Stillinger-Weber (SW) potential with user defined functions

This example demonstrates the (ab)use of the modified embedded atom method (MEAM) potential routine together with user defined functions to create a Stillinger-Weber potential. The potential form and parameters have been taken from [StiWeb84]. The example also illustrates the use of XML Inclusions. Note that the potential is merely evaluated for a couple of simple lattice structures and none of the parameters are fitted.

Location

examples/potential_SW

Input files

  • main.xml: main input file

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    <?xml version='1.0' encoding='iso-8859-1'?>
<job>

  <name>Stillinger and Weber,  Phys. Rev. B, v. 31, p. 5262, (1985)</name>

  <verbosity>medium</verbosity>

  <atom-types>
    <species>Si</species>
  </atom-types>

  <potentials>
    <xi:include href="potential.xml" xmlns:xi="http://www.w3.org/2003/XInclude" />
  </potentials>

  <structures>
    <xi:include href="structures.xml" xmlns:xi="http://www.w3.org/2003/XInclude" />
  </structures>

</job>

  • potential.xml: potential parameter set (included in main input file via XML Inclusions)

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    <meam id='Si potential' species-a='*' species-b='*'>

  <mapping>
    <pair-interaction species-a='*' species-b='*' function='V' />
    <f-function species-a='*' species-b='*' function='f' />
    <g-function species-a='*' species-b='*' species-c='*' function='g' />
    <embedding-energy species='*' function='F' />
  </mapping>

  <functions>

      <user-function id="V">
        <cutoff>3.77118</cutoff>
        <input-var>r</input-var>
        <expression>
          A*epsilon*(B*(sigma/r)^(p) - (sigma/r)^(q)) * exp(sigma/(r-a*sigma))
        </expression>
        <derivative>
          A*exp(sigma/(r - a*sigma))*epsilon*
          (-((B*p*sigma*(sigma/r)^(-1 + p))/r^2) + (q*sigma*(sigma/r)^(-1 + q))/r^2)
          - (A*exp(sigma/(r - a*sigma))*epsilon*sigma*(B*(sigma/r)^p
          - (sigma/r)^q))/(r - a*sigma)^2
        </derivative>
        <param name="epsilon">2.1683</param>
        <param name="sigma">2.0951</param>
        <param name="a">1.80</param>
        <param name="p">4.0</param>
        <param name="q">0.0</param>
        <param name="A">7.049556277</param>
        <param name="B">0.6022245584</param>
      </user-function>

    <user-function id="F">
      <input-var>rho</input-var>
      <expression>
        rho
      </expression>
      <derivative>
        1
      </derivative>
    </user-function>

    <user-function id="f">
      <cutoff>3.771179</cutoff>
      <input-var>r</input-var>
      <expression>
        exp(gamma*sigma/(r-a*sigma))
      </expression>
      <derivative>
        -gamma * sigma * exp(gamma*sigma/(r-a*sigma)) / (r - a*sigma)^2
      </derivative>
      <param name="sigma">2.0951</param>
      <param name="gamma">1.20</param>
      <param name="a">1.80</param>
    </user-function>

    <user-function id="g">
      <input-var>costheta</input-var>
      <expression>
        lambda * epsilon * (costheta - costheta0)^2
      </expression>
      <derivative>
        lambda * epsilon * 2 * (costheta - costheta0)
      </derivative>
      <param name="epsilon">2.1683</param>
      <param name="lambda">21.0</param>
      <param name="costheta0">-0.333333333333</param>
    </user-function>

  </functions>

</meam>

  • structures.xml: input structures (included in main input file via XML Inclusions)

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    <group>

  <fcc-lattice id='A1 (fcc)'>
    <atom-type>Si</atom-type>
    <lattice-parameter>4.14</lattice-parameter>
    <!-- <lattice-parameter>3.6</lattice-parameter> -->
    <relax-dof>
      <lattice-parameter/>
    </relax-dof>
    <properties>
      <atomic-energy/>
      <lattice-parameter/>
      <bulk-modulus/>
    </properties>
  </fcc-lattice>

  <bcc-lattice id='A2 (bcc)'>
    <atom-type>Si</atom-type>
    <lattice-parameter>3.24</lattice-parameter>
    <!-- <lattice-parameter>3.0</lattice-parameter> -->
    <relax-dof>
      <lattice-parameter/>
    </relax-dof>
    <properties>
      <atomic-energy/>
      <lattice-parameter/>
      <bulk-modulus/>
    </properties>
  </bcc-lattice>

  <diamond-lattice id='A4 (diamond)'>
    <atom-type>Si</atom-type>
    <lattice-parameter>5.43</lattice-parameter>
    <!-- <lattice-parameter>5.</lattice-parameter> -->
    <relax-dof>
      <atom-coordinates/>
      <lattice-parameter/>
    </relax-dof>
    <properties>
      <atomic-energy/>
      <lattice-parameter/>
      <bulk-modulus/>
    </properties>
  </diamond-lattice>

</group>

Output (files)

  • The final properties (as well as parameters) are written to standard output.

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    This is program version 0.1.6
Reading job file main.xml
-------------------------------------------------------
Parsing input file(s)
-------------------------------------------------------
-------------------------------------------------------
Computing structure properties
Structure 'A1 (fcc)':
   total-energy: -3.94031 eV
   atomic-energy: -3.94031 eV/atom
   total-volume: 17.8242 A^3
   atomic-volume: 17.8242 A^3/atom
Structure 'A2 (bcc)':
   total-energy: -4.05556 eV
   atomic-energy: -4.05556 eV/atom
   total-volume: 17.0819 A^3
   atomic-volume: 17.0819 A^3/atom
Structure 'A4 (diamond)':
   total-energy: -8.6732 eV
   atomic-energy: -4.3366 eV/atom
   total-volume: 40.0468 A^3
   atomic-volume: 20.0234 A^3/atom
-------------------------------------------------------
-------------------------------------------------------