View source for MEAM Potential for Au-Si

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MEAM Potential for Au-Si</STRONG></font></P>
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<P ALIGN="CENTER"><STRONG>Adriano Satana and Wei Cai</STRONG></P>
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<P ALIGN="CENTER"> Created Aug, 2015, Last modified Sep, 2015</P>
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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.

                                       <math>\alpha_i</math>      <math>\beta_i^{(0)}</math>    <math>\beta_i^{(1)}</math>  <math>\beta_i^{(2)}</math>  <math>\beta_i^{(3)}</math>
 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  

 <math>(R_i^0)</math> <math>E_i^0</math>   <math>A_i</math>   <math>t_i^{(0)}</math>   <math>t_i^{(1)}</math>        <math>t_i^{(2)}</math>         <math>t_i^{(3)}</math>     <math>\rho_0^{\rm Au}</math>
  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 <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

<math>\rho_0^{\rm Au}</math> = '''rozero''' will be important only for cross-potential.  

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

<span style="background:yellow">'''Seunghwa: Can you explain what does ibar mean?  For Au, ibar = 3, and for Si, ibar = 0.'''</span>

===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.  

                                       <math>\alpha_i</math>      <math>\beta_i^{(0)}</math>    <math>\beta_i^{(1)}</math>  <math>\beta_i^{(2)}</math>  <math>\beta_i^{(3)}</math>
 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  



 <math>(R_i^0)</math> <math>E_i^0</math>   <math>A_i</math>   <math>t_i^{(0)}</math>   <math>t_i^{(1)}</math>        <math>t_i^{(2)}</math>         <math>t_i^{(3)}</math>     <math>\rho_0^{\rm Au}</math>
  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 <math> R_i^0 </math> = '''alat''' / <math>\sqrt{2}</math>.

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).

        <math>\alpha</math>          <math>\beta_i^{(0)}</math>  <math>A_i</math>     <math>t_i^{(1)}</math>        <math>t_i^{(2)}</math>         <math>t_i^{(3)}</math>
 '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), <math>t^{(1)} = 2.90</math>, 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  (<math>\gamma</math>)
 repuls(1,1) = 4.0  (<math>\lambda</math>)
 Cmin(1,1,1) = 0.8  (<math>C_{\rm min}</math>)

Note that we label the atomic species of Au as 1.  The variable <math>d = 0.05</math> 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.

                                       <math>\alpha_i</math>      <math>\beta_i^{(0)}</math>    <math>\beta_i^{(1)}</math>  <math>\beta_i^{(2)}</math>  <math>\beta_i^{(3)}</math>
 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   


 <math>(R_i^0)</math> <math>E_i^0</math>   <math>A_i</math>   <math>t_i^{(0)}</math>   <math>t_i^{(1)}</math>        <math>t_i^{(2)}</math>         <math>t_i^{(3)}</math>     <math>\rho_0^{\rm Si}</math>
  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 <math> R_i^0 </math> = '''alat'''  <math>\times \sqrt{3}/4</math> for the diamond cubic structure.

<math>\rho_0^{\rm Si}</math> = '''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 (<math>\gamma</math>)
 repuls(2,2) = 16.0  (<math>\lambda</math>)
 Cmin(2,2,2) = 1.85  (<math>C_{\rm min}</math>)

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    (<math>r_e</math>)
 delta(1,2) = 0.125   (related to <math>E_c</math>, see below)
 lattce(1,2) = b1
 alpha(1,2) = 5.819     (<math>\alpha</math>)
 attrac(1,2) = 0.0      
 repuls(1,2) = 0.26     (<math>\gamma</math>)
 Cmin(1,1,2) = 1.9     (<math>C_{\min}(1,1,2)</math>)
 Cmin(1,2,1) = 0.95     (<math>C_{\min}(1,2,1)</math>)
 Cmin(1,2,2) = 1.85     (<math>C_{\min}(1,2,2)</math>)
 Cmin(2,2,1) = 1.0     (<math>C_{\min}(2,2,1)</math>)

Table 3 of Ryu and Cai (2010) gives <math>E_c (AuSi) = 4.155</math>.  This value is related to delta(1,2) through

<math>E_c (AuSi) = 0.5*[ E_c (Au) + E_c(Si) ] - delta(1,2) = 0.5 * (3.93 + 4.63) - 0.125 = 4.155</math>.