Micro and Nano Mechanics Group - User contributions [en]

Shuffle-Glide dislocation MD and NEB

2018-03-13T18:10:46Z

Xzhang11:

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2018, Last modified Mar, 2018


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

===Test case 2: Energy barrier with SW for strain 5.2%===

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Finite temperature MD with Lammps==

We use lammps-30Jul16 version.

::> cd lammps-30Jul16/lib/meam
::> make -f Makefile.gfortran (for meam)
::> cd lammps-30Jul16/src
::> make yes-manybody
::> make yes-meam
::> make mpi

First, one estimates thermal expansion ratios for a bulk system of si using MEAM and sworig.

::> cd MD++.git/
::> bin1/sworig_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_exp_estimates/bulk_generator.tcl 0
::> cd /home/xzhang11/Planet/Libs/MD++.git/scripts/work/he-si-tf-pit-
md/thermal_init_config/therm_exp_estimates/thermal_equilibrate_load_hold_si_800K
::> lmp_mpi < thermal_equilibrate.sw (meam)

From initial and final equilibrated states, one gets thermal expansion. And one records the coefficents in
scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl

::> sw_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl 0 1 1000

To run the lammps scripts, first create surface pit structure with MD++ as follows,

::> cd MD++.git/scripts/work/he-si-tf-pit-md/he-si-pit-800K-54-thermal-relax-nvt
::> mpirun -np $ncpu lammps-30Jul16/src/lmp_mpi < input.meam

===Test case 3: Nucleation event with SW for strain 5.2%===

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Shuffle-Glide dislocation MD and NEB

2018-03-13T18:09:59Z

Xzhang11:

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2018, Last modified Mar, 2018


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

===Test case 2: Energy barrier with SW for strain 0.0520===

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Finite temperature MD with Lammps==

We use lammps-30Jul16 version.

::> cd lammps-30Jul16/lib/meam
::> make -f Makefile.gfortran (for meam)
::> cd lammps-30Jul16/src
::> make yes-manybody
::> make yes-meam
::> make mpi

First, one estimates thermal expansion ratios for a bulk system of si using MEAM and sworig.

::> cd MD++.git/
::> bin1/sworig_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_exp_estimates/bulk_generator.tcl 0
::> cd /home/xzhang11/Planet/Libs/MD++.git/scripts/work/he-si-tf-pit-
md/thermal_init_config/therm_exp_estimates/thermal_equilibrate_load_hold_si_800K
::> lmp_mpi < thermal_equilibrate.sw (meam)

From initial and final equilibrated states, one gets thermal expansion. And one records the coefficents in
scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl

::> sw_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl 0 1 1000

To run the lammps scripts, first create surface pit structure with MD++ as follows,

::> cd MD++.git/scripts/work/he-si-tf-pit-md/he-si-pit-800K-54-thermal-relax-nvt
::> mpirun -np $ncpu lammps-30Jul16/src/lmp_mpi < input.meam

===Test case 3: Nucleation event with SW for strain 0.0520===

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Shuffle-Glide dislocation MD and NEB

2018-03-13T18:09:16Z

Xzhang11:

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2018, Last modified Mar, 2018


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

===Test case 2: Energy barrier with SW for strain 0.0520===

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Finite temperature MD with Lammps==

We use lammps-30Jul16 version.

::> cd lammps-30Jul16/lib/meam
::> make -f Makefile.gfortran (for meam)
::> cd lammps-30Jul16/src
::> make yes-manybody
::> make yes-meam
::> make mpi

First, one estimates thermal expansion ratios for a bulk system of si using MEAM and sworig.

::> cd MD++.git/
::> bin1/sworig_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_exp_estimates/bulk_generator.tcl 0
::> cd /home/xzhang11/Planet/Libs/MD++.git/scripts/work/he-si-tf-pit-
md/thermal_init_config/therm_exp_estimates/thermal_equilibrate_load_hold_si_800K
::> lmp_mpi < thermal_equilibrate.sw (meam)

From initial and final equilibrated states, one gets thermal expansion. And one records the coefficents in
scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl

::> sw_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl 0 1 1000

To run the lammps scripts, first create surface pit structure with MD++ as follows,

::> cd MD++.git/scripts/work/he-si-tf-pit-md/he-si-pit-800K-54-thermal-relax-nvt
::> mpirun -np $ncpu lammps-30Jul16/src/lmp_mpi < input.meam

===Test case 3: Nucleation event with SW for strain 0.0520===

Shuffle-Glide dislocation MD and NEB

2018-03-13T18:01:25Z

Xzhang11:

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2018, Last modified Mar, 2018


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Benchmark in Lammps==

We use lammps-30Jul16 version.

::> cd lammps-30Jul16/lib/meam
::> make -f Makefile.gfortran (for meam)
::> cd lammps-30Jul16/src
::> make yes-manybody
::> make yes-meam
::> make mpi

First, one estimates thermal expansion ratios for a bulk system of si using MEAM and sworig.

::> cd MD++.git/
::> bin1/sworig_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_exp_estimates/bulk_generator.tcl 0
::> cd /home/xzhang11/Planet/Libs/MD++.git/scripts/work/he-si-tf-pit-
md/thermal_init_config/therm_exp_estimates/thermal_equilibrate_load_hold_si_800K
::> lmp_mpi < thermal_equilibrate.sw (meam)

From initial and final equilibrated states, one gets thermal expansion. And one records the coefficents in
scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl

::> sw_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl 0 1 1000

To run the lammps scripts, first create surface pit structure with MD++ as follows,

::> cd MD++.git/scripts/work/he-si-tf-pit-md/he-si-pit-800K-54-thermal-relax-nvt
::> mpirun -np $ncpu lammps-30Jul16/src/lmp_mpi < input.meam

Shuffle-Glide dislocation MD and NEB

2018-03-12T22:53:52Z

Xzhang11: /* Benchmark in Lammps */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Benchmark in Lammps==

We use lammps-30Jul16 version.

::> cd lammps-30Jul16/lib/meam
::> make -f Makefile.gfortran (for meam)
::> cd lammps-30Jul16/src
::> make yes-manybody
::> make yes-meam
::> make mpi

First, one estimates thermal expansion ratios for a bulk system of si using MEAM and sworig.

::> cd MD++.git/
::> bin1/sworig_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_exp_estimates/bulk_generator.tcl 0
::> cd /home/xzhang11/Planet/Libs/MD++.git/scripts/work/he-si-tf-pit-
md/thermal_init_config/therm_exp_estimates/thermal_equilibrate_load_hold_si_800K
::> lmp_mpi < thermal_equilibrate.sw (meam)

From initial and final equilibrated states, one gets thermal expansion. And one records the coefficents in
scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl

::> sw_mc2 scripts/work/he-si-tf-pit-md/thermal_init_config/therm_initconfig_generator.tcl 0 1 1000

To run the lammps scripts, first create surface pit structure with MD++ as follows,

::> cd MD++.git/scripts/work/he-si-tf-pit-md/he-si-pit-800K-54-thermal-relax-nvt
::> mpirun -np $ncpu lammps-30Jul16/src/lmp_mpi < input.meam

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:59:44Z

Xzhang11: /* Benchmark in MD++ */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Benchmark in Lammps==

We use lammps-30Jul16 version.

::> cd /home/xzhang11/Planet/Codes/lammps-30Jul16/lib/meam
::> make -f Makefile.gfortran (for meam)
::> cd /home/xzhang11/Planet/Codes/lammps-30Jul16/src
::> make yes-manybody
::> make yes-meam
::> make mpi

To run the lammps scripts, first create surface pit structure with MD++ as follows,

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:54:00Z

Xzhang11: /* NEB calculation work flow */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

Note that, dislocation loop size of status == 1 can be adjusted manually in the script by specifying w in make_glide_dislocation_loop_1, for example, minor adjustment is needed to get a smooth energy barrier - strain curve.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:51:52Z

Xzhang11: /* NEB calculation work flow */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 0 0 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 1 0.0520 001 1
::> bin1/sworig_mc2_mpich scripts/work/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/disl_nuc_hetero.tcl 4 0.0520 001 1

The first line executes a thread that
1) creates a thin film of (001) free surface
2) reconstruct surface atoms by perturb the atom positions and forming dimers
3) apply along [110] direction a compression strain by the increments of 0.001 from 0 to 0.06, i.e., 6% compressive strain.

The second line reads in initial config of (3) from above and create a shuffle-glide dislocation complex beneath top free surface, which is then relaxed for several steps. The output configuration can be examined by importing w-loop-compression-surf001-eps0.0520.cfg to ovito/DXA.

The third line needs to be launched within pbs file `cause it execute sworig_mc2_mpich in MPI mode, calling stringrelax_parallel (). The energy barrier curve can be visualized by using octave/matlab such as,

::> load runs/he-si-tf-pit-neb/he-si-tf-pit-special-3-sworig/w-disl-nuc-hetero-001-0.0520.24/stringeng.out
::> plot(stringeng(1:100:end, 3:5:end)', '*')

Apply this work flow for different strain, one gets the energy barrier as a function of applied strain.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:43:58Z

Xzhang11: /* Cross Potential between Ge and Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==NEB calculation work flow==

::> cd MD++.git
::> module list
Currently Loaded Modulefiles:
1) null 2) intel/14 3) mvapich2/2.0rc1-intel-14
::> make sworig build=R SYS=mc2_mpich

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:41:39Z

Xzhang11: /* Test case 1: Potential Calibration for SW and MEAM */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, SiGeHole_sw.cn. (There are also bulk_meam.cn, SiGeHole_meam.cn generated from disl_nuc_hetero.tcl with meam-lammps)

From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:40:26Z

Xzhang11: /* Test case 1: Potential Calibration for SW and MEAM */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, bulk_meam.cn, SiGeHole_meam.cn, SiGeHole_sw.cn. From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:39:53Z

Xzhang11: /* Test case 1: Potential Calibration for SW and MEAM */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, bulk_meam.cn, SiGeHole_meam.cn, SiGeHole_sw.cn. From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8
SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7
SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9
SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26
SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:39:13Z

Xzhang11: /* Test case 1: Potential Calibration for SW and MEAM */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14
::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, bulk_meam.cn, SiGeHole_meam.cn, SiGeHole_sw.cn. From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9

MEAM + SiGeHole_sw.cn: -9.97015.8

SWorig + bulk_sw.cn : -9.58832.6

SWorig + SiGeHole_sw.cn : -9.32569.7

SW + bulk_sw.cn : -1.024081.9

SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9

MEAM + SiGeHole_sw.cn: -997015.9

SWorig + bulk_sw.cn : -958832.17

SWorig + SiGeHole_sw.cn : -932569.26

SW + bulk_sw.cn : -1024081.9

SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:38:35Z

Xzhang11: /* Test case 1: Potential Calibration for SW and MEAM */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14

::> cd MD++.git (svn)

::> make sworig build=R SYS=mc2_mpich

::> make sw build=R SYS=mc2_mpich

::> make meam-lammps build=R SYS=mc2

::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, bulk_meam.cn, SiGeHole_meam.cn, SiGeHole_sw.cn. From MD++, the numbers should be exactly the following:

MEAM + bulk_sw.cn : -1.024081.9

MEAM + SiGeHole_sw.cn: -9.97015.8

SWorig + bulk_sw.cn : -9.58832.6

SWorig + SiGeHole_sw.cn : -9.32569.7

SW + bulk_sw.cn : -1.024081.9

SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9

MEAM + SiGeHole_sw.cn: -997015.9

SWorig + bulk_sw.cn : -958832.17

SWorig + SiGeHole_sw.cn : -932569.26

SW + bulk_sw.cn : -1024081.9

SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:38:15Z

Xzhang11: /* Test case 1: Potential Calibration for SW and MEAM */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14

::> cd MD++.git (svn)

::> make sworig build=R SYS=mc2_mpich

::> make sw build=R SYS=mc2_mpich

::> make meam-lammps build=R SYS=mc2

::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

(0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)

::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, bulk_meam.cn, SiGeHole_meam.cn, SiGeHole_sw.cn. From MD++, the numbers should be exactly the following:

MEAM + bulk_meam.cn : -1.024081.9

MEAM + SiGeHole_sw.cn: -9.97015.8

SWorig + bulk_sw.cn : -9.58832.6

SWorig + SiGeHole_sw.cn : -9.32569.7

SW + bulk_sw.cn : -1.024081.9

SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9

MEAM + SiGeHole_sw.cn: -997015.9

SWorig + bulk_sw.cn : -958832.17

SWorig + SiGeHole_sw.cn : -932569.26

SW + bulk_sw.cn : -1024081.9

SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:37:27Z

Xzhang11: /* MEAM Potential for Ge */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===Test case 1: Potential Calibration for SW and MEAM===
This test case is developed in MD++, but also use lammps executable, to evaluate potential energy of a bulk system and a surface pit structure with both SW (1985, 1992) and MEAM potential. To run the test case, follow the steps below,

Take mc2 as an example, one module load the following:

::> module load mvapich2/2.0rc1-intel-14, intel/14

::> cd MD++.git (svn)
::> make sworig build=R SYS=mc2_mpich
::> make sw build=R SYS=mc2_mpich
::> make meam-lammps build=R SYS=mc2
::> bin1/sworig_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000 (0 and 1000 are useless, but need to be there otherwise the script will complain missing parameters)
::> bin1/sw_mc2_mpich scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000
::> meam-lammps_mc2 scripts/work/sw_meam_calibrations/disl_nuc_hetero.tcl 1 0 1000

change in the script the configuration to read in, choosing from runs/sw_meam_calibrations/bulk_sw.cn, bulk_meam.cn, SiGeHole_meam.cn, SiGeHole_sw.cn. From MD++, the numbers should be exactly the following:

MEAM + bulk_meam.cn : -1.024081.9
MEAM + SiGeHole_sw.cn: -9.97015.8

SWorig + bulk_sw.cn : -9.58832.6
SWorig + SiGeHole_sw.cn : -9.32569.7

SW + bulk_sw.cn : -1.024081.9
SW + SiGeHole_sw.cn : -9.96031.739

From lammps,

MEAM + bulk_sw.cn : -1024081.9
MEAM + SiGeHole_sw.cn: -997015.9

SWorig + bulk_sw.cn : -958832.17
SWorig + SiGeHole_sw.cn : -932569.26

SW + bulk_sw.cn : -1024081.9
SW + SiGeHole_sw.cn : -996031.74

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:04:49Z

Xzhang11: /* MEAM Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), which is explained in SiGe potential tutorial (http://micro.stanford.edu/wiki/MEAM_Potential_for_Si-Ge)

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:03:39Z

Xzhang11: /* MEAM Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR:
Greg Wagner, gjwagne@sandia.gov
CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:03:05Z

Xzhang11: /* MEAM Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponds to the data format of

DATE: 2012-06-29 DATE: 2007-06-11 CONTRIBUTOR: Greg Wagner, gjwagne@sandia.gov CITATION: Baskes, Phys Rev B, 46, 2727-2742 (1992)
meam data from vax files fcc,bcc,dia 11/4/92
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T20:01:54Z

Xzhang11: /* MEAM Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

corresponding to the data format of:
elt lat z ielement atwt
alpha b0 b1 b2 b3 alat esub asub
t0 t1 t2 t3 rozero ibar

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T19:59:42Z

Xzhang11: /* MEAM Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)."

MD++:

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

Lammps:

'Siz' 'dia' 4. 14 28.086
4.87 4.4 5.5 5.5 5.5 5.431 4.63 1.
1.0 3.13 4.47 -1.80 1.600 0

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T19:57:59Z

Xzhang11: /* SW Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T19:57:37Z

Xzhang11: /* SW Potential for Si */

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as follows:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */

Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */

Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T19:57:06Z

Xzhang11:

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. The modified version of SW fits to cohesive energy. Their parameters are listed as following:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

/* sw, Stillinger and Weber, Phys. Rev. B, v. 31, p. 5262, (1985) */
Si Si Si 2.1674166667 2.0951 1.80 21.0 1.20 -0.333333333
7.049827 0.602225 4.0 0.0 0.0

/* PRB 46, 2250 (1992) */
Si Si Si 2.1683 2.0951 1.80 22.4207904718 1.20 -0.333333333333
7.5265059125 0.6022245574 4.0 0.0 0.0

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T18:41:22Z

Xzhang11:

Shuffle Glide Dislocation Complex: NEB and MD 
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial corresponds to paper ``Shuffle-Glide Dislocation Complex Nucleation in Silicon Thin Film''. It explains how to calibrate and specify SW and MEAM-lammps potential parameters in both MD++ and LAMMPs. It explains how to set up and run NEB calculations to measure the energy barrier of a shuffle-glide dislocation complex nucleated in a thin film with a surface pit. Finite temperature MD simulations are performed in Lammps to capture nucleation events as validation to energy barrier calculations.

<HR>

==Potential for Pure Elements==

===SW Potential for Si===
We calibrate both SW (1985) and SW (1992) potentials in both MD++ and Lammps. Their parameters are listed as following:

MD++:
/* original Si version PRB 31, 5262 (1985) */
aa=15.27991323; bb=11.60319228; plam=45.51575;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.0;

/* modified Si parameters PRB 46, 2250 (1992) */
aa=16.31972277; bb=11.60319228; plam=48.61499998;
pgam=2.51412; acut=3.77118; pss=2.0951; rho=4.;

Lammps:

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T18:15:10Z

Xzhang11:

MEAM Potential for Si-Ge
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Shuffle-Glide dislocation MD and NEB

2018-03-12T18:12:51Z

Xzhang11: Created page with "==Potential for Pure Elements== ===MEAM Potential for Si=== We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Frac..."

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

Tutorial:Members Only

2018-03-12T18:12:08Z

Xzhang11: /* Manuals for Group Members */

== Manuals for Group Members ==

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Scientific Articles
|-
| [https://micro.stanford.edu/journal-repository Journal Repository]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | ParaDiS
|-
| [[ParaDiS Cylinder Code Manuals ]]
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!width="500" | MD++
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|-
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|-
| [[MEAM Potential for Si-Ge]]
|-
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|-
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|-
| [[Classical Simulation of GeAu droplet on Ge substrate]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | LAMMPS
|-
| [[Use Au-Si MEAM Potential in LAMMPS]]
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|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Phase Field
|-
| [[Summary of Nanowire Growth Mechanism]]
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| [[Single Phase Field Model with Isotropic Surface Energy]]
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| [[Single Phase Field Model with Anisotropic Surface Energy]]
|-
| [[Multi Phase Field Model with Isotropic Interface Energy]]
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| [[Multi Phase Field Model with Anisotropic Interface Energy]]
|-
| [[Multi Phase Field Model (Revised Formulation)]]
|-
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|-
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|}

{| class="wikitable" cellpadding="2" style="text-align:center"
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!width="500" | FEM Codes
|-
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|}

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|}

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|-
| [[Ab Initio Simulations of Condensed Matter under Arbitrary Magnetic Field | MPBC/Qbox draft1]]
|-
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|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
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|}

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|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
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|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
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|}

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|}

{| class="wikitable" cellpadding="2" style="text-align:center"
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!width="500" | Outreach
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|}

MEAM Potential for Si-Ge

2017-03-06T22:36:17Z

Xzhang11:

MEAM Potential for Si-Ge

2017-03-06T22:31:14Z

Xzhang11: /* Cross Potential between Ge and Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.67 (<math>r_e</math>)
delta(1,2) = 0.071 (related to <math>E_c</math>, see below)
lattce(1,2) = b1 (<math>B</math>)
lattce(1,2) = b1 (<math>Rcut</math>)
lattce(1,2) = b1 (<math>C_{\max}</math>)
lattce(1,2) = b1 (<math>C_{\min}</math>)
d = 0

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T22:29:02Z

Xzhang11: /* Cross Potential between Ge and Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

erose_form = 3
rc = 4.23
re(1,2) = 5.529
delta(1,2) = 0.125
lattce(1,2) = b1
alpha(1,2) = 5.819
attrac(1,1) = -0.182
repuls(1,1) = 4.0
attrac(2,2) = -0.36
repuls(2,2) = 16.0
attrac(1,2) = 0.0
repuls(1,2) = 0.26
Cmin(1,1,1) = 0.8
Cmin(2,2,2) = 1.85
Cmin(1,1,2) = 1.9
Cmin(1,2,1) = 0.95
Cmin(1,2,2) = 1.85
Cmin(2,2,1) = 1.0
augt1 = 1

The values for <math>E_c ({\rm AuGe}) = 3.189</math>.
This value is related to delta(1,2) through

<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US)
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US)

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T22:06:19Z

Xzhang11: /* Benchmark in MD++ */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command on mc2.

make meam-lammps build=R SYS=mc2_mpich

Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T22:04:29Z

Xzhang11: /* Cross Potential between Ge and Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T22:02:39Z

Xzhang11: /* MEAM Potential for Ge */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T22:02:10Z

Xzhang11: /* MEAM Potential for Ge */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T22:00:13Z

Xzhang11: /* MEAM Potential for Ge */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===
We use the 'Ge5' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T21:58:55Z

Xzhang11: /* MEAM Potential for Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T21:58:25Z

Xzhang11: /* MEAM Potential for Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T21:57:33Z

Xzhang11: /* MEAM Potential for Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-06T21:53:28Z

Xzhang11: /* MEAM Potential for Si */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Siz' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-02T00:05:27Z

Xzhang11: /* Impurity energy */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===melting point===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

===phase diagram===

Use the following command to obtain the phase diagram of SiGe.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-02T00:04:03Z

Xzhang11: /* Benchmark in MD++ */

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===Impurity energy===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-02T00:02:55Z

Xzhang11: /* Impurity energy */

MEAM Potential for Si-Ge

2017-03-02T00:02:01Z

Xzhang11:

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

===MEAM Potential for Ge===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Ge and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===Impurity energy===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-01T23:58:45Z

Xzhang11:

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference:

"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

As an example, we first describe the original 'Au' potential whose parameters are given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Au' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Au' 'fcc' 12. 79 196.967 6.34090112 5.449 2.20 6 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.07 3.93 1.04 1.0 1.58956328 1.50776392 2.60609758 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS). It selects the
G(gamma) function in Eq (4) and (5) on the paper by BJ LEE: Phys. Rev. B 64, 184102 (2001)

While the functional form is quite different, the modulus is almost not affected by
the choice of ibar.

===New 2nn MEAM Potential for Au===

We now explain the newer 2nn MEAM potential whose parameters are given by Lee, Shim and Baskes, Phys. Rev. B 68, 144112 (2003), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential are specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines which correspond to 'AuBt' are given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'AuBt' 'fcc' 12. 79 196.967 6.59815965 5.77 2.20 6.0 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.073 3.93 1.00 1.0 1.7 1.64 2.0 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

We can see that from 'Au' to 'AuBt', the following parameters are changed. The new parameters correspond to values given in Table I of Lee, Shim and Baskes, PRB (2003).

<math>\alpha</math> <math>\beta_i^{(0)}</math> <math>A_i</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math>
'Au' 6.34090112 5.449 1.04 1.58956328 1.50776392 2.60609758
'AuBt' 6.59815965 5.77 1.00 1.7 1.64 2.0

Note that in Table I of Lee et al. (2003), <math>t^{(1)} = 2.90</math>, while in the '''meamf''' file, t1 = 1.7. This is because of the '''augt1''' parameter. In '''meam_setup_done.F''', there is a line

t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:)

This means that if '''augt1''' = 1.0, then the ''true'' value of t1 is 1.7 + 0.6 * 2.0 = 2.9.

'''augt1''' is specified in the '''AuSi2nn.meam''' file, as described below.

The '''AuSi2nn.meam''' file contains several lines that are relevant for the pure Au potential. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(1,1) = -0.182 (<math>\gamma</math>)
repuls(1,1) = 4.0 (<math>\lambda</math>)
Cmin(1,1,1) = 0.8 (<math>C_{\rm min}</math>)
augt1 = 1

Note that we label the atomic species of Au as 1. The variable <math>d = 0.05</math> is hard coded in '''meam_setup_done.F''' (when repuls < 5.0).

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===Impurity energy===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-01T23:58:27Z

Xzhang11:

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference "A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

As an example, we first describe the original 'Au' potential whose parameters are given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Au' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Au' 'fcc' 12. 79 196.967 6.34090112 5.449 2.20 6 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.07 3.93 1.04 1.0 1.58956328 1.50776392 2.60609758 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS). It selects the
G(gamma) function in Eq (4) and (5) on the paper by BJ LEE: Phys. Rev. B 64, 184102 (2001)

While the functional form is quite different, the modulus is almost not affected by
the choice of ibar.

===New 2nn MEAM Potential for Au===

We now explain the newer 2nn MEAM potential whose parameters are given by Lee, Shim and Baskes, Phys. Rev. B 68, 144112 (2003), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential are specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines which correspond to 'AuBt' are given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'AuBt' 'fcc' 12. 79 196.967 6.59815965 5.77 2.20 6.0 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.073 3.93 1.00 1.0 1.7 1.64 2.0 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

We can see that from 'Au' to 'AuBt', the following parameters are changed. The new parameters correspond to values given in Table I of Lee, Shim and Baskes, PRB (2003).

<math>\alpha</math> <math>\beta_i^{(0)}</math> <math>A_i</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math>
'Au' 6.34090112 5.449 1.04 1.58956328 1.50776392 2.60609758
'AuBt' 6.59815965 5.77 1.00 1.7 1.64 2.0

Note that in Table I of Lee et al. (2003), <math>t^{(1)} = 2.90</math>, while in the '''meamf''' file, t1 = 1.7. This is because of the '''augt1''' parameter. In '''meam_setup_done.F''', there is a line

t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:)

This means that if '''augt1''' = 1.0, then the ''true'' value of t1 is 1.7 + 0.6 * 2.0 = 2.9.

'''augt1''' is specified in the '''AuSi2nn.meam''' file, as described below.

The '''AuSi2nn.meam''' file contains several lines that are relevant for the pure Au potential. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(1,1) = -0.182 (<math>\gamma</math>)
repuls(1,1) = 4.0 (<math>\lambda</math>)
Cmin(1,1,1) = 0.8 (<math>C_{\rm min}</math>)
augt1 = 1

Note that we label the atomic species of Au as 1. The variable <math>d = 0.05</math> is hard coded in '''meam_setup_done.F''' (when repuls < 5.0).

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===Impurity energy===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-01T23:57:55Z

Xzhang11:

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference ``A modified embedded atom method interatomic potential for alloy SiGe'', Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

As an example, we first describe the original 'Au' potential whose parameters are given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Au' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Au' 'fcc' 12. 79 196.967 6.34090112 5.449 2.20 6 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.07 3.93 1.04 1.0 1.58956328 1.50776392 2.60609758 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS). It selects the
G(gamma) function in Eq (4) and (5) on the paper by BJ LEE: Phys. Rev. B 64, 184102 (2001)

While the functional form is quite different, the modulus is almost not affected by
the choice of ibar.

===New 2nn MEAM Potential for Au===

We now explain the newer 2nn MEAM potential whose parameters are given by Lee, Shim and Baskes, Phys. Rev. B 68, 144112 (2003), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential are specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines which correspond to 'AuBt' are given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'AuBt' 'fcc' 12. 79 196.967 6.59815965 5.77 2.20 6.0 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.073 3.93 1.00 1.0 1.7 1.64 2.0 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

We can see that from 'Au' to 'AuBt', the following parameters are changed. The new parameters correspond to values given in Table I of Lee, Shim and Baskes, PRB (2003).

<math>\alpha</math> <math>\beta_i^{(0)}</math> <math>A_i</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math>
'Au' 6.34090112 5.449 1.04 1.58956328 1.50776392 2.60609758
'AuBt' 6.59815965 5.77 1.00 1.7 1.64 2.0

Note that in Table I of Lee et al. (2003), <math>t^{(1)} = 2.90</math>, while in the '''meamf''' file, t1 = 1.7. This is because of the '''augt1''' parameter. In '''meam_setup_done.F''', there is a line

t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:)

This means that if '''augt1''' = 1.0, then the ''true'' value of t1 is 1.7 + 0.6 * 2.0 = 2.9.

'''augt1''' is specified in the '''AuSi2nn.meam''' file, as described below.

The '''AuSi2nn.meam''' file contains several lines that are relevant for the pure Au potential. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(1,1) = -0.182 (<math>\gamma</math>)
repuls(1,1) = 4.0 (<math>\lambda</math>)
Cmin(1,1,1) = 0.8 (<math>C_{\rm min}</math>)
augt1 = 1

Note that we label the atomic species of Au as 1. The variable <math>d = 0.05</math> is hard coded in '''meam_setup_done.F''' (when repuls < 5.0).

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===Impurity energy===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

MEAM Potential for Si-Ge

2017-03-01T23:54:57Z

Xzhang11: Created page with " MEAM Potential for Au-Si <DIV> Xiaohan Zhang and Wei Cai..."

MEAM Potential for Au-Si
<DIV>
Xiaohan Zhang and Wei Cai
</DIV>
 Created Mar, 2017, Last modified Mar, 2017


This tutorial explains how to specify the parameters for the Au-Si MEAM potential in MD++. It starts with the parameters in pure Au and pure Si potentials, then talks about the Au-Si cross potential.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

As an example, we first describe the original 'Au' potential whose parameters are given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Au' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Au' 'fcc' 12. 79 196.967 6.34090112 5.449 2.20 6 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.07 3.93 1.04 1.0 1.58956328 1.50776392 2.60609758 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS). It selects the
G(gamma) function in Eq (4) and (5) on the paper by BJ LEE: Phys. Rev. B 64, 184102 (2001)

While the functional form is quite different, the modulus is almost not affected by
the choice of ibar.

===New 2nn MEAM Potential for Au===

We now explain the newer 2nn MEAM potential whose parameters are given by Lee, Shim and Baskes, Phys. Rev. B 68, 144112 (2003), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential are specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines which correspond to 'AuBt' are given below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'AuBt' 'fcc' 12. 79 196.967 6.59815965 5.77 2.20 6.0 2.20

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Au}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
4.073 3.93 1.00 1.0 1.7 1.64 2.0 1. 3

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

We can see that from 'Au' to 'AuBt', the following parameters are changed. The new parameters correspond to values given in Table I of Lee, Shim and Baskes, PRB (2003).

<math>\alpha</math> <math>\beta_i^{(0)}</math> <math>A_i</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math>
'Au' 6.34090112 5.449 1.04 1.58956328 1.50776392 2.60609758
'AuBt' 6.59815965 5.77 1.00 1.7 1.64 2.0

Note that in Table I of Lee et al. (2003), <math>t^{(1)} = 2.90</math>, while in the '''meamf''' file, t1 = 1.7. This is because of the '''augt1''' parameter. In '''meam_setup_done.F''', there is a line

t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:)

This means that if '''augt1''' = 1.0, then the ''true'' value of t1 is 1.7 + 0.6 * 2.0 = 2.9.

'''augt1''' is specified in the '''AuSi2nn.meam''' file, as described below.

The '''AuSi2nn.meam''' file contains several lines that are relevant for the pure Au potential. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(1,1) = -0.182 (<math>\gamma</math>)
repuls(1,1) = 4.0 (<math>\lambda</math>)
Cmin(1,1,1) = 0.8 (<math>C_{\rm min}</math>)
augt1 = 1

Note that we label the atomic species of Au as 1. The variable <math>d = 0.05</math> is hard coded in '''meam_setup_done.F''' (when repuls < 5.0).

===MEAM Potential for Si===

We use the 'Si4' potential whose parameters are originally given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010).

The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math>
elt lat z ielement atwt alpha b0 b1 b2 b3
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5

<math>(R_i^0)</math> <math>E_i^0</math> <math>A_i</math> <math>t_i^{(0)}</math> <math>t_i^{(1)}</math> <math>t_i^{(2)}</math> <math>t_i^{(3)}</math> <math>\rho_0^{\rm Si}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.48 0

Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential.

'''ibar''' is a setting used in the equation of state (EOS), and will be explained later.

The modification made in Ryu and Cai JPCM (2010) is specified in the '''AuSi2nn.meam''' file. The variables in Eq.(A.1) of Ryu and Cai JPCM (2010) are given in the parenthesis.

erose_form = 3
rc = 4.5
attrac(2,2) = -0.36 (<math>\gamma</math>)
repuls(2,2) = 16.0 (<math>\lambda</math>)
Cmin(2,2,2) = 1.85 (<math>C_{\rm min}</math>)

Note that we label the atomic species of Si as 2.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

re(1,2) = 2.700 (<math>r_e</math>)
delta(1,2) = 0.125 (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 5.819 (<math>\alpha</math>)
attrac(1,2) = 0.0
repuls(1,2) = 0.26 (<math>\gamma</math>)
Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>)
Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>)
Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>)
Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c ({\rm AuSi}) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c ({\rm AuSi}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Si}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au}</math> = 1.48 because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

Cmax = 2.8 is the default value.

==Benchmark in MD++==

Compile the code using the following command.

make meam-lammps build=R SYS=gpp

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Au (FCC). You can download the [[media:si-au.tcl.txt | si-au.tcl]] from the link.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1

The results are

a0 = 4.07300759775 Angstrom
Ecoh = -3.92996804082 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 eV

Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2

The results are

a0 = 5.4 Angstrom
Ecoh = -4.155000000083061 eV

===Impurity energy===

Use the following command to compute the impurity of a Au atom in Si DC lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4

The results depend slightly on the cell size
cell size, Eimp(eV)
3x3x3 3.914
4x4x4 3.968
5x5x5 3.987
10x10x10 4.005
20x20x20 4.008

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal.
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here.

Use the following command to compute the impurity of a Si atom in Au fcc lattice.

bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3

cell size, Eimp(eV)
2x2x2 0.639
3x3x3 0.660
4x4x4 0.665
5x5x5 0.667
10x10x10 0.669
20x20x20 0.669

The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2,
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal.
So it seems that for a Si in Au FCC crystal, the predicted results here using
the 2x2x2 cell corresponds to the value in JPCM (2010).

Tutorial:Members Only

2017-03-01T23:53:38Z

Xzhang11: /* Manuals for Group Members */

== Manuals for Group Members ==

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Scientific Articles
|-
| [https://micro.stanford.edu/journal-repository Journal Repository]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | ParaDiS
|-
| [[ParaDiS Cylinder Code Manuals ]]
|-
| [[ParaDiS ThinFilm Code Manuals]]
|-
| [[ParaDiS Aniso Code Manuals]]
|-
| [[ Cross-slip in ParaDiS]]
|-
| [[Parallel Cluster Guides]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | MD++
|-
| [[Foward Flux Sampling in MD++]]
|-
| [[Torsion and Bending PBC in MD++]]
|-
| [[A Polygonal Dislocation Loop in MD++]]
|-
| [[Use of Ewald Summation in MD++]]
|-
| [[MEAM Potential for Au-Si]]
|-
| [[MEAM Potential for Au-Ge]]
|-
| [[MEAM Potential for Si-Ge]]
|-
| [[Computing Binary Phase Diagram in MD++]]
|-
| [[Classical Simulation of GeAu droplet on Ge substrate]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | LAMMPS
|-
| [[Use Au-Si MEAM Potential in LAMMPS]]
|-
| [[Compile LAMMPS on GPU on Sherlock]]
|-
| [[Perform Nanoindentation on Al-Mg Alloy]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Phase Field
|-
| [[Summary of Nanowire Growth Mechanism]]
|-
| [[Single Phase Field Model with Isotropic Surface Energy]]
|-
| [[Single Phase Field Model with Anisotropic Surface Energy]]
|-
| [[Multi Phase Field Model with Isotropic Interface Energy]]
|-
| [[Multi Phase Field Model with Anisotropic Interface Energy]]
|-
| [[Multi Phase Field Model (Revised Formulation)]]
|-
| [[Parallelization of the Phase Field Model]]
|-
| [[Phase Field Model for Grain Evolution]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | VASP
|-
| [[VASP Computing Bulk Modulus of Au]]
|-
| [[VASP Computing Bulk Modulus of ZrO2]]
|-
| [[VASP Computing Bulk Modulus of YSZ]]
|-
| [[VASP Computing Density of States of YSZ]]
|-
| [[VASP Computing Generalized Stacking Fault Energy of Au]]
|-
| [[VASP Computing Ideal Shear Strength of Au]]
|-
| [[VASP terminology]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Qbox
|-
| [[Qbox Computing Bulk Modulus of Au]]
|-
| [[Qbox Computing Bulk Modulus of ZrO2]]
|-
| [[Qbox Implemention of Magnetic Field]]
|-
| [[Qbox Generating Pseudopotentials]]
|-
| [[Ab Initio Simulations of Condensed Matter under Arbitrary Magnetic Field | MPBC/Qbox draft1]]
|-
| [[Predicting Molecular and Electronic Response to Magnetic Field from First Principles | MPBC/Qbox draft2]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | C++
|-
| [[BOOST Library]]
|-
| [[Install GCC]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | LaTeX
|-
| [[Install LaTeX from Scratch]]
|-
| [[Beamer Presentations]]
|-
| [[TikZ package]]
|-
| [[PGFPLOTS]]
|-
| [[Asymptote]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Tools
|-
| [[Atom Eye]]
|-
| [[Gnuplot]]
|-
| [[Computational XRD]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Computers
|-
| [[Micro Maintenance]]
|-
| [[Libraries in SU-AHPCRC]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Fatigue Literature Review
|-
| [[2D Dislocation Dynamics]]
|-
| [[3D Dislocation Dynamics]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | Outreach
|-
| [[Simulating Solids in MD++]]
|-
| [[Videos of bucky balls in motion]]
|}

Group Members

2016-03-22T03:54:00Z

Xzhang11: /* Graduate Students */

__NOTOC__
===Professor===
:[[Wei Cai]]

===Graduate Students===
:[[Yanming Wang]]
:[[Ryan Sills]]
:[[Nicolas Bertin]]
:[[Xiaohan Zhang]]

===Former Members===
:[[Amin Aghaei | Amin Aghaei (former postdoc)]]
:[[William Kuykendall | William Kuykendall (former PhD student)]]
:[[William Cash | William Cash (former PhD student)]]
:[[Hark Lee | Hark Lee (former PhD student)]]
:[[Ill Ryu | Ill Ryu (former PhD student)]]
:[[Jie Yin | Jie Yin (former PhD student)]]
:[[Seunghwa Ryu | Seunghwa Ryu (former PhD student) ]]
:[[Seokwoo Lee | Seokwoo Lee (former PhD student) ]]
:[[Haneesh Kesari | Haneesh Kesari (former PhD student)]]
:[[Chris Weinberger | Chris Weinberger (former PhD student)]]
:[[William Fong | William Fong (guest)]]
:[[Alfredo Correa | Alfredo Correa (former postdoc)]]
:[[Keonwook Kang | Keonwook Kang (former PhD student)]]
:[[Eunseok Lee | Eunseok Lee (former PhD student)]]
:[[Sylvie Aubry | Sylvie Aubry (former Research Associate)]]

===Outreach Collaborator===
:[[Alfonso Garcia | Alfonso Garcia (high school teacher)]]