# coding: utf-8
# Distributed under the terms of the MIT License.
""" This submodule implements some useful functions for real/reciprocal
cell manipulation, symmetry checking and sampling (e.g. grids and paths.)
"""
from __future__ import annotations
from typing import Dict, Any, Union, Tuple, List, TYPE_CHECKING
import numpy as np
from matador.data.periodic_table import PERIODIC_TABLE
if TYPE_CHECKING:
from matador.crystal import Crystal
EPS = 1e-12
[docs]def abc2cart(lattice_abc: List[List[float]]) -> List[List[float]]:
"""Converts lattice parameters into Cartesian lattice vectors.
Parameters:
lattice_abc: The lattice parameters [[a, b, c], [alpha, beta, gamma]]
Returns:
Cartesian lattice vectors.
"""
assert len(lattice_abc) == 2
assert len(lattice_abc[0]) == 3
assert len(lattice_abc[1]) == 3
a = lattice_abc[0][0]
b = lattice_abc[0][1]
c = lattice_abc[0][2]
deg2rad = np.pi / 180
alpha = lattice_abc[1][0] * deg2rad
beta = lattice_abc[1][1] * deg2rad
gamma = lattice_abc[1][2] * deg2rad
lattice_cart = []
lattice_cart.append([a, 0.0, 0.0])
bx = b * np.cos(gamma)
by = b * np.sin(gamma)
tol = 1e-12
if abs(bx) < tol:
bx = 0.0
if abs(by) < tol:
by = 0.0
cx = c * np.cos(beta)
if abs(cx) < tol:
cx = 0.0
cy = c * (np.cos(alpha) - np.cos(beta) * np.cos(gamma)) / np.sin(gamma)
if abs(cy) < tol:
cy = 0.0
cz = np.sqrt(c**2 - cx**2 - cy**2)
lattice_cart.append([bx, by, 0.0])
lattice_cart.append([cx, cy, cz])
return lattice_cart
[docs]def cart2abcstar(lattice_cart: List[List[float]]) -> np.ndarray:
"""Convert Cartesian lattice vectors to the reciprocal of the lattice vectors,
NOT the reciprocal lattice vectors (useful when writing PDB files).
Parameters:
lattice_cart: Cartesian lattice vectors.
Returns:
Reciprocal of the lattice vectors.
"""
return np.asarray(real2recip(lattice_cart)) / (2 * np.pi)
[docs]def cart2volume(lattice_cart: List[List[float]]) -> float:
"""Convert lattice_cart to cell volume.
Parameters:
lattice_cart: Cartesian lattice vectors.
Returns:
Cell volume in the same unit as the lattice vectors (cubed).
"""
lattice_cart = np.asarray(lattice_cart)
vol = np.abs(np.dot(np.cross(lattice_cart[0], lattice_cart[1]), lattice_cart[2]))
return vol
[docs]def cart2abc(lattice_cart: List[List[float]]) -> List[List[float]]:
"""Convert Cartesian lattice vectors to lattice parametres.
Parameters:
lattice_cart: Cartesian lattice vectors.
Returns:
The lattice parameters :math:`[(a, b, c), (\\alpha, \\beta, \\gamma)]`.
"""
vecs = lattice_cart
lattice_abc = []
a, b, c = (np.sqrt(sum([val**2 for val in vec])) for vec in vecs)
lattice_abc.append([a, b, c])
# np.cos(alpha) = b.c /|b * c|
radians2deg = 180.0 / np.pi
cos_alpha = sum([val_b * val_c for (val_c, val_b) in zip(vecs[2], vecs[1])]) / (
b * c
)
cos_beta = sum([val_c * val_a for (val_c, val_a) in zip(vecs[2], vecs[0])]) / (
c * a
)
cos_gamma = sum([val_a * val_b for (val_a, val_b) in zip(vecs[0], vecs[1])]) / (
a * b
)
alpha = radians2deg * np.arccos(cos_alpha)
beta = radians2deg * np.arccos(cos_beta)
gamma = radians2deg * np.arccos(cos_gamma)
lattice_abc.append([alpha, beta, gamma])
return lattice_abc
[docs]def frac2cart(
lattice_cart: List[List[float]], positions_frac: List[List[float]]
) -> List[List[float]]:
"""Convert positions_frac block into positions_abs.
Parameters:
lattice_cart: Cartesian lattice vectors.
positions_frac: List of fractional position vectors.
Returns:
List of absolute position vectors.
"""
_positions_frac = np.asarray(positions_frac)
reshaped = False
if len(np.shape(_positions_frac)) == 1:
reshaped = True
_positions_frac = _positions_frac.reshape((1, 3))
_lattice_cart = np.asarray(lattice_cart)
positions_abs = switch_coords(_lattice_cart, _positions_frac)
if reshaped:
positions_abs = positions_abs.reshape(-1)
return positions_abs.tolist()
[docs]def wrap_frac_coords(
positions: Union[List[List[float]], List[float]], remove: bool = False
) -> Union[List[List[float]], List[float]]:
"""Wrap the given fractional coordinates back into the cell.
Parameters:
positions: list of fractional position vectors, or
a single position.
Keyword arguments:
remove: if True, removes points exterior to the cell.
Returns:
List of wrapped fractional position vectors.
"""
from copy import deepcopy
wrapped = deepcopy(positions)
single = False
if len(wrapped) == 3 and isinstance(wrapped[0], float):
wrapped = [wrapped]
single = True
if remove:
to_remove = len(wrapped) * [False]
for ind, pos in enumerate(wrapped):
for k in range(3):
if pos[k] >= 1 or pos[k] < 0:
if remove:
to_remove[ind] = True
break
else:
wrapped[ind][k] %= 1
if remove:
wrapped = [wrapped[ind] for ind, res in enumerate(to_remove) if not res]
if single:
return wrapped[0]
return wrapped
[docs]def switch_coords(
lattice: np.ndarray, pos: np.ndarray, norm: float = None
) -> np.ndarray:
"""Act on coordinates with the relevant lattice
vectors to switch from fractional to absolute coordinates.
Parameters:
lattice: either lattice_cart or reciprocal lattice_cart (3x3 array)
pos: input positions to convert (3xN array for N atoms).
Keyword arguments:
norm (float): divide final coordinates by normalisation factor, e.g.
:math:`2 \\pi` when lattice is recip and positions are cartesian.
Returns:
3xN array of converted positions.
"""
new_pos = np.zeros_like(pos)
for ni, _ in enumerate(pos):
for j in range(3):
new_pos[ni] += lattice[j] * pos[ni][j]
if norm is not None:
new_pos /= norm
return new_pos
[docs]def cart2frac(
lattice_cart: List[List[float]], positions_abs: List[List[float]]
) -> List[List[float]]:
"""Convert positions_abs block into positions_frac (and equivalent
in reciprocal space).
Parameters:
lattice_cart: Cartesian lattice vectors.
positions_abs: list of absolute position vectors.
Returns:
List of fractional position vectors with the same shape
as the input list.
"""
_positions_abs = np.asarray(positions_abs, dtype=np.float64)
reshaped = False
if len(np.shape(_positions_abs)) == 1:
reshaped = True
_positions_abs = _positions_abs.reshape((1, 3))
recip_lat = np.asarray(real2recip(lattice_cart))
recip_lat = recip_lat.T
positions_frac = switch_coords(recip_lat, _positions_abs, norm=2 * np.pi)
if reshaped:
positions_frac = positions_frac.reshape(-1)
return positions_frac.tolist()
[docs]def real2recip(real_lat: List[List[float]]) -> List[List[float]]:
"""Convert the real lattice in Cartesian basis to
the reciprocal space lattice.
Parameters:
real_lat: Cartesian lattice vectors.
Returns:
Cartesian lattice vectors of reciprocal lattice.
"""
real_lat = np.asarray(real_lat)
recip_lat = np.zeros((3, 3))
volume = np.dot(real_lat[0], np.cross(real_lat[1], real_lat[2]))
recip_lat[0] = (2 * np.pi) * np.cross(real_lat[1], real_lat[2])
recip_lat[1] = (2 * np.pi) * np.cross(real_lat[2], real_lat[0])
recip_lat[2] = (2 * np.pi) * np.cross(real_lat[0], real_lat[1])
recip_lat /= volume
return recip_lat.tolist()
[docs]def calc_mp_grid(
lattice_cart: List[List[float]], spacing: float
) -> Tuple[int, int, int]:
"""Return the Monkhorst-Pack grid based on lattice
vectors and desired spacing.
Parameters:
lattice_cart: Cartesian lattice vectors.
spacing: desired maximum grid spacing.
Returns:
List of 3 integers defining the MP grid.
"""
recip_lat = real2recip(lattice_cart)
recip_len = np.zeros((3))
recip_len = np.sqrt(np.sum(np.power(recip_lat, 2), axis=1))
mp_grid = recip_len / (2 * np.pi * spacing)
return [int(np.ceil(elem)) for elem in mp_grid]
[docs]def shift_to_include_gamma(mp_grid: Tuple[int, int, int]) -> Tuple[float, float, float]:
"""Calculate the shift required to include the :math:`\\Gamma`-point
in the Monkhorst-Pack grid.
Parameters:
mp_grid: number of grid points
in each reciprocal space direction.
Returns:
The shift required to include the :math:`\\Gamma`.
"""
shift = [0, 0, 0]
for ind, val in enumerate(mp_grid):
if val % 2 == 0:
shift[ind] = 1.0 / (val * 2)
return shift
[docs]def shift_to_exclude_gamma(mp_grid: Tuple[int, int, int]) -> Tuple[float, float, float]:
"""Calculate the shift required to exclude the :math:`\\Gamma`-point
in the Monkhorst-Pack grid. Returns the "minimal shift", i.e. only
one direction will be shifted.
Parameters:
mp_grid: number of grid points
in each reciprocal space direction.
Returns:
The shift required to exclude :math:`\\Gamma`.
"""
shift = [0, 0, 0]
if all([val % 2 == 1 for val in mp_grid]):
for ind, val in enumerate(mp_grid):
if val % 2 == 1:
shift[ind] = 1.0 / (val * 2)
break
return shift
[docs]def get_best_mp_offset_for_cell(doc: Union[Dict[str, Any], Crystal]) -> List[float]:
"""Calculates the "best" kpoint_mp_offset to use for the passed
cell. If the crystal has a hexagonal space group, then the offset
returned will shift the grid to include :math:`\\Gamma`-point, and vice
versa for non-hexagonal cells.
Parameters:
doc: matador document/Crystal to consider, containing structural
information and a "kpoints_mp_spacing" key.
Returns:
The desired `kpoint_mp_offset`.
"""
gamma = False
if "6" in get_spacegroup_spg(doc, symprec=1e-5):
gamma = True
if "lattice_cart" not in doc or "kpoints_mp_spacing" not in doc:
raise RuntimeError("Unable to calculate offset without lattice or spacing")
mp_grid = calc_mp_grid(doc["lattice_cart"], doc["kpoints_mp_spacing"])
if gamma:
return shift_to_include_gamma(mp_grid)
return shift_to_exclude_gamma(mp_grid)
[docs]def calc_mp_spacing(
real_lat: List[List[float]], mp_grid: Tuple[int, int, int], prec: int = 3
) -> float:
"""Convert real lattice in Cartesian basis and the CASTEP
`kpoint_mp_grid` into a CASTEP grid spacing.
Parameters:
real_lat: Cartesian lattice vectors.
mp_grid: 3 integers defining the MP grid.
Keyword arguments:
prec: desired decimal precision of output.
Returns:
`kpoint_mp_spacing` rounded to `prec` decimal places.
"""
recip_lat = real2recip(real_lat)
recip_len = np.zeros((3))
recip_len = np.sqrt(np.sum(np.power(recip_lat, 2), axis=1))
spacing = recip_len / (2 * np.pi * np.asarray(mp_grid))
max_spacing = np.max(spacing)
exponent = round(np.log10(max_spacing) - prec)
return round(max_spacing + 0.5 * 10**exponent, prec)
[docs]def get_seekpath_kpoint_path(
doc: Union[Dict[str, Any], Tuple],
standardize: bool = True,
explicit: bool = True,
spacing: float = 0.01,
threshold: float = 1e-7,
debug: bool = False,
symmetry_tol: float = None,
) -> Tuple[Dict[str, Any], List[List[float]], Dict[str, Any]]:
"""Return the conventional kpoint path of the relevant crystal system
according to the definitions by "HKPOT" in
Comp. Mat. Sci. 128, 2017:
http://dx.doi.org/10.1016/j.commatsci.2016.10.015
Parameters:
doc: matador doc or spglib tuple to find kpoint path for.
Keyword arguments:
spacing: desired kpoint spacing
threshold: internal seekpath threshold
symmetry_tol: spglib symmetry tolerance
Returns:
dict: standardized version of input doc
list: list of kpoint positions
dict: full dictionary of all seekpath results
"""
try:
from seekpath import get_explicit_k_path, get_path
except ImportError:
raise ImportError(
"SeeK-Path dependency missing, please install it with `pip install seekpath`."
)
if symmetry_tol is None:
symmetry_tol = 1e-5
if isinstance(doc, tuple):
spg_structure = doc
else:
if standardize:
spg_structure = doc2spg(standardize_doc_cell(doc, symprec=symmetry_tol))
else:
spg_structure = doc2spg(doc)
if explicit:
seekpath_results = get_explicit_k_path(
spg_structure,
reference_distance=spacing,
with_time_reversal=True,
symprec=symmetry_tol,
threshold=threshold,
)
kpt_path = seekpath_results["explicit_kpoints_rel"]
else:
seekpath_results = get_path(spg_structure)
kpt_path = []
primitive_doc = dict()
primitive_doc["lattice_cart"] = seekpath_results["primitive_lattice"]
primitive_doc["positions_frac"] = seekpath_results["primitive_positions"]
primitive_doc["atom_types"] = [
list(PERIODIC_TABLE)[i] for i in seekpath_results["primitive_types"]
]
primitive_doc["num_atoms"] = len(primitive_doc["atom_types"])
primitive_doc["lattice_abc"] = cart2abc(primitive_doc["lattice_cart"])
primitive_doc["cell_volume"] = cart2volume(primitive_doc["lattice_cart"])
if debug:
print(
"Found lattice type {}".format(seekpath_results["bravais_lattice_extended"])
)
print("Old lattice:\n", np.asarray(doc["lattice_cart"]))
print("Contained {} atoms".format(doc["num_atoms"]))
print("New lattice:\n", np.asarray(primitive_doc["lattice_cart"]))
print("Contains {} atoms".format(primitive_doc["num_atoms"]))
print("k-point path contains {} points.".format(len(kpt_path)))
if "site_occupancy" in doc:
if min(doc["site_occupancy"]) < 1 - EPS:
print("Ignoring any site occupancy found in this cell.")
primitive_doc["site_occupancy"] = [1 for atom in primitive_doc["atom_types"]]
return primitive_doc, kpt_path, seekpath_results
[docs]def doc2spg(
doc: Union[Dict[str, Any], "Crystal"], check_occ: bool = True
) -> Tuple[List[List[float]], List[List[float]], List[int]]:
"""Return an spglib input tuple from a matador doc.
Parameters:
doc: matador document or Crystal object.
Keyword arguments:
check_occ: check for partial occupancy and raise an error if present.
Returns:
tuple: spglib-style tuple of lattice, positions and types.
"""
from matador.utils.chem_utils import get_atomic_number
try:
if "lattice_cart" not in doc:
doc["lattice_cart"] = abc2cart(doc["lattice_abc"])
except KeyError:
raise RuntimeError("doc2spg failed: unable to find lattice in document.")
required_keys = ("lattice_cart", "positions_frac", "atom_types")
if all(key in doc for key in required_keys):
if "lattice_cart" not in doc:
doc["lattice_cart"] = abc2cart(doc["lattice_abc"])
cell = (
doc["lattice_cart"],
doc["positions_frac"],
[get_atomic_number(elem) for elem in doc["atom_types"]],
)
if check_occ and np.min(doc.get("site_occupancy", [1.0])) < 1.0:
raise RuntimeError("spglib does not support partial occupancy.")
return cell
else:
raise RuntimeError(
f"Unable to use doc2spg, one of {required_keys} was missing."
)
[docs]def get_space_group_label_latex(label: str) -> str:
"""Return the LaTeX format of the passed space group label. Takes
any string, leaves the first character upright, italicses the rest,
handles subscripts and bars over numbers.
Parameters:
label: a given space group in "standard" plain text format,
e.g. P-63m to convert to '$P\\bar{6}3m$'.
Returns:
The best attempt to convert the label to LaTeX format.
"""
import re
return "${}$".format(re.sub("-(?P<number>[0-9])", "\\\\bar{\\g<number>}", label))
[docs]def standardize_doc_cell(
doc: Union["Crystal", Dict[str, Any]], primitive: bool = True, symprec: float = 1e-2
) -> Union["Crystal", Dict[str, Any]]:
"""Return standardized cell data from matador doc.
Parameters:
doc: matador document or Crystal object to standardize.
Keyword arguments:
primitive: whether to reduce cell to primitive.
symprec: spglib symmetry tolerance.
Returns:
A matador document/`Crystal` containing standardized cell.
"""
import spglib as spg
from matador.utils.chem_utils import get_atomic_symbol
from copy import deepcopy
from matador.crystal import Crystal
spg_cell = doc2spg(doc)
spg_standardized = spg.standardize_cell(
spg_cell, to_primitive=primitive, symprec=symprec
)
if not isinstance(doc, Crystal):
std_doc = deepcopy(doc)
else:
std_doc = deepcopy(doc._data)
std_doc["lattice_cart"] = [list(vec) for vec in spg_standardized[0]]
std_doc["lattice_abc"] = cart2abc(std_doc["lattice_cart"])
std_doc["positions_frac"] = [list(atom) for atom in spg_standardized[1]]
std_doc["atom_types"] = [get_atomic_symbol(atom) for atom in spg_standardized[2]]
std_doc["site_occupancy"] = len(std_doc["positions_frac"]) * [1]
std_doc["cell_volume"] = cart2volume(std_doc["lattice_cart"])
std_doc["space_group"] = get_spacegroup_spg(std_doc, symprec=symprec)
# if the original document was a crystal, return a new one
if isinstance(doc, Crystal):
std_doc = Crystal(std_doc)
return std_doc
[docs]def get_spacegroup_spg(
doc: Union[Dict[str, Any], Crystal], symprec: float = 0.01, check_occ: bool = True
):
"""Return spglib spacegroup for a cell.
Parameters:
doc: matador document or Crystal object.
Keyword arguments:
symprec: spglib symmetry tolerance.
Returns:
The H-M space group symbol of structure.
"""
import spglib as spg
spg_cell = doc2spg(doc, check_occ=check_occ)
space_group = spg.get_spacegroup(spg_cell, symprec=symprec)
if space_group is None:
raise RuntimeError("Spglib was unable to calculate space group.")
return space_group.split(" ")[0]
[docs]def get_compatible_spacegroups(
doc: Union[Dict[str, Any], Crystal], symprec_range=(-5, 0)
) -> Dict[float, str]:
"""Return the space group of a given crystal for the range of symprecs.
Parameters:
doc: The crystal to analyse.
symprec_range: The range of symprecs to test (log space).
Returns:
A mapping from symprec to space group symbol.
"""
spgs = {}
for symprec in np.logspace(*symprec_range, num=10):
spgs[symprec] = get_spacegroup_spg(doc, symprec=symprec)
return spgs
[docs]def add_noise(doc: Dict[str, Any], amplitude: float = 0.1) -> Dict[str, Any]:
"""Add random noise to the positions of structure contained in doc.
Useful for force convergence tests.
Parameters:
doc: dictionary containing matador structure.
Keyword arguments:
amplitude: maximum amplitude of noise vector.
Raises:
KeyError if (`lattice_cart` and `positions_frac`) or `positions_abs`
are missing.
Returns:
The randomised structure.
"""
poscart = np.asarray(
doc.get("positions_abs")
or frac2cart(doc["lattice_cart"], doc["positions_frac"])
)
for atom in poscart:
noise_vector = np.random.rand(3)
noise_vector /= np.sqrt(np.sum(noise_vector**2))
noise_vector *= amplitude * (np.random.rand())
atom += noise_vector
doc["positions_abs"] = poscart.tolist()
doc["positions_frac"] = cart2frac(doc["lattice_cart"], doc["positions_abs"])
return doc
[docs]def calc_pairwise_distances_pbc(
poscart,
images,
lattice,
rmax,
poscart_b=None,
compress=False,
debug=False,
filter_zero=False,
per_image=False,
):
"""Calculate PBC distances with SciPy's cdist, given the
image cell vectors.
Parameters:
poscart (numpy.ndarray): list or array of absolute atomic coordinates.
images: iterable of lattice vector multiples (e.g. [2, -1, 3])
required to obtain the translation to desired image cells.
lattice (:obj:`list` if :obj:`list`): list of lattice vectors of
the real cell.
rmax (float): maximum value after which to mask the array.
Keyword arguments:
poscart_b (numpy.ndarray): absolute positions of another type of
atom, where only A-B distances will be calculated.
debug (bool): print timing data and how many distances were masked.
compress (bool): whether or not to compressed the output array,
useful when e.g. creating PDFs but not when atom ID is important.
filter_zero (bool): whether or not to filter out the "self-interaction"
zero distances.
per_image (bool): return a list of distances per image, as opposed to
one large flat. This preserves atom IDs for use elsewhere.
Returns:
distances (numpy.ndarray): pairwise 2-D d_ij masked array with values
or stripped 1-D array containing just the distances, or a list of
numpy arrays if per_image is True.
"""
from scipy.spatial.distance import cdist
import time
if debug:
start = time.time()
_lattice = np.asarray(lattice)
_poscart = np.asarray(poscart)
image_distances = []
if poscart_b is None:
_poscart_b = _poscart
else:
_poscart_b = np.asarray(poscart_b)
num_pairs = len(_poscart) * len(_poscart_b)
if per_image:
for image_ind, prod in enumerate(images):
distances = cdist(_poscart, _poscart_b + prod @ _lattice)
distances = np.ma.masked_where(distances > rmax, distances, copy=False)
image_distances.append(distances)
distances = image_distances
else:
array_size = len(_poscart) * len(images) * len(_poscart_b)
distances = np.empty(array_size)
for image_ind, prod in enumerate(images):
distances[image_ind * num_pairs : (image_ind + 1) * num_pairs] = cdist(
_poscart, _poscart_b + prod @ _lattice
).flatten()
distances = np.ma.masked_where(distances > rmax, distances, copy=False)
if filter_zero:
distances = np.ma.masked_where(distances < EPS, distances, copy=False)
if debug:
print(
"Calculated: {}, Used: {}, Ignored: {}".format(
len(distances),
np.ma.count(distances),
np.ma.count_masked(distances),
)
)
if compress:
distances = distances.compressed()
if debug:
end = time.time()
print("Calculated distances in {} s".format(end - start))
return distances
[docs]def create_simple_supercell(
doc: Union[Dict[str, Any], "Crystal"],
extension: Tuple[int, int, int],
standardize: bool = False,
symmetric: bool = False,
) -> Union[Dict[str, Any], "Crystal"]:
"""Return a document with new supercell, given extension vector.
Parameters:
doc: matador doc to construct cell from.
extension: multiplicity of each lattice vector, e.g. (2,2,1).
Keyword arguments:
standardize: whether or not to use spglib to standardize the cell first.
symmetric: whether or not centre the new cell on the origin.
Returns:
The supercell, either as a `Crystal` or as a dictionary,
depending on the input type.
"""
from itertools import product
from copy import deepcopy
from matador.crystal import Crystal
if not all([elem >= 1 for elem in extension]) or extension == (1, 1, 1):
raise RuntimeError("Bad/null supercell {} requested...".format(extension))
if isinstance(doc, Crystal):
supercell_doc = deepcopy(doc._data)
else:
supercell_doc = deepcopy(doc)
# copy new doc and delete data that will not be corrected
keys_to_copy = set(
["positions_frac", "lattice_cart", "atom_types", "source", "stoichiometry"]
)
supercell_doc = {key: deepcopy(doc[key]) for key in keys_to_copy}
# standardize cell with spglib
if standardize:
supercell_doc = standardize_doc_cell(supercell_doc)
for i, elem in enumerate(extension):
supercell_doc["lattice_cart"] = np.asarray(supercell_doc["lattice_cart"])
for k in range(3):
supercell_doc["lattice_cart"][i][k] = (
elem * supercell_doc["lattice_cart"][i][k]
)
for ind, atom in enumerate(supercell_doc["positions_frac"]):
supercell_doc["positions_frac"][ind][i] /= elem
images = product(*[list(range(elem)) for elem in extension])
new_positions = []
new_atoms = []
for image in images:
if image != (0, 0, 0):
for ind, atom in enumerate(supercell_doc["atom_types"]):
new_pos = deepcopy(supercell_doc["positions_frac"][ind])
for i, elem in enumerate(image):
new_pos[i] += image[i] / extension[i]
new_positions.append(new_pos)
new_atoms.append(atom)
supercell_doc["atom_types"].extend(new_atoms)
supercell_doc["positions_frac"].extend(new_positions)
if symmetric:
supercell_doc["positions_frac"] = np.asarray(supercell_doc["positions_frac"])
supercell_doc["positions_frac"] -= np.mean(
supercell_doc["positions_frac"], axis=0
)
supercell_doc["positions_frac"] = supercell_doc["positions_frac"].tolist()
supercell_doc["num_atoms"] = len(supercell_doc["atom_types"])
supercell_doc["cell_volume"] = cart2volume(supercell_doc["lattice_cart"])
supercell_doc["lattice_abc"] = cart2abc(supercell_doc["lattice_cart"])
supercell_doc["source"] = doc["source"]
supercell_doc["stoichiometry"] = doc["stoichiometry"]
assert np.isclose(
supercell_doc["cell_volume"],
np.prod(extension) * cart2volume(doc["lattice_cart"]),
)
if isinstance(doc, Crystal):
return Crystal(supercell_doc)
return supercell_doc
[docs]def create_supercell_with_minimum_side_length(
doc: Union[Dict[str, Any], "Crystal"], target: float
):
"""Pad the cell such that the minimum side length is greater than the target length.
Parameters:
doc: The crystal structure to pad.
target: The target minimum side length.
Returns:
The supercell.
"""
extension = [1, 1, 1]
for ind, lat in enumerate(doc.cell.lengths):
if lat < target:
extension[ind] = int(-(target // -lat))
return create_simple_supercell(doc, extension, standardize=False)