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"""Function-like objects creating cubic lattices (SC, FCC, BCC and Diamond).
The following lattice creators are defined:
SimpleCubic
FaceCenteredCubic
BodyCenteredCubic
Diamond
"""
import numpy as np
from ase.data import reference_states as _refstate
from ase.lattice.bravais import Bravais, reduceindex
class SimpleCubicFactory(Bravais):
"A factory for creating simple cubic lattices."
# The name of the crystal structure in ChemicalElements
xtal_name = "sc"
# 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
# For checking the basis volume
atoms_in_unit_cell = 1
def get_lattice_constant(self):
"Get the lattice constant of an element with cubic 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]['a']
def make_crystal_basis(self):
"""Make the basis matrix for the crystal unit cell and the
system unit cell."""
self.crystal_basis = (self.latticeconstant * self.basis_factor
* self.int_basis)
self.miller_basis = self.latticeconstant * np.identity(3)
self.basis = np.dot(self.directions, self.crystal_basis)
self.check_basis_volume()
def check_basis_volume(self):
"Check the volume of the unit cell."
vol1 = abs(np.linalg.det(self.basis))
cellsize = self.atoms_in_unit_cell
if self.bravais_basis is not None:
cellsize *= len(self.bravais_basis)
vol2 = (self.calc_num_atoms() * self.latticeconstant**3 / cellsize)
assert abs(vol1 - vol2) < 1e-5
def find_directions(self, directions, miller):
"Find missing directions and miller indices from the specified ones."
directions = list(directions)
miller = list(miller)
# Process keyword "orthogonal"
self.find_ortho(directions)
self.find_ortho(miller)
Bravais.find_directions(self, directions, miller)
def find_ortho(self, idx):
"Replace keyword 'ortho' or 'orthogonal' with a direction."
for i in range(3):
if (isinstance(idx[i], str)
and (idx[i].lower() == "ortho" or
idx[i].lower() == "orthogonal")):
if self.debug:
print("Calculating orthogonal direction", i)
print(idx[i - 2], "X", idx[i - 1], end=' ')
idx[i] = reduceindex(np.cross(idx[i - 2], idx[i - 1]))
if self.debug:
print("=", idx[i])
SimpleCubic = SimpleCubicFactory()
class FaceCenteredCubicFactory(SimpleCubicFactory):
"A factory for creating face-centered cubic lattices."
xtal_name = "fcc"
int_basis = np.array([[0, 1, 1],
[1, 0, 1],
[1, 1, 0]])
basis_factor = 0.5
inverse_basis = np.array([[-1, 1, 1],
[1, -1, 1],
[1, 1, -1]])
inverse_basis_factor = 1.0
atoms_in_unit_cell = 4
FaceCenteredCubic = FaceCenteredCubicFactory()
class BodyCenteredCubicFactory(SimpleCubicFactory):
"A factory for creating body-centered cubic lattices."
xtal_name = "bcc"
int_basis = np.array([[-1, 1, 1],
[1, -1, 1],
[1, 1, -1]])
basis_factor = 0.5
inverse_basis = np.array([[0, 1, 1],
[1, 0, 1],
[1, 1, 0]])
inverse_basis_factor = 1.0
atoms_in_unit_cell = 2
BodyCenteredCubic = BodyCenteredCubicFactory()
class DiamondFactory(FaceCenteredCubicFactory):
"A factory for creating diamond lattices."
xtal_name = "diamond"
bravais_basis = [[0, 0, 0], [0.25, 0.25, 0.25]]
Diamond = DiamondFactory()
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