MEAM Potential for Au-Ge

MEAM Potential for Au-Ge

Adriano Santana and Wei Cai

Created Aug, 2015, Last modified Dec, 2016

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.

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Potential for Pure Elements

Original MEAM Potential for Au

The details for the original 'Au' potential can be found here:

http://micro.stanford.edu/wiki/MEAM_Potential_for_Au-Si

MEAM Potential for Ge

We use the 'Ge5' potential whose parameters are originally given in M. I. Baskes, The main parameters in the MEAM potential are specified in the meamf file. (In MD++, this file is in the potentials/MEAMDATA folder.) The lines corresponding to 'Ge5' are given below. Most of these parameters correspond to Table III of Baskes PRB (1992), as shown below.

                                      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}
       $\beta _{i}^{(0)}$     $\beta _{i}^{(1)}$   $\beta _{i}^{(2)}$  $\beta _{i}^{(3)}$
elt    lat   z    ielement  atwt     alpha    b0       b1     b2    b3      
'Ge5' 'dia'  4.     32      72.64     4.98   4.55      5.5    5.5  5.5 

$(R_{i}^{0})$    $E_{i}^{0}$   $A_{i}$   $t_{i}^{(0)}$   $t_{i}^{(1)}$         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 Ge}}

 alat  esub  asub t0     t1          t2           t3     rozero  ibar
 5.6575 3.85  1.0 1.0   4.02       5.23          -1.6    1.5228   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 Ge}} = rozero will be important only for cross-potential. In our fitting it takes the value 1.5228 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 (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 \gamma}
)
repuls(2,2) = 16.0  (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 \lambda}
)
Cmin(2,2,2) = 1.85  (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_{\rm min}}
)

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/US.

Similar values are found in Table 3 of "AuGe mean potential fitted to the binary phase diagram", Yanming Wang, Adriano Santana and Wei Cai,25, 025004, (2017)

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
alpha(1,2) = 5.4219      (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}
)
attrac(1,2) = 0.0      
repuls(1,2) = 0.168     (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 \gamma}
)
Cmin(1,1,2) = 1.9      (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}(1,1,2)}
)
Cmin(1,2,1) = 0.70     (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}(1,2,1)}
)
Cmin(1,2,2) = 2.0     (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 C_{\min}(1,2,2)}
)
Cmin(2,2,1) = 1.0      (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 C_{\min}(2,2,1)}
)

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.

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 si-au.tcl from the link.

bin/meam-lammps_gpp scripts/work/ge_au/ge_au_benchmark.tcl 1

The results are

a0 = xxx Angstrom
Ecoh = xxx eV

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

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

The results are

 a0 = xxx Angstrom 
 Ecoh = xxx eV

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

bin/meam-lammps_gpp scripts/work/ge_au/ge_au_benchmark.tcl 2

The results are

 a0 = xxx Angstrom 
 Ecoh = xxx eV

Impurity energy

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

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

Mention paper....