MEAM Potential for Au-Si

MEAM Potential for Au-Si

Adriano Satana and Wei Cai

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.

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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.

                                      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)}}
    $\beta _{i}^{(1)}$  $\beta _{i}^{(2)}$  $\beta _{i}^{(3)}$
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  

$(R_{i}^{0})$ $E_{i}^{0}$   $A_{i}$   $t_{i}^{(0)}$   $t_{i}^{(1)}$        $t_{i}^{(2)}$         $t_{i}^{(3)}$     $\rho _{0}^{\rm {Au}}$
 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 $R_{i}^{0}$ = alat / ${\sqrt {2}}$.

$\rho _{0}^{\rm {Au}}$ = 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.

                                      $\alpha _{i}$      $\beta _{i}^{(0)}$    $\beta _{i}^{(1)}$  $\beta _{i}^{(2)}$  $\beta _{i}^{(3)}$
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  

$(R_{i}^{0})$ $E_{i}^{0}$   $A_{i}$   $t_{i}^{(0)}$   $t_{i}^{(1)}$        $t_{i}^{(2)}$         $t_{i}^{(3)}$     $\rho _{0}^{\rm {Au}}$
 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 $R_{i}^{0}$ = alat / ${\sqrt {2}}$.

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).

       $\alpha$          $\beta _{i}^{(0)}$  $A_{i}$     $t_{i}^{(1)}$        $t_{i}^{(2)}$         $t_{i}^{(3)}$
'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), $t^{(1)}=2.90$, 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  ($\gamma$)
repuls(1,1) = 4.0  ($\lambda$)
Cmin(1,1,1) = 0.8  ($C_{\rm {min}}$)
augt1 = 1

Note that we label the atomic species of Au as 1. The variable $d=0.05$ 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.

                                      $\alpha _{i}$      $\beta _{i}^{(0)}$    $\beta _{i}^{(1)}$  $\beta _{i}^{(2)}$  $\beta _{i}^{(3)}$
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   

$(R_{i}^{0})$ $E_{i}^{0}$   $A_{i}$   $t_{i}^{(0)}$   $t_{i}^{(1)}$        $t_{i}^{(2)}$         $t_{i}^{(3)}$     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      1.48    0

Note that the nearest neighbor distance $R_{i}^{0}$ = 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.

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 (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 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    (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) = 0.125   (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) = 5.819     (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 \alpha}
)
attrac(1,2) = 0.0      
repuls(1,2) = 0.26     (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) = 0.95     (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) = 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_{\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)}
)

Table 3 of Ryu and Cai (2010) gives 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 AuSi}) = 4.155} . 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 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} .

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} / \rho_0^{\rm Au}} = 1.48 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 Si}} 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.

Cmax = 2.8 is the default value.