MEAM Potential for Au-Ge

MEAM Potential for Au-Ge

Adriano Santana and Wei Cai

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.

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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.

                                      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)}}
       $\rho _{0}^{\rm {Ge}}$
 alat  esub  asub t0     t1          t2           t3     rozero  ibar
 5.6575 3.85  1.0 1.0   4.02       5.23          -1.6     0.9861   0

Note that the nearest neighbor distance $R_{i}^{0}$ = alat $\times {\sqrt {3}}/4$ for the diamond cubic structure.

$\rho _{0}^{\rm {Ge}}$ = 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 ($\gamma$)
repuls(2,2) = 16.0  ($\lambda$)
Cmin(2,2,2) = 1.85  ($C_{\rm {min}}$)

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/PAW.

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

re(1,2) = 2.6495         ($r_{e}$)
delta(1,2) = -0.844      (related to $E_{c}$, see below)
lattce(1,2) = b1
alpha(1,2) = 4.927      ($\alpha$)
attrac(1,2) = 0.0      
repuls(1,2) = 0.26     ($\gamma$)
Cmin(1,1,2) = 1.9      ($C_{\min }(1,1,2)$)
Cmin(1,2,1) = 0.95     ($C_{\min }(1,2,1)$)
Cmin(1,2,2) = 1.85     ($C_{\min }(1,2,2)$)
Cmin(2,2,1) = 1.0      ($C_{\min }(2,2,1)$)

The values for $E_{c}({\rm {AuGe}})=4.734$. This value is related to delta(1,2) through

$E_{c}({\rm {AuGe}})=0.5*[E_{c}({\rm {Au}})+E_{c}({\rm {Ge}})]-{\rm {delta}}(1,2)=0.5*(3.93+3.85)-(-0.844)=4.734$.

$\rho _{0}^{\rm {Ge}}/\rho _{0}^{\rm {Au}}$ = 0.9861 because of the $\rho _{0}^{\rm {Ge}}$ 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 = 0.310 }
 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 = 1.169 }
 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 = 0.31 }
 eV   Ge impurity in FCC Au (VASP/LDA/PAW)
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 = 1.02 }
 eV   Au impurity in DC  Ge (VASP/LDA/PAW)

In a similar way as above, the values for delta(1,2), re(1,2) 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 r_e} and alpha(1,2) 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 \alpha} , can be calculated with VASP LDA/US potential obtaining the results:

re(1,2)    = 2.6505 (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) = -0.832
alpha(1,2) = 4.880  (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}
)    

Cmax = 2.8 is the default value.