def test_translation_integers_for_simple_cubic_cell(self):
"""
For a cubic system, expect the naive expression
ceil(cutoff / |a|) to give the same maximum integer as
translation_integers_for_radial_cutoff function,
where a is the cubic lattice vector
"""
lattice_vectors = simple_cubic(5)
cutoff = 21
integers = lattice.simple_cubic_cell_translation_integers(
lattice_vectors, cutoff)
integers2 = lattice.translation_integers_for_radial_cutoff(
lattice_vectors, cutoff)
self.assertTrue(np.all(integers == integers2))
def simple_cubic():
system_label = 'cubic_silicon'
al = 10.33
species = ['Si'] * 8
positions = al * np.array([[0.25000000, 0.75000000, 0.25000000],
[0.00000000, 0.00000000, 0.50000000],
[0.25000000, 0.25000000, 0.75000000],
[0.00000000, 0.50000000, 0.00000000],
[0.75000000, 0.75000000, 0.75000000],
[0.50000000, 0.00000000, 0.00000000],
[0.75000000, 0.25000000, 0.25000000],
[0.50000000, 0.50000000, 0.50000000]])
unit_cell = atoms.Atoms(species, positions)
lattice = bravais.simple_cubic(al)
return System(system_label, unit_cell, lattice)
def cubic_point_groups():
point_groups = []
al = 1
cubic_lattice = bravais.simple_cubic(al)
pg = find_point_group(cubic_lattice)
point_groups.append(pg)
print(' Real lattice of simple cubic:', pg)
recip_lattice = lattice.reciprocal_lattice_vectors(cubic_lattice)
pg = find_point_group(recip_lattice)
point_groups.append(pg)
print(' Reciprocal lattice of simple cubic:', pg)
bcc_lattice = bravais.body_centred_cubic(al)
pg = find_point_group(bcc_lattice)
point_groups.append(pg)
print(' Real lattice of BCC:', pg)
recip_lattice = lattice.reciprocal_lattice_vectors(bcc_lattice)
pg = find_point_group(recip_lattice)
point_groups.append(pg)
print(' Reciprocal lattice of BCC:', pg)
fcc_lattice = bravais.face_centred_cubic(al)
pg = find_point_group(fcc_lattice)
point_groups.append(pg)
print(' Real lattice of FCC:', pg)
recip_lattice = lattice.reciprocal_lattice_vectors(fcc_lattice)
pg = find_point_group(recip_lattice)
point_groups.append(pg)
print(' Reciprocal lattice of FCC:', pg, "\n")
assert check_all_equal(point_groups, 'm-3m')
return
# Silicon cells for gamma point calculation with Grimme gfn1
import numpy as np
from modules.electronic_structure.structure import atoms, bravais, crystals, supercell
from modules.electronic_structure.basis import gfn1
from modules.parameters import crystals as params
from modules.fileio import write
from modules import entos
# Silicon cubic unit cell in angstrom
al = params.silicon['lattice_constant']['angstrom']
fractional_basis_positions = crystals.silicon('conventional')
lattice = bravais.simple_cubic(al)
unit_cell = []
for atom in fractional_basis_positions:
pos_angstrom = np.matmul(lattice, atom.position)
unit_cell.append(atoms.Atom(atom.species, pos_angstrom))
def silicon_supercell(n, centred_on_zero=None):
if centred_on_zero == None:
centred_on_zero = (n[0] * n[1] * n[2]) % 2 != 0
translations = supercell.translation_vectors(
lattice, n, centred_on_zero=centred_on_zero)
super_cell = supercell.build_supercell(unit_cell, translations)
# Information
def test_parallelpiped_volume_simple_cubic(self):
""" Test volume for simple cubic lattice"""
al = 5
lattice_vectors = simple_cubic(5)
vol = lattice.parallelpiped_volume(lattice_vectors)
self.assertEqual(vol, al**3)