"""Build crystalline systems"""
from math import sqrt
from typing import Any
from ase.atoms import Atoms
from ase.data import atomic_numbers, chemical_symbols, reference_states
from ase.symbols import string2symbols
from ase.utils import plural
def incompatible_cell(*, want, have):
return RuntimeError(f'Cannot create {want} cell for {have} structure')
[docs]
def bulk(
name: str,
crystalstructure: str = None,
a: float = None,
b: float = None,
c: float = None,
*,
alpha: float = None,
covera: float = None,
u: float = None,
orthorhombic: bool = False,
cubic: bool = False,
basis=None,
) -> Atoms:
"""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, mcl, 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 = ''
ref: Any = {}
if name in chemical_symbols: # single element
atomic_number = atomic_numbers[name]
ref = reference_states[atomic_number]
if ref is None:
ref = {} # easier to 'get' things from empty dictionary than None
else:
xref = ref['symmetry']
if crystalstructure is None:
# `ref` requires `basis` but not given and not pre-defined
if basis is None and 'basis' in ref and ref['basis'] is None:
raise ValueError('This structure requires an atomic basis')
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 ValueError(
f'The reference structure of {name} is not implemented')
# 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(f'No suitable reference data for bulk {name}.'
f' Reference data: {ref}')
magmom_per_atom = None
if crystalstructure == xref:
magmom_per_atom = ref.get('magmom_per_atom')
if crystalstructure not in structures:
raise ValueError(f'Unknown structure: {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.')
if 'a' in ref:
a = ref['a']
else:
raise KeyError(f'No reference lattice parameter "a" for "{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 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 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)
elif orthorhombic:
atoms = _orthorhombic_bulk(name, crystalstructure, a, covera, u)
elif cubic:
atoms = _cubic_bulk(name, crystalstructure, a)
else:
atoms = _primitive_bulk(name, crystalstructure, a, covera, u)
if magmom_per_atom is not None:
magmoms = [magmom_per_atom] * len(atoms)
atoms.set_initial_magnetic_moments(magmoms)
if cubic or orthorhombic:
assert atoms.cell.orthorhombic
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 in ('sc', 'bcc', 'cesiumchloride'):
atoms = _cubic_bulk(name, crystalstructure, a)
elif crystalstructure == 'fcc':
b = a / sqrt(2)
cell = (b, b, a)
scaled_positions = ((0.0, 0.0, 0.0), (0.5, 0.5, 0.5))
atoms = Atoms(2 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'hcp':
cell = (a, a * sqrt(3), covera * a)
scaled_positions = [
(0.0, 0 / 6, 0.0),
(0.5, 3 / 6, 0.0),
(0.5, 1 / 6, 0.5),
(0.0, 4 / 6, 0.5),
]
atoms = Atoms(4 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'diamond':
b = a / sqrt(2)
cell = (b, b, a)
scaled_positions = [
(0.0, 0.0, 0.0), (0.5, 0.0, 0.25),
(0.5, 0.5, 0.5), (0.0, 0.5, 0.75),
]
atoms = Atoms(4 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'rocksalt':
b = a / sqrt(2)
cell = (b, b, a)
scaled_positions = [
(0.0, 0.0, 0.0), (0.5, 0.5, 0.0),
(0.5, 0.5, 0.5), (0.0, 0.0, 0.5),
]
atoms = Atoms(2 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'zincblende':
symbol0, symbol1 = string2symbols(name)
atoms = _orthorhombic_bulk(symbol0, 'diamond', a)
atoms.symbols[[1, 3]] = symbol1
elif crystalstructure == 'wurtzite':
cell = (a, a * sqrt(3), covera * a)
u = u or 0.25 + 1 / 3 / covera**2
scaled_positions = [
(0.0, 0 / 6, 0.0), (0.0, 2 / 6, 0.5 - u),
(0.0, 2 / 6, 0.5), (0.0, 0 / 6, 1.0 - u),
(0.5, 3 / 6, 0.0), (0.5, 5 / 6, 0.5 - u),
(0.5, 5 / 6, 0.5), (0.5, 3 / 6, 1.0 - u),
]
atoms = Atoms(4 * name, cell=cell, scaled_positions=scaled_positions)
else:
raise incompatible_cell(want='orthorhombic', have=crystalstructure)
atoms.pbc = True
return atoms
def _cubic_bulk(name: str, crystalstructure: str, a: float) -> Atoms:
cell = (a, a, a)
if crystalstructure == 'sc':
atoms = Atoms(name, cell=cell)
elif crystalstructure == 'fcc':
scaled_positions = [
(0.0, 0.0, 0.0),
(0.0, 0.5, 0.5),
(0.5, 0.0, 0.5),
(0.5, 0.5, 0.0),
]
atoms = Atoms(4 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'bcc':
scaled_positions = [
(0.0, 0.0, 0.0),
(0.5, 0.5, 0.5),
]
atoms = Atoms(2 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'diamond':
scaled_positions = [
(0.0, 0.0, 0.0), (0.25, 0.25, 0.25),
(0.0, 0.5, 0.5), (0.25, 0.75, 0.75),
(0.5, 0.0, 0.5), (0.75, 0.25, 0.75),
(0.5, 0.5, 0.0), (0.75, 0.75, 0.25),
]
atoms = Atoms(8 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'cesiumchloride':
symbol0, symbol1 = string2symbols(name)
atoms = _cubic_bulk(symbol0, 'bcc', a)
atoms.symbols[[1]] = symbol1
elif crystalstructure == 'zincblende':
symbol0, symbol1 = string2symbols(name)
atoms = _cubic_bulk(symbol0, 'diamond', a)
atoms.symbols[[1, 3, 5, 7]] = symbol1
elif crystalstructure == 'rocksalt':
scaled_positions = [
(0.0, 0.0, 0.0), (0.5, 0.0, 0.0),
(0.0, 0.5, 0.5), (0.5, 0.5, 0.5),
(0.5, 0.0, 0.5), (0.0, 0.0, 0.5),
(0.5, 0.5, 0.0), (0.0, 0.5, 0.0),
]
atoms = Atoms(4 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'fluorite':
scaled_positions = [
(0.00, 0.00, 0.00), (0.25, 0.25, 0.25), (0.75, 0.75, 0.75),
(0.00, 0.50, 0.50), (0.25, 0.75, 0.75), (0.75, 0.25, 0.25),
(0.50, 0.00, 0.50), (0.75, 0.25, 0.75), (0.25, 0.75, 0.25),
(0.50, 0.50, 0.00), (0.75, 0.75, 0.25), (0.25, 0.25, 0.75),
]
atoms = Atoms(4 * name, cell=cell, scaled_positions=scaled_positions)
else:
raise incompatible_cell(want='cubic', have=crystalstructure)
atoms.pbc = True
return atoms
def _primitive_bulk(name, crystalstructure, a, covera=None, u=None):
if crystalstructure == 'sc':
atoms = Atoms(name, cell=(a, a, a))
elif crystalstructure == 'fcc':
b = 0.5 * a
cell = ((0, b, b), (b, 0, b), (b, b, 0))
atoms = Atoms(name, cell=cell)
elif crystalstructure == 'bcc':
b = 0.5 * a
cell = ((-b, b, b), (b, -b, b), (b, b, -b))
atoms = Atoms(name, cell=cell)
elif crystalstructure == 'hcp':
c = covera * a
cell = ((a, 0, 0), (-0.5 * a, 0.5 * sqrt(3) * a, 0), (0, 0, c))
scaled_positions = [
(0 / 3, 0 / 3, 0.0),
(1 / 3, 2 / 3, 0.5),
]
atoms = Atoms(2 * name, cell=cell, scaled_positions=scaled_positions)
elif crystalstructure == 'diamond':
atoms = \
_primitive_bulk(name, 'fcc', a) + \
_primitive_bulk(name, 'fcc', a)
atoms.positions[1, :] += 0.25 * a
elif crystalstructure == 'rocksalt':
symbol0, symbol1 = string2symbols(name)
atoms = \
_primitive_bulk(symbol0, 'fcc', a) + \
_primitive_bulk(symbol1, 'fcc', a)
atoms.positions[1, 0] += 0.5 * a
elif crystalstructure == 'cesiumchloride':
symbol0, symbol1 = string2symbols(name)
atoms = \
_primitive_bulk(symbol0, 'sc', a) + \
_primitive_bulk(symbol1, 'sc', a)
atoms.positions[1, :] += 0.5 * a
elif crystalstructure == 'zincblende':
symbol0, symbol1 = string2symbols(name)
atoms = \
_primitive_bulk(symbol0, 'fcc', a) + \
_primitive_bulk(symbol1, 'fcc', a)
atoms.positions[1, :] += 0.25 * a
elif crystalstructure == 'fluorite':
symbol0, symbol1, symbol2 = string2symbols(name)
atoms = \
_primitive_bulk(symbol0, 'fcc', a) + \
_primitive_bulk(symbol1, 'fcc', a) + \
_primitive_bulk(symbol2, 'fcc', a)
atoms.positions[1, :] += 0.25 * a
atoms.positions[2, :] += 0.75 * a
elif crystalstructure == 'wurtzite':
c = covera * a
cell = ((a, 0, 0), (-0.5 * a, 0.5 * sqrt(3) * a, 0), (0, 0, c))
u = u or 0.25 + 1 / 3 / covera**2
scaled_positions = [
(0 / 3, 0 / 3, 0.0), (1 / 3, 2 / 3, 0.5 - u),
(1 / 3, 2 / 3, 0.5), (0 / 3, 0 / 3, 1.0 - u),
]
atoms = Atoms(2 * name, cell=cell, scaled_positions=scaled_positions)
else:
raise incompatible_cell(want='primitive', have=crystalstructure)
atoms.pbc = True
return atoms