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1"""Function-like object creating triclinic lattices.
3The following lattice creator is defined:
4 Triclinic
5"""
7from ase.lattice.bravais import Bravais
8import numpy as np
9from ase.data import reference_states as _refstate
12class TriclinicFactory(Bravais):
13 "A factory for creating triclinic lattices."
15 # The name of the crystal structure in ChemicalElements
16 xtal_name = "triclinic"
18 # The natural basis vectors of the crystal structure
19 int_basis = np.array([[1, 0, 0],
20 [0, 1, 0],
21 [0, 0, 1]])
22 basis_factor = 1.0
24 # Converts the natural basis back to the crystallographic basis
25 inverse_basis = np.array([[1, 0, 0],
26 [0, 1, 0],
27 [0, 0, 1]])
28 inverse_basis_factor = 1.0
30 def get_lattice_constant(self):
31 """Get the lattice constant of an element with triclinic
32 crystal structure."""
33 if _refstate[self.atomicnumber]['symmetry'] != self.xtal_name:
34 raise ValueError(('Cannot guess the %s lattice constant of'
35 + ' an element with crystal structure %s.')
36 % (self.xtal_name,
37 _refstate[self.atomicnumber]['symmetry']))
38 return _refstate[self.atomicnumber].copy()
40 def make_crystal_basis(self):
41 """Make the basis matrix for the crystal unit cell and the system
42 unit cell."""
43 lattice = self.latticeconstant
44 if isinstance(lattice, type({})):
45 a = lattice['a']
46 try:
47 b = lattice['b']
48 except KeyError:
49 b = a * lattice['b/a']
50 try:
51 c = lattice['c']
52 except KeyError:
53 c = a * lattice['c/a']
54 alpha = lattice['alpha']
55 beta = lattice['beta']
56 gamma = lattice['gamma']
57 else:
58 if len(lattice) == 6:
59 (a, b, c, alpha, beta, gamma) = lattice
60 else:
61 raise ValueError(
62 "Improper lattice constants for triclinic crystal.")
64 degree = np.pi / 180.0
65 cosa = np.cos(alpha * degree)
66 cosb = np.cos(beta * degree)
67 sinb = np.sin(beta * degree)
68 cosg = np.cos(gamma * degree)
69 sing = np.sin(gamma * degree)
70 lattice = np.array(
71 [[a, 0, 0],
72 [b * cosg, b * sing, 0],
73 [c * cosb, c * (cosa - cosb * cosg) / sing,
74 c * np.sqrt(sinb**2 - ((cosa - cosb * cosg) / sing)**2)]])
75 self.latticeconstant = lattice
76 self.miller_basis = lattice
77 self.crystal_basis = (self.basis_factor *
78 np.dot(self.int_basis, lattice))
79 self.basis = np.dot(self.directions, self.crystal_basis)
80 assert abs(np.dot(lattice[0], lattice[1]) - a * b * cosg) < 1e-5
81 assert abs(np.dot(lattice[0], lattice[2]) - a * c * cosb) < 1e-5
82 assert abs(np.dot(lattice[1], lattice[2]) - b * c * cosa) < 1e-5
83 assert abs(np.dot(lattice[0], lattice[0]) - a * a) < 1e-5
84 assert abs(np.dot(lattice[1], lattice[1]) - b * b) < 1e-5
85 assert abs(np.dot(lattice[2], lattice[2]) - c * c) < 1e-5
88Triclinic = TriclinicFactory()