from math import sqrt
from ase.atoms import Atoms
from ase.symbols import string2symbols
from ase.data import reference_states, atomic_numbers, chemical_symbols
from ase.utils import plural
def incompatible_cell(*, want, have):
return RuntimeError('Cannot create {} cell for {} structure'
.format(want, have))
[docs]def bulk(name, crystalstructure=None, a=None, b=None, c=None, *, alpha=None,
covera=None, u=None, orthorhombic=False, cubic=False,
basis=None):
"""Creating bulk systems.
Crystal structure and lattice constant(s) will be guessed if not
provided.
name: str
Chemical symbol or symbols as in 'MgO' or 'NaCl'.
crystalstructure: str
Must be one of sc, fcc, bcc, tetragonal, bct, hcp, rhombohedral,
orthorhombic, mlc, diamond, zincblende, rocksalt, cesiumchloride,
fluorite or wurtzite.
a: float
Lattice constant.
b: float
Lattice constant. If only a and b is given, b will be interpreted
as c instead.
c: float
Lattice constant.
alpha: float
Angle in degrees for rhombohedral lattice.
covera: float
c/a ratio used for hcp. Default is ideal ratio: sqrt(8/3).
u: float
Internal coordinate for Wurtzite structure.
orthorhombic: bool
Construct orthorhombic unit cell instead of primitive cell
which is the default.
cubic: bool
Construct cubic unit cell if possible.
"""
if c is None and b is not None:
# If user passes (a, b) positionally, we want it as (a, c) instead:
c, b = b, c
if covera is not None and c is not None:
raise ValueError("Don't specify both c and c/a!")
xref = None
ref = {}
if name in chemical_symbols:
Z = atomic_numbers[name]
ref = reference_states[Z]
if ref is not None:
xref = ref['symmetry']
# If user did not specify crystal structure, and no basis
# is given, and the reference state says we need one, but
# does not have one, then we can't proceed.
if (crystalstructure is None and basis is None
and 'basis' in ref and ref['basis'] is None):
# XXX This is getting much too complicated, we need to split
# this function up. A lot.
raise RuntimeError('This structure requires an atomic basis')
if ref is None:
ref = {} # easier to 'get' things from empty dictionary than None
if xref == 'cubic':
# P and Mn are listed as 'cubic' but the lattice constants
# are 7 and 9. They must be something other than simple cubic
# then. We used to just return the cubic one but that must
# have been wrong somehow. --askhl
raise RuntimeError('Only simple cubic ("sc") supported')
# Mapping of name to number of atoms in primitive cell.
structures = {'sc': 1, 'fcc': 1, 'bcc': 1,
'tetragonal': 1,
'bct': 1,
'hcp': 1,
'rhombohedral': 1,
'orthorhombic': 1,
'mcl': 1,
'diamond': 1,
'zincblende': 2, 'rocksalt': 2, 'cesiumchloride': 2,
'fluorite': 3, 'wurtzite': 2}
if crystalstructure is None:
crystalstructure = xref
if crystalstructure not in structures:
raise ValueError('No suitable reference data for bulk {}.'
' Reference data: {}'
.format(name, ref))
if crystalstructure not in structures:
raise ValueError('Unknown structure: {}.'
.format(crystalstructure))
# Check name:
natoms = len(string2symbols(name))
natoms0 = structures[crystalstructure]
if natoms != natoms0:
raise ValueError('Please specify {} for {} and not {}'
.format(plural(natoms0, 'atom'),
crystalstructure, natoms))
if alpha is None:
alpha = ref.get('alpha')
if a is None:
if xref != crystalstructure:
raise ValueError('You need to specify the lattice constant.')
try:
a = ref['a']
except KeyError:
raise KeyError('No reference lattice parameter "a" for "{}"'
.format(name))
if b is None:
bovera = ref.get('b/a')
if bovera is not None and a is not None:
b = bovera * a
if crystalstructure in ['hcp', 'wurtzite']:
if cubic:
raise incompatible_cell(want='cubic', have=crystalstructure)
if c is not None:
covera = c / a
elif covera is None:
if xref == crystalstructure:
covera = ref['c/a']
else:
covera = sqrt(8 / 3)
if covera is None:
covera = ref.get('c/a')
if c is None and covera is not None:
c = covera * a
if orthorhombic and crystalstructure not in ['sc', 'tetragonal',
'orthorhombic']:
return _orthorhombic_bulk(name, crystalstructure, a, covera, u)
if cubic and crystalstructure in ['bcc', 'cesiumchloride']:
return _orthorhombic_bulk(name, crystalstructure, a, covera)
if cubic and crystalstructure != 'sc':
return _cubic_bulk(name, crystalstructure, a)
if crystalstructure == 'sc':
atoms = Atoms(name, cell=(a, a, a), pbc=True)
elif crystalstructure == 'fcc':
b = a / 2
atoms = Atoms(name, cell=[(0, b, b), (b, 0, b), (b, b, 0)], pbc=True)
elif crystalstructure == 'bcc':
b = a / 2
atoms = Atoms(name, cell=[(-b, b, b), (b, -b, b), (b, b, -b)],
pbc=True)
elif crystalstructure == 'hcp':
atoms = Atoms(2 * name,
scaled_positions=[(0, 0, 0),
(1 / 3, 2 / 3, 0.5)],
cell=[(a, 0, 0),
(-a / 2, a * sqrt(3) / 2, 0),
(0, 0, covera * a)],
pbc=True)
elif crystalstructure == 'diamond':
atoms = bulk(2 * name, 'zincblende', a)
elif crystalstructure == 'zincblende':
s1, s2 = string2symbols(name)
atoms = bulk(s1, 'fcc', a) + bulk(s2, 'fcc', a)
atoms.positions[1] += a / 4
elif crystalstructure == 'rocksalt':
s1, s2 = string2symbols(name)
atoms = bulk(s1, 'fcc', a) + bulk(s2, 'fcc', a)
atoms.positions[1, 0] += a / 2
elif crystalstructure == 'cesiumchloride':
s1, s2 = string2symbols(name)
atoms = bulk(s1, 'sc', a) + bulk(s2, 'sc', a)
atoms.positions[1, :] += a / 2
elif crystalstructure == 'fluorite':
s1, s2, s3 = string2symbols(name)
atoms = bulk(s1, 'fcc', a) + bulk(s2, 'fcc', a) + bulk(s3, 'fcc', a)
atoms.positions[1, :] += a / 4
atoms.positions[2, :] += a * 3 / 4
elif crystalstructure == 'wurtzite':
u = u or 0.25 + 1 / 3 / covera**2
atoms = Atoms(2 * name,
scaled_positions=[(0, 0, 0),
(1 / 3, 2 / 3, 0.5 - u),
(1 / 3, 2 / 3, 0.5),
(0, 0, 1 - u)],
cell=[(a, 0, 0),
(-a / 2, a * sqrt(3) / 2, 0),
(0, 0, a * covera)],
pbc=True)
elif crystalstructure == 'bct':
from ase.lattice import BCT
if basis is None:
basis = ref.get('basis')
if basis is not None:
natoms = len(basis)
lat = BCT(a=a, c=c)
atoms = Atoms([name] * natoms, cell=lat.tocell(), pbc=True,
scaled_positions=basis)
elif crystalstructure == 'rhombohedral':
atoms = _build_rhl(name, a, alpha, basis)
elif crystalstructure == 'orthorhombic':
atoms = Atoms(name, cell=[a, b, c], pbc=True)
else:
raise ValueError('Unknown crystal structure: ' + crystalstructure)
if orthorhombic:
assert atoms.cell.orthorhombic
if cubic:
assert abs(atoms.cell.angles() - 90).all() < 1e-10
return atoms
def _build_rhl(name, a, alpha, basis):
from ase.lattice import RHL
lat = RHL(a, alpha)
cell = lat.tocell()
if basis is None:
# RHL: Given by A&M as scaled coordinates "x" of cell.sum(0):
basis_x = reference_states[atomic_numbers[name]]['basis_x']
basis = basis_x[:, None].repeat(3, axis=1)
natoms = len(basis)
return Atoms([name] * natoms, cell=cell, scaled_positions=basis, pbc=True)
def _orthorhombic_bulk(name, crystalstructure, a, covera=None, u=None):
if crystalstructure == 'fcc':
b = a / sqrt(2)
atoms = Atoms(2 * name, cell=(b, b, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.5, 0.5, 0.5)])
elif crystalstructure == 'bcc':
atoms = Atoms(2 * name, cell=(a, a, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.5, 0.5, 0.5)])
elif crystalstructure == 'hcp':
atoms = Atoms(4 * name,
cell=(a, a * sqrt(3), covera * a),
scaled_positions=[(0, 0, 0),
(0.5, 0.5, 0),
(0.5, 1 / 6, 0.5),
(0, 2 / 3, 0.5)],
pbc=True)
elif crystalstructure == 'diamond':
atoms = _orthorhombic_bulk(2 * name, 'zincblende', a)
elif crystalstructure == 'zincblende':
s1, s2 = string2symbols(name)
b = a / sqrt(2)
atoms = Atoms(2 * name, cell=(b, b, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.5, 0, 0.25),
(0.5, 0.5, 0.5), (0, 0.5, 0.75)])
elif crystalstructure == 'rocksalt':
s1, s2 = string2symbols(name)
b = a / sqrt(2)
atoms = Atoms(2 * name, cell=(b, b, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.5, 0.5, 0),
(0.5, 0.5, 0.5), (0, 0, 0.5)])
elif crystalstructure == 'cesiumchloride':
atoms = Atoms(name, cell=(a, a, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.5, 0.5, 0.5)])
elif crystalstructure == 'wurtzite':
u = u or 0.25 + 1 / 3 / covera**2
atoms = Atoms(4 * name,
cell=(a, a * 3**0.5, covera * a),
scaled_positions=[(0, 0, 0),
(0, 1 / 3, 0.5 - u),
(0, 1 / 3, 0.5),
(0, 0, 1 - u),
(0.5, 0.5, 0),
(0.5, 5 / 6, 0.5 - u),
(0.5, 5 / 6, 0.5),
(0.5, 0.5, 1 - u)],
pbc=True)
else:
raise incompatible_cell(want='orthorhombic', have=crystalstructure)
return atoms
def _cubic_bulk(name, crystalstructure, a):
if crystalstructure == 'fcc':
atoms = Atoms(4 * name, cell=(a, a, a), pbc=True,
scaled_positions=[(0, 0, 0), (0, 0.5, 0.5),
(0.5, 0, 0.5), (0.5, 0.5, 0)])
elif crystalstructure == 'diamond':
atoms = _cubic_bulk(2 * name, 'zincblende', a)
elif crystalstructure == 'zincblende':
atoms = Atoms(4 * name, cell=(a, a, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.25, 0.25, 0.25),
(0, 0.5, 0.5), (0.25, 0.75, 0.75),
(0.5, 0, 0.5), (0.75, 0.25, 0.75),
(0.5, 0.5, 0), (0.75, 0.75, 0.25)])
elif crystalstructure == 'rocksalt':
atoms = Atoms(4 * name, cell=(a, a, a), pbc=True,
scaled_positions=[(0, 0, 0), (0.5, 0, 0),
(0, 0.5, 0.5), (0.5, 0.5, 0.5),
(0.5, 0, 0.5), (0, 0, 0.5),
(0.5, 0.5, 0), (0, 0.5, 0)])
else:
raise incompatible_cell(want='cubic', have=crystalstructure)
return atoms