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"""Function-like object creating triclinic lattices.
The following lattice creator is defined:
Triclinic
"""
import numpy as np
from ase.data import reference_states as _refstate
from ase.lattice.bravais import Bravais
class TriclinicFactory(Bravais):
"A factory for creating triclinic lattices."
# The name of the crystal structure in ChemicalElements
xtal_name = "triclinic"
# The natural basis vectors of the crystal structure
int_basis = np.array([[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
basis_factor = 1.0
# Converts the natural basis back to the crystallographic basis
inverse_basis = np.array([[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
inverse_basis_factor = 1.0
def get_lattice_constant(self):
"""Get the lattice constant of an element with triclinic
crystal structure."""
if _refstate[self.atomicnumber]['symmetry'] != self.xtal_name:
raise ValueError(('Cannot guess the %s lattice constant of'
+ ' an element with crystal structure %s.')
% (self.xtal_name,
_refstate[self.atomicnumber]['symmetry']))
return _refstate[self.atomicnumber].copy()
def make_crystal_basis(self):
"""Make the basis matrix for the crystal unit cell and the system
unit cell."""
lattice = self.latticeconstant
if isinstance(lattice, type({})):
a = lattice['a']
try:
b = lattice['b']
except KeyError:
b = a * lattice['b/a']
try:
c = lattice['c']
except KeyError:
c = a * lattice['c/a']
alpha = lattice['alpha']
beta = lattice['beta']
gamma = lattice['gamma']
else:
if len(lattice) == 6:
(a, b, c, alpha, beta, gamma) = lattice
else:
raise ValueError(
"Improper lattice constants for triclinic crystal.")
degree = np.pi / 180.0
cosa = np.cos(alpha * degree)
cosb = np.cos(beta * degree)
sinb = np.sin(beta * degree)
cosg = np.cos(gamma * degree)
sing = np.sin(gamma * degree)
lattice = np.array(
[[a, 0, 0],
[b * cosg, b * sing, 0],
[c * cosb, c * (cosa - cosb * cosg) / sing,
c * np.sqrt(sinb**2 - ((cosa - cosb * cosg) / sing)**2)]])
self.latticeconstant = lattice
self.miller_basis = lattice
self.crystal_basis = (self.basis_factor *
np.dot(self.int_basis, lattice))
self.basis = np.dot(self.directions, self.crystal_basis)
assert abs(np.dot(lattice[0], lattice[1]) - a * b * cosg) < 1e-5
assert abs(np.dot(lattice[0], lattice[2]) - a * c * cosb) < 1e-5
assert abs(np.dot(lattice[1], lattice[2]) - b * c * cosa) < 1e-5
assert abs(np.dot(lattice[0], lattice[0]) - a * a) < 1e-5
assert abs(np.dot(lattice[1], lattice[1]) - b * b) < 1e-5
assert abs(np.dot(lattice[2], lattice[2]) - c * c) < 1e-5
Triclinic = TriclinicFactory()
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