def get_integer_formula_and_factor(self, max_denominator=10000):
"""
Calculates an integer formula and factor.
Args:
max_denominator (int): all amounts in the el:amt dict are
first converted to a Fraction with this maximum denominator
Returns:
A pretty normalized formula and a multiplicative factor, i.e.,
Li0.5O0.25 returns (Li2O, 0.25). O0.25 returns (O2, 0.125)
"""
vals = [
Fraction(v).limit_denominator(max_denominator)
for v in self.values()
]
denom = lcm(*(f.denominator for f in vals))
mul = gcd(*[int(v * denom) for v in vals])
d = {
k: round(v / mul * denom)
for k, v in self.get_el_amt_dict().items()
}
(formula, factor) = reduce_formula(d)
if formula in Composition.special_formulas:
formula = Composition.special_formulas[formula]
factor /= 2
return formula, factor * mul / denom
def determine_min_cell(cls, structure, mag_species_spin, order_parameter):
"""
Determine the smallest supercell that is able to enumerate
the provided structure with the given order parameter
"""
def lcm(n1, n2):
"""
Find least common multiple of two numbers
"""
return n1 * n2 / gcd(n1, n2)
denom = Fraction(order_parameter).limit_denominator(100).denominator
atom_per_specie = [structure.composition[m]
for m in mag_species_spin.keys()]
n_gcd = six.moves.reduce(gcd, atom_per_specie)
if not n_gcd:
raise ValueError(
'The specified species do not exist in the structure'
' to be enumerated')
return lcm(int(n_gcd), denom) / n_gcd
def determine_min_cell(cls, structure, mag_species_spin, order_parameter):
"""
Determine the smallest supercell that is able to enumerate
the provided structure with the given order parameter
"""
def lcm(n1, n2):
"""
Find least common multiple of two numbers
"""
return n1 * n2 / gcd(n1, n2)
denom = Fraction(order_parameter).limit_denominator(100).denominator
atom_per_specie = [
structure.composition[m] for m in mag_species_spin.keys()
]
n_gcd = six.moves.reduce(gcd, atom_per_specie)
if not n_gcd:
raise ValueError(
'The specified species do not exist in the structure'
' to be enumerated')
return lcm(n_gcd, denom) / n_gcd
def get_integer_formula_and_factor(self, max_denominator=10000):
"""
Calculates an integer formula and factor.
Args:
max_denominator (int): all amounts in the el:amt dict are
first converted to a Fraction with this maximum denominator
Returns:
A pretty normalized formula and a multiplicative factor, i.e.,
Li0.5O0.25 returns (Li2O, 0.25). O0.25 returns (O2, 0.125)
"""
vals = [Fraction(v).limit_denominator(max_denominator)
for v in self.values()]
denom = lcm(*(f.denominator for f in vals))
mul = gcd(*[int(v * denom) for v in vals])
d = {k: round(v / mul * denom) for k, v in self.get_el_amt_dict().items()}
(formula, factor) = reduce_formula(d)
if formula in Composition.special_formulas:
formula = Composition.special_formulas[formula]
factor /= 2
return formula, factor * mul / denom
def determine_min_cell(disordered_structure):
"""
Determine the smallest supercell that is able to enumerate
the provided structure with the given order parameter
"""
def lcm(n1, n2):
"""
Find least common multiple of two numbers
"""
return n1 * n2 / gcd(n1, n2)
# assumes all order parameters for a given species are the same
mag_species_order_parameter = {}
mag_species_occurrences = {}
for idx, site in enumerate(disordered_structure):
if not site.is_ordered:
op = max(site.species_and_occu.values())
# this very hacky bit of code only works because we know
# that on disordered sites in this class, all species are the same
# but have different spins, and this is comma-delimited
sp = str(list(site.species_and_occu.keys())[0]).split(",")[0]
if sp in mag_species_order_parameter:
mag_species_occurrences[sp] += 1
else:
mag_species_order_parameter[sp] = op
mag_species_occurrences[sp] = 1
smallest_n = []
for sp, order_parameter in mag_species_order_parameter.items():
denom = Fraction(order_parameter).limit_denominator(
100).denominator
num_atom_per_specie = mag_species_occurrences[sp]
n_gcd = gcd(denom, num_atom_per_specie)
smallest_n.append(lcm(int(n_gcd), denom) / n_gcd)
return max(smallest_n)
def determine_min_cell(disordered_structure):
"""
Determine the smallest supercell that is able to enumerate
the provided structure with the given order parameter
"""
def lcm(n1, n2):
"""
Find least common multiple of two numbers
"""
return n1 * n2 / gcd(n1, n2)
# assumes all order parameters for a given species are the same
mag_species_order_parameter = {}
mag_species_occurrences = {}
for idx, site in enumerate(disordered_structure):
if not site.is_ordered:
op = max(site.species_and_occu.values())
# this very hacky bit of code only works because we know
# that on disordered sites in this class, all species are the same
# but have different spins, and this is comma-delimited
sp = str(list(site.species_and_occu.keys())[0]).split(",")[0]
if sp in mag_species_order_parameter:
mag_species_occurrences[sp] += 1
else:
mag_species_order_parameter[sp] = op
mag_species_occurrences[sp] = 1
smallest_n = []
for sp, order_parameter in mag_species_order_parameter.items():
denom = Fraction(order_parameter).limit_denominator(100).denominator
num_atom_per_specie = mag_species_occurrences[sp]
n_gcd = gcd(denom, num_atom_per_specie)
smallest_n.append(lcm(int(n_gcd), denom) / n_gcd)
return max(smallest_n)
def __init__(self,
initial_structure,
miller_index,
min_slab_size,
min_vacuum_size,
lll_reduce=False,
center_slab=False,
primitive=True,
max_normal_search=None):
"""
Calculates the slab scale factor and uses it to generate a unit cell
of the initial structure that has been oriented by its miller index.
Also stores the initial information needed later on to generate a slab.
Args:
initial_structure (Structure): Initial input structure. Note that to
ensure that the miller indices correspond to usual
crystallographic definitions, you should supply a conventional
unit cell structure.
miller_index ([h, k, l]): Miller index of plane parallel to
surface. Note that this is referenced to the input structure. If
you need this to be based on the conventional cell,
you should supply the conventional structure.
min_slab_size (float): In Angstroms
min_vac_size (float): In Angstroms
lll_reduce (bool): Whether to perform an LLL reduction on the
eventual structure.
center_slab (bool): Whether to center the slab in the cell with
equal vacuum spacing from the top and bottom.
primitive (bool): Whether to reduce any generated slabs to a
primitive cell (this does **not** mean the slab is generated
from a primitive cell, it simply means that after slab
generation, we attempt to find shorter lattice vectors,
which lead to less surface area and smaller cells).
max_normal_search (int): If set to a positive integer, the code will
conduct a search for a normal lattice vector that is as
perpendicular to the surface as possible by considering
multiples linear combinations of lattice vectors up to
max_normal_search. This has no bearing on surface energies,
but may be useful as a preliminary step to generating slabs
for absorption and other sizes. It is typical that this will
not be the smallest possible cell for simulation. Normality
is not guaranteed, but the oriented cell will have the c
vector as normal as possible (within the search range) to the
surface. A value of up to the max absolute Miller index is
usually sufficient.
"""
latt = initial_structure.lattice
miller_index = reduce_vector(miller_index)
#Calculate the surface normal using the reciprocal lattice vector.
recp = latt.reciprocal_lattice_crystallographic
normal = recp.get_cartesian_coords(miller_index)
normal /= np.linalg.norm(normal)
slab_scale_factor = []
non_orth_ind = []
eye = np.eye(3, dtype=np.int)
for i, j in enumerate(miller_index):
if j == 0:
# Lattice vector is perpendicular to surface normal, i.e.,
# in plane of surface. We will simply choose this lattice
# vector as one of the basis vectors.
slab_scale_factor.append(eye[i])
else:
#Calculate projection of lattice vector onto surface normal.
d = abs(np.dot(normal, latt.matrix[i])) / latt.abc[i]
non_orth_ind.append((i, d))
# We want the vector that has maximum magnitude in the
# direction of the surface normal as the c-direction.
# Results in a more "orthogonal" unit cell.
c_index, dist = max(non_orth_ind, key=lambda t: t[1])
if len(non_orth_ind) > 1:
lcm_miller = lcm(*[miller_index[i] for i, d in non_orth_ind])
for (i, di), (j, dj) in itertools.combinations(non_orth_ind, 2):
l = [0, 0, 0]
l[i] = -int(round(lcm_miller / miller_index[i]))
l[j] = int(round(lcm_miller / miller_index[j]))
slab_scale_factor.append(l)
if len(slab_scale_factor) == 2:
break
if max_normal_search is None:
slab_scale_factor.append(eye[c_index])
else:
index_range = sorted(reversed(
range(-max_normal_search, max_normal_search + 1)),
key=lambda x: abs(x))
candidates = []
for uvw in itertools.product(index_range, index_range,
index_range):
if (not any(uvw)) or abs(
np.linalg.det(slab_scale_factor + [uvw])) < 1e-8:
continue
vec = latt.get_cartesian_coords(uvw)
l = np.linalg.norm(vec)
cosine = abs(np.dot(vec, normal) / l)
candidates.append((uvw, cosine, l))
if abs(abs(cosine) - 1) < 1e-8:
# If cosine of 1 is found, no need to search further.
break
# We want the indices with the maximum absolute cosine,
# but smallest possible length.
uvw, cosine, l = max(candidates, key=lambda x: (x[1], -l))
slab_scale_factor.append(uvw)
slab_scale_factor = np.array(slab_scale_factor)
# Let's make sure we have a left-handed crystallographic system
if np.linalg.det(slab_scale_factor) < 0:
slab_scale_factor *= -1
# Make sure the slab_scale_factor is reduced to avoid
# unnecessarily large slabs
reduced_scale_factor = [reduce_vector(v) for v in slab_scale_factor]
slab_scale_factor = np.array(reduced_scale_factor)
single = initial_structure.copy()
single.make_supercell(slab_scale_factor)
self.oriented_unit_cell = Structure.from_sites(single,
to_unit_cell=True)
self.parent = initial_structure
self.lll_reduce = lll_reduce
self.center_slab = center_slab
self.slab_scale_factor = slab_scale_factor
self.miller_index = miller_index
self.min_vac_size = min_vacuum_size
self.min_slab_size = min_slab_size
self.primitive = primitive
self._normal = normal
a, b, c = self.oriented_unit_cell.lattice.matrix
self._proj_height = abs(np.dot(normal, c))
def test_lcm(self):
self.assertEqual(lcm(2, 3, 4), 12)
def _gen_input_file(self):
"""
Generate the necessary struct_enum.in file for enumlib. See enumlib
documentation for details.
"""
coord_format = "{:.6f} {:.6f} {:.6f}"
# Using symmetry finder, get the symmetrically distinct sites.
fitter = SpacegroupAnalyzer(self.structure, self.symm_prec)
symmetrized_structure = fitter.get_symmetrized_structure()
logger.debug("Spacegroup {} ({}) with {} distinct sites".format(
fitter.get_space_group_symbol(), fitter.get_space_group_number(),
len(symmetrized_structure.equivalent_sites)))
"""
Enumlib doesn"t work when the number of species get too large. To
simplify matters, we generate the input file only with disordered sites
and exclude the ordered sites from the enumeration. The fact that
different disordered sites with the exact same species may belong to
different equivalent sites is dealt with by having determined the
spacegroup earlier and labelling the species differently.
"""
# index_species and index_amounts store mappings between the indices
# used in the enum input file, and the actual species and amounts.
index_species = []
index_amounts = []
# Stores the ordered sites, which are not enumerated.
ordered_sites = []
disordered_sites = []
coord_str = []
for sites in symmetrized_structure.equivalent_sites:
if sites[0].is_ordered:
ordered_sites.append(sites)
else:
sp_label = []
species = {k: v for k, v in sites[0].species.items()}
if sum(species.values()) < 1 - EnumlibAdaptor.amount_tol:
# Let us first make add a dummy element for every single
# site whose total occupancies don't sum to 1.
species[DummySpecie("X")] = 1 - sum(species.values())
for sp in species.keys():
if sp not in index_species:
index_species.append(sp)
sp_label.append(len(index_species) - 1)
index_amounts.append(species[sp] * len(sites))
else:
ind = index_species.index(sp)
sp_label.append(ind)
index_amounts[ind] += species[sp] * len(sites)
sp_label = "/".join(["{}".format(i) for i in sorted(sp_label)])
for site in sites:
coord_str.append("{} {}".format(
coord_format.format(*site.coords), sp_label))
disordered_sites.append(sites)
def get_sg_info(ss):
finder = SpacegroupAnalyzer(Structure.from_sites(ss),
self.symm_prec)
return finder.get_space_group_number()
target_sgnum = get_sg_info(symmetrized_structure.sites)
curr_sites = list(itertools.chain.from_iterable(disordered_sites))
sgnum = get_sg_info(curr_sites)
ordered_sites = sorted(ordered_sites, key=lambda sites: len(sites))
logger.debug("Disordered sites has sg # %d" % (sgnum))
self.ordered_sites = []
# progressively add ordered sites to our disordered sites
# until we match the symmetry of our input structure
if self.check_ordered_symmetry:
while sgnum != target_sgnum and len(ordered_sites) > 0:
sites = ordered_sites.pop(0)
temp_sites = list(curr_sites) + sites
new_sgnum = get_sg_info(temp_sites)
if sgnum != new_sgnum:
logger.debug("Adding %s in enum. New sg # %d" %
(sites[0].specie, new_sgnum))
index_species.append(sites[0].specie)
index_amounts.append(len(sites))
sp_label = len(index_species) - 1
for site in sites:
coord_str.append("{} {}".format(
coord_format.format(*site.coords), sp_label))
disordered_sites.append(sites)
curr_sites = temp_sites
sgnum = new_sgnum
else:
self.ordered_sites.extend(sites)
for sites in ordered_sites:
self.ordered_sites.extend(sites)
self.index_species = index_species
lattice = self.structure.lattice
output = [self.structure.formula, "bulk"]
for vec in lattice.matrix:
output.append(coord_format.format(*vec))
output.append("%d" % len(index_species))
output.append("%d" % len(coord_str))
output.extend(coord_str)
output.append("{} {}".format(self.min_cell_size, self.max_cell_size))
output.append(str(self.enum_precision_parameter))
output.append("full")
ndisordered = sum([len(s) for s in disordered_sites])
base = int(ndisordered * lcm(*[
f.limit_denominator(ndisordered * self.max_cell_size).denominator
for f in map(fractions.Fraction, index_amounts)
]))
# This multiplicative factor of 10 is to prevent having too small bases
# which can lead to rounding issues in the next step.
# An old bug was that a base was set to 8, with a conc of 0.4:0.6. That
# resulted in a range that overlaps and a conc of 0.5 satisfying this
# enumeration. See Cu7Te5.cif test file.
base *= 10
# base = ndisordered #10 ** int(math.ceil(math.log10(ndisordered)))
# To get a reasonable number of structures, we fix concentrations to the
# range expected in the original structure.
total_amounts = sum(index_amounts)
for amt in index_amounts:
conc = amt / total_amounts
if abs(conc * base - round(conc * base)) < 1e-5:
output.append("{} {} {}".format(int(round(conc * base)),
int(round(conc * base)), base))
else:
min_conc = int(math.floor(conc * base))
output.append("{} {} {}".format(min_conc - 1, min_conc + 1,
base))
output.append("")
logger.debug("Generated input file:\n{}".format("\n".join(output)))
with open("struct_enum.in", "w") as f:
f.write("\n".join(output))
def apply_transformation(self, structure, return_ranked_list=False):
"""
Args:
structure (Structure): Input structure to dope
Returns:
[{"structure": Structure, "energy": float}]
"""
comp = structure.composition
logger.info("Composition: %s" % comp)
for sp in comp:
try:
sp.oxi_state
except AttributeError:
analyzer = BVAnalyzer()
structure = analyzer.get_oxi_state_decorated_structure(
structure)
comp = structure.composition
break
ox = self.dopant.oxi_state
radius = self.dopant.ionic_radius
compatible_species = [
sp for sp in comp if sp.oxi_state == ox and
abs(sp.ionic_radius / radius - 1) < self.ionic_radius_tol]
if (not compatible_species) and self.alio_tol:
# We only consider aliovalent doping if there are no compatible
# isovalent species.
compatible_species = [
sp for sp in comp
if abs(sp.oxi_state - ox) <= self.alio_tol and
abs(sp.ionic_radius / radius - 1) < self.ionic_radius_tol and
sp.oxi_state * ox >= 0]
if self.allowed_doping_species is not None:
# Only keep allowed doping species.
compatible_species = [
sp for sp in compatible_species
if sp in [get_el_sp(s) for s in self.allowed_doping_species]]
logger.info("Compatible species: %s" % compatible_species)
lengths = structure.lattice.abc
scaling = [max(1, int(round(math.ceil(self.min_length/x))))
for x in lengths]
logger.info("Lengths are %s" % str(lengths))
logger.info("Scaling = %s" % str(scaling))
all_structures = []
t = EnumerateStructureTransformation(**self.kwargs)
for sp in compatible_species:
supercell = structure * scaling
nsp = supercell.composition[sp]
if sp.oxi_state == ox:
supercell.replace_species({sp: {sp: (nsp - 1)/nsp,
self.dopant: 1/nsp}})
logger.info("Doping %s for %s at level %.3f" % (
sp, self.dopant, 1 / nsp))
elif self.codopant:
codopant = _find_codopant(sp, 2 * sp.oxi_state - ox)
supercell.replace_species({sp: {sp: (nsp - 2) / nsp,
self.dopant: 1 / nsp,
codopant: 1 / nsp}})
logger.info("Doping %s for %s + %s at level %.3f" % (
sp, self.dopant, codopant, 1 / nsp))
elif abs(sp.oxi_state) < abs(ox):
# Strategy: replace the target species with a
# combination of dopant and vacancy.
# We will choose the lowest oxidation state species as a
# vacancy compensation species as it is likely to be lower in
# energy
sp_to_remove = min([s for s in comp if s.oxi_state * ox > 0],
key=lambda ss: abs(ss.oxi_state))
if sp_to_remove == sp:
common_charge = lcm(int(abs(sp.oxi_state)), int(abs(ox)))
ndopant = common_charge / abs(ox)
nsp_to_remove = common_charge / abs(sp.oxi_state)
logger.info("Doping %d %s with %d %s." %
(nsp_to_remove, sp, ndopant, self.dopant))
supercell.replace_species(
{sp: {sp: (nsp - nsp_to_remove) / nsp,
self.dopant: ndopant / nsp}})
else:
ox_diff = int(abs(round(sp.oxi_state - ox)))
vac_ox = int(abs(sp_to_remove.oxi_state))
common_charge = lcm(vac_ox, ox_diff)
ndopant = common_charge / ox_diff
nx_to_remove = common_charge / vac_ox
nx = supercell.composition[sp_to_remove]
logger.info("Doping %d %s with %s and removing %d %s." %
(ndopant, sp, self.dopant,
nx_to_remove, sp_to_remove))
supercell.replace_species(
{sp: {sp: (nsp - ndopant) / nsp,
self.dopant: ndopant / nsp},
sp_to_remove: {
sp_to_remove: (nx - nx_to_remove) / nx}})
elif abs(sp.oxi_state) > abs(ox):
# Strategy: replace the target species with dopant and also
# remove some opposite charged species for charge neutrality
if ox > 0:
sp_to_remove = max(supercell.composition.keys(),
key=lambda el: el.X)
else:
sp_to_remove = min(supercell.composition.keys(),
key=lambda el: el.X)
# Confirm species are of opposite oxidation states.
assert sp_to_remove.oxi_state * sp.oxi_state < 0
ox_diff = int(abs(round(sp.oxi_state - ox)))
anion_ox = int(abs(sp_to_remove.oxi_state))
nx = supercell.composition[sp_to_remove]
common_charge = lcm(anion_ox, ox_diff)
ndopant = common_charge / ox_diff
nx_to_remove = common_charge / anion_ox
logger.info("Doping %d %s with %s and removing %d %s." %
(ndopant, sp, self.dopant,
nx_to_remove, sp_to_remove))
supercell.replace_species(
{sp: {sp: (nsp - ndopant) / nsp,
self.dopant: ndopant / nsp},
sp_to_remove: {sp_to_remove: (nx - nx_to_remove)/nx}})
ss = t.apply_transformation(
supercell, return_ranked_list=self.max_structures_per_enum)
logger.info("%s distinct structures" % len(ss))
all_structures.extend(ss)
logger.info("Total %s doped structures" % len(all_structures))
if return_ranked_list:
return all_structures[:return_ranked_list]
return all_structures[0]["structure"]
def apply_transformation(self, structure, return_ranked_list=False):
"""
Args:
structure (Structure): Input structure to dope
Returns:
[{"structure": Structure, "energy": float}]
"""
comp = structure.composition
logger.info("Composition: %s" % comp)
for sp in comp:
try:
sp.oxi_state
except AttributeError:
analyzer = BVAnalyzer()
structure = analyzer.get_oxi_state_decorated_structure(
structure)
comp = structure.composition
break
ox = self.dopant.oxi_state
radius = self.dopant.ionic_radius
compatible_species = [
sp for sp in comp
if sp.oxi_state == ox and abs(sp.ionic_radius / radius -
1) < self.ionic_radius_tol
]
if (not compatible_species) and self.alio_tol:
# We only consider aliovalent doping if there are no compatible
# isovalent species.
compatible_species = [
sp for sp in comp if abs(sp.oxi_state - ox) <= self.alio_tol
and abs(sp.ionic_radius / radius -
1) < self.ionic_radius_tol and sp.oxi_state * ox >= 0
]
if self.allowed_doping_species is not None:
# Only keep allowed doping species.
compatible_species = [
sp for sp in compatible_species
if sp in [get_el_sp(s) for s in self.allowed_doping_species]
]
logger.info("Compatible species: %s" % compatible_species)
lengths = structure.lattice.abc
scaling = [
max(1, int(round(math.ceil(self.min_length / x)))) for x in lengths
]
logger.info("Lengths are %s" % str(lengths))
logger.info("Scaling = %s" % str(scaling))
all_structures = []
t = EnumerateStructureTransformation(**self.kwargs)
for sp in compatible_species:
supercell = structure * scaling
nsp = supercell.composition[sp]
if sp.oxi_state == ox:
supercell.replace_species(
{sp: {
sp: (nsp - 1) / nsp,
self.dopant: 1 / nsp
}})
logger.info("Doping %s for %s at level %.3f" %
(sp, self.dopant, 1 / nsp))
elif self.codopant:
codopant = _find_codopant(sp, 2 * sp.oxi_state - ox)
supercell.replace_species({
sp: {
sp: (nsp - 2) / nsp,
self.dopant: 1 / nsp,
codopant: 1 / nsp
}
})
logger.info("Doping %s for %s + %s at level %.3f" %
(sp, self.dopant, codopant, 1 / nsp))
elif abs(sp.oxi_state) < abs(ox):
# Strategy: replace the target species with a
# combination of dopant and vacancy.
# We will choose the lowest oxidation state species as a
# vacancy compensation species as it is likely to be lower in
# energy
sp_to_remove = min([s for s in comp if s.oxi_state * ox > 0],
key=lambda ss: abs(ss.oxi_state))
if sp_to_remove == sp:
common_charge = lcm(int(abs(sp.oxi_state)), int(abs(ox)))
ndopant = common_charge / abs(ox)
nsp_to_remove = common_charge / abs(sp.oxi_state)
logger.info("Doping %d %s with %d %s." %
(nsp_to_remove, sp, ndopant, self.dopant))
supercell.replace_species({
sp: {
sp: (nsp - nsp_to_remove) / nsp,
self.dopant: ndopant / nsp
}
})
else:
ox_diff = int(abs(round(sp.oxi_state - ox)))
vac_ox = int(abs(sp_to_remove.oxi_state))
common_charge = lcm(vac_ox, ox_diff)
ndopant = common_charge / ox_diff
nx_to_remove = common_charge / vac_ox
nx = supercell.composition[sp_to_remove]
logger.info(
"Doping %d %s with %s and removing %d %s." %
(ndopant, sp, self.dopant, nx_to_remove, sp_to_remove))
supercell.replace_species({
sp: {
sp: (nsp - ndopant) / nsp,
self.dopant: ndopant / nsp
},
sp_to_remove: {
sp_to_remove: (nx - nx_to_remove) / nx
}
})
elif abs(sp.oxi_state) > abs(ox):
# Strategy: replace the target species with dopant and also
# remove some opposite charged species for charge neutrality
if ox > 0:
sp_to_remove = max(supercell.composition.keys(),
key=lambda el: el.X)
else:
sp_to_remove = min(supercell.composition.keys(),
key=lambda el: el.X)
# Confirm species are of opposite oxidation states.
assert sp_to_remove.oxi_state * sp.oxi_state < 0
ox_diff = int(abs(round(sp.oxi_state - ox)))
anion_ox = int(abs(sp_to_remove.oxi_state))
nx = supercell.composition[sp_to_remove]
common_charge = lcm(anion_ox, ox_diff)
ndopant = common_charge / ox_diff
nx_to_remove = common_charge / anion_ox
logger.info(
"Doping %d %s with %s and removing %d %s." %
(ndopant, sp, self.dopant, nx_to_remove, sp_to_remove))
supercell.replace_species({
sp: {
sp: (nsp - ndopant) / nsp,
self.dopant: ndopant / nsp
},
sp_to_remove: {
sp_to_remove: (nx - nx_to_remove) / nx
}
})
ss = t.apply_transformation(
supercell, return_ranked_list=self.max_structures_per_enum)
logger.info("%s distinct structures" % len(ss))
all_structures.extend(ss)
logger.info("Total %s doped structures" % len(all_structures))
if return_ranked_list:
return all_structures[:return_ranked_list]
return all_structures[0]["structure"]
def __init__(self, initial_structure, miller_index, min_slab_size,
min_vacuum_size, lll_reduce=False, center_slab=False,
primitive=True, max_normal_search=None):
"""
Calculates the slab scale factor and uses it to generate a unit cell
of the initial structure that has been oriented by its miller index.
Also stores the initial information needed later on to generate a slab.
Args:
initial_structure (Structure): Initial input structure. Note that to
ensure that the miller indices correspond to usual
crystallographic definitions, you should supply a conventional
unit cell structure.
miller_index ([h, k, l]): Miller index of plane parallel to
surface. Note that this is referenced to the input structure. If
you need this to be based on the conventional cell,
you should supply the conventional structure.
min_slab_size (float): In Angstroms
min_vac_size (float): In Angstroms
lll_reduce (bool): Whether to perform an LLL reduction on the
eventual structure.
center_slab (bool): Whether to center the slab in the cell with
equal vacuum spacing from the top and bottom.
primitive (bool): Whether to reduce any generated slabs to a
primitive cell (this does **not** mean the slab is generated
from a primitive cell, it simply means that after slab
generation, we attempt to find shorter lattice vectors,
which lead to less surface area and smaller cells).
max_normal_search (int): If set to a positive integer, the code will
conduct a search for a normal lattice vector that is as
perpendicular to the surface as possible by considering
multiples linear combinations of lattice vectors up to
max_normal_search. This has no bearing on surface energies,
but may be useful as a preliminary step to generating slabs
for absorption and other sizes. It is typical that this will
not be the smallest possible cell for simulation. Normality
is not guaranteed, but the oriented cell will have the c
vector as normal as possible (within the search range) to the
surface. A value of up to the max absolute Miller index is
usually sufficient.
"""
latt = initial_structure.lattice
miller_index = reduce_vector(miller_index)
#Calculate the surface normal using the reciprocal lattice vector.
recp = latt.reciprocal_lattice_crystallographic
normal = recp.get_cartesian_coords(miller_index)
normal /= np.linalg.norm(normal)
slab_scale_factor = []
non_orth_ind = []
eye = np.eye(3, dtype=np.int)
for i, j in enumerate(miller_index):
if j == 0:
# Lattice vector is perpendicular to surface normal, i.e.,
# in plane of surface. We will simply choose this lattice
# vector as one of the basis vectors.
slab_scale_factor.append(eye[i])
else:
#Calculate projection of lattice vector onto surface normal.
d = abs(np.dot(normal, latt.matrix[i])) / latt.abc[i]
non_orth_ind.append((i, d))
# We want the vector that has maximum magnitude in the
# direction of the surface normal as the c-direction.
# Results in a more "orthogonal" unit cell.
c_index, dist = max(non_orth_ind, key=lambda t: t[1])
if len(non_orth_ind) > 1:
lcm_miller = lcm(*[miller_index[i] for i, d in non_orth_ind])
for (i, di), (j, dj) in itertools.combinations(non_orth_ind, 2):
l = [0, 0, 0]
l[i] = -int(round(lcm_miller / miller_index[i]))
l[j] = int(round(lcm_miller / miller_index[j]))
slab_scale_factor.append(l)
if len(slab_scale_factor) == 2:
break
if max_normal_search is None:
slab_scale_factor.append(eye[c_index])
else:
index_range = sorted(
reversed(range(-max_normal_search, max_normal_search + 1)),
key=lambda x: abs(x))
candidates = []
for uvw in itertools.product(index_range, index_range, index_range):
if (not any(uvw)) or abs(
np.linalg.det(slab_scale_factor + [uvw])) < 1e-8:
continue
vec = latt.get_cartesian_coords(uvw)
l = np.linalg.norm(vec)
cosine = abs(np.dot(vec, normal) / l)
candidates.append((uvw, cosine, l))
if abs(abs(cosine) - 1) < 1e-8:
# If cosine of 1 is found, no need to search further.
break
# We want the indices with the maximum absolute cosine,
# but smallest possible length.
uvw, cosine, l = max(candidates, key=lambda x: (x[1], -l))
slab_scale_factor.append(uvw)
slab_scale_factor = np.array(slab_scale_factor)
# Let's make sure we have a left-handed crystallographic system
if np.linalg.det(slab_scale_factor) < 0:
slab_scale_factor *= -1
# Make sure the slab_scale_factor is reduced to avoid
# unnecessarily large slabs
reduced_scale_factor = [reduce_vector(v) for v in slab_scale_factor]
slab_scale_factor = np.array(reduced_scale_factor)
single = initial_structure.copy()
single.make_supercell(slab_scale_factor)
self.oriented_unit_cell = Structure.from_sites(single,
to_unit_cell=True)
self.parent = initial_structure
self.lll_reduce = lll_reduce
self.center_slab = center_slab
self.slab_scale_factor = slab_scale_factor
self.miller_index = miller_index
self.min_vac_size = min_vacuum_size
self.min_slab_size = min_slab_size
self.primitive = primitive
self._normal = normal
a, b, c = self.oriented_unit_cell.lattice.matrix
self._proj_height = abs(np.dot(normal, c))
def __init__(self, initial_structure, miller_index, min_slab_size,
min_vacuum_size, lll_reduce=False, center_slab=False,
primitive=True):
"""
Calculates the slab scale factor and uses it to generate a unit cell
of the initial structure that has been oriented by its miller index.
Also stores the initial information needed later on to generate a slab.
Args:
initial_structure (Structure): Initial input structure.
miller_index ([h, k, l]): Miller index of plane parallel to
surface. Note that this is referenced to the input structure. If
you need this to be based on the conventional cell,
you should supply the conventional structure.
min_slab_size (float): In Angstroms
min_vac_size (float): In Angstroms
lll_reduce (bool): Whether to perform an LLL reduction on the
eventual structure.
center_slab (bool): Whether to center the slab in the cell with
equal vacuum spacing from the top and bottom.
primitive (bool): Whether to reduce any generated slabs to a
primitive cell (this does **not** mean the slab is generated
from a primitive cell, it simply means that after slab
generation, we attempt to find shorter lattice vectors,
which lead to less surface area and smaller cells).
"""
latt = initial_structure.lattice
d = abs(reduce(gcd, miller_index))
miller_index = tuple([int(i / d) for i in miller_index])
#Calculate the surface normal using the reciprocal lattice vector.
recp = latt.reciprocal_lattice_crystallographic
normal = recp.get_cartesian_coords(miller_index)
normal /= np.linalg.norm(normal)
slab_scale_factor = []
non_orth_ind = []
eye = np.eye(3, dtype=np.int)
for i, j in enumerate(miller_index):
if j == 0:
# Lattice vector is perpendicular to surface normal, i.e.,
# in plane of surface. We will simply choose this lattice
# vector as one of the basis vectors.
slab_scale_factor.append(eye[i])
else:
#Calculate projection of lattice vector onto surface normal.
d = abs(np.dot(normal, latt.matrix[i])) / latt.abc[i]
non_orth_ind.append((i, d))
# We want the vector that has maximum magnitude in the
# direction of the surface normal as the c-direction.
# Results in a more "orthogonal" unit cell.
c_index, dist = max(non_orth_ind, key=lambda t: t[1])
if len(non_orth_ind) > 1:
lcm_miller = lcm(*[miller_index[i] for i, d in non_orth_ind])
for (i, di), (j, dj) in itertools.combinations(non_orth_ind, 2):
l = [0, 0, 0]
l[i] = -int(round(lcm_miller / miller_index[i]))
l[j] = int(round(lcm_miller / miller_index[j]))
slab_scale_factor.append(l)
if len(slab_scale_factor) == 2:
break
slab_scale_factor.append(eye[c_index])
slab_scale_factor = np.array(slab_scale_factor)
# Let's make sure we have a left-handed crystallographic system
if np.linalg.det(slab_scale_factor) < 0:
slab_scale_factor *= -1
single = initial_structure.copy()
single.make_supercell(slab_scale_factor)
self.oriented_unit_cell = Structure.from_sites(single,
to_unit_cell=True)
self.parent = initial_structure
self.lll_reduce = lll_reduce
self.center_slab = center_slab
self.slab_scale_factor = slab_scale_factor
self.miller_index = miller_index
self.min_vac_size = min_vacuum_size
self.min_slab_size = min_slab_size
self.primitive = primitive
self._normal = normal
a, b, c = self.oriented_unit_cell.lattice.matrix
self._proj_height = abs(np.dot(normal, c))
def test_lcm(self):
self.assertEqual(lcm(2, 3, 4), 12)
def _gen_input_file(self):
"""
Generate the necessary struct_enum.in file for enumlib. See enumlib
documentation for details.
"""
coord_format = "{:.6f} {:.6f} {:.6f}"
# Using symmetry finder, get the symmetrically distinct sites.
fitter = SpacegroupAnalyzer(self.structure, self.symm_prec)
symmetrized_structure = fitter.get_symmetrized_structure()
logger.debug("Spacegroup {} ({}) with {} distinct sites".format(
fitter.get_space_group_symbol(),
fitter.get_space_group_number(),
len(symmetrized_structure.equivalent_sites))
)
"""
Enumlib doesn"t work when the number of species get too large. To
simplify matters, we generate the input file only with disordered sites
and exclude the ordered sites from the enumeration. The fact that
different disordered sites with the exact same species may belong to
different equivalent sites is dealt with by having determined the
spacegroup earlier and labelling the species differently.
"""
# index_species and index_amounts store mappings between the indices
# used in the enum input file, and the actual species and amounts.
index_species = []
index_amounts = []
# Stores the ordered sites, which are not enumerated.
ordered_sites = []
disordered_sites = []
coord_str = []
for sites in symmetrized_structure.equivalent_sites:
if sites[0].is_ordered:
ordered_sites.append(sites)
else:
sp_label = []
species = {k: v for k, v in sites[0].species.items()}
if sum(species.values()) < 1 - EnumlibAdaptor.amount_tol:
# Let us first make add a dummy element for every single
# site whose total occupancies don't sum to 1.
species[DummySpecie("X")] = 1 - sum(species.values())
for sp in species.keys():
if sp not in index_species:
index_species.append(sp)
sp_label.append(len(index_species) - 1)
index_amounts.append(species[sp] * len(sites))
else:
ind = index_species.index(sp)
sp_label.append(ind)
index_amounts[ind] += species[sp] * len(sites)
sp_label = "/".join(["{}".format(i) for i in sorted(sp_label)])
for site in sites:
coord_str.append("{} {}".format(
coord_format.format(*site.coords),
sp_label))
disordered_sites.append(sites)
def get_sg_info(ss):
finder = SpacegroupAnalyzer(Structure.from_sites(ss),
self.symm_prec)
return finder.get_space_group_number()
target_sgnum = get_sg_info(symmetrized_structure.sites)
curr_sites = list(itertools.chain.from_iterable(disordered_sites))
sgnum = get_sg_info(curr_sites)
ordered_sites = sorted(ordered_sites, key=lambda sites: len(sites))
logger.debug("Disordered sites has sg # %d" % (sgnum))
self.ordered_sites = []
# progressively add ordered sites to our disordered sites
# until we match the symmetry of our input structure
if self.check_ordered_symmetry:
while sgnum != target_sgnum and len(ordered_sites) > 0:
sites = ordered_sites.pop(0)
temp_sites = list(curr_sites) + sites
new_sgnum = get_sg_info(temp_sites)
if sgnum != new_sgnum:
logger.debug("Adding %s in enum. New sg # %d"
% (sites[0].specie, new_sgnum))
index_species.append(sites[0].specie)
index_amounts.append(len(sites))
sp_label = len(index_species) - 1
for site in sites:
coord_str.append("{} {}".format(
coord_format.format(*site.coords),
sp_label))
disordered_sites.append(sites)
curr_sites = temp_sites
sgnum = new_sgnum
else:
self.ordered_sites.extend(sites)
for sites in ordered_sites:
self.ordered_sites.extend(sites)
self.index_species = index_species
lattice = self.structure.lattice
output = [self.structure.formula, "bulk"]
for vec in lattice.matrix:
output.append(coord_format.format(*vec))
output.append("%d" % len(index_species))
output.append("%d" % len(coord_str))
output.extend(coord_str)
output.append("{} {}".format(self.min_cell_size, self.max_cell_size))
output.append(str(self.enum_precision_parameter))
output.append("partial")
ndisordered = sum([len(s) for s in disordered_sites])
base = int(ndisordered*lcm(*[f.limit_denominator(ndisordered *
self.max_cell_size).denominator
for f in map(fractions.Fraction,
index_amounts)]))
# This multiplicative factor of 10 is to prevent having too small bases
# which can lead to rounding issues in the next step.
# An old bug was that a base was set to 8, with a conc of 0.4:0.6. That
# resulted in a range that overlaps and a conc of 0.5 satisfying this
# enumeration. See Cu7Te5.cif test file.
base *= 10
# base = ndisordered #10 ** int(math.ceil(math.log10(ndisordered)))
# To get a reasonable number of structures, we fix concentrations to the
# range expected in the original structure.
total_amounts = sum(index_amounts)
for amt in index_amounts:
conc = amt / total_amounts
if abs(conc * base - round(conc * base)) < 1e-5:
output.append("{} {} {}".format(int(round(conc * base)),
int(round(conc * base)),
base))
else:
min_conc = int(math.floor(conc * base))
output.append("{} {} {}".format(min_conc - 1, min_conc + 1,
base))
output.append("")
logger.debug("Generated input file:\n{}".format("\n".join(output)))
with open("struct_enum.in", "w") as f:
f.write("\n".join(output))
def __init__(self, initial_structure, miller_index, min_slab_size,
min_vacuum_size, lll_reduce=False, center_slab=False,
primitive=True):
"""
Calculates the slab scale factor and uses it to generate a unit cell
of the initial structure that has been oriented by its miller index.
Also stores the initial information needed later on to generate a slab.
Args:
initial_structure (Structure): Initial input structure.
miller_index ([h, k, l]): Miller index of plane parallel to
surface. Note that this is referenced to the input structure. If
you need this to be based on the conventional cell,
you should supply the conventional structure.
min_slab_size (float): In Angstroms
min_vac_size (float): In Angstroms
lll_reduce (bool): Whether to perform an LLL reduction on the
eventual structure.
center_slab (bool): Whether to center the slab in the cell with
equal vacuum spacing from the top and bottom.
primitive (bool): Whether to reduce any generated slabs to a
primitive cell (this does **not** mean the slab is generated
from a primitive cell, it simply means that after slab
generation, we attempt to find shorter lattice vectors,
which lead to less surface area and smaller cells).
"""
latt = initial_structure.lattice
d = abs(reduce(gcd, miller_index))
miller_index = tuple([int(i / d) for i in miller_index])
#Calculate the surface normal using the reciprocal lattice vector.
recp = latt.reciprocal_lattice_crystallographic
normal = recp.get_cartesian_coords(miller_index)
normal /= np.linalg.norm(normal)
slab_scale_factor = []
non_orth_ind = []
eye = np.eye(3, dtype=np.int)
for i, j in enumerate(miller_index):
if j == 0:
# Lattice vector is perpendicular to surface normal, i.e.,
# in plane of surface. We will simply choose this lattice
# vector as one of the basis vectors.
slab_scale_factor.append(eye[i])
else:
#Calculate projection of lattice vector onto surface normal.
d = abs(np.dot(normal, latt.matrix[i])) / latt.abc[i]
non_orth_ind.append((i, d))
# We want the vector that has maximum magnitude in the
# direction of the surface normal as the c-direction.
# Results in a more "orthogonal" unit cell.
c_index, dist = max(non_orth_ind, key=lambda t: t[1])
if len(non_orth_ind) > 1:
lcm_miller = lcm(*[miller_index[i] for i, d in non_orth_ind])
for (i, di), (j, dj) in itertools.combinations(non_orth_ind, 2):
l = [0, 0, 0]
l[i] = -int(round(lcm_miller / miller_index[i]))
l[j] = int(round(lcm_miller / miller_index[j]))
slab_scale_factor.append(l)
if len(slab_scale_factor) == 2:
break
slab_scale_factor.append(eye[c_index])
slab_scale_factor = np.array(slab_scale_factor)
# Let's make sure we have a left-handed crystallographic system
if np.linalg.det(slab_scale_factor) < 0:
slab_scale_factor *= -1
single = initial_structure.copy()
single.make_supercell(slab_scale_factor)
self.oriented_unit_cell = Structure.from_sites(single,
to_unit_cell=True)
self.parent = initial_structure
self.lll_reduce = lll_reduce
self.center_slab = center_slab
self.slab_scale_factor = slab_scale_factor
self.miller_index = miller_index
self.min_vac_size = min_vacuum_size
self.min_slab_size = min_slab_size
self.primitive = primitive
self._normal = normal
a, b, c = self.oriented_unit_cell.lattice.matrix
self._proj_height = abs(np.dot(normal, c))
