MEAM Potential for Au-Si

From Micro and Nano Mechanics Group
Jump to navigation Jump to search

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.

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. 

                                                    
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  

                                
 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 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 \sqrt{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 \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.

New 2nn MEAM Potential for Au

We now explain use the 'AuBt' potential whose parameters are given by S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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. 

                                      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   
'AuBt' 'fcc' 12.     79      196.967 6.59815965 5.77   2.20   6.0   2.20  



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 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 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 \sqrt{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 \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.

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 S. Ryu, et al. Model. Simul. Mater. Sci. Eng. 17, 075008 (2009).

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. 

                                      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^{(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
 5.431 4.63  1.  1.0    3.13        4.47          -1.8      1.48    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.

ibar is a setting used in the equation of state (EOS), and will be explained later.

Cross Potential between Au and Si

The parameters for the cross potential are specified in AuSi2nn.meam file. The content is shown below. 

erose_form = 3
rc = 4.5
re(1,2) = 2.700
delta(1,2) = 0.125
lattce(1,2) = b1
alpha(1,2) = 5.819
attrac(1,1) = -0.182
repuls(1,1) = 4.0
attrac(2,2) = -0.36
repuls(2,2) = 16.0
attrac(1,2) = 0.0
repuls(1,2) = 0.26
Cmin(1,1,1) = 0.8
Cmin(2,2,2) = 1.85
Cmin(1,1,2) = 1.9
Cmin(1,2,1) = 0.95
Cmin(1,2,2) = 1.85
Cmin(2,2,1) = 1.0
augt1 = 1

re(1,2), alpha(1,2), Cmin(1,1,2),Cmin(1,2,1), Cmin(1,2,2), Cmin(2,2,1) correspond to values given in Table 3 of Ryu and Cai, J. Phys. Condens. Matter, 22, 055401 (2010).

We will explain erose_form, rc, delta, attract, repuls, augt1.

Where are 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 max}} 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 \gamma} specified.

Retrieved from "http://micro.stanford.edu/mediawiki/index.php?title=MEAM_Potential_for_Au-Si&oldid=6208"