Shuffle-Glide dislocation MD and NEB: Difference between revisions
(Created page with "==Potential for Pure Elements== ===MEAM Potential for Si=== We use the 'Siz' potential as those used in Kang, et al "Size and Temperature Effects on Brittle and Ductile Frac...") |
No edit summary |
||
| Line 1: | Line 1: | ||
<P ALIGN="CENTER"> |
|||
<FONT SIZE="+3" color="darkred"><STRONG> |
|||
MEAM Potential for Si-Ge</STRONG></font></P> |
|||
<DIV> |
|||
<P ALIGN="CENTER"><STRONG>Xiaohan Zhang and Wei Cai</STRONG></P> |
|||
</DIV> |
|||
<P ALIGN="CENTER"> Created Mar, 2017, Last modified Mar, 2017</P> |
|||
<P> |
|||
This tutorial explains how to specify the parameters for the Si-Ge MEAM potential in MD++. It starts with the parameters in pure Si and pure Ge potentials, then walks through SiGe cross potential, based on the reference: |
|||
"A modified embedded atom method interatomic potential for alloy SiGe", Gregory Grochola, Salvy P.Russo, Ian K. Snook, Chemical Physics Letters 493 (2010) 57-60. |
|||
<HR> |
|||
==Potential for Pure Elements== |
==Potential for Pure Elements== |
||
| Line 35: | Line 49: | ||
<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. |
||
==Cross Potential between Ge and Si== |
|||
The parameters for the cross potential are specified in '''SiGe.meam''' file. The lines relevant for the cross potential (i.e. between species 1 and 2) are shown below. The values correspond to Table 1 of G. Grochola et al. / Chemical Physics Letters 493 (2010) 57–60 59. |
|||
re(1,2) = 2.67 (<math>r_e</math>) |
|||
delta(1,2) = 0.071 (related to <math>E_c</math>, see below) |
|||
lattce(1,2) = b1 (<math>B</math>) |
|||
lattce(1,2) = b1 (<math>Rcut</math>) |
|||
lattce(1,2) = b1 (<math>C_{\max}</math>) |
|||
lattce(1,2) = b1 (<math>C_{\min}</math>) |
|||
d = 0 |
|||
The values for <math>E_c ({\rm AuGe}) = 3.189</math>. |
|||
This value is related to delta(1,2) through |
|||
<math>E_c ({\rm AuGe}) = 0.5*[ E_c ({\rm Au}) + E_c({\rm Ge}) ] - {\rm delta}(1,2) = 0.5 * (3.93 + 3.85) - 0.071 = 3.819</math>. |
|||
<math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> = 1.5228 because of the <math>\rho_0^{\rm Ge}</math> and <math>\rho_0^{\rm Au}</math> values specified above. This value of <math>\rho_0^{\rm Ge} / \rho_0^{\rm Au}</math> leads to the following impurity formation energies |
|||
<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (MEAM) |
|||
<math>E_2 = 1.387 </math> eV Au impurity in DC Ge (MEAM) |
|||
These values are to be compared with VASP predictions |
|||
<math>E_1 = 0.331 </math> eV Ge impurity in FCC Au (VASP/LDA/US) |
|||
<math>E_2 = 1.130 </math> eV Au impurity in DC Ge (VASP/LDA/US) |
|||
Cmax = 2.8 is the default value. |
|||
==Benchmark in MD++== |
|||
Compile the code using the following command on mc2. |
|||
make meam-lammps build=R SYS=mc2_mpich |
|||
Use the following command to compute the melting point of pure Si, Ge, and Si0.5Ge0.5. |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 1 |
|||
The results are |
|||
a0 = 4.07300759775 Angstrom |
|||
Ecoh = -3.92996804082 eV |
|||
Use the following command to compute the equilibrium lattice constant and cohesive energy of pure Si (DC). |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 0 |
|||
The results are |
|||
a0 = 5.43100051581 Angstrom |
|||
Ecoh = -4.63000000205 eV |
|||
Use the following command to compute the equilibrium lattice constant and cohesive energy of Au-Si (B1). |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 2 |
|||
The results are |
|||
a0 = 5.4 Angstrom |
|||
Ecoh = -4.155000000083061 eV |
|||
===melting point=== |
|||
Use the following command to compute the impurity of a Au atom in Si DC lattice. |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4 |
|||
The results depend slightly on the cell size |
|||
cell size, Eimp(eV) |
|||
3x3x3 3.914 |
|||
4x4x4 3.968 |
|||
5x5x5 3.987 |
|||
10x10x10 4.005 |
|||
20x20x20 4.008 |
|||
The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, |
|||
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal. |
|||
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here. |
|||
Use the following command to compute the impurity of a Si atom in Au fcc lattice. |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3 |
|||
cell size, Eimp(eV) |
|||
2x2x2 0.639 |
|||
3x3x3 0.660 |
|||
4x4x4 0.665 |
|||
5x5x5 0.667 |
|||
10x10x10 0.669 |
|||
20x20x20 0.669 |
|||
The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, |
|||
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal. |
|||
So it seems that for a Si in Au FCC crystal, the predicted results here using |
|||
the 2x2x2 cell corresponds to the value in JPCM (2010). |
|||
===phase diagram=== |
|||
Use the following command to obtain the phase diagram of SiGe. |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 4 |
|||
The results depend slightly on the cell size |
|||
cell size, Eimp(eV) |
|||
3x3x3 3.914 |
|||
4x4x4 3.968 |
|||
5x5x5 3.987 |
|||
10x10x10 4.005 |
|||
20x20x20 4.008 |
|||
The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, |
|||
is <math>E_2 = 3.968</math> (eV) for a Au atom in Si DC crystal. |
|||
So it seems that the result in JPCM (2010) corresponds to the 4x4x4 cell here. |
|||
Use the following command to compute the impurity of a Si atom in Au fcc lattice. |
|||
bin/meam-lammps_gpp scripts/work/si_au/si_au_benchmark.tcl 3 |
|||
cell size, Eimp(eV) |
|||
2x2x2 0.639 |
|||
3x3x3 0.660 |
|||
4x4x4 0.665 |
|||
5x5x5 0.667 |
|||
10x10x10 0.669 |
|||
20x20x20 0.669 |
|||
The result in the paper (S. Ryu and W.Cai JPCM 22 055401 (2010), Table 2, |
|||
is <math>E_1 = 0.636</math> (eV) for a Si atom in Au FCC crystal. |
|||
So it seems that for a Si in Au FCC crystal, the predicted results here using |
|||
the 2x2x2 cell corresponds to the value in JPCM (2010). |
|||
Revision as of 18:15, 12 March 2018
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.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha_i}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(0)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(1)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(2)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(3)}}
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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (R_i^0)}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_i^0}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_i}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(0)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(2)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(3)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}}
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_i^0 } = alat Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \times \sqrt{3}/4} for the diamond cubic structure.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}} = 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.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha_i}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(0)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(1)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(2)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta_i^{(3)}}
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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (R_i^0)}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_i^0}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_i}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(0)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(1)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(2)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_i^{(3)}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}}
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R_i^0 } = alat Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \times \sqrt{3}/4} for the diamond cubic structure.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Si}} = 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 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r_e}
)
delta(1,2) = 0.071 (related to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_c}
, see below)
lattce(1,2) = b1 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B}
)
lattce(1,2) = b1 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Rcut}
)
lattce(1,2) = b1 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\max}}
)
lattce(1,2) = b1 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_{\min}}
)
d = 0
The values for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_c ({\rm AuGe}) = 3.189} . This value is related to delta(1,2) through
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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} .
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Ge} / \rho_0^{\rm Au}} = 1.5228 because of the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Ge}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Au}} values specified above. This value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_0^{\rm Ge} / \rho_0^{\rm Au}} leads to the following impurity formation energies
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_1 = 0.331 }
eV Ge impurity in FCC Au (MEAM)
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_2 = 1.387 }
eV Au impurity in DC Ge (MEAM)
These values are to be compared with VASP predictions
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_1 = 0.331 }
eV Ge impurity in FCC Au (VASP/LDA/US)
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_2 = 1.130 }
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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_2 = 3.968} (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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_1 = 0.636} (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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_2 = 3.968} (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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_1 = 0.636} (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).