Using deformations with user defined structures

This example demonstrates the use of the deformations. It employs the embedded atom method (EAM) potential routine together with user defined functions [MisMehPap01]. The example also illustrates the use of XML Inclusions.

Location

examples/imposing_a_deformation

Input files

  • main.xml: main input file

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
    <?xml version="1.0" encoding="iso-8859-1"?>
<job>

  <name> Demonstrating the usage of deformations </name>

  <verbosity>maximum</verbosity>
  
  <atom-types>
    <species>Cu</species>
  </atom-types>

  <potentials>
    <xi:include href="potential.xml" xmlns:xi="http://www.w3.org/2003/XInclude" />
  </potentials>
  
  <deformations>
    <deformation id="lattice_constant">
      <scale> 3.615 </scale>
    </deformation>

    <deformation id="tetragonal_strain">
      <scale> 3.615 </scale>
      <matrix>
	<s1 x="1.05" y="0.0" z="0.0"/>
	<s2 x="0.0"  y="1.0" z="0.0"/>
	<s3 x="0.0"  y="0.0" z="1.0"/>
      </matrix>
    </deformation>
  </deformations>

  <structures>
    <user-structure id="conventional_fcc_cell1">
      <pbc x="true" y="true" z="true" />
      <cell>
	<a1 x="1" y="0" z="0" />
	<a2 x="0" y="1" z="0" />
	<a3 x="0" y="0" z="1" />
	<atoms>
	  <atom type="Cu" x="0.0" y="0.0" z="0.0" reduced="true" />
	  <atom type="Cu" x="0.0" y="0.5" z="0.5" reduced="true" />
	  <atom type="Cu" x="0.5" y="0.0" z="0.5" reduced="true" />
	  <atom type="Cu" x="0.5" y="0.5" z="0.0" reduced="true" />
	</atoms>
      </cell>
      <deformation>lattice_constant</deformation>
      <relax-dof>
	<atom-coordinates/>
      </relax-dof>
    </user-structure>

    <user-structure id="conventional_fcc_cell2">
      <pbc x="true" y="true" z="true" />
      <cell>
	<a1 x="1" y="0" z="0" />
	<a2 x="0" y="1" z="0" />
	<a3 x="0" y="0" z="1" />
	<atoms>
	  <atom type="Cu" x="0.0" y="0.0" z="0.0" reduced="true" />
	  <atom type="Cu" x="0.0" y="0.5" z="0.5" reduced="true" />
	  <atom type="Cu" x="0.5" y="0.0" z="0.5" reduced="true" />
	  <atom type="Cu" x="0.5" y="0.5" z="0.0" reduced="true" />
	</atoms>
      </cell>
      <deformation>tetragonal_strain</deformation>
      <relax-dof>
	<atom-coordinates/>
      </relax-dof>
    </user-structure>

  </structures>

</job>

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

      1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
    <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'>2.24000</param>
	<param name='rs2'>1.80000</param>
	<param name='rs3'>1.20000</param>
	<param name='S1'>4.00000</param>
	<param name='S2'>40.00000</param>
	<param name='S3'>1.15000e3</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>

Output

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

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
    This is program version 0.1.6
Reading job file main.xml
-------------------------------------------------------
Parsing input file(s)
-------------------------------------------------------
 EAM potential - maximum cutoff : 5.50679
Neighbor lists of structure 'conventional_fcc_cell1' will be built for the first time.
Neighbor lists of structure 'conventional_fcc_cell2' will be built for the first time.
-------------------------------------------------------
Computing structure properties
Relaxing atomic d.o.f. of structure conventional_fcc_cell1 (#dof=9):
Neighbor lists of structure 'conventional_fcc_cell1' need to be rebuilt because of cell deformation (skin=0, cell_def=0 threshold=0).
        force_rlx_iter=1 E=-14.2315 fnorm=9.68342e-17
Structure 'conventional_fcc_cell1':
   total-energy: -14.2315 eV
   atomic-energy: -3.55787 eV/atom
   total-volume: 47.2416 A^3
   atomic-volume: 11.8104 A^3/atom
Relaxing atomic d.o.f. of structure conventional_fcc_cell2 (#dof=9):
Neighbor lists of structure 'conventional_fcc_cell2' need to be rebuilt because of cell deformation (skin=0, cell_def=0 threshold=0).
        force_rlx_iter=1 E=-14.17 fnorm=5.74558e-17
Structure 'conventional_fcc_cell2':
   total-energy: -14.17 eV
   atomic-energy: -3.54249 eV/atom
   total-volume: 49.6037 A^3
   atomic-volume: 12.4009 A^3/atom
-------------------------------------------------------
-------------------------------------------------------