Embedded atom method (EAM) potential with user defined functions¶

This example demonstrates the use of the embedded atom method (EAM) potential routine together with user defined functions. The potential form and parameters have been taken from [MisMehPap01]. 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_EAM

Input files¶

main.xml: main input file

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

<eam id="elemental EAM potential" species-a="*" species-b="*">

  <mapping>
    <pair-interaction species-a="*" species-b="*" function="V" />
    <electron-density species-a="*" species-b="*" function="rho" />
    <embedding-energy species="*" function="F" />			
  </mapping>

  <functions>

    <sum id="V">
      <user-function id="V_term1">
	<input-var>r</input-var>
	<expression>
	  ( E1 * (exp(-2 * alpha1 * (r - r01))
	  - 2 * exp(-alpha1 * (r - r01)))
	  + E2 * (exp(-2 * alpha2 * (r - r02))
	  - 2 * exp(-alpha2 * (r - r02))) + delta) 
	</expression>
	<derivative>
	  E1 * (2 * alpha1 * exp(-alpha1 * (r - r01))
	  - 2 * alpha1 * exp(-2 * alpha1 * (r - r01))) 
	  + E2 * (2 * alpha2 * exp(-alpha2 * (r - r02))
	  - 2 * alpha2 * exp(-2 * alpha2 * (r - r02)))
	</derivative>
	<param name="E1">2.01458e2</param>
	<param name="alpha1">2.97758</param>
	<param name="r01">0.83591</param>
	<param name="E2">6.59288e-3</param>
	<param name="alpha2">1.54927</param>
	<param name="r02">4.46867</param>
	<param name="delta">0.86225e-2</param>
	<screening>
	  <user-function id="rho_screening">
	    <cutoff>5.50679</cutoff>
	    <input-var>r</input-var>
	    <expression>
	      1 - 1/(1 + ((r - cutoff) / h)^4)
	    </expression>
	    <derivative>
	      4 * h^4 * (r-cutoff)^3 / ((h^4 + (r-cutoff)^4)^2)
	    </derivative>
	    <param name="h">0.50037</param>
	  </user-function>
	</screening>
      </user-function>
      <user-function id="V_term2">
	<cutoff>5.50679</cutoff>
	<input-var>r</input-var>
	<expression>
	  - (r &lt; rs1 ? S1*(rs1-r)^4 : 0)
	  - (r &lt; rs2 ? S2*(rs2-r)^4 : 0)
	  - (r &lt; rs3 ? S3*(rs3-r)^4 : 0)
	</expression>
	<derivative>
	  - (r &lt; rs1 ? -4*S1*(rs1-r)^3 : 0)
	  - (r &lt; rs2 ? -4*S2*(rs2-r)^3 : 0)
	  - (r &lt; rs3 ? -4*S3*(rs3-r)^3 : 0)
	</derivative>
	<param name="rs1">2.24</param>
	<param name="rs2">1.80</param>
	<param name="rs3">1.20</param>
	<param name="S1">4.0</param>
	<param name="S2">40.0</param>
	<param name="S3">1.15e3</param>
      </user-function>
    </sum>

    <user-function id="rho">
      <input-var>r</input-var>
      <expression>
	a * exp(-beta1*(r - r03)^2)
        + exp(-beta2*(r - r04))
      </expression>
      <derivative>
        beta2 * (-exp(-beta1 * (r - r04)))
	- 2 * a * beta1 * (r - r03) * exp(-beta1 * (r - r03)^2)
      </derivative>
      <param name="a">3.80362</param>
      <param name="r03">-2.19885</param>
      <param name="r04">-2.61984e2</param>
      <param name="beta1">0.17394</param>
      <param name="beta2">5.35661e2</param>
      <screening>
	<user-function id="rho_screening">
	  <cutoff>5.50679</cutoff>
	  <input-var>r</input-var>
	  <expression>
	    1 - 1/(1 + ((r - cutoff) / h)^4)
	  </expression>
	  <derivative>
	    4 * h^4 * (r - cutoff)^3 / ((h^4 + (r - cutoff)^4)^2)
	  </derivative>
	  <param name="h">0.5</param>
	</user-function>
      </screening>
    </user-function>

    <user-function id="F">
      <input-var>rho</input-var>
      <expression>
	(rho &lt; 1) ?
	(F0 + 0.5 * F2 * (rho - 1)^2 + q1 * (rho - 1)^3
	+ q2 * (rho - 1)^4 + q3 * (rho - 1)^5 + q4 * (rho - 1)^6)
	: 
	(F0 + 0.5 * F2 * (rho - 1)^2 + q1 * (rho - 1)^3
	+ Q1 * (rho - 1)^4) / (1 + Q2 * (rho - 1)^3)
      </expression>
      <derivative>
	(rho &lt; 1) ?
	(rho - 1) * ( F2
	+ 3 * q1 * (rho - 1)
	+ 4 * q2 * (rho - 1)^2
	+ 5 * q3 * (rho - 1)^3
	+ 6 * q4 * (rho - 1)^4 )
	:
	(F2 * (rho - 1) + 3 * q1 * (rho - 1)^2
	+ 4 * Q1 * (rho - 1)^3)/(Q2 * (rho - 1)^3 + 1)
	- (3 * Q2 * (rho - 1)^2 * (F0 + 0.5 * F2 * (rho - 1)^2
	+ q1 * (rho - 1)^3 + Q1 * (rho - 1)^4))
	/ ((Q2 * (rho - 1)^3 + 1)^2)
      </derivative>
      <param name="F0">-2.3</param>
      <param name="F2">1.4</param>
      <param name="q1">-1.3</param>
      <param name="q2">-0.9</param>
      <param name="q3">1.8</param>
      <param name="q4">3.0</param>
      <param name="Q1">0.4</param>
      <param name="Q2">0.3</param>
    </user-function>

  </functions>

</eam>

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

Output (files)¶

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