Elastic properties of gallium nitride

This example demonstrates the relaxation and property evaluation for compound structures. In particular, it shows how to handle the computation of elastic constants for structure with internal relaxation due to deformation, such as zincblende and wurtzite. The example employs the analytic bond-order potential (ABOP) from [NorAlbErh03].

Location

examples/elastic_constants_GaN

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
 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
    <?xml version='1.0' encoding='iso-8859-1'?>
<job>
	<name>Relaxation of structures</name>
	<verbosity>medium</verbosity>

	<atom-types>
	  <species>Ga</species>
	  <species>N</species>
	</atom-types>

	<potentials>
	  <tersoff id='GaN potential' species-a='*' species-b='*'>
	    <param-file>GaN.tersoff</param-file>
	  </tersoff>
	</potentials>
	
	<structures>

	  <B1-lattice id='B1 (rocksalt)'>
	    <atom-type-A>Ga</atom-type-A>
	    <atom-type-B>N</atom-type-B>
	    <lattice-parameter>4.5</lattice-parameter>
	    <properties>
	      <atomic-energy/>
	      <lattice-parameter/>
	      <bulk-modulus/>
	      <C11/>
	      <C12/>
	      <C44/>
	    </properties>
	  </B1-lattice>

	  <B2-lattice id='B2 (cesium chloride)'>
	    <atom-type-A>Ga</atom-type-A>
	    <atom-type-B>N</atom-type-B>
	    <lattice-parameter>2.5</lattice-parameter>
	    <properties>
	      <atomic-energy/>
	      <lattice-parameter/>
	      <bulk-modulus/>
	      <C11/>
	      <C12/>
	      <C44/>
	    </properties>
	  </B2-lattice>

	  <B3-lattice id='B3 (zincblende)'>
	    <atom-type-A>Ga</atom-type-A>
	    <atom-type-B>N</atom-type-B>
	    <lattice-parameter>4.3</lattice-parameter>
	    <properties>
	      <atomic-energy/>
	      <lattice-parameter/>
	      <bulk-modulus/>
	      <C11/>
	      <C12/>
	      <C44/>
	    </properties>
	  </B3-lattice>

	  <B4-lattice id='B4 (wurtzite); relaxed ion'>
	    <atom-type-A>Ga</atom-type-A>
	    <atom-type-B>N</atom-type-B>
	    <lattice-parameter>3.25</lattice-parameter>
	    <ca-ratio>1.6</ca-ratio>
	    <u-parameter>0.37</u-parameter>
	    <properties>
	      <atomic-energy/>
	      <lattice-parameter/>
	      <ca-ratio/>
	      <u-parameter/>
	      <C11/>
	      <C33/>
	      <C12/>
	      <C13/>
	      <C44/>
	      <C66/>
	    </properties>
	    <relax-dof>
	      <atom-coordinates/>
	    </relax-dof>
	  </B4-lattice>

	  <B4-lattice id='B4 (wurtzite); clamped ion'>
	    <atom-type-A>Ga</atom-type-A>
	    <atom-type-B>N</atom-type-B>
	    <lattice-parameter>3.18</lattice-parameter>
	    <ca-ratio>1.6</ca-ratio>
	    <u-parameter>0.37</u-parameter>
	    <properties>
	      <atomic-energy/>
	      <lattice-parameter/>
	      <ca-ratio/>
	      <u-parameter/>
	      <bulk-modulus/>
	      <C11/>
	      <C33/>
	      <C12/>
	      <C13/>
	      <C44/>
	      <C66/>
	    </properties>
	  </B4-lattice>

	</structures>
</job>

  • GaN.tersoff: initial parameter set in Lammps/Tersoff format

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
    # Tersoff parameters for various elements and mixtures
# multiple entries can be added to this file, LAMMPS reads the ones it needs
# these entries are in LAMMPS "metal" units:
#   A,B = eV; lambda1,lambda2,lambda3 = 1/Angstroms; R,D = Angstroms
#   other quantities are unitless

# format of a single entry (one or more lines):
#   element 1, element 2, element 3, 
#   m, gamma, lambda3, c, d, costheta0, n, beta, lambda2, B, R, D, lambda1, A

# The following GaN potential is from J. Nord, K. Albe, P. Erhart
# and K. Nordlund, J. Phys.: Condens. Matter, 15, 5649(2003).
# This file is from Xiaowang Zhou, xzhou @ sandia.gov

 Ga Ga Ga 1.0 0.007874 1.846 1.918000 0.75000 -0.301300 1.0 1.0 1.44970 410.132 2.87 0.15 1.60916 535.199
 N  N  N  1.0 0.766120 0.000 0.178493 0.20172 -0.045238 1.0 1.0 2.38426 423.769 2.20 0.20 3.55779 1044.77
 Ga Ga N  1.0 0.001632 0.000 65.20700 2.82100 -0.518000 1.0 0.0 0.00000 0.00000 2.90 0.20 0.00000 0.00000
 Ga N  N  1.0 0.001632 0.000 65.20700 2.82100 -0.518000 1.0 1.0 2.63906 3864.27 2.90 0.20 2.93516 6136.44
 N  Ga Ga 1.0 0.001632 0.000 65.20700 2.82100 -0.518000 1.0 1.0 2.63906 3864.27 2.90 0.20 2.93516 6136.44
 N  Ga N  1.0 0.766120 0.000 0.178493 0.20172 -0.045238 1.0 0.0 0.00000 0.00000 2.20 0.20 0.00000 0.00000
 N  N  Ga 1.0 0.001632 0.000 65.20700 2.82100 -0.518000 1.0 0.0 0.00000 0.00000 2.90 0.20 0.00000 0.00000
 Ga N  Ga 1.0 0.007874 1.846 1.918000 0.75000 -0.301300 1.0 0.0 0.00000 0.00000 2.87 0.15 0.00000 0.00000

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
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
    This is program version 0.1.6
Reading job file main.xml
-------------------------------------------------------
Parsing input file(s)
-------------------------------------------------------
-------------------------------------------------------
Computing structure properties
Structure 'B1 (rocksalt)':
   total-energy: -7.22833 eV
   atomic-energy: -3.61417 eV/atom
   total-volume: 22.7812 A^3
   atomic-volume: 11.3906 A^3/atom
   bulk-modulus: 111.402 GPa
   C11: 379.642 GPa
   C12: -22.7132 GPa
   C44: 64.3545 GPa
   lattice-parameter: 4.5 A [0:]
Structure 'B2 (cesium chloride)':
   total-energy: -1.42416 eV
   atomic-energy: -0.71208 eV/atom
   total-volume: 15.625 A^3
   atomic-volume: 7.8125 A^3/atom
   bulk-modulus: 877.28 GPa
   C11: 1089.46 GPa
   C12: 771.19 GPa
   C44: 352.373 GPa
   lattice-parameter: 2.5 A [0:]
Structure 'B3 (zincblende)':
   total-energy: -8.75112 eV
   atomic-energy: -4.37556 eV/atom
   total-volume: 19.8767 A^3
   atomic-volume: 9.93837 A^3/atom
   bulk-modulus: 368.64 GPa
   C11: 430.608 GPa
   C12: 337.658 GPa
   C44: 367.577 GPa
   lattice-parameter: 4.3 A [0:]
Structure 'B4 (wurtzite); relaxed ion':
   total-energy: -18.0458 eV
   atomic-energy: -4.51146 eV/atom
   total-volume: 47.5664 A^3
   atomic-volume: 11.8916 A^3/atom
   C11: 303.342 GPa
   C12: 111.249 GPa
   C13: 84.503 GPa
   C33: 333.85 GPa
   C44: 78.5184 GPa
   C66: 96.0925 GPa
   lattice-parameter: 3.25 A [0:]
   ca-ratio: 1.6
   u-parameter: 0.37
Structure 'B4 (wurtzite); clamped ion':
   total-energy: -18.0277 eV
   atomic-energy: -4.50692 eV/atom
   total-volume: 44.5586 A^3
   atomic-volume: 11.1397 A^3/atom
   bulk-modulus: 230.898 GPa
   C11: 473.56 GPa
   C12: 105.933 GPa
   C13: 43.9617 GPa
   C33: 704.804 GPa
   C44: 108.291 GPa
   C66: 183.813 GPa
   lattice-parameter: 3.18 A [0:]
   ca-ratio: 1.6
   u-parameter: 0.37
-------------------------------------------------------
-------------------------------------------------------

Other files

  • lammps_runs/data.lammps: elastic constants computed using Lammps; the original runs can be found in the tgz-archive wurtzite.tgz in the lammps_runs subdirectory.

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
    # 1st col: target pressure (GPa)
# 2nd col: final pressure (GPa)
# 3rd col: lattice constant (A)
# 4th col: cohesive energy (eV/atom)
# 5th col: c11 (GPa)
# 6th col: c12 (GPa)
# 7th col: c13 (GPa)
# 8th col: c33 (GPa)
# 9th col: c44 (GPa)
# 10th col: c66 (GPa)
# 11th col: iteration until pressure converged
# 12th col: number of atoms

  -4.00   -4.00    3.2023   -4.5249  325.4  138.1  104.8  358.7   82.2   93.6     102     192
  -2.00   -2.00    3.1914   -4.5271  335.1  147.8  113.7  369.2   82.2   93.6      68     192
   0.00   -0.00    3.1809   -4.5278  344.6  157.4  122.6  379.4   82.2   93.6      35     192
   2.00    2.00    3.1710   -4.5272  353.8  166.9  131.4  389.4   82.0   93.5      38     192
   4.00    4.00    3.1615   -4.5253  362.8  176.3  140.1  399.0   81.9   93.3      68     192
   6.00    6.00    3.1523   -4.5222  371.7  185.6  148.8  408.4   81.6   93.0      97     192
   8.00    8.00    3.1436   -4.5182  380.3  194.8  157.4  417.6   81.3   92.7     124     192
  10.00   10.00    3.1352   -4.5133  388.7  203.9  166.0  426.6   81.0   92.4     151     192