Enumerate derivative structures with composition and site constraints

This example shows how to specify a composition of derivative structures and restrict each site to be occupied by only allowed species.

Import modules

from pathlib import Path

import numpy as np
from pymatgen.core import Lattice, Structure
from pymatgen.core.periodic_table import DummySpecie

from dsenum import ZddStructureEnumerator
from dsenum.utils import write_cif

from dsenum import __version__
print(f"dsenum {__version__}")

dsenum 0.3.16.dev19+gc2b1184.d20220615

Enumerate derivative structures with site constraints

Here, we enumerate Rutile-like SnO\(_{2-x}\) derivative structures.

def get_rutile_structure():
    # rutile structure taken from mp-856
    a = 4.832
    c = 3.243
    x_4f = 0.3066

    lattice = Lattice.from_parameters(a, a, c, 90, 90, 90)
    species = ["Sn", "Sn", "O", "O", "O", "O"]
    frac_coords = np.array([
        [0, 0, 0],                      # Sn(2a)
        [0.5, 0.5, 0.5],                # Sn(2a)
        [x_4f, x_4f, 0],                # O(4f)
        [1 - x_4f, 1 - x_4f, 0],        # O(4f)
        [0.5 - x_4f, 0.5 + x_4f, 0.5],  # O(4f)
        [0.5 + x_4f, 0.5 - x_4f, 0.5],  # O(4f)
    ])
    structure = Structure(lattice, species, frac_coords)
    return structure

base_structure = get_rutile_structure()
mapping_color_species = [DummySpecie("X"), "O", "Sn"]

# Only O sites are disordered.
base_site_constraints = [
    [2],  # 2a
    [2],  # 2a
    [0, 1],  # 4f
    [0, 1],  # 4f
    [0, 1],  # 4f
    [0, 1],  # 4f
]

max_index = 4

# root = Path("./SnO2-x")
# root.mkdir(exist_ok=True)

for index in range(1, max_index + 1):
    se = ZddStructureEnumerator(
        base_structure,
        index=index,
        num_types=len(mapping_color_species),
        mapping_color_species=mapping_color_species,
        base_site_constraints=base_site_constraints,
        remove_superperiodic=True,
        remove_incomplete=False,
    )
    list_dstructs = se.generate()

    for i, dstruct in enumerate(list_dstructs):
        # remove void
        dstruct.remove_species([mapping_color_species[0]])

        # Save structure here
        # filename = root / f"SnO2-x_{index}_{i}.cif"
        # write_cif(filename, dstruct, refine_cell=True)

100%|██████████| 1/1 [00:00<00:00, 33.30it/s]

total: 6 (Time: 0.03666sec)

100%|██████████| 5/5 [00:00<00:00, 22.48it/s]

total: 132 (Time: 0.2258sec)

100%|██████████| 5/5 [00:00<00:00,  9.69it/s]

total: 1756 (Time: 0.5191sec)

100%|██████████| 17/17 [00:09<00:00,  1.81it/s]

total: 47827 (Time: 9.396sec)

Enumerate derivative structures with composition constraints

Here, we enumerate oxygen-deficient derivative structures of SrTiO\(_{3-x}\) \((0 \leq x \leq 1)\) in perovskite prototype.

def get_perovskite_structure():
    lattice = Lattice(3.945 * np.eye(3))
    species = ["Sr", "Ti", "O", "O", "O"]
    frac_coords = np.array(
        [[0, 0, 0], [0.5, 0.5, 0.5], [0.0, 0.5, 0.5], [0.5, 0.0, 0.5], [0.5, 0.5, 0.0]]
    )
    return Structure(lattice, species, frac_coords)

aristo = get_perovskite_structure()

# Remove cation sites that are nothing to do with oxygen-deficient ordering!
base_structure = aristo.copy()
base_structure.remove_species(["Sr", "Ti"])
# Later append Sr and Ti sites with `additional_species` and `additional_frac_coords`
additional_species = aristo.species[:2]
additional_frac_coords = aristo.frac_coords[:2]

mapping_color_species = [DummySpecie("X"), "O"]
base_site_constraints = []

# root = Path("./SrTiO3-x")
# root.mkdir(exist_ok=True)

max_index = 6
counts = {}

for index in range(1, max_index + 1):
    # Enumerate possible compositions
    list_compositions = []
    for num_oxygen in range(2 * index, 3 * index + 1):
        num_vacancy = 3 * index - num_oxygen
        list_compositions.append([num_vacancy, num_oxygen])

    poscars = []
    for composition_constraints in list_compositions:
        zse = ZddStructureEnumerator(
            base_structure,
            index=index,
            num_types=len(mapping_color_species),
            mapping_color_species=mapping_color_species,
            composition_constraints=composition_constraints,
            remove_superperiodic=True,
            remove_incomplete=False,
            verbose=False,
        )
        list_dstructs = zse.generate(
            additional_species=additional_species, additional_frac_coords=additional_frac_coords,
            output='poscar',
        )
        poscars.extend(list_dstructs)
    counts[index] = len(poscars)

assert counts[1] == 2
assert counts[2] == 11
assert counts[3] == 45
assert counts[4] == 455
assert counts[5] == 1296
assert counts[6] == 17111