Micro and Nano Mechanics Group - User contributions [en]

Computing Melting Point by Free Energy Method

2020-08-05T22:53:10Z

Caiwei: Add link to python jupyter notebook on GitLab

Computing Melting Point by Free Eneregy Method
<DIV>
Seunghwa Ryu and Wei Cai
</DIV>
Modified by Yanming Wang (Sep 2015)

This tutorial describes how to compute melting points from free energy methods. We provide the [https://gitlab.com/micronano_public/MDpp MD++] script files and describe how to use them in detail. The theoretical background is published in

Comparison of Thermal Properties Predicted by Interatomic Potential Models, ''Modelling and Simulation in Materials Science and Engineering'', '''16''', 085005 (2008). [http://micro.stanford.edu/~caiwei/papers/Ryu08msmse-meltingT.pdf (PDF)] (Paper selected as [http://www.iop.org/EJ/journal/-page=featured/0965-0393 MSMSE featured article]).

This case study is also available in the form of a Python [https://gitlab.com/micronano_public/MDpp/-/blob/release/scripts/ME346B/Tutorial%2027%20-%20Melting%20Point%20by%20Free%20Energy%20Method.ipynb jupyter notebook].
<HR>

==Download files==

First, you need to install MD++ on your computer by following the instructions on [[MD++_Manuals | MD++ Manuals]].

Second, copy files [[media:melting_cubic.tcl.txt‎ | melting_cubic.tcl]] and
[[media:melting_noncubic.tcl.txt‎ | melting_noncubic.tcl]] to your input file directory of MD++. You can do so by the following commands (assuming you have installed MD++ in <tt>~/Codes/MD++</tt>).

<pre>
export MDPP=~/Codes/MD++
mkdir -p ${MDPP}/scripts/work/melting
cd ${MDPP}/scripts/work/melting
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melting_cubic.tcl.txt -O melting_cubic.tcl
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melting_noncubic.tcl.txt -O melting_noncubic.tcl
</pre>

Both files contain a big comment section in the beginning that describes in detail the (16) steps to compute the melting point. These steps are fully automated. In this tutorial, we describe how to run these scripts on a parallel cluster (using wcr.stanford.edu as an example) and what kind of results you should expect.

==Compile executable file==

Different executables in MD++ contains different interatomic potentials, for example,
<pre>
sw - Stillinger-Weber Silicon (modified by Balamane et al.)
sworig - Original version of SW Silicon
swge - Stillinger-Weber Germanium
tersoff - Tersoff potential for Silicon
meam-lammps - MEAM (taken from lammps)
meam-baskes - MEAM (taken from Baskes's code dynamo)
meam - MEAM (directly implemented in MD++)
eam - Embedded Atom Method
fs - Finnis-Sinclair
</pre>

Here we use Si as an example. You can compile <tt>sworig</tt> by typing
<pre>
cd ${MDPP}
make sworig build=R SYS=wcr
</pre>
If compilation is successful, this will create binary file <tt>sworig_wcr</tt> file in your <tt>${MDPP}/bin</tt> directory.

The script [[media:melting_cubic.tcl.txt‎ | melting_cubic.tcl]] can be used with many potentials (i.e. executables), which are explained in the header region of the file. Contact <tt>shryu@stanford.edu</tt> if you have further questions.

==Submit jobs==

Here are the PBS scripts ([[media:melt1.pbs.txt‎ |melt1.pbs]] and
[[media:melt2.pbs.txt‎ |melt2.pbs]]) for submitting the jobs on wcr.stanford.edu. You can submit jobs by typing the following commands. This is a test case that computes the melting points of silicon described by the Stillinger-Weber (SW) potential on the parallel cluster wcr.stanford.edu.

<pre>
cd ${MDPP}
mkdir runs/Single_Elem_Tm
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melt1.pbs.txt -O melt1.pbs
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melt2.pbs.txt -O melt2.pbs
qsub melt1.pbs
qsub melt2.pbs
</pre>

After the calculation is finished (within 24 hours), the free energy data will be stored in the following two directories.

<pre>
${MDPP}/runs/Single_Elem_Tm/SW_Si_Solid/
${MDPP}/runs/Single_Elem_Tm/SW_Si_Liquid/
</pre>

==Analyse data==

At the end of the calculation, data files and Matlab files will be automatically generated. Transfer these files to a location where you have Matlab installed. Run the following commands in Matlab and you will get the free energy plot (for solid and liquid phases). The melting point is the temperature at which the two free energy curves cross.

In this test case, the analysis files are generated in directory
<tt>${MDPP}/runs/Single_Elem_Tm</tt>. They are

<pre>
Hessian_SW_Si.m
Free_Energy_of_SW_Si.m
tar_SW_Si
</pre>

Run the following command to zip all data
<pre>
cd ${MDPP}/runs/Single_Elem_Tm
./tar_SW_Si
</pre>
into a tar file <tt>inter_SW_Si.tar</tt>.

Copy this file to your local computer and unzip the data. Next, run the following command in Matlab.
<pre>
Hessian_SW_Si.m
Free_Energy_of_SW_Si.m
</pre>

You'll see the following output files that contain all free energy data and the error analysis.

<pre>
Solid Free Energy Info

lattice const = 5.43095
strain = 0.00518
E_0 = -2218.74337 eV ( -4.33348 eV/atom)
F_w = -253.34582 eV ( -0.49482 eV/atom)
F_ha = E_0 + F_w = -2472.08919 eV ( -4.82830 eV/atom)
W_re_to_ha = 5.99169 eV ( 0.01170 eV/atom)
W_ha_to_re = -7.30068 eV ( -0.01426 eV/atom)
F_re - F_ha = (W_ha_to_re - W_re_to_ha)/2 = -6.64619 eV ( -0.01298 eV/atom)
F_re at 1600.000000 = -2478.73538 eV ( -4.84128 eV/atom)
W_T1_to_T11 = 417.87095 eV ( 0.81615 eV/atom)
W_T11_to_T1 = -417.87508 eV ( -0.81616 eV/atom)
dW1 = (W_T1_to_T11 - W_T11_to_T1)/2 = 417.87302 eV ( 0.81616 eV/atom)
F_re at 2000.000000 = -2605.55266 eV ( -5.08897 eV/atom)
</pre>

<pre>
Liquid Free Energy Info

strain = -0.01894
F_ideal = -919.36940 ( -1.79564 eV/atom)
W_re_to_ga = 1888.21102 eV ( 3.68791 eV/atom)
W_ga_to_re = -1887.53306 eV ( -3.68659 eV/atom)
F_re - F_ga = (W_ga_to_re - W_re_to_ga)/2 = -1887.87204 eV ( -3.68725 eV/atom)
W_ga_to_id = -256.29295 eV ( -0.50057 eV/atom)
W_id_to_ga = 256.52177 eV ( 0.50102 eV/atom)
F_ga - F_id = (W_id_to_ga - W_ga_to_id)/2 = 256.40736 eV ( 0.50080 eV/atom)
F_re at 1800.000000 = -2550.83408 eV ( -4.98210 eV/atom)
W_T2_to_T22 = -583.02785 eV ( -1.13873 eV/atom)
W_T22_to_T2 = 583.06542 eV ( 1.13880 eV/atom)
dW2 = (W_T2_to_T22 - W_T22_to_T2)/2 = -583.04664 eV ( -1.13876 eV/atom)
F_re at 1384.615385 = -2386.68534 eV ( -4.66149 eV/atom)
</pre>

<pre>
Error Analysis

Solid Side
Err_re_to_ha = 0.02769 eV ( 0.00005407 eV/atom)( 0.628 K)
Err_ha_to_re = 0.02815 eV ( 0.00005498 eV/atom)( 0.638 K)
Err_T1_to_T11 = 0.00374 eV ( 0.00000730 eV/atom)( 0.085 K)
Err_T11_to_T1 = 0.00441 eV ( 0.00000861 eV/atom)( 0.100 K)

Liquid Side
Err_re_to_ga = 0.04793 eV ( 0.00009362 eV/atom)( 1.086 K)
Err_ga_to_re = 0.06601 eV ( 0.00012893 eV/atom)( 1.496 K)
Err_ga_to_id = 0.02557 eV ( 0.00004993 eV/atom)( 0.580 K)
Err_id_to_ga = 0.03421 eV ( 0.00006682 eV/atom)( 0.776 K)
Err_T2_to_T22 = 0.01488 eV ( 0.00002906 eV/atom)( 0.337 K)
Err_T22_to_T2 = 0.01183 eV ( 0.00002311 eV/atom)( 0.268 K)
Max dT = 2.315
Tm= 1695.08000 (K), err= 1.044 Fm = -4.89779 (eV/atom)
L= 165.8833097832 (eV) Ss=0.308452 Sl=0.406313
L= 0.3239908394 (eV/atom) ss=0.000602 sl=0.000794
L= 31206.7976529696 (J/mol) ss=58.027496 sl=76.437718
L= 1111115.7748689589 (J/kg) ss=2066.064819 sl=2721.559412
</pre>

<gallery caption="The Gibbs free energy (in eV/atom) as a function of temperature (in K) of the solid (blue) and liquid (green) phases of silicon described by the Stillinger-Weber (SW) potential. The intersection of the two curves determines the melting point." widths="300px" height="200px" perrow="1">
Image:SW_Si_Tm.jpg
</gallery>

== Melting point of Other Elements ==

===MEAM Si===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1140.1</math> K, <math>L = 1315 J/g </math>, <math>S_S = 48.70 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.91 J/(\mbox{mol}\cdot K) </math>.

The above results are in good agreement with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1411.3 \pm 0.4</math> K, <math>L = 1309 J/g </math>, <math>S_S = 48.74 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 74.79 J/(\mbox{mol}\cdot K) </math>.

===MEAM Au===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1145</math> K, <math>L = 92.4 J/g </math>, <math>S_S = 77.63 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 93.52 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1120.0 \pm 0.6</math> K, <math>L = 92 J/g </math>, <math>S_S = 77.47 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 93.72 J/(\mbox{mol}\cdot K) </math>.

The agreement on <math>L</math>, <math>S_S</math>, and <math>S_L</math> is pretty good. The values of <math>T_m</math> do not agree so well.

===EAM Au===
Following the same procedure, we can evaluate the melting point of Cu with the '''eam''' potential. The results are <math>T_m = 1229.6</math> K, <math>L = 161 J/g </math>, <math>S_S = 71.57 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 79.90 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1239.6 \pm 2.3</math> K, <math>L = 164 J/g </math>, <math>S_S = 71.78 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 80.17 J/(\mbox{mol}\cdot K) </math>.

The relative differences in <math>T_m</math>, <math>L</math>, <math>S_S</math>, and <math>S_L</math> are all around or less 1%.

===MEAM Ge===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1216.5 </math> K, <math>L = 426.8 J/g </math>, <math>S_S = 58.36 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.85 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1216.2 \pm 0.6</math> K, <math>L = 427 J/g </math>, <math>S_S = 58.34 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.84 J/(\mbox{mol}\cdot K) </math>.

The agreement is fantastic

===SW Ge===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 2902.1</math> K, <math>L = 836.3 J/g </math>, <math>S_S = 84.4 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 105.3 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 2898.0 \pm 1.7</math> K, <math>L = 847 J/g </math>, <math>S_S = 84.07 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 105.30 J/(\mbox{mol}\cdot K) </math>.

The agreement is OK, not too outside the error bar.

Wei Cai

2019-09-17T20:57:30Z

Caiwei:

Professor 
Mechanics and Computation 
Mechanical Engineering Department 
Stanford University

Building 520 Room 126 
452 Escondido Mall 
Stanford, CA 94305-4040 
Phone: 650-736-1671

[http://www.stanford.edu/~caiwei Wei Cai's home page]

[[Wei's Bookshelf]]

Computing Melting Point by Free Energy Method

2019-04-02T21:21:25Z

Caiwei: /* Melting point of Other Elements */

Computing Melting Point by Free Eneregy Method
<DIV>
Seunghwa Ryu and Wei Cai
</DIV>
Modified by Yanming Wang (Sep 2015)

This tutorial describes how to compute melting points from free energy methods. We provide the MD++ script files and describe how to use them in detail. The theoretical background is published in

Comparison of Thermal Properties Predicted by Interatomic Potential Models, ''Modelling and Simulation in Materials Science and Engineering'', '''16''', 085005 (2008). [http://micro.stanford.edu/~caiwei/papers/Ryu08msmse-meltingT.pdf (PDF)] (Paper selected as [http://www.iop.org/EJ/journal/-page=featured/0965-0393 MSMSE featured article]).
<HR>

==Download files==

First, you need to install MD++ on your computer by following the instructions on [[MD++_Manuals | MD++ Manuals]].

Second, copy files [[media:melting_cubic.tcl.txt‎ | melting_cubic.tcl]] and
[[media:melting_noncubic.tcl.txt‎ | melting_noncubic.tcl]] to your input file directory of MD++. You can do so by the following commands (assuming you have installed MD++ in <tt>~/Codes/MD++</tt>).

<pre>
export MDPP=~/Codes/MD++
mkdir -p ${MDPP}/scripts/work/melting
cd ${MDPP}/scripts/work/melting
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melting_cubic.tcl.txt -O melting_cubic.tcl
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melting_noncubic.tcl.txt -O melting_noncubic.tcl
</pre>

Both files contain a big comment section in the beginning that describes in detail the (16) steps to compute the melting point. These steps are fully automated. In this tutorial, we describe how to run these scripts on a parallel cluster (using wcr.stanford.edu as an example) and what kind of results you should expect.

==Compile executable file==

Different executables in MD++ contains different interatomic potentials, for example,
<pre>
sw - Stillinger-Weber Silicon (modified by Balamane et al.)
sworig - Original version of SW Silicon
swge - Stillinger-Weber Germanium
tersoff - Tersoff potential for Silicon
meam-lammps - MEAM (taken from lammps)
meam-baskes - MEAM (taken from Baskes's code dynamo)
meam - MEAM (directly implemented in MD++)
eam - Embedded Atom Method
fs - Finnis-Sinclair
</pre>

Here we use Si as an example. You can compile <tt>sworig</tt> by typing
<pre>
cd ${MDPP}
make sworig build=R SYS=wcr
</pre>
If compilation is successful, this will create binary file <tt>sworig_wcr</tt> file in your <tt>${MDPP}/bin</tt> directory.

The script [[media:melting_cubic.tcl.txt‎ | melting_cubic.tcl]] can be used with many potentials (i.e. executables), which are explained in the header region of the file. Contact <tt>shryu@stanford.edu</tt> if you have further questions.

==Submit jobs==

Here are the PBS scripts ([[media:melt1.pbs.txt‎ |melt1.pbs]] and
[[media:melt2.pbs.txt‎ |melt2.pbs]]) for submitting the jobs on wcr.stanford.edu. You can submit jobs by typing the following commands. This is a test case that computes the melting points of silicon described by the Stillinger-Weber (SW) potential on the parallel cluster wcr.stanford.edu.

<pre>
cd ${MDPP}
mkdir runs/Single_Elem_Tm
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melt1.pbs.txt -O melt1.pbs
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melt2.pbs.txt -O melt2.pbs
qsub melt1.pbs
qsub melt2.pbs
</pre>

After the calculation is finished (within 24 hours), the free energy data will be stored in the following two directories.

<pre>
${MDPP}/runs/Single_Elem_Tm/SW_Si_Solid/
${MDPP}/runs/Single_Elem_Tm/SW_Si_Liquid/
</pre>

==Analyse data==

At the end of the calculation, data files and Matlab files will be automatically generated. Transfer these files to a location where you have Matlab installed. Run the following commands in Matlab and you will get the free energy plot (for solid and liquid phases). The melting point is the temperature at which the two free energy curves cross.

In this test case, the analysis files are generated in directory
<tt>${MDPP}/runs/Single_Elem_Tm</tt>. They are

<pre>
Hessian_SW_Si.m
Free_Energy_of_SW_Si.m
tar_SW_Si
</pre>

Run the following command to zip all data
<pre>
cd ${MDPP}/runs/Single_Elem_Tm
./tar_SW_Si
</pre>
into a tar file <tt>inter_SW_Si.tar</tt>.

Copy this file to your local computer and unzip the data. Next, run the following command in Matlab.
<pre>
Hessian_SW_Si.m
Free_Energy_of_SW_Si.m
</pre>

You'll see the following output files that contain all free energy data and the error analysis.

<pre>
Solid Free Energy Info

lattice const = 5.43095
strain = 0.00518
E_0 = -2218.74337 eV ( -4.33348 eV/atom)
F_w = -253.34582 eV ( -0.49482 eV/atom)
F_ha = E_0 + F_w = -2472.08919 eV ( -4.82830 eV/atom)
W_re_to_ha = 5.99169 eV ( 0.01170 eV/atom)
W_ha_to_re = -7.30068 eV ( -0.01426 eV/atom)
F_re - F_ha = (W_ha_to_re - W_re_to_ha)/2 = -6.64619 eV ( -0.01298 eV/atom)
F_re at 1600.000000 = -2478.73538 eV ( -4.84128 eV/atom)
W_T1_to_T11 = 417.87095 eV ( 0.81615 eV/atom)
W_T11_to_T1 = -417.87508 eV ( -0.81616 eV/atom)
dW1 = (W_T1_to_T11 - W_T11_to_T1)/2 = 417.87302 eV ( 0.81616 eV/atom)
F_re at 2000.000000 = -2605.55266 eV ( -5.08897 eV/atom)
</pre>

<pre>
Liquid Free Energy Info

strain = -0.01894
F_ideal = -919.36940 ( -1.79564 eV/atom)
W_re_to_ga = 1888.21102 eV ( 3.68791 eV/atom)
W_ga_to_re = -1887.53306 eV ( -3.68659 eV/atom)
F_re - F_ga = (W_ga_to_re - W_re_to_ga)/2 = -1887.87204 eV ( -3.68725 eV/atom)
W_ga_to_id = -256.29295 eV ( -0.50057 eV/atom)
W_id_to_ga = 256.52177 eV ( 0.50102 eV/atom)
F_ga - F_id = (W_id_to_ga - W_ga_to_id)/2 = 256.40736 eV ( 0.50080 eV/atom)
F_re at 1800.000000 = -2550.83408 eV ( -4.98210 eV/atom)
W_T2_to_T22 = -583.02785 eV ( -1.13873 eV/atom)
W_T22_to_T2 = 583.06542 eV ( 1.13880 eV/atom)
dW2 = (W_T2_to_T22 - W_T22_to_T2)/2 = -583.04664 eV ( -1.13876 eV/atom)
F_re at 1384.615385 = -2386.68534 eV ( -4.66149 eV/atom)
</pre>

<pre>
Error Analysis

Solid Side
Err_re_to_ha = 0.02769 eV ( 0.00005407 eV/atom)( 0.628 K)
Err_ha_to_re = 0.02815 eV ( 0.00005498 eV/atom)( 0.638 K)
Err_T1_to_T11 = 0.00374 eV ( 0.00000730 eV/atom)( 0.085 K)
Err_T11_to_T1 = 0.00441 eV ( 0.00000861 eV/atom)( 0.100 K)

Liquid Side
Err_re_to_ga = 0.04793 eV ( 0.00009362 eV/atom)( 1.086 K)
Err_ga_to_re = 0.06601 eV ( 0.00012893 eV/atom)( 1.496 K)
Err_ga_to_id = 0.02557 eV ( 0.00004993 eV/atom)( 0.580 K)
Err_id_to_ga = 0.03421 eV ( 0.00006682 eV/atom)( 0.776 K)
Err_T2_to_T22 = 0.01488 eV ( 0.00002906 eV/atom)( 0.337 K)
Err_T22_to_T2 = 0.01183 eV ( 0.00002311 eV/atom)( 0.268 K)
Max dT = 2.315
Tm= 1695.08000 (K), err= 1.044 Fm = -4.89779 (eV/atom)
L= 165.8833097832 (eV) Ss=0.308452 Sl=0.406313
L= 0.3239908394 (eV/atom) ss=0.000602 sl=0.000794
L= 31206.7976529696 (J/mol) ss=58.027496 sl=76.437718
L= 1111115.7748689589 (J/kg) ss=2066.064819 sl=2721.559412
</pre>

<gallery caption="The Gibbs free energy (in eV/atom) as a function of temperature (in K) of the solid (blue) and liquid (green) phases of silicon described by the Stillinger-Weber (SW) potential. The intersection of the two curves determines the melting point." widths="300px" height="200px" perrow="1">
Image:SW_Si_Tm.jpg
</gallery>

== Melting point of Other Elements ==

===MEAM Si===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1140.1</math> K, <math>L = 1315 J/g </math>, <math>S_S = 48.70 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.91 J/(\mbox{mol}\cdot K) </math>.

The above results are in good agreement with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1411.3 \pm 0.4</math> K, <math>L = 1309 J/g </math>, <math>S_S = 48.74 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 74.79 J/(\mbox{mol}\cdot K) </math>.

===MEAM Au===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1145</math> K, <math>L = 92.4 J/g </math>, <math>S_S = 77.63 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 93.52 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1120.0 \pm 0.6</math> K, <math>L = 92 J/g </math>, <math>S_S = 77.47 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 93.72 J/(\mbox{mol}\cdot K) </math>.

The agreement on <math>L</math>, <math>S_S</math>, and <math>S_L</math> is pretty good. The values of <math>T_m</math> do not agree so well.

===EAM Au===
Following the same procedure, we can evaluate the melting point of Cu with the '''eam''' potential. The results are <math>T_m = 1229.6</math> K, <math>L = 161 J/g </math>, <math>S_S = 71.57 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 79.90 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1239.6 \pm 2.3</math> K, <math>L = 164 J/g </math>, <math>S_S = 71.78 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 80.17 J/(\mbox{mol}\cdot K) </math>.

The relative differences in <math>T_m</math>, <math>L</math>, <math>S_S</math>, and <math>S_L</math> are all around or less 1%.

===MEAM Ge===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1216.5 </math> K, <math>L = 426.8 J/g </math>, <math>S_S = 58.36 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.85 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1216.2 \pm 0.6</math> K, <math>L = 427 J/g </math>, <math>S_S = 58.34 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.84 J/(\mbox{mol}\cdot K) </math>.

The agreement is fantastic

===SW Ge===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 2902.1</math> K, <math>L = 836.3 J/g </math>, <math>S_S = 84.4 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 105.3 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 2898.0 \pm 1.7</math> K, <math>L = 847 J/g </math>, <math>S_S = 84.07 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 105.30 J/(\mbox{mol}\cdot K) </math>.

The agreement is OK, not too outside the error bar.

How to install Moose

2017-06-11T18:04:02Z

Caiwei: /* Create MOOSE Profile */

How to install MOOSE
<DIV>
Yanming Wang
June, 2017
 <HR>

[http://mooseframework.org MOOSE], short for Multiphysics Object-Oriented Simulation Environment, is a finite-element multi-physics framework developed by Idaho National Laboratory. Here we briefly describe how to install MOOSE on the [https://web.stanford.edu/group/hpcc/cgi-bin/certainty/index.php/Main_Page Certainty cluster].

== System requirements ==
The installation of MOOSE requires Compiler: C++11 Compliant GCC 4.8.4, Clang 3.4.0, Intel20130607, and Python 2.7+. On Certainty, they are provided as modules, so you can simply type the following commands to load them,

module load gnu/4.7.2
module load clang/3.5.2
module load gnu/5.2
module load openmpi/1.10.2-gnu-5.2
module load cmake/2.8.12.2

Or you can copy and paste them in your '''~/.bashrc''' file, which will load the modules automatically when you login to Certainty. Notice that on Certainty '''clang''' requires some libraries from '''gnu/4.7.2''', so that you have to load '''gnu/4.7.2''' first and update it later (to '''gnu/5.2''' in this case) to satisfy the MOOSE requirement. Also, the version of '''openmpi''' compiler should be compatible with the '''gcc''' compiler.

== Installation ==
The procedures of MOOSE installation is given in details on their [http://mooseframework.org/getting-started/ official website].
=== PETSc ===
First, you need to install PETSc following the following steps. (mostly follow the official tutorial)
==== PREFIX Setup ====
export CLUSTER_TEMP=`mktemp -d /tmp/cluster_temp.XXXXXX`
export PACKAGES_DIR=$HOME/moose-compilers
==== Download Software ====
cd $CLUSTER_TEMP
curl -L -O http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-3.6.4.tar.gz
==== Extract Software ====
cd $CLUSTER_TEMP
tar -xf petsc-3.6.4.tar.gz
==== Create MOOSE Profile ====
Make note of your $PACKAGES_DIR:

echo $PACKAGES_DIR
Edit the following file:

$HOME/.moose-profile
Add the following content to that file:

export PACKAGES_DIR=INSERT-PACKAGES-DIR-HERE!!!!

export CC=mpicc
export CXX=mpicxx
export F90=mpif90
export F77=mpif77
export FC=mpif90

export ARCH=gcc
export PETSC_DIR=$PACKAGES_DIR/petsc/petsc-3.6.4/$ARCH-opt

And run,
source ~/.moose-profile

==== Build and Install PETSc ====
cd $CLUSTER_TEMP/petsc-3.6.4

./configure \
--prefix=$PETSC_DIR \
--download-hypre=1 \
--with-ssl=0 \
--with-debugging=yes \
--with-pic=1 \
--with-shared-libraries=1 \
--with-cc=mpicc \
--with-cxx=mpicxx \
--with-fc=mpif90 \
--download-fblaslapack=1 \
--download-metis=1 \
--download-parmetis=1 \
--download-superlu_dist=1 \
--download-scalapack=1 \
--download-mumps=1 \
CC=mpicc CXX=mpicxx FC=mpif90 F77=mpif77 F90=mpif90 \
CFLAGS='-fPIC -fopenmp' \
CXXFLAGS='-fPIC -fopenmp' \
FFLAGS='-fPIC -fopenmp' \
FCFLAGS='-fPIC -fopenmp' \
F90FLAGS='-fPIC -fopenmp' \
F77FLAGS='-fPIC -fopenmp' \
PETSC_DIR=`pwd`

At the end of the configure step, the system will print out messages on your terminal window. The last printed section contains the make command you will need to enter on your terminal window. At the end of the make step, there will be another message about the make install commands. Just follow them to complete the setup. An example is the following. The specific folder you will need to enter will be different. Just copy and paste the printed out message.

make PETSC_DIR=/tmp/cluster_temp.wowSIm/petsc-3.6.4 PETSC_ARCH=arch-linux2-c-debug all
make PETSC_DIR=/tmp/cluster_temp.wowSIm/petsc-3.6.4 PETSC_ARCH=arch-linux2-c-debug install

== Clone MOOSE ==
You can do exactly the same as suggested by their official tutorial.

mkdir ~/projects
cd ~/projects
git clone https://github.com/idaholab/moose.git
cd ~/projects/moose
git checkout master

== Compile libMesh ==
This step is straight forward, but you may need some patience. The compilation may take up to an hour.
cd ~/projects/moose
scripts/update_and_rebuild_libmesh.sh

== Test ==
cd ~/projects/moose/test
make -j8
./run_tests -j8

The test results should look like
Ran 1329 tests in 191.7 seconds
1328 passed, 51 skipped, 0 pending, 1 FAILED
You may receive one message regarding the failed item,
preconditioners/pbp.lots_of_variables....................................................... FAILED (TIMEOUT)
Don't worry about it. This is a timed test, which most likely indicates that the computer is running slow (or the machine is overburdened).

How to install Moose

2017-06-11T17:48:35Z

Caiwei: /* Build and Install PETSc */

How to install MOOSE
<DIV>
Yanming Wang
June, 2017
 <HR>

[http://mooseframework.org MOOSE], short for Multiphysics Object-Oriented Simulation Environment, is a finite-element multi-physics framework developed by Idaho National Laboratory. Here we briefly describe how to install MOOSE on the [https://web.stanford.edu/group/hpcc/cgi-bin/certainty/index.php/Main_Page Certainty cluster].

== System requirements ==
The installation of MOOSE requires Compiler: C++11 Compliant GCC 4.8.4, Clang 3.4.0, Intel20130607, and Python 2.7+. On Certainty, they are provided as modules, so you can simply type the following commands to load them,

module load gnu/4.7.2
module load clang/3.5.2
module load gnu/5.2
module load openmpi/1.10.2-gnu-5.2
module load cmake/2.8.12.2

Or you can copy and paste them in your '''~/.bashrc''' file, which will load the modules automatically when you login to Certainty. Notice that on Certainty '''clang''' requires some libraries from '''gnu/4.7.2''', so that you have to load '''gnu/4.7.2''' first and update it later (to '''gnu/5.2''' in this case) to satisfy the MOOSE requirement. Also, the version of '''openmpi''' compiler should be compatible with the '''gcc''' compiler.

== Installation ==
The procedures of MOOSE installation is given in details on their [http://mooseframework.org/getting-started/ official website].
=== PETSc ===
First, you need to install PETSc following the following steps. (mostly follow the official tutorial)
==== PREFIX Setup ====
export CLUSTER_TEMP=`mktemp -d /tmp/cluster_temp.XXXXXX`
export PACKAGES_DIR=$HOME/moose-compilers
==== Download Software ====
cd $CLUSTER_TEMP
curl -L -O http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-3.6.4.tar.gz
==== Extract Software ====
cd $CLUSTER_TEMP
tar -xf petsc-3.6.4.tar.gz
==== Create MOOSE Profile ====
Make note of your $PACKAGES_DIR:

echo $PACKAGES_DIR
Edit the following file:

$HOME/.moose-profile
Add the following content to that file:

export PACKAGES_DIR=INSERT-PACKAGES-DIR-HERE!!!!

export CC=mpicc
export CXX=mpicxx
export F90=mpif90
export F77=mpif77
export FC=mpif90

export ARCH=gcc
export PETSC_DIR=$PACKAGES_DIR/petsc/petsc-3.6.4/$ARCH-opt

And run,
source ~/.moose-profile
==== Build and Install PETSc ====
cd $CLUSTER_TEMP/petsc-3.6.4

./configure \
--prefix=$PETSC_DIR \
--download-hypre=1 \
--with-ssl=0 \
--with-debugging=yes \
--with-pic=1 \
--with-shared-libraries=1 \
--with-cc=mpicc \
--with-cxx=mpicxx \
--with-fc=mpif90 \
--download-fblaslapack=1 \
--download-metis=1 \
--download-parmetis=1 \
--download-superlu_dist=1 \
--download-scalapack=1 \
--download-mumps=1 \
CC=mpicc CXX=mpicxx FC=mpif90 F77=mpif77 F90=mpif90 \
CFLAGS='-fPIC -fopenmp' \
CXXFLAGS='-fPIC -fopenmp' \
FFLAGS='-fPIC -fopenmp' \
FCFLAGS='-fPIC -fopenmp' \
F90FLAGS='-fPIC -fopenmp' \
F77FLAGS='-fPIC -fopenmp' \
PETSC_DIR=`pwd`

At the end of the configure step, the system will print out messages on your terminal window. The last printed section contains the make command you will need to enter on your terminal window. At the end of the make step, there will be another message about the make install commands. Just follow them to complete the setup. An example is the following. The specific folder you will need to enter will be different. Just copy and paste the printed out message.

make PETSC_DIR=/tmp/cluster_temp.wowSIm/petsc-3.6.4 PETSC_ARCH=arch-linux2-c-debug all
make PETSC_DIR=/tmp/cluster_temp.wowSIm/petsc-3.6.4 PETSC_ARCH=arch-linux2-c-debug install

== Clone MOOSE ==
You can do exactly the same as suggested by their official tutorial.

mkdir ~/projects
cd ~/projects
git clone https://github.com/idaholab/moose.git
cd ~/projects/moose
git checkout master

== Compile libMesh ==
This step is straight forward, but you may need some patience. The compilation may take up to an hour.
cd ~/projects/moose
scripts/update_and_rebuild_libmesh.sh

== Test ==
cd ~/projects/moose/test
make -j8
./run_tests -j8

The test results should look like
Ran 1329 tests in 191.7 seconds
1328 passed, 51 skipped, 0 pending, 1 FAILED
You may receive one message regarding the failed item,
preconditioners/pbp.lots_of_variables....................................................... FAILED (TIMEOUT)
Don't worry about it. This is a timed test, which most likely indicates that the computer is running slow (or the machine is overburdened).

How to install Moose

2017-06-11T17:45:34Z

Caiwei: /* Installation */

How to install MOOSE
<DIV>
Yanming Wang
June, 2017
 <HR>

[http://mooseframework.org MOOSE], short for Multiphysics Object-Oriented Simulation Environment, is a finite-element multi-physics framework developed by Idaho National Laboratory. Here we briefly describe how to install MOOSE on the [https://web.stanford.edu/group/hpcc/cgi-bin/certainty/index.php/Main_Page Certainty cluster].

== System requirements ==
The installation of MOOSE requires Compiler: C++11 Compliant GCC 4.8.4, Clang 3.4.0, Intel20130607, and Python 2.7+. On Certainty, they are provided as modules, so you can simply type the following commands to load them,

module load gnu/4.7.2
module load clang/3.5.2
module load gnu/5.2
module load openmpi/1.10.2-gnu-5.2
module load cmake/2.8.12.2

Or you can copy and paste them in your '''~/.bashrc''' file, which will load the modules automatically when you login to Certainty. Notice that on Certainty '''clang''' requires some libraries from '''gnu/4.7.2''', so that you have to load '''gnu/4.7.2''' first and update it later (to '''gnu/5.2''' in this case) to satisfy the MOOSE requirement. Also, the version of '''openmpi''' compiler should be compatible with the '''gcc''' compiler.

== Installation ==
The procedures of MOOSE installation is given in details on their [http://mooseframework.org/getting-started/ official website].
=== PETSc ===
First, you need to install PETSc following the following steps. (mostly follow the official tutorial)
==== PREFIX Setup ====
export CLUSTER_TEMP=`mktemp -d /tmp/cluster_temp.XXXXXX`
export PACKAGES_DIR=$HOME/moose-compilers
==== Download Software ====
cd $CLUSTER_TEMP
curl -L -O http://ftp.mcs.anl.gov/pub/petsc/release-snapshots/petsc-3.6.4.tar.gz
==== Extract Software ====
cd $CLUSTER_TEMP
tar -xf petsc-3.6.4.tar.gz
==== Create MOOSE Profile ====
Make note of your $PACKAGES_DIR:

echo $PACKAGES_DIR
Edit the following file:

$HOME/.moose-profile
Add the following content to that file:

export PACKAGES_DIR=INSERT-PACKAGES-DIR-HERE!!!!

export CC=mpicc
export CXX=mpicxx
export F90=mpif90
export F77=mpif77
export FC=mpif90

export ARCH=gcc
export PETSC_DIR=$PACKAGES_DIR/petsc/petsc-3.6.4/$ARCH-opt

And run,
source ~/.moose-profile
==== Build and Install PETSc ====
cd $CLUSTER_TEMP/petsc-3.6.4

./configure \
--prefix=$PETSC_DIR \
--download-hypre=1 \
--with-ssl=0 \
--with-debugging=yes \
--with-pic=1 \
--with-shared-libraries=1 \
--with-cc=mpicc \
--with-cxx=mpicxx \
--with-fc=mpif90 \
--download-fblaslapack=1 \
--download-metis=1 \
--download-parmetis=1 \
--download-superlu_dist=1 \
--download-scalapack=1 \
--download-mumps=1 \
CC=mpicc CXX=mpicxx FC=mpif90 F77=mpif77 F90=mpif90 \
CFLAGS='-fPIC -fopenmp' \
CXXFLAGS='-fPIC -fopenmp' \
FFLAGS='-fPIC -fopenmp' \
FCFLAGS='-fPIC -fopenmp' \
F90FLAGS='-fPIC -fopenmp' \
F77FLAGS='-fPIC -fopenmp' \
PETSC_DIR=`pwd`

During the installation, the system will pop up messages on your terminal window, suggesting make / make install commands. Just follow them to complete the setup. An example is the following.

make PETSC_DIR=/tmp/cluster_temp.wowSIm/petsc-3.6.4 PETSC_ARCH=arch-linux2-c-debug all
make PETSC_DIR=/tmp/cluster_temp.wowSIm/petsc-3.6.4 PETSC_ARCH=arch-linux2-c-debug install

== Clone MOOSE ==
You can do exactly the same as suggested by their official tutorial.

mkdir ~/projects
cd ~/projects
git clone https://github.com/idaholab/moose.git
cd ~/projects/moose
git checkout master

== Compile libMesh ==
This step is straight forward, but you may need some patience. The compilation may take up to an hour.
cd ~/projects/moose
scripts/update_and_rebuild_libmesh.sh

== Test ==
cd ~/projects/moose/test
make -j8
./run_tests -j8

The test results should look like
Ran 1329 tests in 191.7 seconds
1328 passed, 51 skipped, 0 pending, 1 FAILED
You may receive one message regarding the failed item,
preconditioners/pbp.lots_of_variables....................................................... FAILED (TIMEOUT)
Don't worry about it. This is a timed test, which most likely indicates that the computer is running slow (or the machine is overburdened).

How to install deal.II

2017-05-16T22:36:11Z

Caiwei: Created page with " How to install deal.II <DIV> Yanming Wang <P ALIGN="CENT..."

How to install deal.II
<DIV>
Yanming Wang
May, 2017
 <HR>

Deal.II is an open Finite Element Method (FEM) code. Let's give a link. Here we explain how to install it on the Sherlock cluster...

(The following is copied from the wiki LAMMPS compilation.)

This page discusses how to compile LAMMPS on the clusters at Stanford. An executable file can be created for running MD simulation with MEAM potential following this instruction. Before we start to compile LAMMPS, we assume the LAMMPS package was downloaded from our '''svn''' server and was unzipped into the directory Codes/LAMMPS.svn/.

== LAMMPS on mc2 ==

The following command can be used to checkout a specific reversion of LAMMPS from our '''svn''' server.

svn checkout -r 23 http://micro.stanford.edu/svn/LAMMPS ~/Codes/LAMMPS.svn/

1. Copy Makefile.mc2 into Codes/LAMMPS.svn/src/MAKE/ directory using the following commands
cd ~/Codes/LAMMPS.svn
wget http://micro.stanford.edu/mediawiki/images/f/fb/Makefile.mc2.txt -O ./src/MAKE/Makefile.mc2

2. In any directory, type the following command
Export TARGET=mc2

3. In your home directory, make a folder named '''usr'''
mkdir ~/usr

4. Download the fftw library and unzip it using the following commands
cd ~/usr
wget http://micro.stanford.edu/mediawiki/images/9/9e/Fftw.tar -O fftw.tar
tar –zxvf fftw.tar

5. Make sure you have the modules for using '''icc''' and '''mpi''' complier, you can load the modules by adding the below two lines to your '''bash_profile''' file.
vi ~/.bash_profile (You can use whatever text editor to open the file and add the following lines)

module load intel/intel-11
module load mvapich/1.2rc1-intel-11-dell-gen2

Save the file and log out. Next time when you log in, the compilers should work for you.

To confirm the compiler is ready, you can inquiry the location of the compiler by typing
which icc
which mpicc
This will tell you where are the compilers.

6. Go to LAMMPS.svn directory
cd ~/Codes/LAMMPS.svn
make clean
make
This will make the executable file lmp_mc2 in LAMMPS.svn/src directory.

== LAMMPS on WCR ==

The system of WCR was rebuilt in June 2014 and the new Intel 14 compiler and MVAPICH2 wrappers were introduced onto the cluster. After this update, the old version LAMMPS on our '''svn''' server (before revision 24) cannot compile anymore. Accordingly, we updated a new version '''svn''' LAMMPS based on the Feb1-2014 package from the official LAMMPS website. The following command can be used to download this LAMMPS package to your current directory.

svn checkout -r 24 https://micro.stanford.edu/svn/LAMMPS ./

The compilation can be accomplished by the following steps.

1. Revise the ~/.bashrc file to add the needed modules for Intel 14 and MVAPICH2 compiler by adding the following words at the end of your ~/.bashrc file. You need to logout and re-login for the changes to take effect.

module load null intel/14 mvapich2/2.0rc1-intel-14

2. Install the FFTW library. First, in your home directory, make a folder named '''usr'''

mkdir ~/usr

Then download the fftw library and unzip it using the following commands
cd ~/usr
wget http://micro.stanford.edu/mediawiki/images/9/9e/Fftw.tar -O fftw.tar
tar –zxvf fftw.tar

3. If you only want to build LAMMPS with basic packages, you can do the followings.
cd ~/Codes/LAMMPS.svn/src/
make wcr
This will make the executable lmp_wcr in LAMMPS.svn/src directory. To speed up the compilation, you can use the "-j" switch with the make command.

4. If you want to build LAMMPS with optional packages, e.g., MEAM, see the below section.
First, type the following command. This will build the needed library for MEAM.
cd ~/Codes/LAMMPS.svn/lib/meam/
make -f Makefile.ifort
Then, go to the /src folder and install the meam package.
cd ~/Codes/LAMMPS.svn/src/
make yes-meam
Finally, do the compilation.
cd ~/Codes/LAMMPS.svn/src/
make -j wcr
You should get the executable lmp_wcr when the build is complete.

== LAMMPS compilation on WCR before June 2014 ==

1. Open Codes/LAMMPS.svn/Makefile file, add the following line below SYS = $(TARGET)
libFC.wcr = ifort

2. Copy Makefile.wcr into Codes/LAMMPS.svn/src/MAKE/ directory using the following commands/
cd ~/Codes/LAMMPS.svn
wget http://micro.stanford.edu/mediawiki/images/8/80/Makefile.wcr.txt -O ./src/MAKE/Makefile.wcr

3. In any directory, type the following command
Export TARGET=wcr

4. In your home directory, make a folder named usr
mkdir ~/usr

5. Download the fftw library and unzip it using the following commands
cd ~/usr
wget http://micro.stanford.edu/mediawiki/images/9/9e/Fftw.tar -O fftw.tar
tar –zxvf fftw.tar

6. Choose the modules for the compliers.
The following command can list the available modules on the cluster.
module avail
And the below command can give you the names of the modules you are currently using
module list
By default, one module is intel/intel-9, and we need to change it to intel/intel-11, which can be done by typing the commands.
module rm intel/intel-9
module load intel/intel-11
Still, you can make changes to your bash_profile to let the system load the modules automatically for you. So the following lines could be added to your ~/.bash_profile file.
module rm intel/intel-9
module load intel/intel-11
module load mvapich/1.2RC1-intel-11-gen2

7. Go to LAMMPS.svn directory
cd ~/Codes/LAMMPS.svn
make clean
make
This will make lmp_wcr in LAMMPS.svn/src directory.

== References ==

The below webpages would be useful when you are new to using the clusters.

https://www.stanford.edu/group/hpcc/cgi-bin/mediawiki/index.php/Main_Page

https://www.stanford.edu/group/hpcc/cgi-bin/mediawiki/index.php/I%27m_new_%26_don%27t_know_what_to_do

https://www.stanford.edu/group/hpcc/cgi-bin/mediawiki/index.php/New_to_Cluster_Computing

Tutorial:Members Only

2017-05-16T22:27:14Z

Caiwei: /* 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" | FEM Codes
|-
| [[How to install deal.II]]
|}

{| 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

2016-07-18T19:10:34Z

Caiwei:

__NOTOC__
===Professor===
:[[Wei Cai]]

===Graduate Students===
:[[Yanming Wang]]
:[[Yikai Yin]]

===Postocs===
:[[Nicolas Bertin]]
:[[Xiaohan Zhang]]
:[[Lihua Jin]]

===Former Members===
:[[Ryan Sills | Ryan Sills (former PhD student)]]
:[[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)]]

Wei Cai

2016-04-02T21:32:34Z

Caiwei:

Associate Professor 
Mechanics and Computation 
Mechanical Engineering Department 
Stanford University

Building 520 Room 126 
452 Escondido Mall 
Stanford, CA 94305-4040 
Phone: 650-736-1671

[http://www.stanford.edu/~caiwei Wei Cai's home page]

[[Wei's Bookshelf]]

Tutorial:Members Only

2016-03-18T05:55:18Z

Caiwei: /* 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]]
|-
| [[Computing Binary Phase Diagram in MD++]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | LAMMPS
|-
| [[Use Au-Si MEAM Potential in LAMMPS]]
|-
| [[Compile LAMMPS on GPU on Sherlock]]
|}

{| 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]]
|}

M04 Binary Junction

2016-03-18T05:53:12Z

Caiwei:

not available yet (someone still has to write it).

See [[From DDLab to ParaDiS]]

ParaDiS Manuals

2016-03-18T05:51:25Z

Caiwei:

<UL>

<LI> [[Overview of ParaDiS 2.2]]

<LI> [[Before You Start: Known Bugs in ParaDiS]]

<LI> [[M01 How to Obtain and Run ParaDiS]]

<LI> [[M02 Straight dislocations]]

<LI> [[M03 Frank-Read Source]]

<LI> [[M04 Binary Junction]]

<LI> [[M05 ParaDiS Flowchart]]

<LI> [[Create Straight Dislocations for ParaDiS Input]]

<LI> [[Programming tips for ParaDiS]]

<LI> [[ParaDiS FAQs]]

<LI> [[ParaDiS Manual Updated]]

</UL>

M03 Frank-Read Source

2016-03-18T05:45:59Z

Caiwei:

not available yet (somebody still has to write it)

Tutorial:Members Only

2015-10-15T01:08:10Z

Caiwei: /* 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]]
|}

{| 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]]
|-
| [[Computing Binary Phase Diagram in MD++]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | LAMMPS
|-
| [[Use Au-Si MEAM Potential in LAMMPS]]
|-
| [[Compile LAMMPS on GPU on Sherlock]]
|}

{| 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]]
|}

MEAM Potential for Au-Ge

2015-09-08T05:45:54Z

Caiwei: /* MEAM Potential for Ge */

MEAM Potential for Au-Ge
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


This tutorial explains how to specify the parameters for the Au-Ge MEAM potential in MD++. It starts with the parameters in pure Au and pure Ge potentials, then talks about the Au-Ge cross potential.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

The details for the original 'Au' potential can be found here
JUST REFER TO OTHER PAGE....!

UNDER CONSTRUCTION!!!!!

===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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Ge' 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
'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 Ge}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1.0 1.0 4.02 5.23 -1.6 0.9861 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 Ge}</math> = '''rozero''' will be important only for cross-potential. In our fitting it takes the value 0.9861 instead of the original one of 1.35 in Baskes paper.

'''ibar''' is a setting used in the equation of state (EOS). ibar selects the G(gamma) function in Eq (4) and (5) of the paper by BJ Lee, PRB 68, 144112 (2003).

While the functional form is quite different, the modulus is almost not affected by the choice of ibar.

The parameters for the cross potential are specified in the '''AuGe2nn.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 Ge==

The parameters for the cross potential are specified in '''AuGe2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below.
They are calculated from VASP LDA/PAW.

Similar values are found in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

RECALCULATE THIS VALUES FOR MY POTENTIAL AU-GE!!!
re(1,2) = 2.6495 new! (<math>r_e</math>)
delta(1,2) = -0.844 new! (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 4.927 new! (<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>)

The values for <math>E_c ({\rm AuGe}) = 4.734</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) - (-0.844) = 4.734</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 0.9861 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 = 0.310 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.169 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.31 </math> eV Ge impurity in FCC Au (VASP/LDA/PAW)
<math>E_2 = 1.02 </math> eV Au impurity in DC Ge (VASP/LDA/PAW)

The VASP values will need to be recalculated to US pseudopotential.

Cmax = 2.8 is the default value.

MEAM Potential for Au-Ge

2015-09-08T05:44:48Z

Caiwei: /* Cross Potential between Au and Ge */

MEAM Potential for Au-Ge
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


This tutorial explains how to specify the parameters for the Au-Ge MEAM potential in MD++. It starts with the parameters in pure Au and pure Ge potentials, then talks about the Au-Ge cross potential.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

The details for the original 'Au' potential can be found here
JUST REFER TO OTHER PAGE....!

UNDER CONSTRUCTION!!!!!

===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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Ge' 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
'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 Ge}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1.0 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 Ge}</math> = '''rozero''' will be important only for cross-potential. In our fitting it takes the value 0.861 instead of the original one of 1.35 in Baskes paper.

'''ibar''' is a setting used in the equation of state (EOS). ibar selects the G(gamma) function in Eq (4) and (5) of the paper by BJ Lee, PRB 68, 144112 (2003).

While the functional form is quite different, the modulus is almost not affected by the choice of ibar.

The parameters for the cross potential are specified in the '''AuGe2nn.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 Ge==

The parameters for the cross potential are specified in '''AuGe2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below.
They are calculated from VASP LDA/PAW.

Similar values are found in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

RECALCULATE THIS VALUES FOR MY POTENTIAL AU-GE!!!
re(1,2) = 2.6495 new! (<math>r_e</math>)
delta(1,2) = -0.844 new! (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 4.927 new! (<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>)

The values for <math>E_c ({\rm AuGe}) = 4.734</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) - (-0.844) = 4.734</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 0.9861 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 = 0.310 </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = 1.169 </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.31 </math> eV Ge impurity in FCC Au (VASP/LDA/PAW)
<math>E_2 = 1.02 </math> eV Au impurity in DC Ge (VASP/LDA/PAW)

The VASP values will need to be recalculated to US pseudopotential.

Cmax = 2.8 is the default value.

MEAM Potential for Au-Ge

2015-09-08T05:37:34Z

Caiwei: /* Cross Potential between Au and Ge */

MEAM Potential for Au-Ge
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


This tutorial explains how to specify the parameters for the Au-Ge MEAM potential in MD++. It starts with the parameters in pure Au and pure Ge potentials, then talks about the Au-Ge cross potential.
<HR>

==Potential for Pure Elements==

===Original MEAM Potential for Au===

The details for the original 'Au' potential can be found here
JUST REFER TO OTHER PAGE....!

UNDER CONSTRUCTION!!!!!

===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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Ge' 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
'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 Ge}</math>
alat esub asub t0 t1 t2 t3 rozero ibar
5.6575 3.85 1.0 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 Ge}</math> = '''rozero''' will be important only for cross-potential. In our fitting it takes the value 0.861 instead of the original one of 1.35 in Baskes paper.

'''ibar''' is a setting used in the equation of state (EOS). ibar selects the G(gamma) function in Eq (4) and (5) of the paper by BJ Lee, PRB 68, 144112 (2003).

While the functional form is quite different, the modulus is almost not affected by the choice of ibar.

The parameters for the cross potential are specified in the '''AuGe2nn.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 Ge==

The parameters for the cross potential are specified in '''AuGe2nn.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below.
They are calculated from VASP LDA/PAW.

Similar values are found in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

RECALCULATE THIS VALUES FOR MY POTENTIAL AU-GE!!!
re(1,2) = 2.6495 new! (<math>r_e</math>)
delta(1,2) = -0.844 new! (related to <math>E_c</math>, see below)
lattce(1,2) = b1
alpha(1,2) = 4.927 new! (<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>)

The values for <math>E_c ({\rm AuGe}) = 4.734</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) - (-0.844) = 4.734</math>.

<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 0.9861 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 = ?? </math> eV Ge impurity in FCC Au (MEAM)
<math>E_2 = ?? </math> eV Au impurity in DC Ge (MEAM)

These values are to be compared with VASP predictions

<math>E_1 = 0.31 </math> eV Ge impurity in FCC Au (VASP/LDA/PAW)
<math>E_2 = 1.02 </math> eV Au impurity in DC Ge (VASP/LDA/PAW)

The VASP values will need to be recalculated to US pseudopotential.

Cmax = 2.8 is the default value.

MEAM Potential for Au-Si

2015-09-08T03:03:33Z

Caiwei: /* Impurity energy */

MEAM Potential for Au-Si
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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 use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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 Au-Si

2015-09-08T02:59:46Z

Caiwei: /* Benchmark in MD++ */

MEAM Potential for Au-Si
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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 use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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.
Seunghwa: please confirm.

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 MEAM potential by MD++) does not agree well with the value in JPCM (2010) regardless of the cell size.

Use Au-Si MEAM Potential in LAMMPS

2015-09-08T02:49:08Z

Caiwei: /* MD++ test case */

Use Au-Si MEAM Potential in LAMMPS 
<DIV>
Yanming Wang, Seunghwa Ryu and Wei Cai
</DIV>
 Created June, 2012, Last modified July, 2014


This tutorial explains how to use Au-Si MEAM potential in LAMMPS on a cluster like '''mc2'''. It starts with the installation of LAMMPS on '''mc2''', then talks about the compiling of the Au-Si MEAM potential. This tutorial also includes a test case to make sure the result from LAMMPS with this MEAM potential is consistent with that from MD++.
<HR>

==Installing LAMMPS on '''mc2'''==

[http://lammps.sandia.gov/ LAMMPS] is a classical molecular dynamics code for large-scale atomic/molecular massively parallel simulation. On '''mc2''', you can get LAMMPS from our SVN server using the following commands.

mkdir -p ~/Codes/LAMMPS.svn
cd ~/Codes/LAMMPS.svn
svn co https://micro.stanford.edu/svn/LAMMPS .

Typing the following SVN command from within the "LAMMPS.svn" directory, you can update your LAMMPS package.

svn update

== Compiling MEAM potential in LAMMPS==

The compilation of MEAM potential has been changed starting from LAMMPS '''svn''' revision 24. For detailed instruction, please refer to [http://micro.stanford.edu/wiki/How_to_compile_LAMMPS How to compile LAMMPS].

Please notice the following content is only for the older version LAMMPS.

=== Preparing for parallel run ===

First, you need to download the [[media:fftw.tar.gz |fftw.tar.gz]] and upload this archive file to your account on '''mc2'''. In your home directory, make a new folder named usr, then type the following command to unzip the fftw library in your '''usr''' folder.

cd ~/usr
tar zxvf fftw.tar.gz

ALso add the following lines at the end of your '''~/.bash_profile''' file to clarify the compiler.

module load intel/intel-11
module load mvapich/1.2rc1-intel-11-dell-gen2

=== Preparing for compiling MEAM potential ===

Au-Si MEAM potential is a potential developed by Dr. Seunghwa Ryu and Prof. Wei Cai<ref>
[http://iopscience.iop.org/0953-8984/22/5/055401 Seunghwa Ryu and Wei Cai, "Molecular Dynamics Simulations of Gold-Catalyzed Growth of Silicon Bulk Crystals and Nanowires", Journal of Materials Research, 26, 2199 (2011).]</ref><ref>[http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8368065 Seunghwa Ryu and Wei Cai, "A Gold-Silicon Potential Fitted to the Binary Phase Diagram", Journal of Physics Condensed Matter, 22, 055401 (2010).]
</ref>for gold-silicon binary system. To compile this potential in LAMMPS, you need to open the Makefile file under the '''LAMMPS.svn''' directory, finding the following line

cd lib/meam; make -f Makefile.$(libFC.$(SYS)) F90FLAGS="-O -D_EROSE_FUNCTION=1"

and replace it with

cd lib/meam; make -f Makefile.$(libFC.$(SYS)) F90FLAGS="-O -D_EROSE_FUNCTION=3"

Next, in the '''~/.bash_profile''' file, add the following line to specify the system you are using.

export TARGET=mc2

Finally, go to LAMMPS.svn directory and type

make

This will make lmp_mc2 in LAMMPS.svn/src/ directory.

==Test cases==

===MD++ test cases===
Assuming you've got the latest MD++ package (e.g., revision 452 or later) from the '''svn''' server, you can download [[Media:Md++_meam_test_r452.tar |MD++ test case]] that contains one input '''tcl'''scripts and two configuration '''cn''' files, and unzip it under the MD++ home directory using the command
cd ~/Codes/MD++.svn/
tar -xvf Md++_meam_test_r452.tar

The compilation of MEAM on cluster (for example mc2) can be done with the following command,
make meam-lammps build=R SYS=mc2

Run the below command within the MD++ home folder to start the test cases.

Test case 1:
bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase1
Test case 2:
bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase2

The two runs will create two folders named as '''AuSiTestCase1''' and '''AuSiTestCase2''' in the '''Codes/MD++.svn/runs'''folder. In inside each folder, you can find one '''energy.txt''' file that stores the total potential energy value and one '''force.txt''' file that lists the forces act on each atom. You can download this Matlab code [[Media:Matlab_meam_check.tar |Energy and force check]] to test if your results are correct. When you unzip the tar file, you will have a folder named '''TEST''' that contains one Matlab script '''data_compare.m''' and several standard test case results for comparison. You need to put your '''force.txt''' and '''force.txt''' in the same folder, then the Matlab code will tell you if you pass the tests.

===LAMMPS test cases===

Assuming you've followed the previous instruction and compiled the LAMMPS executable successfully, you can start the test cases by downloading [[Media:Lammps_meam_test_r24.tar |LAMMPS test case]] and unzipping it within the LAMMPS home folder.
cd ~/Codes/LAMMPS.svn/
tar -xvf Lammps_meam_test_r24.tar

For mc2 test cases, you need to enter the folder created for each test case and submit your simulation request via a '''PBS''' script by typing

Test case 1:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase1/
qsub golammps.pbs

Test case 2:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase2/
qsub golammps.pbs

If you prefer to work on WCR, you can avoid touching the '''PBS''' scripts. Instead you can type

Test case 1:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase1/
../../src/lmp_wcr -in in.md

Test case 2:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase2/
../../src/lmp_wcr -in in.md

When the simulation is finished, in the same folder, it will create a '''log.md''' file contains potential energy value and a '''dump.md''' file contains force information. To check these results with the provided Matlab code, you need to copy these two files into the '''TEST''' folder generated by unzipping [[Media:Matlab_meam_check.tar |Energy and force check]]. The Matlab code will tell you if you pass the tests via the messages displayed on screen.

==Test case:Comparsion with MD++ ==
===(for LAMMPS before revision 24 and MD++ before revision 452)===
This section illustrates how to compare the simulation result from LAMMPS using the MEAM potential with that from MD++. A successful test will show MD++ and LAMMPS report the same potential energy and forces from a given atoms' configuration.

===MD++ test case===

Supposing you've known how to run MD++ code from [http://micro.stanford.edu/wiki/MD%2B%2B_Manuals our manuals] and downloaded the MD++ package from our SVN server, you can do the following test case.

Download [[media:md++_meam_testcase.tar.gz |md++_meam_testcase.tar.gz]], which contains a input '''tcl''' script, three configuration '''cn''' files and a help text file.

Unzip this '''gz''' file under the certain folder using the command

mkdir -p ~/Codes/MD++.svn/scripts/work/si_au
cd ~/Codes/MD++.svn/scripts/work/si_au
tar zxvf md++_meam_testcase.tar.gz

Compile the MEAM potential typing the below command and make sure that in src/Makefile file '''-D_EROSE_FUNCTION=3''' is specified under meam-lammps.

make meam-lammps build=R SYS=mc2

Run the simulation within the MD++ home folder. For example,

bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase1

This will read the atoms' configuration from AuSiTestCase1.cn, visualize the atoms and calculate the potential and forces of the system. Meanwhile, it provides one '''.lammps''' file for '''LAMMPS''' and one '''.cfg''' file for '''Atomeye'''. The potential energy in this case should be

EPOT = -18874.6969309944

You can compare this value with the number from LAMMPS later.

Run the second test case,

bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase2

You should get this potential energy

EPOT=-19301.21011320015

You can compare this value with the number from LAMMPS later.

===LAMMPS test case===

Download [[Media:lammps_meam_testcase.tar.gz |lammps_meam_testcase.tar.gz]] and unzip it by the command

mkdir ~/Codes/LAMMPS.svn/runs/AuSi_meam_test
cd ~/Codes/LAMMPS.svn/runs/AuSi_meam_test
tar zxvf lammps_meam_testcase.tar.gz

In this archive file, the '''in.md''' is the input script for[http://lammps.sandia.gov/doc/Manual.html LAMMPS]. The '''golammps.pbs''' can submit your simulation request onto the server. Run this LAMMPS test case, you should type

qsub golammps.pbs

When the simulation is finished, in the same folder, you can check the potential information in the '''lammps.out''' file and the forces information in the '''dump.md'''file. Specifically, if you read the configuration from '''AuSiTestCase1.lammpsdata''', you would expect the potential and forces results are exactly the same as those come from MD++ simulation, like the potential should be -1.88746969e+04.

==Seunghwa's Instructions on How to Use MEAM Au-Si Potential==

Adriano: please past the content here.

<references/>

Use Au-Si MEAM Potential in LAMMPS

2015-09-08T01:46:42Z

Caiwei: /* Test case:Comparsion with MD++ */

Use Au-Si MEAM Potential in LAMMPS 
<DIV>
Yanming Wang, Seunghwa Ryu and Wei Cai
</DIV>
 Created June, 2012, Last modified July, 2014


This tutorial explains how to use Au-Si MEAM potential in LAMMPS on a cluster like '''mc2'''. It starts with the installation of LAMMPS on '''mc2''', then talks about the compiling of the Au-Si MEAM potential. This tutorial also includes a test case to make sure the result from LAMMPS with this MEAM potential is consistent with that from MD++.
<HR>

==Installing LAMMPS on '''mc2'''==

[http://lammps.sandia.gov/ LAMMPS] is a classical molecular dynamics code for large-scale atomic/molecular massively parallel simulation. On '''mc2''', you can get LAMMPS from our SVN server using the following commands.

mkdir -p ~/Codes/LAMMPS.svn
cd ~/Codes/LAMMPS.svn
svn co https://micro.stanford.edu/svn/LAMMPS .

Typing the following SVN command from within the "LAMMPS.svn" directory, you can update your LAMMPS package.

svn update

== Compiling MEAM potential in LAMMPS==

The compilation of MEAM potential has been changed starting from LAMMPS '''svn''' revision 24. For detailed instruction, please refer to [http://micro.stanford.edu/wiki/How_to_compile_LAMMPS How to compile LAMMPS].

Please notice the following content is only for the older version LAMMPS.

=== Preparing for parallel run ===

First, you need to download the [[media:fftw.tar.gz |fftw.tar.gz]] and upload this archive file to your account on '''mc2'''. In your home directory, make a new folder named usr, then type the following command to unzip the fftw library in your '''usr''' folder.

cd ~/usr
tar zxvf fftw.tar.gz

ALso add the following lines at the end of your '''~/.bash_profile''' file to clarify the compiler.

module load intel/intel-11
module load mvapich/1.2rc1-intel-11-dell-gen2

=== Preparing for compiling MEAM potential ===

Au-Si MEAM potential is a potential developed by Dr. Seunghwa Ryu and Prof. Wei Cai<ref>
[http://iopscience.iop.org/0953-8984/22/5/055401 Seunghwa Ryu and Wei Cai, "Molecular Dynamics Simulations of Gold-Catalyzed Growth of Silicon Bulk Crystals and Nanowires", Journal of Materials Research, 26, 2199 (2011).]</ref><ref>[http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8368065 Seunghwa Ryu and Wei Cai, "A Gold-Silicon Potential Fitted to the Binary Phase Diagram", Journal of Physics Condensed Matter, 22, 055401 (2010).]
</ref>for gold-silicon binary system. To compile this potential in LAMMPS, you need to open the Makefile file under the '''LAMMPS.svn''' directory, finding the following line

cd lib/meam; make -f Makefile.$(libFC.$(SYS)) F90FLAGS="-O -D_EROSE_FUNCTION=1"

and replace it with

cd lib/meam; make -f Makefile.$(libFC.$(SYS)) F90FLAGS="-O -D_EROSE_FUNCTION=3"

Next, in the '''~/.bash_profile''' file, add the following line to specify the system you are using.

export TARGET=mc2

Finally, go to LAMMPS.svn directory and type

make

This will make lmp_mc2 in LAMMPS.svn/src/ directory.

==Test cases==

===MD++ test cases===
Assuming you've got the latest MD++ package (e.g., revision 452 or later) from the '''svn''' server, you can download [[Media:Md++_meam_test_r452.tar |MD++ test case]] that contains one input '''tcl'''scripts and two configuration '''cn''' files, and unzip it under the MD++ home directory using the command
cd ~/Codes/MD++.svn/
tar -xvf Md++_meam_test_r452.tar

The compilation of MEAM on cluster (for example mc2) can be done with the following command,
make meam-lammps build=R SYS=mc2

Run the below command within the MD++ home folder to start the test cases.

Test case 1:
bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase1
Test case 2:
bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase2

The two runs will create two folders named as '''AuSiTestCase1''' and '''AuSiTestCase2''' in the '''Codes/MD++.svn/runs'''folder. In inside each folder, you can find one '''energy.txt''' file that stores the total potential energy value and one '''force.txt''' file that lists the forces act on each atom. You can download this Matlab code [[Media:Matlab_meam_check.tar |Energy and force check]] to test if your results are correct. When you unzip the tar file, you will have a folder named '''TEST''' that contains one Matlab script '''data_compare.m''' and several standard test case results for comparison. You need to put your '''force.txt''' and '''force.txt''' in the same folder, then the Matlab code will tell you if you pass the tests.

===LAMMPS test cases===

Assuming you've followed the previous instruction and compiled the LAMMPS executable successfully, you can start the test cases by downloading [[Media:Lammps_meam_test_r24.tar |LAMMPS test case]] and unzipping it within the LAMMPS home folder.
cd ~/Codes/LAMMPS.svn/
tar -xvf Lammps_meam_test_r24.tar

For mc2 test cases, you need to enter the folder created for each test case and submit your simulation request via a '''PBS''' script by typing

Test case 1:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase1/
qsub golammps.pbs

Test case 2:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase2/
qsub golammps.pbs

If you prefer to work on WCR, you can avoid touching the '''PBS''' scripts. Instead you can type

Test case 1:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase1/
../../src/lmp_wcr -in in.md

Test case 2:
cd ~/Codes/LAMMPS.svn/runs/AuSiTestCase2/
../../src/lmp_wcr -in in.md

When the simulation is finished, in the same folder, it will create a '''log.md''' file contains potential energy value and a '''dump.md''' file contains force information. To check these results with the provided Matlab code, you need to copy these two files into the '''TEST''' folder generated by unzipping [[Media:Matlab_meam_check.tar |Energy and force check]]. The Matlab code will tell you if you pass the tests via the messages displayed on screen.

==Test case:Comparsion with MD++ ==
===(for LAMMPS before revision 24 and MD++ before revision 452)===
This section illustrates how to compare the simulation result from LAMMPS using the MEAM potential with that from MD++. A successful test will show MD++ and LAMMPS report the same potential energy and forces from a given atoms' configuration.

===MD++ test case===

Supposing you've known how to run MD++ code from [http://micro.stanford.edu/wiki/MD%2B%2B_Manuals our manuals] and downloaded the MD++ package from our SVN server, you can do the following test case.

Downlaod [[media:md++_meam_testcase.tar.gz |md++_meam_testcase.tar.gz]], which contains a input '''tcl''' script, three configuration '''cn''' files and a help text file.

Unzip this '''gz''' file under the certain folder using the command

mkdir -p ~/Codes/MD++.svn/scripts/work/si_au
cd ~/Codes/MD++.svn/scripts/work/si_au
tar zxvf md++_meam_testcase.tar.gz

Compile the MEAM potential typing the below command and make sure that in src/Makefile file '''-D_EROSE_FUNCTION=3''' is specified under meam-lammps.

make meam-lammps build=R SYS=mc2

Run the simulation within the MD++ home folder. for example,

bin/meam-lammps_mc2 scripts/work/si_au/si_au_compare.tcl AuSiTestCase1

This will read the atoms' configuration from AuSiTestCase1.cn, visualize the atoms and calculate the potential and forces of the system. Meanwhile, it provides one '''.lammps''' file for '''LAMMPS''' and one '''.cfg''' file for '''Atomeye'''. The potential energy in this case should be -18874.6969309944. You can compare this value with the number from LAMMPS later.

===LAMMPS test case===

Download [[Media:lammps_meam_testcase.tar.gz |lammps_meam_testcase.tar.gz]] and unzip it by the command

mkdir ~/Codes/LAMMPS.svn/runs/AuSi_meam_test
cd ~/Codes/LAMMPS.svn/runs/AuSi_meam_test
tar zxvf lammps_meam_testcase.tar.gz

In this archive file, the '''in.md''' is the input script for[http://lammps.sandia.gov/doc/Manual.html LAMMPS]. The '''golammps.pbs''' can submit your simulation request onto the server. Run this LAMMPS test case, you should type

qsub golammps.pbs

When the simulation is finished, in the same folder, you can check the potential information in the '''lammps.out''' file and the forces information in the '''dump.md'''file. Specifically, if you read the configuration from '''AuSiTestCase1.lammpsdata''', you would expect the potential and forces results are exactly the same as those come from MD++ simulation, like the potential should be -1.88746969e+04.

==Seunghwa's Instructions on How to Use MEAM Au-Si Potential==

Adriano: please past the content here.

<references/>

Computing Melting Point by Free Energy Method

2015-09-07T07:21:10Z

Caiwei: /* Melting point of MEAM Au */

Computing Melting Point by Free Eneregy Method
<DIV>
Seunghwa Ryu and Wei Cai
</DIV>
Modified by Yanming Wang (Sep 2015)

This tutorial describes how to compute melting points from free energy methods. We provide the MD++ script files and describe how to use them in detail. The theoretical background is published in

Comparison of Thermal Properties Predicted by Interatomic Potential Models, ''Modelling and Simulation in Materials Science and Engineering'', '''16''', 085005 (2008). [http://micro.stanford.edu/~caiwei/papers/Ryu08msmse-meltingT.pdf (PDF)] (Paper selected as [http://www.iop.org/EJ/journal/-page=featured/0965-0393 MSMSE featured article]).
<HR>

==Download files==

First, you need to install MD++ on your computer by following the instructions on [[MD++_Manuals | MD++ Manuals]].

Second, copy files [[media:melting_cubic.tcl.txt‎ | melting_cubic.tcl]] and
[[media:melting_noncubic.tcl.txt‎ | melting_noncubic.tcl]] to your input file directory of MD++. You can do so by the following commands (assuming you have installed MD++ in <tt>~/Codes/MD++</tt>).

<pre>
export MDPP=~/Codes/MD++
mkdir -p ${MDPP}/scripts/work/melting
cd ${MDPP}/scripts/work/melting
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melting_cubic.tcl.txt -O melting_cubic.tcl
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melting_noncubic.tcl.txt -O melting_noncubic.tcl
</pre>

Both files contain a big comment section in the beginning that describes in detail the (16) steps to compute the melting point. These steps are fully automated. In this tutorial, we describe how to run these scripts on a parallel cluster (using wcr.stanford.edu as an example) and what kind of results you should expect.

==Compile executable file==

Different executables in MD++ contains different interatomic potentials, for example,
<pre>
sw - Stillinger-Weber Silicon (modified by Balamane et al.)
sworig - Original version of SW Silicon
swge - Stillinger-Weber Germanium
tersoff - Tersoff potential for Silicon
meam-lammps - MEAM (taken from lammps)
meam-baskes - MEAM (taken from Baskes's code dynamo)
meam - MEAM (directly implemented in MD++)
eam - Embedded Atom Method
fs - Finnis-Sinclair
</pre>

Here we use Si as an example. You can compile <tt>sworig</tt> by typing
<pre>
cd ${MDPP}
make sworig build=R SYS=wcr
</pre>
If compilation is successful, this will create binary file <tt>sworig_wcr</tt> file in your <tt>${MDPP}/bin</tt> directory.

The script [[media:melting_cubic.tcl.txt‎ | melting_cubic.tcl]] can be used with many potentials (i.e. executables), which are explained in the header region of the file. Contact <tt>shryu@stanford.edu</tt> if you have further questions.

==Submit jobs==

Here are the PBS scripts ([[media:melt1.pbs.txt‎ |melt1.pbs]] and
[[media:melt2.pbs.txt‎ |melt2.pbs]]) for submitting the jobs on wcr.stanford.edu. You can submit jobs by typing the following commands. This is a test case that computes the melting points of silicon described by the Stillinger-Weber (SW) potential on the parallel cluster wcr.stanford.edu.

<pre>
cd ${MDPP}
mkdir runs/Single_Elem_Tm
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melt1.pbs.txt -O melt1.pbs
wget http://micro.stanford.edu/mediawiki-1.11.0/images/Melt2.pbs.txt -O melt2.pbs
qsub melt1.pbs
qsub melt2.pbs
</pre>

After the calculation is finished (within 24 hours), the free energy data will be stored in the following two directories.

<pre>
${MDPP}/runs/Single_Elem_Tm/SW_Si_Solid/
${MDPP}/runs/Single_Elem_Tm/SW_Si_Liquid/
</pre>

==Analyse data==

At the end of the calculation, data files and Matlab files will be automatically generated. Transfer these files to a location where you have Matlab installed. Run the following commands in Matlab and you will get the free energy plot (for solid and liquid phases). The melting point is the temperature at which the two free energy curves cross.

In this test case, the analysis files are generated in directory
<tt>${MDPP}/runs/Single_Elem_Tm</tt>. They are

<pre>
Hessian_SW_Si.m
Free_Energy_of_SW_Si.m
tar_SW_Si
</pre>

Run the following command to zip all data
<pre>
cd ${MDPP}/runs/Single_Elem_Tm
./tar_SW_Si
</pre>
into a tar file <tt>inter_SW_Si.tar</tt>.

Copy this file to your local computer and unzip the data. Next, run the following command in Matlab.
<pre>
Hessian_SW_Si.m
Free_Energy_of_SW_Si.m
</pre>

You'll see the following output files that contain all free energy data and the error analysis.

<pre>
Solid Free Energy Info

lattice const = 5.43095
strain = 0.00518
E_0 = -2218.74337 eV ( -4.33348 eV/atom)
F_w = -253.34582 eV ( -0.49482 eV/atom)
F_ha = E_0 + F_w = -2472.08919 eV ( -4.82830 eV/atom)
W_re_to_ha = 5.99169 eV ( 0.01170 eV/atom)
W_ha_to_re = -7.30068 eV ( -0.01426 eV/atom)
F_re - F_ha = (W_ha_to_re - W_re_to_ha)/2 = -6.64619 eV ( -0.01298 eV/atom)
F_re at 1600.000000 = -2478.73538 eV ( -4.84128 eV/atom)
W_T1_to_T11 = 417.87095 eV ( 0.81615 eV/atom)
W_T11_to_T1 = -417.87508 eV ( -0.81616 eV/atom)
dW1 = (W_T1_to_T11 - W_T11_to_T1)/2 = 417.87302 eV ( 0.81616 eV/atom)
F_re at 2000.000000 = -2605.55266 eV ( -5.08897 eV/atom)
</pre>

<pre>
Liquid Free Energy Info

strain = -0.01894
F_ideal = -919.36940 ( -1.79564 eV/atom)
W_re_to_ga = 1888.21102 eV ( 3.68791 eV/atom)
W_ga_to_re = -1887.53306 eV ( -3.68659 eV/atom)
F_re - F_ga = (W_ga_to_re - W_re_to_ga)/2 = -1887.87204 eV ( -3.68725 eV/atom)
W_ga_to_id = -256.29295 eV ( -0.50057 eV/atom)
W_id_to_ga = 256.52177 eV ( 0.50102 eV/atom)
F_ga - F_id = (W_id_to_ga - W_ga_to_id)/2 = 256.40736 eV ( 0.50080 eV/atom)
F_re at 1800.000000 = -2550.83408 eV ( -4.98210 eV/atom)
W_T2_to_T22 = -583.02785 eV ( -1.13873 eV/atom)
W_T22_to_T2 = 583.06542 eV ( 1.13880 eV/atom)
dW2 = (W_T2_to_T22 - W_T22_to_T2)/2 = -583.04664 eV ( -1.13876 eV/atom)
F_re at 1384.615385 = -2386.68534 eV ( -4.66149 eV/atom)
</pre>

<pre>
Error Analysis

Solid Side
Err_re_to_ha = 0.02769 eV ( 0.00005407 eV/atom)( 0.628 K)
Err_ha_to_re = 0.02815 eV ( 0.00005498 eV/atom)( 0.638 K)
Err_T1_to_T11 = 0.00374 eV ( 0.00000730 eV/atom)( 0.085 K)
Err_T11_to_T1 = 0.00441 eV ( 0.00000861 eV/atom)( 0.100 K)

Liquid Side
Err_re_to_ga = 0.04793 eV ( 0.00009362 eV/atom)( 1.086 K)
Err_ga_to_re = 0.06601 eV ( 0.00012893 eV/atom)( 1.496 K)
Err_ga_to_id = 0.02557 eV ( 0.00004993 eV/atom)( 0.580 K)
Err_id_to_ga = 0.03421 eV ( 0.00006682 eV/atom)( 0.776 K)
Err_T2_to_T22 = 0.01488 eV ( 0.00002906 eV/atom)( 0.337 K)
Err_T22_to_T2 = 0.01183 eV ( 0.00002311 eV/atom)( 0.268 K)
Max dT = 2.315
Tm= 1695.08000 (K), err= 1.044 Fm = -4.89779 (eV/atom)
L= 165.8833097832 (eV) Ss=0.308452 Sl=0.406313
L= 0.3239908394 (eV/atom) ss=0.000602 sl=0.000794
L= 31206.7976529696 (J/mol) ss=58.027496 sl=76.437718
L= 1111115.7748689589 (J/kg) ss=2066.064819 sl=2721.559412
</pre>

<gallery caption="The Gibbs free energy (in eV/atom) as a function of temperature (in K) of the solid (blue) and liquid (green) phases of silicon described by the Stillinger-Weber (SW) potential. The intersection of the two curves determines the melting point." widths="300px" height="200px" perrow="1">
Image:SW_Si_Tm.jpg
</gallery>

== Melting point of Other Elements ==

===MEAM Si===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = ??</math> K, <math>L = ?? J/g </math>, <math>S_S = ?? J/(\mbox{mol}\cdot K) </math> and <math>S_L = ?? J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1411.3 \pm 0.4</math> K, <math>L = 1309 J/g </math>, <math>S_S = 48.74 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 74.79 J/(\mbox{mol}\cdot K) </math>.

The agreement is good / not-so-good ???

===MEAM Au===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = 1145</math> K, <math>L = 92.4 J/g </math>, <math>S_S = 77.63 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 93.52 J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1120.0 \pm 0.6</math> K, <math>L = 92 J/g </math>, <math>S_S = 77.47 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 93.72 J/(\mbox{mol}\cdot K) </math>.

The agreement on <math>L</math>, <math>S_S</math>, and <math>S_L</math> is pretty good. The values of <math>T_m</math> do not agree so well.

===EAM Au===
Still waiting for results...

===MEAM Ge===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = ???</math> K, <math>L = ??? J/g </math>, <math>S_S = ??? J/(\mbox{mol}\cdot K) </math> and <math>S_L = ??? J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 1216.2 \pm 0.6</math> K, <math>L = 427 J/g </math>, <math>S_S = 58.34 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 83.84 J/(\mbox{mol}\cdot K) </math>.

The agreement is good / not-so-good ???

===SW Ge===
Following the same procedure, we can evaluate the melting point of Au with the '''meam-lammps''' potential. The results are <math>T_m = ???</math> K, <math>L = ??? J/g </math>, <math>S_S = ??? J/(\mbox{mol}\cdot K) </math> and <math>S_L = ??? J/(\mbox{mol}\cdot K) </math>.

This is to be compared with MSMSE 16, 085005 (2008), Table 1, in which <math>T_m = 2898.0 \pm 1.7</math> K, <math>L = 847 J/g </math>, <math>S_S = 84.07 J/(\mbox{mol}\cdot K) </math> and <math>S_L = 105.30 J/(\mbox{mol}\cdot K) </math>.

The agreement is good / not-so-good ???

MEAM Potential for Au-Si

2015-09-07T05:05:45Z

Caiwei: /* Benchmark in MD++ */

MEAM Potential for Au-Si
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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 use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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.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.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 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.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.
Seunghwa: please confirm.

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.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 MEAM potential by MD++) does not agree well with the value in JPCM (2010) regardless of the cell size.

MEAM Potential for Au-Si

2015-09-07T05:03:47Z

Caiwei: /* Benchmark in MD++ */

MEAM Potential for Au-Si
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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 use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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.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.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 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.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.
Seunghwa: please confirm.

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.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 MEAM potential by MD++) does not agree well with the value in JPCM (2010) regardless of the cell size.

MEAM Potential for Au-Si

2015-09-07T04:48:27Z

Caiwei: /* Impurity energy */

MEAM Potential for Au-Si
<DIV>
Adriano Santana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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 use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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).

bin/meam-lammps_gpp scripts/work/si_au/si-au.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.tcl 0

The results are

a0 = 5.43100051581 Angstrom
Ecoh = -4.63000000205 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.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.
Seunghwa: please confirm.

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.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 MEAM potential by MD++) does not agree well with the value in JPCM (2010) regardless of the cell size.

MEAM Potential for Au-Si

2015-08-31T07:07:24Z

Caiwei: /* New 2nn MEAM Potential for Au */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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.

MEAM Potential for Au-Si

2015-08-31T07:06:19Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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.

MEAM Potential for Au-Si

2015-08-31T07:05:20Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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 (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}) ] - 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.

MEAM Potential for Au-Si

2015-08-31T07:03:37Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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 (AuSi) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c (AuSi) = 0.5*[ E_c (Au) + E_c(Si) ] - 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.

MEAM Potential for Au-Si

2015-08-31T07:03:11Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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 (AuSi) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c (AuSi) = 0.5*[ E_c (Au) + E_c(Si) ] - delta(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

<math>\rho_0^{\rm Si} / \rho_0^{\rm Au} = 1.38</math> because of the <math>\rho_0^{\rm Si}</math> and <math>\rho_0^{\rm Au}</math> values specified above.

MEAM Potential for Au-Si

2015-08-31T06:34:11Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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 (AuSi) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c (AuSi) = 0.5*[ E_c (Au) + E_c(Si) ] - delta(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

MEAM Potential for Au-Si

2015-08-31T06:33:11Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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 (??????)
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 (AuSi) = 4.155</math>. This value is related to delta(1,2) through

<math>E_c (AuSi) = 0.5*[ E_c (Au) + E_c(Si) ] - delta(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.

MEAM Potential for Au-Si

2015-08-31T06:22:17Z

Caiwei: /* MEAM Potential for Si */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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 content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T06:21:35Z

Caiwei: /* Original MEAM Potential for Au */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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>)

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T06:20:05Z

Caiwei: /* Potential for Pure Elements */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

'''Seunghwa: Can you explain what does ibar mean? For Au, ibar = 3, and for Si, ibar = 0.'''

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

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>)

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T06:07:50Z

Caiwei: /* New 2nn MEAM Potential for Au */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

===New 2nn MEAM Potential for Au===

We now explain use 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 is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'AuBt' 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
'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>)

Note that we label the atomic species of Au as 1.

===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 S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T05:45:16Z

Caiwei: /* Potential for Pure Elements */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

===New 2nn MEAM Potential for Au===

We now explain use the 'AuBt' potential whose parameters are given by S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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 'AuBt' 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
'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.

<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 1.0 1.7 1.64 2.0

===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 S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T05:36:53Z

Caiwei: /* New 2nn MEAM Potential for Au */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

===New 2nn MEAM Potential for Au===

We now explain use the 'AuBt' potential whose parameters are given by S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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 'AuBt' 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
'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>.

<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), and will be explained later.

===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 S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T05:33:38Z

Caiwei: /* MEAM Potential for Au */

MEAM Potential for Au-Si
<DIV>
Adriano Satana and Wei Cai
</DIV>
 Created Aug, 2015, Last modified Sep, 2015


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), and will be explained later.

===New 2nn MEAM Potential for Au===

We now explain use the 'Aubt' potential whose parameters are given by S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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 'AuBt' 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
'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>.

<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), and will be explained later.

===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 S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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.

==Cross Potential between Au and Si==

The parameters for the cross potential are specified in '''AuSi2nn.meam''' file. The content is shown below.

erose_form = 3
rc = 4.5
re(1,2) = 2.700
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

'''re'''(1,2), '''alpha'''(1,2), '''Cmin'''(1,1,2),'''Cmin'''(1,2,1), '''Cmin'''(1,2,2), '''Cmin'''(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain '''erose_form''', '''rc''', '''delta''', '''attract''', '''repuls''', '''augt1'''.

Where are <math>C_{\rm max}</math> and <math>\gamma</math> specified.

MEAM Potential for Au-Si

2015-08-31T05:21:10Z

Caiwei: /* Cross Potential between Au and Si */

MEAM Potential for Au-Si

2015-08-31T05:10:03Z

Caiwei: /* Potential for Pure Elements */

MEAM Potential for Au-Si

2015-08-31T04:58:27Z

Caiwei: /* Potential for Pure Elements */

MEAM Potential for Au-Si

2015-08-31T04:49:19Z

Caiwei: /* MEAM Potential for Au */

MEAM Potential for Au-Si

2015-08-31T04:33:40Z

Caiwei: /* MEAM Potential for Au */

MEAM Potential for Au-Si

2015-08-31T04:25:00Z

Caiwei: Created page with " MEAM Potential for Au-Si <DIV> Adriano Satana and Wei Cai</P..."

Tutorial:Members Only

2015-08-31T03:32:47Z

Caiwei:

== 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]]
|}

{| 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]]
|}

{| class="wikitable" cellpadding="2" style="text-align:center"
|-
!width="500" | LAMMPS
|-
| [[Use Au-Si MEAM Potential in LAMMPS]]
|-
| [[Compile LAMMPS on GPU on Sherlock]]
|}

{| 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]]
|}

File:Fit a0EB.m.txt

2015-08-25T09:16:35Z

Caiwei: Caiwei uploaded a new version of "File:Fit a0EB.m.txt"

VASP Computing Elastic Constants of Au

2015-08-24T01:04:47Z

Caiwei: Created page with " VASP: Computing Elastic Constants of Au <DIV> </DIV> ..."

VASP: Computing Elastic Constants of Au
<DIV>
 
</DIV>

===Input files===

(Under construction!!!)

Here we give an example of how to use VASP to compute the bulk modulus of LDA-Au. We performed this calculation on <tt>MC-CC</tt> in serial model in the <tt>~/Codes/VASP/runs/Au/LDA/perfect.21x21x21</tt> directory. This directory contains the following files.

'''INCAR'''

<pre>
ENCUT = 400
ISMEAR = 1
SIGMA = 0.1
</pre>

'''KPOINTS'''

<pre>
21x21x21
0 0 = automatic generation of k-points
Monkhorst
21 21 21
0 0 0
</pre>

'''POSCAR'''

<pre>
POSCAR for FCC Au (created manually)
4.068
0 0.5 0.5
0.5 0 0.5
0.5 0.5 0
1
Cartesian (real coordinates r)
0 0 0
</pre>

To do this calculation, you also need to put the LDA pseudopotential file as <tt>POTCAR</tt> in this directory.

===Run VASP===

Now we are ready to run

vasp

To compute the equilibrium lattice constant, cohesive energy and bulk modulus, we use the following script <tt>auto.B.serial</tt> to run <tt>vasp</tt> repeated with different lattice constants.

<pre>
#!/bin/bash
rm WAVECAR
for a in 4.056 4.058 4.060 4.062 4.064 4.066 4.068
do
cat > POSCAR << FIN
POSCAR for FCC Au (created manually)
$a
0 0.5 0.5
0.5 0 0.5
0.5 0.5 0
1
Cartesian (real coordinates r)
0 0 0
FIN

echo "a=$a"
./vasp

E=`tail -1 OSZICAR`
echo $a $E | sed -s 's/F=//; s/E0=//; s/d E =//;' >> Elatt.B.dat

p=`grep pressure OUTCAR | cut -b 25-34`
echo $a $p >> platt.B.dat

done
</pre>

===Analyze data===

After running it as <tt>./auto.B.serial</tt>, it will create data files <tt>Elatt.B.dat</tt> and <tt>platt.B.dat</tt>.

Launch <tt>octave</tt> and run the following functions [[media:fit_a0EB.m.txt | fit_a0EB.m]] and [[media:fit_a0B.m.txt | fit_a0B.m]],

fit_a0EB('Elatt.B.dat');
fit_a0B ('platt.B.dat');

The first line fits the energy data to a quadratic curve and computes the equilibrium lattice constant, cohesive energy and bulk modulus. The second line fits the pressure data to a linear curve and computes the equilibrium lattice constant and bulk modulus. In this example, the result is a0 = 4.06 angstrom, Ecoh = -4.39 eV, B = 190 GPa.

===Parallel computation===

To run <tt>vasp</tt> in parallel, you need to submit [[media:vasp.pbs.txt | vasp.pbs]] as

qsub vasp.pbs

You will need the following two files to do this calculation in parallel on SU-AHPCRC:
[[media:auto.B.par.Au.txt | auto.B.par]] and
[[media:B.pbs.Au.txt | B.pbs]].

VASP Manuals

2015-08-24T01:02:33Z

Caiwei: added new page for VASP elastic constants of Au

<H3>Manuals</H3>
<UL>
<LI>[[How to compile VASP]]
<LI>[[VASP Computing Bulk Modulus of Au]]
<LI>[[VASP Computing Elastic Constants of Au]]
<LI>[[VASP Computing Ideal Shear Strength of Au]]
</UL>