MEAM Potential for Si-Ge: Difference between revisions
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<FONT SIZE="+3" color="darkred"><STRONG> |
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MEAM Potential for |
MEAM Potential for Si-Ge</STRONG></font></P> |
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<P ALIGN="CENTER"><STRONG>Xiaohan Zhang and Wei Cai</STRONG></P> |
<P ALIGN="CENTER"><STRONG>Xiaohan Zhang and Wei Cai</STRONG></P> |
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This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference |
This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference: |
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"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60. |
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==Potential for Pure Elements== |
==Potential for Pure Elements== |
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=== |
===MEAM Potential for Si=== |
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We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below. |
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As an example, we first describe the original 'Au' potential whose parameters are given in M. I. Baskes, Phys. Rev. B 46, 2727 (1992). |
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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. |
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<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math> |
<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math> |
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elt lat z ielement atwt alpha b0 b1 b2 b3 |
elt lat z ielement atwt alpha b0 b1 b2 b3 |
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' |
'Si4' 'dia' 4. 14 28.086 4.87 4.4 5.5 5.5 5.5 |
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<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> |
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alat esub asub t0 t1 t2 t3 rozero ibar |
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4.07 3.93 1.04 1.0 1.58956328 1.50776392 2.60609758 1. 3 |
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<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> |
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Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>. |
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<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential. |
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'''ibar''' is a setting used in the equation of state (EOS). It selects the |
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G(gamma) function in Eq (4) and (5) on the paper by BJ LEE: Phys. Rev. B 64, 184102 (2001) |
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While the functional form is quite different, the modulus is almost not affected by |
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the choice of ibar. |
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===New 2nn MEAM Potential for Au=== |
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We now explain the newer 2nn MEAM potential whose parameters are given by Lee, Shim and Baskes, Phys. Rev. B 68, 144112 (2003), and later modified by Ryu and Cai, J. Phys. Condens. Matter 22, 055401 (2010). |
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The main parameters in the MEAM potential are specified in the '''meamf''' file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines which correspond to 'AuBt' are given below. |
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<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math> |
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elt lat z ielement atwt alpha b0 b1 b2 b3 |
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'AuBt' 'fcc' 12. 79 196.967 6.59815965 5.77 2.20 6.0 2.20 |
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<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> |
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alat esub asub t0 t1 t2 t3 rozero ibar |
alat esub asub t0 t1 t2 t3 rozero ibar |
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5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0 |
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Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' |
Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure. |
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<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. And note that this is the only different from Si4 line. |
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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). |
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'''ibar''' is a setting used in the equation of state (EOS), and will be explained later. |
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<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> |
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'Au' 6.34090112 5.449 1.04 1.58956328 1.50776392 2.60609758 |
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'AuBt' 6.59815965 5.77 1.00 1.7 1.64 2.0 |
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===MEAM Potential for Ge=== |
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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 |
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We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below. |
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t1_meam(:) = t1_meam(:) + augt1 * 3.d0/5.d0 * t3_meam(:) |
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This means that if '''augt1''' = 1.0, then the ''true'' value of t1 is 1.7 + 0.6 * 2.0 = 2.9. |
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'''augt1''' is specified in the '''AuSi2nn.meam''' file, as described below. |
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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. |
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erose_form = 3 |
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rc = 4.5 |
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attrac(1,1) = -0.182 (<math>\gamma</math>) |
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repuls(1,1) = 4.0 (<math>\lambda</math>) |
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Cmin(1,1,1) = 0.8 (<math>C_{\rm min}</math>) |
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augt1 = 1 |
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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). |
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===MEAM Potential for Si=== |
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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). |
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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. |
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<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math> |
<math>\alpha_i</math> <math>\beta_i^{(0)}</math> <math>\beta_i^{(1)}</math> <math>\beta_i^{(2)}</math> <math>\beta_i^{(3)}</math> |
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elt lat z ielement atwt alpha b0 b1 b2 b3 |
elt lat z ielement atwt alpha b0 b1 b2 b3 |
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' |
'Ge' 'dia' 4. 32 72.64 4.98 4.55 5.5 5.5 5.5 |
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<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> |
<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> |
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alat esub asub t0 t1 t2 t3 rozero ibar |
alat esub asub t0 t1 t2 t3 rozero ibar |
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5. |
5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0 |
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Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure. |
Note that the nearest neighbor distance <math> R_i^0 </math> = '''alat''' <math>\times \sqrt{3}/4</math> for the diamond cubic structure. |
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<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. |
<math>\rho_0^{\rm Si}</math> = '''rozero''' will be important only for cross-potential. |
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==Cross Potential between Ge and Si== |
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'''ibar''' is a setting used in the equation of state (EOS), and will be explained later. |
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The |
The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59. |
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re(1,2) = 2.67 (<math>r_e</math>) |
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erose_form = 3 |
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delta(1,2) = 0.071 (related to <math>E_c</math>, see below) |
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rc = 4.5 |
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lattce(1,2) = b1 (<math>B</math>) |
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lattce(1,2) = b1 (<math>Rcut</math>) |
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lattce(1,2) = b1 (<math>C_{\max}</math>) |
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lattce(1,2) = b1 (<math>C_{\min}</math>) |
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d = 0 |
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The values for <math>E_c ({\rm AuGe}) = 3.189</math>. |
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Note that we label the atomic species of Si as 2. |
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This value is related to delta(1,2) through |
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<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>. |
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==Cross Potential between Au and Si== |
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<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies |
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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). |
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<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM) |
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re(1,2) = 2.700 (<math>r_e</math>) |
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<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM) |
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delta(1,2) = 0.125 (related to <math>E_c</math>, see below) |
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lattce(1,2) = b1 |
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alpha(1,2) = 5.819 (<math>\alpha</math>) |
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attrac(1,2) = 0.0 |
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repuls(1,2) = 0.26 (<math>\gamma</math>) |
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Cmin(1,1,2) = 1.9 (<math>C_{\min}(1,1,2)</math>) |
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Cmin(1,2,1) = 0.95 (<math>C_{\min}(1,2,1)</math>) |
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Cmin(1,2,2) = 1.85 (<math>C_{\min}(1,2,2)</math>) |
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Cmin(2,2,1) = 1.0 (<math>C_{\min}(2,2,1)</math>) |
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These values are to be compared with VASP predictions |
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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 |
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<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US) |
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<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>. |
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<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US) |
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<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. |
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Cmax = 2.8 is the default value. |
Cmax = 2.8 is the default value. |
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==Benchmark in MD++== |
==Benchmark in MD++== |
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Compile the code using the following command. |
Compile the code using the following command on mc2. |
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make meam-lammps build=R SYS= |
make meam-lammps build=R SYS=mc2_mpich |
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Use the following command to compute the |
Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5. |
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bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1 |
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1 |
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| Line 168: | Line 113: | ||
Ecoh = -4.155000000083061 eV |
Ecoh = -4.155000000083061 eV |
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=== |
===melting point=== |
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Use the following command to compute the impurity of a Au atom in Si DC lattice. |
Use the following command to compute the impurity of a Au atom in Si DC lattice. |
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bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4 |
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The results depend slightly on the cell size |
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cell size, Eimp(eV) |
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3x3x3 3.914 |
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4x4x4 3.968 |
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5x5x5 3.987 |
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10x10x10 4.005 |
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20x20x20 4.008 |
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The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, |
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is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal. |
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So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here. |
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Use the following command to compute the impurity of a Si atom in Au fcc lattice. |
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bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3 |
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cell size, Eimp(eV) |
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2x2x2 0.639 |
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3x3x3 0.660 |
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4x4x4 0.665 |
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5x5x5 0.667 |
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10x10x10 0.669 |
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20x20x20 0.669 |
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The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, |
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is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal. |
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So it seems that for a Si in Au FCC crystal, the predicted results here using |
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the 2x2x2 cell corresponds to the value in JPCM (2010). |
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===phase diagram=== |
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Use the following command to obtain the phase diagram of SiGe. |
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bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4 |
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4 |
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Latest revision as of 22:36, 6 March 2017
MEAM Potential for Si-Ge
Xiaohan Zhang and Wei Cai
Created Mar, 2017, Last modified Mar, 2017
This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference: "A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60.
Potential for Pure Elements
MEAM Potential for Si
We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Fracture of Silicon Nanowires", International Journal of Plasticity, 26, 1387 (2010" and "Brittle and Ductile Fracture of Semiconductor Nanowires – Molecular Dynamics Simulations", Philosophical Magazine, 87, 2169, (2007)." The main parameters in the MEAM potential is specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines correspond to 'Siz' is given below.
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
alat esub asub t0 t1 t2 t3 rozero ibar 5.431 4.63 1. 1.0 3.13 4.47 -1.8 1.60 0
Note that the nearest neighbor distance = alat for the diamond cubic structure.
= rozero will be important only for cross-potential. And note that this is the only different from Si4 line.
ibar is a setting used in the equation of state (EOS), and will be explained later.
MEAM Potential for Ge
We use the 'Ge' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.
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
alat esub asub t0 t1 t2 t3 rozero ibar 5.6575 3.85 1. 1.0 4.02 5.23 -1.6 1.35 0
Note that the nearest neighbor distance = alat for the diamond cubic structure.
= rozero will be important only for cross-potential.
Cross Potential between Ge and Si
The parameters for the cross potential are specified in SiGe.meam file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59.
re(1,2) = 2.67 () delta(1,2) = 0.071 (related to , see below) lattce(1,2) = b1 () lattce(1,2) = b1 () lattce(1,2) = b1 () lattce(1,2) = b1 () d = 0
The values for . This value is related to delta(1,2) through
.
![{\displaystyle E_{c}({\rm {AuGe}})=0.5*[E_{c}({\rm {Au}})+E_{c}({\rm {Ge}})]-{\rm {delta}}(1,2)=0.5*(3.93+3.85)-0.071=3.819}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a756b119f43bbbcc97a26ebef3d8d83561fde1)
= 1.5228 because of the and values specified above. This value of leads to the following impurity formation energies
eV Ge impurity in FCC Au (MEAM) eV Au impurity in DC Ge (MEAM)
These values are to be compared with VASP predictions
eV Ge impurity in FCC Au (VASP/LDA/US) eV Au impurity in DC Ge (VASP/LDA/US)
Cmax = 2.8 is the default value.
Benchmark in MD++
Compile the code using the following command on mc2.
make meam-lammps build=R SYS=mc2_mpich
Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5.
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1
The results are
a0 = 4.07300759775 Angstrom Ecoh = -3.92996804082 eV
Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC).
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0
The results are
a0 = 5.43100051581 Angstrom Ecoh = -4.63000000205 eV
Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1).
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2
The results are
a0 = 5.4 Angstrom Ecoh = -4.155000000083061 eV
melting point
Use the following command to compute the impurity of a Au atom in Si DC lattice.
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4
The results depend slightly on the cell size
cell size, Eimp(eV) 3x3x3 3.914 4x4x4 3.968 5x5x5 3.987 10x10x10 4.005 20x20x20 4.008
The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, is (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 (eV) for a Si atom in Au FCC crystal. So it seems that for a Si in Au FCC crystal, the predicted results here using the 2x2x2 cell corresponds to the value in JPCM (2010).
phase diagram
Use the following command to obtain the phase diagram of SiGe.
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4
The results depend slightly on the cell size
cell size, Eimp(eV) 3x3x3 3.914 4x4x4 3.968 5x5x5 3.987 10x10x10 4.005 20x20x20 4.008
The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, is (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 (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).