def __init__(self, structure, min_cell_size=1, max_cell_size=1,
symm_prec=0.1, enum_precision_parameter=0.001,
refine_structure=False):
"""
Initializes the adapter with a structure and some parameters.
Args:
structure: An input structure.
min_cell_size (int): The minimum cell size wanted. Defaults to 1.
max_cell_size (int): The maximum cell size wanted. Defaults to 1.
symm_prec (float): Symmetry precision. Defaults to 0.1.
enum_precision_parameter (float): Finite precision parameter for
enumlib. Default of 0.001 is usually ok, but you might need to
tweak it for certain cells.
refine_structure (bool): If you are starting from a structure that
has been relaxed via some electronic structure code,
it is usually much better to start with symmetry determination
and then obtain a refined structure. The refined structure have
cell parameters and atomic positions shifted to the expected
symmetry positions, which makes it much less sensitive precision
issues in enumlib. If you are already starting from an
experimental cif, refinement should have already been done and
it is not necessary. Defaults to False.
"""
if refine_structure:
finder = SpacegroupAnalyzer(structure, symm_prec)
self.structure = finder.get_refined_structure()
else:
self.structure = structure
self.min_cell_size = min_cell_size
self.max_cell_size = max_cell_size
self.symm_prec = symm_prec
self.enum_precision_parameter = enum_precision_parameter
def get_pattern(self, structure: Structure, scaled: bool = None, two_theta_range: Tuple[float, float] = None) \
-> pd.DataFrame:
"""
Returns all relevant TEM DP info in a pandas dataframe.
Args:
structure (Structure): The input structure.
scaled (boolean): Required value for inheritance, does nothing in TEM pattern
two_theta_range (Tuple): Required value for inheritance, does nothing in TEM pattern
Returns:
PandasDataFrame
"""
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
points = self.generate_points(-10, 11)
tem_dots = self.tem_dots(structure, points)
field_names = [
"Position", "(hkl)", "Intensity (norm)", "Film radius",
"Interplanar Spacing"
]
rows_list = []
for dot in tem_dots:
dict1 = {
'Pos': dot.position,
'(hkl)': dot.hkl,
'Intnsty (norm)': dot.intensity,
'Film rad': dot.film_radius,
'Interplanar Spacing': dot.d_spacing
}
rows_list.append(dict1)
df = pd.DataFrame(rows_list, columns=field_names)
return df
def high_index_surface(
self,
element,
crystal_structure,
lattice_constant,
terrace_orientation=None,
step_orientation=None,
kink_orientation=None,
step_down_vector=None,
length_step=3,
length_terrace=3,
length_kink=1,
layers=60,
vacuum=10,
):
"""
Gives a slab positioned at the bottom with the high index surface computed by high_index_surface_info().
Args:
element (str): The parent element eq. "N", "O", "Mg" etc.
crystal_structure (str): The crystal structure of the lattice
lattice_constant (float): The lattice constant
terrace_orientation (list): The miller index of the terrace. default: [1,1,1]
step_orientation (list): The miller index of the step. default: [1,1,0]
kink_orientation (list): The miller index of the kink. default: [1,1,1]
step_down_vector (list): The direction for stepping down from the step to next terrace. default: [1,1,0]
length_terrace (int): The length of the terrace along the kink direction in atoms. default: 3
length_step (int): The length of the step along the step direction in atoms. default: 3
length_kink (int): The length of the kink along the kink direction in atoms. default: 1
layers (int): Number of layers of the high_index_surface. default: 60
vacuum (float): Thickness of vacuum on the top of the slab. default:10
Returns:
slab: pyiron_atomistics.atomistics.structure.atoms.Atoms instance Required surface
"""
basis = self.crystal(
element=element,
bravais_basis=crystal_structure,
lattice_constant=lattice_constant,
)
high_index_surface, _, _ = self.high_index_surface_info(
element=element,
crystal_structure=crystal_structure,
lattice_constant=lattice_constant,
terrace_orientation=terrace_orientation,
step_orientation=step_orientation,
kink_orientation=kink_orientation,
step_down_vector=step_down_vector,
length_step=length_step,
length_terrace=length_terrace,
length_kink=length_kink,
)
surf = ase_surf(basis, high_index_surface, layers, vacuum)
sga = SpacegroupAnalyzer(pyiron_to_pymatgen(ase_to_pyiron(surf)))
pmg_refined = sga.get_refined_structure()
slab = pymatgen_to_pyiron(pmg_refined)
slab.positions[:,
2] = slab.positions[:, 2] - np.min(slab.positions[:, 2])
slab.set_pbc(True)
return slab
def test_ferrimagnetic(self):
trans = MagOrderingTransformation({"Fe": 5}, order_parameter=0.75, max_cell_size=1)
p = Poscar.from_file(os.path.join(PymatgenTest.TEST_FILES_DIR, "POSCAR.LiFePO4"), check_for_POTCAR=False)
s = p.structure
a = SpacegroupAnalyzer(s, 0.1)
s = a.get_refined_structure()
alls = trans.apply_transformation(s, 10)
self.assertEqual(len(alls), 1)
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
structure = self.get_structure("Li2O")
structure.add_site_property("magmom", [1.0] * len(structure))
sg = SpacegroupAnalyzer(structure, 0.01)
refined_struct = sg.get_refined_structure(keep_site_properties=True)
self.assertEqual(refined_struct.site_properties["magmom"], [1.0] * len(refined_struct))
structure = self.get_structure("Li2O")
structure.add_site_property("magmom", [1.0] * len(structure))
sg = SpacegroupAnalyzer(structure, 0.01)
refined_struct = sg.get_refined_structure(keep_site_properties=False)
self.assertEqual(refined_struct.site_properties.get("magmom", None), None)
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
s = self.get_structure('Li2O')
sg = SpacegroupAnalyzer(s, 0.001)
self.assertEqual(sg.get_refined_structure().num_sites, 4 * s.num_sites)
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
s = self.get_structure('Li2O')
sg = SpacegroupAnalyzer(s, 0.01)
self.assertEqual(sg.get_refined_structure().num_sites, 4 * s.num_sites)
def __init__(
self,
structure,
min_cell_size=1,
max_cell_size=1,
symm_prec=0.1,
enum_precision_parameter=0.001,
refine_structure=False,
check_ordered_symmetry=True,
timeout=None,
):
"""
Initializes the adapter with a structure and some parameters.
Args:
structure: An input structure.
min_cell_size (int): The minimum cell size wanted. Defaults to 1.
max_cell_size (int): The maximum cell size wanted. Defaults to 1.
symm_prec (float): Symmetry precision. Defaults to 0.1.
enum_precision_parameter (float): Finite precision parameter for
enumlib. Default of 0.001 is usually ok, but you might need to
tweak it for certain cells.
refine_structure (bool): If you are starting from a structure that
has been relaxed via some electronic structure code,
it is usually much better to start with symmetry determination
and then obtain a refined structure. The refined structure have
cell parameters and atomic positions shifted to the expected
symmetry positions, which makes it much less sensitive precision
issues in enumlib. If you are already starting from an
experimental cif, refinement should have already been done and
it is not necessary. Defaults to False.
check_ordered_symmetry (bool): Whether to check the symmetry of
the ordered sites. If the symmetry of the ordered sites is
lower, the lowest symmetry ordered sites is included in the
enumeration. This is important if the ordered sites break
symmetry in a way that is important getting possible
structures. But sometimes including ordered sites
slows down enumeration to the point that it cannot be
completed. Switch to False in those cases. Defaults to True.
timeout (float): If specified, will kill enumlib after specified
time in minutes. This can be useful for gracefully handling
enumerations in a high-throughput context, for some enumerations
which will not terminate in a realistic length of time.
"""
if refine_structure:
finder = SpacegroupAnalyzer(structure, symm_prec)
self.structure = finder.get_refined_structure()
else:
self.structure = structure
self.min_cell_size = min_cell_size
self.max_cell_size = max_cell_size
self.symm_prec = symm_prec
self.enum_precision_parameter = enum_precision_parameter
self.check_ordered_symmetry = check_ordered_symmetry
self.timeout = timeout
def refined(src="POSCAR"):
"""
refined poscar を 作成する
"""
srcpos = Poscar.from_file(src)
finder = SpacegroupAnalyzer(srcpos.structure, symprec=5e-1, angle_tolerance=8)
std = finder.get_refined_structure()
dstpos = Poscar(std)
dst = "POSCAR_refined"
Cabinet.reserve_file(dst)
dstpos.write_file(dst)
def output_struc(entry, eng, tol):
id = entry.entry_id
todo = mpr.get_structure_by_material_id(id)
finder = SpacegroupAnalyzer(todo, symprec=tol, angle_tolerance=5)
newStruc = finder.get_refined_structure()
if len(newStruc.frac_coords) > 16:
newStruc = newStruc.get_primitive_structure()
p1 = ['{:6.3f}'.format(j) for j in newStruc.lattice.abc]
p2 = ['{:6.2f}'.format(j) for j in newStruc.lattice.angles]
sym = finder.get_space_group_symbol()
s = ' '.join(map(str, p1 + p2))
print('%-16s %40s %6.3f %10s [%s]' % (id, s, eng, sym, newStruc.formula))
return newStruc
def __init__(
self,
structure,
min_cell_size=1,
max_cell_size=1,
symm_prec=0.1,
enum_precision_parameter=0.001,
refine_structure=False,
check_ordered_symmetry=True,
):
"""
Initializes the adapter with a structure and some parameters.
Args:
structure: An input structure.
min_cell_size (int): The minimum cell size wanted. Defaults to 1.
max_cell_size (int): The maximum cell size wanted. Defaults to 1.
symm_prec (float): Symmetry precision. Defaults to 0.1.
enum_precision_parameter (float): Finite precision parameter for
enumlib. Default of 0.001 is usually ok, but you might need to
tweak it for certain cells.
refine_structure (bool): If you are starting from a structure that
has been relaxed via some electronic structure code,
it is usually much better to start with symmetry determination
and then obtain a refined structure. The refined structure have
cell parameters and atomic positions shifted to the expected
symmetry positions, which makes it much less sensitive precision
issues in enumlib. If you are already starting from an
experimental cif, refinement should have already been done and
it is not necessary. Defaults to False.
check_ordered_symmetry (bool): Whether to check the symmetry of
the ordered sites. If the symmetry of the ordered sites is
lower, the lowest symmetry ordered sites is included in the
enumeration. This is important if the ordered sites break
symmetry in a way that is important getting possible
structures. But sometimes including ordered sites
slows down enumeration to the point that it cannot be
completed. Switch to False in those cases. Defaults to True.
"""
if refine_structure:
finder = SpacegroupAnalyzer(structure, symm_prec)
self.structure = finder.get_refined_structure()
else:
self.structure = structure
self.min_cell_size = min_cell_size
self.max_cell_size = max_cell_size
self.symm_prec = symm_prec
self.enum_precision_parameter = enum_precision_parameter
self.check_ordered_symmetry = check_ordered_symmetry
self.structures = None
def test_apply_transformation(self):
structure = PymatgenTest.get_structure("LiFePO4")
a = SpacegroupAnalyzer(structure, 0.1)
structure = a.get_refined_structure()
t = DopingTransformation("Ca2+", min_length=10)
ss = t.apply_transformation(structure, 100)
self.assertEqual(len(ss), 1)
t = DopingTransformation("Al3+", min_length=15, ionic_radius_tol=0.1)
ss = t.apply_transformation(structure, 100)
self.assertEqual(len(ss), 0)
# Aliovalent doping with vacancies
for dopant, nstructures in [("Al3+", 2), ("N3-", 235), ("Cl-", 8)]:
t = DopingTransformation(dopant,
min_length=4,
alio_tol=1,
max_structures_per_enum=1000)
ss = t.apply_transformation(structure, 1000)
self.assertEqual(len(ss), nstructures)
for d in ss:
self.assertEqual(d["structure"].charge, 0)
# Aliovalent doping with codopant
for dopant, nstructures in [("Al3+", 3), ("N3-", 37), ("Cl-", 37)]:
t = DopingTransformation(
dopant,
min_length=4,
alio_tol=1,
codopant=True,
max_structures_per_enum=1000,
)
ss = t.apply_transformation(structure, 1000)
self.assertEqual(len(ss), nstructures)
for d in ss:
self.assertEqual(d["structure"].charge, 0)
# Make sure compensation is done with lowest oxi state
structure = PymatgenTest.get_structure("SrTiO3")
t = DopingTransformation(
"Nb5+",
min_length=5,
alio_tol=1,
max_structures_per_enum=1000,
allowed_doping_species=["Ti4+"],
)
ss = t.apply_transformation(structure, 1000)
self.assertEqual(len(ss), 3)
for d in ss:
self.assertEqual(d["structure"].formula, "Sr7 Ti6 Nb2 O24")
def test_niggli(self):
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
from pymatgen.core.structure import Structure
from pymatgen.core.lattice import Lattice
from pymatgen.core.sites import PeriodicSite
from supercellor.supercell import make_supercell
import numpy as np
import itertools
np.random.seed(4)
DIST = 0.99
lattice = Lattice(1 * np.eye(3) + 0.5 *
(np.random.random((3, 3)) - 0.5))
sites = []
for pos in itertools.product([-0.5, 0.5], repeat=3):
sites.append(
PeriodicSite("H", pos, lattice, coords_are_cartesian=True))
structure = Structure.from_sites(sites)
supercell1, scale1 = make_supercell(structure,
distance=DIST,
verbosity=1,
wrap=True,
standardize=True,
do_niggli_first=False)
supercell2, scale2 = make_supercell(structure,
distance=DIST,
verbosity=1,
wrap=True,
standardize=True,
do_niggli_first=True)
sa = SpacegroupAnalyzer(supercell1, symprec=1e-21, angle_tolerance=-1)
supercell_refine = sa.get_refined_structure()
for i in range(3):
for j in range(3):
self.assertTrue(
abs(supercell1._lattice.matrix[i, j] -
supercell2._lattice.matrix[i, j]) < 1e-1,
'{} != {} for i,j={},{}'.format(
supercell1._lattice.matrix[i, j],
supercell2._lattice.matrix[i, j], i, j))
self.assertTrue(
abs(supercell1._lattice.matrix[i, j] -
supercell_refine._lattice.matrix[i, j]) < 1e-1,
'{} != {} for i,j={},{}'.format(
supercell1._lattice.matrix[i, j],
supercell_refine._lattice.matrix[i, j], i, j))
def get_jmol3(structure):
analyzer = SpacegroupAnalyzer(structure)
structure = analyzer.get_refined_structure()
#structure.make_supercell([2, 2, 2])
xyz_structure = [str(structure.num_sites),structure.composition.reduced_formula]
for site in structure.sites:
element = site._species.reduced_formula.replace('2', '')
atom = '{} {} {} {}'.format(element, str(site.x), str(site.y),str(site.z))
xyz_structure.append(atom)
string = str(xyz_structure)
string = string.replace('[', '')
string = string.replace(']', '')
string = string.replace(', ', r'\n')
string = string.replace("'", "")
return string
def run_task(self, fw_spec):
self.user_incar_settings.update({"NPAR": 2})
# Get kpoint density per vol
vol = Poscar.from_file("POSCAR").structure.volume
kppra_vol = self.kpoints_density / vol
new_set = MPStaticSet.from_prev_calc(
os.getcwd(),
user_incar_settings=self.user_incar_settings,
reciprocal_density=kppra_vol)
new_set.write_input('.')
structure = new_set.structure
sga = SpacegroupAnalyzer(structure, 0.1)
return FWAction(stored_data={
'refined_structure': sga.get_refined_structure().as_dict(),
'conventional_standard_structure': sga.get_conventional_standard_structure().as_dict(),
'symmetry_dataset': sga.get_symmetry_dataset(),
'symmetry_operations': [x.as_dict() for x in sga.get_symmetry_operations()]})
def abi_sanitize(self, symprec=1e-3, primitive=True):
"""
Returns a new structure in which:
* Oxidation states are removed.
* Structure is refined.
* Reduced to primitive settings.
* Lattice vectors are exchanged if the triple product is negative
Args:
symprec: Symmetry precision used to refine the structure.
if `symprec` is None, so structure refinement is peformed.
primitive (bool): Whether to convert to a primitive cell.
"""
from pymatgen.transformations.standard_transformations import OxidationStateRemovalTransformation, \
PrimitiveCellTransformation, SupercellTransformation
# Remove oxidation states.
remove_ox = OxidationStateRemovalTransformation()
structure = remove_ox.apply_transformation(self)
# Refine structure
if symprec is not None:
sym_finder = SpacegroupAnalyzer(structure=structure,
symprec=symprec)
structure = sym_finder.get_refined_structure()
# Convert to primitive structure.
if primitive:
get_prim = PrimitiveCellTransformation()
structure = get_prim.apply_transformation(structure)
# Exchange last two lattice vectors if triple product is negative.
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
if x_prod < 0:
trans = SupercellTransformation(((1, 0, 0), (0, 0, 1), (0, 1, 0)))
structure = trans.apply_transformation(structure)
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
if x_prod < 0: raise RuntimeError("x_prod is still negative!")
return structure
def add_cifs(doc):
symprec = 0.1
struc = Structure.from_dict(doc["structure"])
sym_finder = SpacegroupAnalyzer(struc, symprec=symprec)
doc["cif"] = str(CifWriter(struc))
doc["cifs"] = {}
try:
primitive = sym_finder.get_primitive_standard_structure()
conventional = sym_finder.get_conventional_standard_structure()
refined = sym_finder.get_refined_structure()
doc["cifs"]["primitive"] = str(CifWriter(primitive))
doc["cifs"]["refined"] = str(CifWriter(refined, symprec=symprec))
doc["cifs"]["conventional_standard"] = str(
CifWriter(conventional, symprec=symprec))
doc["cifs"]["computed"] = str(CifWriter(struc, symprec=symprec))
except:
doc["cifs"]["primitive"] = None
doc["cifs"]["refined"] = None
doc["cifs"]["conventional_standard"] = None
def refine_structure(structure, symprec=1e-3):
remove_ox = OxidationStateRemovalTransformation()
structure = remove_ox.apply_transformation(structure)
sym_finder = SpacegroupAnalyzer(structure=structure, symprec=symprec)
structure = sym_finder.get_refined_structure()
get_prim = PrimitiveCellTransformation()
structure = get_prim.apply_transformation(structure)
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
if x_prod < 0:
print(x_prod)
trans = SupercellTransformation(((1, 0, 0), (0, 0, 1), (0, 1, 0)))
structure = trans.apply_transformation(structure)
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
print(x_prod)
if x_prod < 0:
raise RuntimeError
return structure
def abi_sanitize(self, symprec=1e-3, angle_tolerance=5, primitive=True, primitive_standard=False):
"""
Returns a new structure in which:
* Structure is refined.
* Reduced to primitive settings.
* Lattice vectors are exchanged if the triple product is negative
Args:
symprec: Symmetry precision used to refine the structure.
if `symprec` is None, so structure refinement is peformed.
primitive (bool): Whether to convert to a primitive cell.
"""
from pymatgen.transformations.standard_transformations import PrimitiveCellTransformation, SupercellTransformation
structure = self.__class__.from_sites(self)
# Refine structure
if symprec is not None and angle_tolerance is not None:
sym_finder = SpacegroupAnalyzer(structure=structure, symprec=symprec, angle_tolerance=angle_tolerance)
structure = sym_finder.get_refined_structure()
# Convert to primitive structure.
if primitive:
if primitive_standard:
sym_finder_prim = SpacegroupAnalyzer(structure=structure, symprec=symprec, angle_tolerance=angle_tolerance)
structure = sym_finder_prim.get_primitive_standard_structure()
else:
get_prim = PrimitiveCellTransformation()
structure = get_prim.apply_transformation(structure)
# Exchange last two lattice vectors if triple product is negative.
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
if x_prod < 0:
trans = SupercellTransformation(((1, 0, 0), (0, 0, 1), (0, 1, 0)))
structure = trans.apply_transformation(structure)
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
if x_prod < 0: raise RuntimeError("x_prod is still negative!")
return structure
def refine_structure(structure, symprec=1e-3):
remove_ox = OxidationStateRemovalTransformation()
structure = remove_ox.apply_transformation(structure)
sym_finder = SpacegroupAnalyzer(structure=structure, symprec=symprec)
structure = sym_finder.get_refined_structure()
get_prim = PrimitiveCellTransformation()
structure = get_prim.apply_transformation(structure)
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
if x_prod < 0:
print(x_prod)
trans = SupercellTransformation(((1, 0, 0), (0, 0, 1), (0, 1, 0)))
structure = trans.apply_transformation(structure)
m = structure.lattice.matrix
x_prod = np.dot(np.cross(m[0], m[1]), m[2])
print(x_prod)
if x_prod < 0:
raise RuntimeError
return structure
def add_cifs(doc):
struc = Structure.from_dict(doc["structure"])
sym_finder = SpacegroupAnalyzer(struc, symprec=0.1)
doc["cif"] = str(CifWriter(struc))
doc["cifs"] = {}
if sym_finder.get_hall():
primitive = sym_finder.get_primitive_standard_structure()
conventional = sym_finder.get_conventional_standard_structure()
refined = sym_finder.get_refined_structure()
doc["cifs"]["primitive"] = str(CifWriter(primitive))
doc["cifs"]["refined"] = str(CifWriter(refined))
doc["cifs"]["conventional_standard"] = str(CifWriter(conventional))
doc["cifs"]["computed"] = str(CifWriter(struc))
doc["spacegroup"]["symbol"] = sym_finder.get_space_group_symbol()
doc["spacegroup"]["number"] = sym_finder.get_space_group_number()
doc["spacegroup"]["point_group"] = sym_finder.get_point_group_symbol()
doc["spacegroup"]["crystal_system"] = sym_finder.get_crystal_system()
doc["spacegroup"]["hall"] = sym_finder.get_hall()
else:
doc["cifs"]["primitive"] = None
doc["cifs"]["refined"] = None
doc["cifs"]["conventional_standard"] = None
def get_jmol3(self):
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
structure = StructureP.from_file(
BASE_DIR + self.entry.path.split('/var/www/materialsweb')[-1] +
'/POSCAR')
analyzer = SpacegroupAnalyzer(structure)
structure = analyzer.get_refined_structure()
structure.make_supercell([2, 2, 2])
xyz_structure = [
str(structure.num_sites), structure.composition.reduced_formula
]
for site in structure.sites:
element = site._species.reduced_formula.replace('2', '')
atom = '{} {} {} {}'.format(element, str(site.x), str(site.y),
str(site.z))
xyz_structure.append(atom)
string = str(xyz_structure)
string = string.replace('[', '')
string = string.replace(']', '')
string = string.replace(', ', r'\n')
string = string.replace("'", "")
return string
def get_plot_2d_concise(self, structure: Structure) -> go.Figure:
"""
Generates the concise 2D diffraction pattern of the input structure of a smaller size and without layout.
Does not display.
Args:
structure (Structure): The input structure.
Returns:
Figure
"""
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
points = self.generate_points(-10, 11)
tem_dots = self.tem_dots(structure, points)
xs = []
ys = []
hkls = []
intensities = []
for dot in tem_dots:
if dot.hkl != (0, 0, 0):
xs.append(dot.position[0])
ys.append(dot.position[1])
hkls.append(dot.hkl)
intensities.append(dot.intensity)
data = [
go.Scatter(
x=xs,
y=ys,
text=hkls,
mode="markers",
hoverinfo="skip",
marker=dict(
size=4,
cmax=1,
cmin=0,
color=intensities,
colorscale=[[0, "black"], [1.0, "white"]],
),
showlegend=False,
)
]
layout = go.Layout(
xaxis=dict(
range=[-4, 4],
showgrid=False,
zeroline=False,
showline=False,
ticks="",
showticklabels=False,
),
yaxis=dict(
range=[-4, 4],
showgrid=False,
zeroline=False,
showline=False,
ticks="",
showticklabels=False,
),
plot_bgcolor="black",
margin={"l": 0, "r": 0, "t": 0, "b": 0},
width=121,
height=121,
)
fig = go.Figure(data=data, layout=layout)
fig.layout.update(showlegend=False)
return fig
def get_plot_2d(self, structure: Structure) -> go.Figure:
"""
Generates the 2D diffraction pattern of the input structure.
Args:
structure (Structure): The input structure.
Returns:
Figure
"""
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
points = self.generate_points(-10, 11)
tem_dots = self.tem_dots(structure, points)
xs = []
ys = []
hkls = []
intensities = []
for dot in tem_dots:
xs.append(dot.position[0])
ys.append(dot.position[1])
hkls.append(str(dot.hkl))
intensities.append(dot.intensity)
hkls = list(map(unicodeify_spacegroup, list(map(latexify_spacegroup, hkls))))
data = [
go.Scatter(
x=xs,
y=ys,
text=hkls,
hoverinfo="text",
mode="markers",
marker=dict(
size=8,
cmax=1,
cmin=0,
color=intensities,
colorscale=[[0, "black"], [1.0, "white"]],
),
showlegend=False,
),
go.Scatter(
x=[0],
y=[0],
text="(0, 0, 0): Direct beam",
hoverinfo="text",
mode="markers",
marker=dict(size=14, cmax=1, cmin=0, color="white"),
showlegend=False,
),
]
layout = go.Layout(
title="2D Diffraction Pattern<br>Beam Direction: " + "".join(str(e) for e in self.beam_direction),
font=dict(size=14, color="#7f7f7f"),
hovermode="closest",
xaxis=dict(
range=[-4, 4],
showgrid=False,
zeroline=False,
showline=False,
ticks="",
showticklabels=False,
),
yaxis=dict(
range=[-4, 4],
showgrid=False,
zeroline=False,
showline=False,
ticks="",
showticklabels=False,
),
width=550,
height=550,
paper_bgcolor="rgba(100,110,110,0.5)",
plot_bgcolor="black",
)
fig = go.Figure(data=data, layout=layout)
return fig
def __init__(self, struct, symprec=None):
format_str = "{:.8f}"
block = OrderedDict()
loops = []
spacegroup = ("P 1", 1)
if symprec is not None:
sf = SpacegroupAnalyzer(struct, symprec)
spacegroup = (sf.get_space_group_symbol(),
sf.get_space_group_number())
# Needs the refined struture when using symprec. This converts
# primitive to conventional structures, the standard for CIF.
struct = sf.get_refined_structure()
latt = struct.lattice
comp = struct.composition
no_oxi_comp = comp.element_composition
block["_symmetry_space_group_name_H-M"] = spacegroup[0]
for cell_attr in ['a', 'b', 'c']:
block["_cell_length_" + cell_attr] = format_str.format(
getattr(latt, cell_attr))
for cell_attr in ['alpha', 'beta', 'gamma']:
block["_cell_angle_" + cell_attr] = format_str.format(
getattr(latt, cell_attr))
block["_symmetry_Int_Tables_number"] = spacegroup[1]
block["_chemical_formula_structural"] = no_oxi_comp.reduced_formula
block["_chemical_formula_sum"] = no_oxi_comp.formula
block["_cell_volume"] = latt.volume.__str__()
reduced_comp, fu = no_oxi_comp.get_reduced_composition_and_factor()
block["_cell_formula_units_Z"] = str(int(fu))
if symprec is None:
block["_symmetry_equiv_pos_site_id"] = ["1"]
block["_symmetry_equiv_pos_as_xyz"] = ["x, y, z"]
else:
sf = SpacegroupAnalyzer(struct, symprec)
def round_symm_trans(i):
for t in TRANSLATIONS.values():
if abs(i - t) < symprec:
return t
if abs(i - round(i)) < symprec:
return 0
raise ValueError("Invalid translation!")
symmops = []
for op in sf.get_symmetry_operations():
v = op.translation_vector
v = [round_symm_trans(i) for i in v]
symmops.append(SymmOp.from_rotation_and_translation(
op.rotation_matrix, v))
ops = [op.as_xyz_string() for op in symmops]
block["_symmetry_equiv_pos_site_id"] = \
["%d" % i for i in range(1, len(ops) + 1)]
block["_symmetry_equiv_pos_as_xyz"] = ops
loops.append(["_symmetry_equiv_pos_site_id",
"_symmetry_equiv_pos_as_xyz"])
contains_oxidation = True
try:
symbol_to_oxinum = OrderedDict([
(el.__str__(), float(el.oxi_state))
for el in sorted(comp.elements)])
except AttributeError:
symbol_to_oxinum = OrderedDict([(el.symbol, 0) for el in
sorted(comp.elements)])
contains_oxidation = False
if contains_oxidation:
block["_atom_type_symbol"] = symbol_to_oxinum.keys()
block["_atom_type_oxidation_number"] = symbol_to_oxinum.values()
loops.append(["_atom_type_symbol", "_atom_type_oxidation_number"])
atom_site_type_symbol = []
atom_site_symmetry_multiplicity = []
atom_site_fract_x = []
atom_site_fract_y = []
atom_site_fract_z = []
atom_site_label = []
atom_site_occupancy = []
count = 1
if symprec is None:
for site in struct:
for sp, occu in site.species_and_occu.items():
atom_site_type_symbol.append(sp.__str__())
atom_site_symmetry_multiplicity.append("1")
atom_site_fract_x.append("{0:f}".format(site.a))
atom_site_fract_y.append("{0:f}".format(site.b))
atom_site_fract_z.append("{0:f}".format(site.c))
atom_site_label.append("{}{}".format(sp.symbol, count))
atom_site_occupancy.append(occu.__str__())
count += 1
else:
# The following just presents a deterministic ordering.
unique_sites = [
(sorted(sites, key=lambda s: tuple([abs(x) for x in
s.frac_coords]))[0],
len(sites))
for sites in sf.get_symmetrized_structure().equivalent_sites
]
for site, mult in sorted(
unique_sites,
key=lambda t: (t[0].species_and_occu.average_electroneg,
-t[1], t[0].a, t[0].b, t[0].c)):
for sp, occu in site.species_and_occu.items():
atom_site_type_symbol.append(sp.__str__())
atom_site_symmetry_multiplicity.append("%d" % mult)
atom_site_fract_x.append("{0:f}".format(site.a))
atom_site_fract_y.append("{0:f}".format(site.b))
atom_site_fract_z.append("{0:f}".format(site.c))
atom_site_label.append("{}{}".format(sp.symbol, count))
atom_site_occupancy.append(occu.__str__())
count += 1
block["_atom_site_type_symbol"] = atom_site_type_symbol
block["_atom_site_label"] = atom_site_label
block["_atom_site_symmetry_multiplicity"] = \
atom_site_symmetry_multiplicity
block["_atom_site_fract_x"] = atom_site_fract_x
block["_atom_site_fract_y"] = atom_site_fract_y
block["_atom_site_fract_z"] = atom_site_fract_z
block["_atom_site_occupancy"] = atom_site_occupancy
loops.append(["_atom_site_type_symbol",
"_atom_site_label",
"_atom_site_symmetry_multiplicity",
"_atom_site_fract_x",
"_atom_site_fract_y",
"_atom_site_fract_z",
"_atom_site_occupancy"])
d = OrderedDict()
d[comp.reduced_formula] = CifBlock(block, loops, comp.reduced_formula)
self._cf = CifFile(d)
def __init__(self, struct, symprec=None):
format_str = "{:.8f}"
block = OrderedDict()
loops = []
spacegroup = ("P 1", 1)
if symprec is not None:
sf = SpacegroupAnalyzer(struct, symprec)
spacegroup = (sf.get_spacegroup_symbol(),
sf.get_spacegroup_number())
# Needs the refined struture when using symprec. This converts
# primitive to conventional structures, the standard for CIF.
struct = sf.get_refined_structure()
latt = struct.lattice
comp = struct.composition
no_oxi_comp = comp.element_composition
block["_symmetry_space_group_name_H-M"] = spacegroup[0]
for cell_attr in ['a', 'b', 'c']:
block["_cell_length_" + cell_attr] = format_str.format(
getattr(latt, cell_attr))
for cell_attr in ['alpha', 'beta', 'gamma']:
block["_cell_angle_" + cell_attr] = format_str.format(
getattr(latt, cell_attr))
block["_symmetry_Int_Tables_number"] = spacegroup[1]
block["_chemical_formula_structural"] = no_oxi_comp.reduced_formula
block["_chemical_formula_sum"] = no_oxi_comp.formula
block["_cell_volume"] = latt.volume.__str__()
reduced_comp, fu = no_oxi_comp.get_reduced_composition_and_factor()
block["_cell_formula_units_Z"] = str(int(fu))
if symprec is None:
block["_symmetry_equiv_pos_site_id"] = ["1"]
block["_symmetry_equiv_pos_as_xyz"] = ["x, y, z"]
else:
sf = SpacegroupAnalyzer(struct, symprec)
def round_symm_trans(i):
for t in TRANSLATIONS.values():
if abs(i - t) < symprec:
return t
if abs(i - round(i)) < symprec:
return 0
raise ValueError("Invalid translation!")
symmops = []
for op in sf.get_symmetry_operations():
v = op.translation_vector
v = [round_symm_trans(i) for i in v]
symmops.append(
SymmOp.from_rotation_and_translation(
op.rotation_matrix, v))
ops = [op.as_xyz_string() for op in symmops]
block["_symmetry_equiv_pos_site_id"] = \
["%d" % i for i in range(1, len(ops) + 1)]
block["_symmetry_equiv_pos_as_xyz"] = ops
loops.append(
["_symmetry_equiv_pos_site_id", "_symmetry_equiv_pos_as_xyz"])
contains_oxidation = True
try:
symbol_to_oxinum = OrderedDict([(el.__str__(), float(el.oxi_state))
for el in sorted(comp.elements)])
except AttributeError:
symbol_to_oxinum = OrderedDict([(el.symbol, 0)
for el in sorted(comp.elements)])
contains_oxidation = False
if contains_oxidation:
block["_atom_type_symbol"] = symbol_to_oxinum.keys()
block["_atom_type_oxidation_number"] = symbol_to_oxinum.values()
loops.append(["_atom_type_symbol", "_atom_type_oxidation_number"])
atom_site_type_symbol = []
atom_site_symmetry_multiplicity = []
atom_site_fract_x = []
atom_site_fract_y = []
atom_site_fract_z = []
atom_site_label = []
atom_site_occupancy = []
count = 1
if symprec is None:
for site in struct:
for sp, occu in site.species_and_occu.items():
atom_site_type_symbol.append(sp.__str__())
atom_site_symmetry_multiplicity.append("1")
atom_site_fract_x.append("{0:f}".format(site.a))
atom_site_fract_y.append("{0:f}".format(site.b))
atom_site_fract_z.append("{0:f}".format(site.c))
atom_site_label.append("{}{}".format(sp.symbol, count))
atom_site_occupancy.append(occu.__str__())
count += 1
else:
# The following just presents a deterministic ordering.
unique_sites = [
(sorted(sites,
key=lambda s: tuple([abs(x)
for x in s.frac_coords]))[0],
len(sites))
for sites in sf.get_symmetrized_structure().equivalent_sites
]
for site, mult in sorted(unique_sites,
key=lambda t:
(t[0].species_and_occu.average_electroneg,
-t[1], t[0].a, t[0].b, t[0].c)):
for sp, occu in site.species_and_occu.items():
atom_site_type_symbol.append(sp.__str__())
atom_site_symmetry_multiplicity.append("%d" % mult)
atom_site_fract_x.append("{0:f}".format(site.a))
atom_site_fract_y.append("{0:f}".format(site.b))
atom_site_fract_z.append("{0:f}".format(site.c))
atom_site_label.append("{}{}".format(sp.symbol, count))
atom_site_occupancy.append(occu.__str__())
count += 1
block["_atom_site_type_symbol"] = atom_site_type_symbol
block["_atom_site_label"] = atom_site_label
block["_atom_site_symmetry_multiplicity"] = \
atom_site_symmetry_multiplicity
block["_atom_site_fract_x"] = atom_site_fract_x
block["_atom_site_fract_y"] = atom_site_fract_y
block["_atom_site_fract_z"] = atom_site_fract_z
block["_atom_site_occupancy"] = atom_site_occupancy
loops.append([
"_atom_site_type_symbol", "_atom_site_label",
"_atom_site_symmetry_multiplicity", "_atom_site_fract_x",
"_atom_site_fract_y", "_atom_site_fract_z", "_atom_site_occupancy"
])
d = OrderedDict()
d[comp.reduced_formula] = CifBlock(block, loops, comp.reduced_formula)
self._cf = CifFile(d)
def get_pattern(self, structure, scaled=True, two_theta_range=(0, 90)):
"""
Calculates the diffraction pattern for a structure.
Args:
structure (Structure): Input structure
scaled (bool): Whether to return scaled intensities. The maximum
peak is set to a value of 100. Defaults to True. Use False if
you need the absolute values to combine XRD plots.
two_theta_range ([float of length 2]): Tuple for range of
two_thetas to calculate in degrees. Defaults to (0, 90). Set to
None if you want all diffracted beams within the limiting
sphere of radius 2 / wavelength.
Returns:
(XRDPattern)
"""
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
wavelength = self.wavelength
latt = structure.lattice
is_hex = latt.is_hexagonal()
# Obtained from Bragg condition. Note that reciprocal lattice
# vector length is 1 / d_hkl.
min_r, max_r = (
(0, 2 / wavelength)
if two_theta_range is None
else [2 * sin(radians(t / 2)) / wavelength for t in two_theta_range]
)
# Obtain crystallographic reciprocal lattice points within range
recip_latt = latt.reciprocal_lattice_crystallographic
recip_pts = recip_latt.get_points_in_sphere([[0, 0, 0]], [0, 0, 0], max_r)
if min_r:
recip_pts = [pt for pt in recip_pts if pt[1] >= min_r]
peaks = {}
two_thetas = []
for hkl, g_hkl, ind, _ in sorted(
recip_pts, key=lambda i: (i[1], -i[0][0], -i[0][1], -i[0][2])
):
# Force miller indices to be integers.
hkl = [int(round(i)) for i in hkl]
if g_hkl != 0:
d_hkl = 1 / g_hkl
# Bragg condition
theta = asin(wavelength * g_hkl / 2)
two_theta = degrees(2 * theta)
if is_hex:
# Use Miller-Bravais indices for hexagonal lattices.
hkl = (hkl[0], hkl[1], -hkl[0] - hkl[1], hkl[2])
# Deal with floating point precision issues.
ind = np.where(
np.abs(np.subtract(two_thetas, two_theta))
< AbstractDiffractionPatternCalculator.TWO_THETA_TOL
)
if len(ind[0]) > 0:
peaks[two_thetas[ind[0][0]]][0] += 1.0
peaks[two_thetas[ind[0][0]]][1].append(tuple(hkl))
else:
peaks[two_theta] = [1.0, [tuple(hkl)], d_hkl]
two_thetas.append(two_theta)
x = []
y = []
hkls = []
d_hkls = []
for k in sorted(peaks.keys()):
v = peaks[k]
fam = get_unique_families(v[1])
x.append(k)
y.append(v[0])
hkls.append(
[{"hkl": hkl, "multiplicity": mult} for hkl, mult in fam.items()]
)
d_hkls.append(v[2])
xrd = DiffractionPattern(x, y, hkls, d_hkls)
return xrd
class SpacegroupAnalyzerTest(PymatgenTest):
def setUp(self):
p = Poscar.from_file(os.path.join(test_dir, 'POSCAR'))
self.structure = p.structure
self.sg = SpacegroupAnalyzer(self.structure, 0.001)
self.disordered_structure = self.get_structure('Li10GeP2S12')
self.disordered_sg = SpacegroupAnalyzer(self.disordered_structure, 0.001)
s = p.structure.copy()
site = s[0]
del s[0]
s.append(site.species_and_occu, site.frac_coords)
self.sg3 = SpacegroupAnalyzer(s, 0.001)
graphite = self.get_structure('Graphite')
graphite.add_site_property("magmom", [0.1] * len(graphite))
self.sg4 = SpacegroupAnalyzer(graphite, 0.001)
def test_get_space_symbol(self):
self.assertEqual(self.sg.get_spacegroup_symbol(), "Pnma")
self.assertEqual(self.disordered_sg.get_spacegroup_symbol(),
"P4_2/nmc")
self.assertEqual(self.sg3.get_spacegroup_symbol(), "Pnma")
self.assertEqual(self.sg4.get_spacegroup_symbol(), "P6_3/mmc")
def test_get_space_number(self):
self.assertEqual(self.sg.get_spacegroup_number(), 62)
self.assertEqual(self.disordered_sg.get_spacegroup_number(), 137)
self.assertEqual(self.sg4.get_spacegroup_number(), 194)
def test_get_hall(self):
self.assertEqual(self.sg.get_hall(), '-P 2ac 2n')
self.assertEqual(self.disordered_sg.get_hall(), 'P 4n 2n -1n')
def test_get_pointgroup(self):
self.assertEqual(self.sg.get_point_group(), 'mmm')
self.assertEqual(self.disordered_sg.get_point_group(), '4/mmm')
def test_get_symmetry_dataset(self):
ds = self.sg.get_symmetry_dataset()
self.assertEqual(ds['international'], 'Pnma')
def test_get_crystal_system(self):
crystal_system = self.sg.get_crystal_system()
self.assertEqual('orthorhombic', crystal_system)
self.assertEqual('tetragonal', self.disordered_sg.get_crystal_system())
def test_get_symmetry_operations(self):
fracsymmops = self.sg.get_symmetry_operations()
symmops = self.sg.get_symmetry_operations(True)
self.assertEqual(len(symmops), 8)
latt = self.structure.lattice
for fop, op in zip(fracsymmops, symmops):
for site in self.structure:
newfrac = fop.operate(site.frac_coords)
newcart = op.operate(site.coords)
self.assertTrue(np.allclose(latt.get_fractional_coords(newcart),
newfrac))
found = False
newsite = PeriodicSite(site.species_and_occu, newcart, latt,
coords_are_cartesian=True)
for testsite in self.structure:
if newsite.is_periodic_image(testsite, 1e-3):
found = True
break
self.assertTrue(found)
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
s = self.get_structure('Li2O')
sg = SpacegroupAnalyzer(s, 0.001)
self.assertEqual(sg.get_refined_structure().num_sites, 4 * s.num_sites)
def test_get_symmetrized_structure(self):
symm_struct = self.sg.get_symmetrized_structure()
for a in symm_struct.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(len(symm_struct.equivalent_sites), 5)
symm_struct = self.disordered_sg.get_symmetrized_structure()
self.assertEqual(len(symm_struct.equivalent_sites), 8)
self.assertEqual([len(i) for i in symm_struct.equivalent_sites],
[16,4,8,4,2,8,8,8])
s1 = symm_struct.equivalent_sites[1][1]
s2 = symm_struct[symm_struct.equivalent_indices[1][1]]
self.assertEqual(s1, s2)
self.assertEqual(self.sg4.get_symmetrized_structure()[0].magmom, 0.1)
def test_find_primitive(self):
"""
F m -3 m Li2O testing of converting to primitive cell
"""
parser = CifParser(os.path.join(test_dir, 'Li2O.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive()
self.assertEqual(primitive_structure.formula, "Li2 O1")
# This isn't what is expected. All the angles should be 60
self.assertAlmostEqual(primitive_structure.lattice.alpha, 60)
self.assertAlmostEqual(primitive_structure.lattice.beta, 60)
self.assertAlmostEqual(primitive_structure.lattice.gamma, 60)
self.assertAlmostEqual(primitive_structure.lattice.volume,
structure.lattice.volume / 4.0)
def test_get_ir_reciprocal_mesh(self):
grid=self.sg.get_ir_reciprocal_mesh()
self.assertEqual(len(grid), 216)
self.assertAlmostEquals(grid[1][0][0], 0.1)
self.assertAlmostEquals(grid[1][0][1], 0.0)
self.assertAlmostEquals(grid[1][0][2], 0.0)
self.assertEqual(grid[1][1], 2)
def test_get_conventional_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.b, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.c, 9.1980270633769461)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.b, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.c, 4.2327080177761687)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 2.9542233922299999)
self.assertAlmostEqual(conv.lattice.b, 4.6330325651443296)
self.assertAlmostEqual(conv.lattice.c, 5.373703587040775)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 4.1430033493799998)
self.assertAlmostEqual(conv.lattice.b, 31.437979757624728)
self.assertAlmostEqual(conv.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 117.53832420192903)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 14.033435583000625)
self.assertAlmostEqual(conv.lattice.b, 3.96052850731)
self.assertAlmostEqual(conv.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'hex_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 120)
self.assertAlmostEqual(conv.lattice.a, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.b, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.c, 6.9779585500000003)
def test_get_primitive_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.beta, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.gamma, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.a, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.b, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.c, 7.9657251015812145)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 105.015053349)
self.assertAlmostEqual(prim.lattice.beta, 105.015053349)
self.assertAlmostEqual(prim.lattice.gamma, 118.80658411899999)
self.assertAlmostEqual(prim.lattice.a, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.b, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.c, 4.1579321075608791)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 134.78923546600001)
self.assertAlmostEqual(prim.lattice.beta, 105.856239333)
self.assertAlmostEqual(prim.lattice.gamma, 91.276341676000001)
self.assertAlmostEqual(prim.lattice.a, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.b, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.c, 3.8428217771014852)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 164.985257335)
self.assertAlmostEqual(prim.lattice.a, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.b, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 63.579155761999999)
self.assertAlmostEqual(prim.lattice.beta, 116.42084423747779)
self.assertAlmostEqual(prim.lattice.gamma, 148.47965136208569)
self.assertAlmostEqual(prim.lattice.a, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.b, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'hex_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 120)
self.assertAlmostEqual(prim.lattice.a, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.b, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.c, 6.9779585500000003)
parser = CifParser(os.path.join(test_dir, 'rhomb_3478_conv.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.beta, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.gamma, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.a, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.b, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.c, 5.9352627428399982)
class SpacegroupAnalyzerTest(PymatgenTest):
def setUp(self):
p = Poscar.from_file(os.path.join(test_dir, 'POSCAR'))
self.structure = p.structure
self.sg = SpacegroupAnalyzer(self.structure, 0.001)
self.disordered_structure = self.get_structure('Li10GeP2S12')
self.disordered_sg = SpacegroupAnalyzer(self.disordered_structure, 0.001)
s = p.structure.copy()
site = s[0]
del s[0]
s.append(site.species_and_occu, site.frac_coords)
self.sg3 = SpacegroupAnalyzer(s, 0.001)
graphite = self.get_structure('Graphite')
graphite.add_site_property("magmom", [0.1] * len(graphite))
self.sg4 = SpacegroupAnalyzer(graphite, 0.001)
self.structure4 = graphite
def test_primitive(self):
s = Structure.from_spacegroup("Fm-3m", np.eye(3) * 3, ["Cu"],
[[0, 0, 0]])
a = SpacegroupAnalyzer(s)
self.assertEqual(len(s), 4)
self.assertEqual(len(a.find_primitive()), 1)
def test_is_laue(self):
s = Structure.from_spacegroup("Fm-3m", np.eye(3) * 3, ["Cu"],
[[0, 0, 0]])
a = SpacegroupAnalyzer(s)
self.assertTrue(a.is_laue())
def test_magnetic(self):
lfp = PymatgenTest.get_structure("LiFePO4")
sg = SpacegroupAnalyzer(lfp, 0.1)
self.assertEqual(sg.get_space_group_symbol(), "Pnma")
magmoms = [0] * len(lfp)
magmoms[4] = 1
magmoms[5] = -1
magmoms[6] = 1
magmoms[7] = -1
lfp.add_site_property("magmom", magmoms)
sg = SpacegroupAnalyzer(lfp, 0.1)
self.assertEqual(sg.get_space_group_symbol(), "Pnma")
def test_get_space_symbol(self):
self.assertEqual(self.sg.get_space_group_symbol(), "Pnma")
self.assertEqual(self.disordered_sg.get_space_group_symbol(),
"P4_2/nmc")
self.assertEqual(self.sg3.get_space_group_symbol(), "Pnma")
self.assertEqual(self.sg4.get_space_group_symbol(), "P6_3/mmc")
def test_get_space_number(self):
self.assertEqual(self.sg.get_space_group_number(), 62)
self.assertEqual(self.disordered_sg.get_space_group_number(), 137)
self.assertEqual(self.sg4.get_space_group_number(), 194)
def test_get_hall(self):
self.assertEqual(self.sg.get_hall(), '-P 2ac 2n')
self.assertEqual(self.disordered_sg.get_hall(), 'P 4n 2n -1n')
def test_get_pointgroup(self):
self.assertEqual(self.sg.get_point_group_symbol(), 'mmm')
self.assertEqual(self.disordered_sg.get_point_group_symbol(), '4/mmm')
def test_get_symmetry_dataset(self):
ds = self.sg.get_symmetry_dataset()
self.assertEqual(ds['international'], 'Pnma')
def test_get_crystal_system(self):
crystal_system = self.sg.get_crystal_system()
self.assertEqual('orthorhombic', crystal_system)
self.assertEqual('tetragonal', self.disordered_sg.get_crystal_system())
def test_get_symmetry_operations(self):
for sg, structure in [(self.sg, self.structure),
(self.sg4, self.structure4)]:
pgops = sg.get_point_group_operations()
fracsymmops = sg.get_symmetry_operations()
symmops = sg.get_symmetry_operations(True)
latt = structure.lattice
for fop, op, pgop in zip(fracsymmops, symmops, pgops):
# translation vector values should all be 0 or 0.5
t = fop.translation_vector * 2
self.assertArrayAlmostEqual(t - np.round(t), 0)
self.assertArrayAlmostEqual(fop.rotation_matrix,
pgop.rotation_matrix)
for site in structure:
newfrac = fop.operate(site.frac_coords)
newcart = op.operate(site.coords)
self.assertTrue(np.allclose(latt.get_fractional_coords(newcart),
newfrac))
found = False
newsite = PeriodicSite(site.species_and_occu, newcart, latt,
coords_are_cartesian=True)
for testsite in structure:
if newsite.is_periodic_image(testsite, 1e-3):
found = True
break
self.assertTrue(found)
# Make sure this works for any position, not just the atomic
# ones.
random_fcoord = np.random.uniform(size=(3))
random_ccoord = latt.get_cartesian_coords(random_fcoord)
newfrac = fop.operate(random_fcoord)
newcart = op.operate(random_ccoord)
self.assertTrue(np.allclose(latt.get_fractional_coords(newcart),
newfrac))
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
s = self.get_structure('Li2O')
sg = SpacegroupAnalyzer(s, 0.01)
self.assertEqual(sg.get_refined_structure().num_sites, 4 * s.num_sites)
def test_get_symmetrized_structure(self):
symm_struct = self.sg.get_symmetrized_structure()
for a in symm_struct.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(len(symm_struct.equivalent_sites), 5)
symm_struct = self.disordered_sg.get_symmetrized_structure()
self.assertEqual(len(symm_struct.equivalent_sites), 8)
self.assertEqual([len(i) for i in symm_struct.equivalent_sites],
[16,4,8,4,2,8,8,8])
s1 = symm_struct.equivalent_sites[1][1]
s2 = symm_struct[symm_struct.equivalent_indices[1][1]]
self.assertEqual(s1, s2)
self.assertEqual(self.sg4.get_symmetrized_structure()[0].magmom, 0.1)
self.assertEqual(symm_struct.wyckoff_symbols[0], '16h')
# self.assertEqual(symm_struct[0].wyckoff, "16h")
def test_find_primitive(self):
"""
F m -3 m Li2O testing of converting to primitive cell
"""
parser = CifParser(os.path.join(test_dir, 'Li2O.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive()
self.assertEqual(primitive_structure.formula, "Li2 O1")
# This isn't what is expected. All the angles should be 60
self.assertAlmostEqual(primitive_structure.lattice.alpha, 60)
self.assertAlmostEqual(primitive_structure.lattice.beta, 60)
self.assertAlmostEqual(primitive_structure.lattice.gamma, 60)
self.assertAlmostEqual(primitive_structure.lattice.volume,
structure.lattice.volume / 4.0)
def test_get_ir_reciprocal_mesh(self):
grid = self.sg.get_ir_reciprocal_mesh()
self.assertEqual(len(grid), 216)
self.assertAlmostEqual(grid[1][0][0], 0.1)
self.assertAlmostEqual(grid[1][0][1], 0.0)
self.assertAlmostEqual(grid[1][0][2], 0.0)
self.assertAlmostEqual(grid[1][1], 2)
def test_get_conventional_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.b, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.c, 9.1980270633769461)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.b, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.c, 4.2327080177761687)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 2.9542233922299999)
self.assertAlmostEqual(conv.lattice.b, 4.6330325651443296)
self.assertAlmostEqual(conv.lattice.c, 5.373703587040775)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 4.1430033493799998)
self.assertAlmostEqual(conv.lattice.b, 31.437979757624728)
self.assertAlmostEqual(conv.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'orac_632475.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 3.1790663399999999)
self.assertAlmostEqual(conv.lattice.b, 9.9032878699999998)
self.assertAlmostEqual(conv.lattice.c, 3.5372412099999999)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 117.53832420192903)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 14.033435583000625)
self.assertAlmostEqual(conv.lattice.b, 3.96052850731)
self.assertAlmostEqual(conv.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'hex_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 120)
self.assertAlmostEqual(conv.lattice.a, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.b, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.c, 6.9779585500000003)
def test_get_primitive_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.beta, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.gamma, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.a, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.b, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.c, 7.9657251015812145)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 105.015053349)
self.assertAlmostEqual(prim.lattice.beta, 105.015053349)
self.assertAlmostEqual(prim.lattice.gamma, 118.80658411899999)
self.assertAlmostEqual(prim.lattice.a, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.b, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.c, 4.1579321075608791)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 134.78923546600001)
self.assertAlmostEqual(prim.lattice.beta, 105.856239333)
self.assertAlmostEqual(prim.lattice.gamma, 91.276341676000001)
self.assertAlmostEqual(prim.lattice.a, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.b, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.c, 3.8428217771014852)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 164.985257335)
self.assertAlmostEqual(prim.lattice.a, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.b, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'orac_632475.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 144.40557588533386)
self.assertAlmostEqual(prim.lattice.a, 5.2005185662155391)
self.assertAlmostEqual(prim.lattice.b, 5.2005185662155391)
self.assertAlmostEqual(prim.lattice.c, 3.5372412099999999)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 63.579155761999999)
self.assertAlmostEqual(prim.lattice.beta, 116.42084423747779)
self.assertAlmostEqual(prim.lattice.gamma, 148.47965136208569)
self.assertAlmostEqual(prim.lattice.a, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.b, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'hex_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 120)
self.assertAlmostEqual(prim.lattice.a, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.b, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.c, 6.9779585500000003)
parser = CifParser(os.path.join(test_dir, 'rhomb_3478_conv.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.beta, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.gamma, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.a, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.b, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.c, 5.9352627428399982)
def convert_to_ieee(self, structure, atol=0.1, ltol=0.05):
"""
Given a structure associated with a tensor, attempts a
calculation of the tensor in IEEE format according to
the 1987 IEEE standards.
Args:
structure (Structure): a structure associated with the
tensor to be converted to the IEEE standard
atol (float): angle tolerance for conversion routines
ltol (float): length tolerance for conversion routines
"""
def get_uvec(vec):
""" Gets a unit vector parallel to input vector"""
return vec / np.linalg.norm(vec)
vecs = structure.lattice.matrix
lengths = np.array(structure.lattice.abc)
angles = np.array(structure.lattice.angles)
# Check conventional setting:
sga = SpacegroupAnalyzer(structure)
xtal_sys = sga.get_crystal_system()
conv_struct = sga.get_refined_structure()
conv_lengths = np.array(conv_struct.lattice.abc)
conv_angles = np.array(conv_struct.lattice.angles)
rhombohedral = xtal_sys == "trigonal" and \
(angles - angles[0] < atol).all()
if ((np.sort(lengths) - np.sort(conv_lengths) > ltol).any() \
or (np.sort(angles) - np.sort(conv_angles) > atol).any() \
or len(structure.sites) != len(conv_struct.sites)) \
and not rhombohedral:
raise ValueError("{} structure not in conventional cell, IEEE "\
"conversion from non-conventional settings "\
"is not yet supported.".format(xtal_sys))
a = b = c = None
rotation = np.zeros((3, 3))
# IEEE rules: a,b,c || x1,x2,x3
if xtal_sys == "cubic":
rotation = [vecs[i] / lengths[i] for i in range(3)]
# IEEE rules: a=b in length; c,a || x3, x1
elif xtal_sys == "tetragonal":
rotation = np.array(
[vec / mag for (mag, vec) in sorted(zip(lengths, vecs))])
if abs(lengths[2] - lengths[1]) < ltol:
rotation[0], rotation[2] = rotation[2], rotation[0].copy()
rotation[1] = get_uvec(np.cross(rotation[2], rotation[0]))
# IEEE rules: c<a<b; c,a || x3,x1
elif xtal_sys == "orthorhombic":
rotation = [vec / mag for (mag, vec) in sorted(zip(lengths, vecs))]
rotation = np.roll(rotation, 2, axis=0)
# IEEE rules: c,a || x3,x1, c is threefold axis
elif xtal_sys in ("trigonal", "hexagonal"):
# Rhombohedral lattice
if rhombohedral:
rotation[0] = get_uvec(vecs[2] - vecs[0])
rotation[2] = get_uvec(np.sum(vecs, axis=0))
rotation[1] = get_uvec(np.cross(rotation[2], rotation[0]))
# Standard hexagonal lattice
else:
# find threefold axis:
tf_mask = np.where(abs(angles - 120.0) < atol)
non_tf_mask = np.logical_not(tf_mask)
rotation[2] = get_uvec(vecs[tf_mask])
rotation[0] = get_uvec(vecs[non_tf_mask][0])
rotation[1] = get_uvec(np.cross(rotation[2], rotation[0]))
# IEEE rules: b,c || x2,x3; alpha=beta=90, c<a
elif xtal_sys == "monoclinic":
# Find unique axis
umask = abs(angles - 90.0) > atol
n_umask = np.logical_not(umask)
rotation[1] = get_uvec(vecs[umask])
# Shorter of remaining lattice vectors for c axis
c = [
vec / mag
for (mag, vec) in sorted(zip(lengths[n_umask], vecs[n_umask]))
][0]
rotation[2] = np.array(c)
rotation[0] = np.cross(rotation[1], rotation[2])
# IEEE rules: c || x3
elif xtal_sys == "triclinic":
rotation = [vec / mag for (mag, vec) in sorted(zip(lengths, vecs))]
rotation = np.roll(rotation, 2, axis=0)
rotation[1] = get_uvec(np.cross(rotation[2], rotation[1]))
rotation[0] = np.cross(rotation[1], rotation[2])
return self.rotate(rotation)
class SpacegroupAnalyzerTest(PymatgenTest):
def setUp(self):
p = Poscar.from_file(os.path.join(test_dir, 'POSCAR'))
self.structure = p.structure
self.sg = SpacegroupAnalyzer(self.structure, 0.001)
self.disordered_structure = self.get_structure('Li10GeP2S12')
self.disordered_sg = SpacegroupAnalyzer(self.disordered_structure,
0.001)
s = p.structure.copy()
site = s[0]
del s[0]
s.append(site.species_and_occu, site.frac_coords)
self.sg3 = SpacegroupAnalyzer(s, 0.001)
graphite = self.get_structure('Graphite')
graphite.add_site_property("magmom", [0.1] * len(graphite))
self.sg4 = SpacegroupAnalyzer(graphite, 0.001)
self.structure4 = graphite
def test_primitive(self):
s = Structure.from_spacegroup("Fm-3m",
np.eye(3) * 3, ["Cu"], [[0, 0, 0]])
a = SpacegroupAnalyzer(s)
self.assertEqual(len(s), 4)
self.assertEqual(len(a.find_primitive()), 1)
def test_is_laue(self):
s = Structure.from_spacegroup("Fm-3m",
np.eye(3) * 3, ["Cu"], [[0, 0, 0]])
a = SpacegroupAnalyzer(s)
self.assertTrue(a.is_laue())
def test_magnetic(self):
lfp = PymatgenTest.get_structure("LiFePO4")
sg = SpacegroupAnalyzer(lfp, 0.1)
self.assertEqual(sg.get_space_group_symbol(), "Pnma")
magmoms = [0] * len(lfp)
magmoms[4] = 1
magmoms[5] = -1
magmoms[6] = 1
magmoms[7] = -1
lfp.add_site_property("magmom", magmoms)
sg = SpacegroupAnalyzer(lfp, 0.1)
self.assertEqual(sg.get_space_group_symbol(), "Pnma")
def test_get_space_symbol(self):
self.assertEqual(self.sg.get_space_group_symbol(), "Pnma")
self.assertEqual(self.disordered_sg.get_space_group_symbol(),
"P4_2/nmc")
self.assertEqual(self.sg3.get_space_group_symbol(), "Pnma")
self.assertEqual(self.sg4.get_space_group_symbol(), "P6_3/mmc")
def test_get_space_number(self):
self.assertEqual(self.sg.get_space_group_number(), 62)
self.assertEqual(self.disordered_sg.get_space_group_number(), 137)
self.assertEqual(self.sg4.get_space_group_number(), 194)
def test_get_hall(self):
self.assertEqual(self.sg.get_hall(), '-P 2ac 2n')
self.assertEqual(self.disordered_sg.get_hall(), 'P 4n 2n -1n')
def test_get_pointgroup(self):
self.assertEqual(self.sg.get_point_group_symbol(), 'mmm')
self.assertEqual(self.disordered_sg.get_point_group_symbol(), '4/mmm')
def test_get_symmetry_operations(self):
coordinates = np.array([[0.5, 0.0, 0.0], [0.0, 0.5, 0.0],
[0.5, 1.0, 0.0], [1.0, 0.5, 0.0]])
species = ['H'] * len(coordinates)
molecule = Molecule(species, coordinates)
so = PointGroupAnalyzer(molecule, 0.3).get_symmetry_operations()
self.assertEqual(len(so), 16) # D4h contains 16 symmetry elements
for o in so:
self.assertEqual(isinstance(o, SymmOp), True)
def test_get_symmetry_dataset(self):
ds = self.sg.get_symmetry_dataset()
self.assertEqual(ds['international'], 'Pnma')
def test_get_crystal_system(self):
crystal_system = self.sg.get_crystal_system()
self.assertEqual('orthorhombic', crystal_system)
self.assertEqual('tetragonal', self.disordered_sg.get_crystal_system())
def test_get_symmetry_operations(self):
for sg, structure in [(self.sg, self.structure),
(self.sg4, self.structure4)]:
pgops = sg.get_point_group_operations()
fracsymmops = sg.get_symmetry_operations()
symmops = sg.get_symmetry_operations(True)
latt = structure.lattice
for fop, op, pgop in zip(fracsymmops, symmops, pgops):
# translation vector values should all be 0 or 0.5
t = fop.translation_vector * 2
self.assertArrayAlmostEqual(t - np.round(t), 0)
self.assertArrayAlmostEqual(fop.rotation_matrix,
pgop.rotation_matrix)
for site in structure:
newfrac = fop.operate(site.frac_coords)
newcart = op.operate(site.coords)
self.assertTrue(
np.allclose(latt.get_fractional_coords(newcart),
newfrac))
found = False
newsite = PeriodicSite(site.species_and_occu,
newcart,
latt,
coords_are_cartesian=True)
for testsite in structure:
if newsite.is_periodic_image(testsite, 1e-3):
found = True
break
self.assertTrue(found)
# Make sure this works for any position, not just the atomic
# ones.
random_fcoord = np.random.uniform(size=(3))
random_ccoord = latt.get_cartesian_coords(random_fcoord)
newfrac = fop.operate(random_fcoord)
newcart = op.operate(random_ccoord)
self.assertTrue(
np.allclose(latt.get_fractional_coords(newcart), newfrac))
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
s = self.get_structure('Li2O')
sg = SpacegroupAnalyzer(s, 0.01)
self.assertEqual(sg.get_refined_structure().num_sites, 4 * s.num_sites)
def test_get_symmetrized_structure(self):
symm_struct = self.sg.get_symmetrized_structure()
for a in symm_struct.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(len(symm_struct.equivalent_sites), 5)
symm_struct = self.disordered_sg.get_symmetrized_structure()
self.assertEqual(len(symm_struct.equivalent_sites), 8)
self.assertEqual([len(i) for i in symm_struct.equivalent_sites],
[16, 4, 8, 4, 2, 8, 8, 8])
s1 = symm_struct.equivalent_sites[1][1]
s2 = symm_struct[symm_struct.equivalent_indices[1][1]]
self.assertEqual(s1, s2)
self.assertEqual(self.sg4.get_symmetrized_structure()[0].magmom, 0.1)
self.assertEqual(symm_struct.wyckoff_symbols[0], '16h')
# self.assertEqual(symm_struct[0].wyckoff, "16h")
def test_find_primitive(self):
"""
F m -3 m Li2O testing of converting to primitive cell
"""
parser = CifParser(os.path.join(test_dir, 'Li2O.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive()
self.assertEqual(primitive_structure.formula, "Li2 O1")
# This isn't what is expected. All the angles should be 60
self.assertAlmostEqual(primitive_structure.lattice.alpha, 60)
self.assertAlmostEqual(primitive_structure.lattice.beta, 60)
self.assertAlmostEqual(primitive_structure.lattice.gamma, 60)
self.assertAlmostEqual(primitive_structure.lattice.volume,
structure.lattice.volume / 4.0)
def test_get_ir_reciprocal_mesh(self):
grid = self.sg.get_ir_reciprocal_mesh()
self.assertEqual(len(grid), 216)
self.assertAlmostEqual(grid[1][0][0], 0.1)
self.assertAlmostEqual(grid[1][0][1], 0.0)
self.assertAlmostEqual(grid[1][0][2], 0.0)
self.assertAlmostEqual(grid[1][1], 2)
def test_get_conventional_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.b, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.c, 9.1980270633769461)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.b, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.c, 4.2327080177761687)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 2.9542233922299999)
self.assertAlmostEqual(conv.lattice.b, 4.6330325651443296)
self.assertAlmostEqual(conv.lattice.c, 5.373703587040775)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 4.1430033493799998)
self.assertAlmostEqual(conv.lattice.b, 31.437979757624728)
self.assertAlmostEqual(conv.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'orac_632475.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 3.1790663399999999)
self.assertAlmostEqual(conv.lattice.b, 9.9032878699999998)
self.assertAlmostEqual(conv.lattice.c, 3.5372412099999999)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 117.53832420192903)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 14.033435583000625)
self.assertAlmostEqual(conv.lattice.b, 3.96052850731)
self.assertAlmostEqual(conv.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'hex_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 120)
self.assertAlmostEqual(conv.lattice.a, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.b, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.c, 6.9779585500000003)
def test_get_primitive_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.beta, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.gamma, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.a, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.b, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.c, 7.9657251015812145)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 105.015053349)
self.assertAlmostEqual(prim.lattice.beta, 105.015053349)
self.assertAlmostEqual(prim.lattice.gamma, 118.80658411899999)
self.assertAlmostEqual(prim.lattice.a, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.b, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.c, 4.1579321075608791)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 134.78923546600001)
self.assertAlmostEqual(prim.lattice.beta, 105.856239333)
self.assertAlmostEqual(prim.lattice.gamma, 91.276341676000001)
self.assertAlmostEqual(prim.lattice.a, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.b, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.c, 3.8428217771014852)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 164.985257335)
self.assertAlmostEqual(prim.lattice.a, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.b, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'orac_632475.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 144.40557588533386)
self.assertAlmostEqual(prim.lattice.a, 5.2005185662155391)
self.assertAlmostEqual(prim.lattice.b, 5.2005185662155391)
self.assertAlmostEqual(prim.lattice.c, 3.5372412099999999)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 63.579155761999999)
self.assertAlmostEqual(prim.lattice.beta, 116.42084423747779)
self.assertAlmostEqual(prim.lattice.gamma, 148.47965136208569)
self.assertAlmostEqual(prim.lattice.a, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.b, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'hex_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 120)
self.assertAlmostEqual(prim.lattice.a, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.b, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.c, 6.9779585500000003)
parser = CifParser(os.path.join(test_dir, 'rhomb_3478_conv.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.beta, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.gamma, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.a, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.b, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.c, 5.9352627428399982)
def get_pattern(self, structure, scaled=True, two_theta_range=(0, 90)):
"""
Calculates the diffraction pattern for a structure.
Args:
structure (Structure): Input structure
scaled (bool): Whether to return scaled intensities. The maximum
peak is set to a value of 100. Defaults to True. Use False if
you need the absolute values to combine XRD plots.
two_theta_range ([float of length 2]): Tuple for range of
two_thetas to calculate in degrees. Defaults to (0, 90). Set to
None if you want all diffracted beams within the limiting
sphere of radius 2 / wavelength.
Returns:
(XRDPattern)
"""
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
wavelength = self.wavelength
latt = structure.lattice
is_hex = latt.is_hexagonal()
# Obtained from Bragg condition. Note that reciprocal lattice
# vector length is 1 / d_hkl.
min_r, max_r = (0, 2 / wavelength) if two_theta_range is None else \
[2 * sin(radians(t / 2)) / wavelength for t in two_theta_range]
# Obtain crystallographic reciprocal lattice points within range
recip_latt = latt.reciprocal_lattice_crystallographic
recip_pts = recip_latt.get_points_in_sphere(
[[0, 0, 0]], [0, 0, 0], max_r)
if min_r:
recip_pts = [pt for pt in recip_pts if pt[1] >= min_r]
# Create a flattened array of zs, coeffs, fcoords and occus. This is
# used to perform vectorized computation of atomic scattering factors
# later. Note that these are not necessarily the same size as the
# structure as each partially occupied specie occupies its own
# position in the flattened array.
zs = []
coeffs = []
fcoords = []
occus = []
dwfactors = []
for site in structure:
for sp, occu in site.species.items():
zs.append(sp.Z)
try:
c = ATOMIC_SCATTERING_PARAMS[sp.symbol]
except KeyError:
raise ValueError("Unable to calculate XRD pattern as "
"there is no scattering coefficients for"
" %s." % sp.symbol)
coeffs.append(c)
dwfactors.append(self.debye_waller_factors.get(sp.symbol, 0))
fcoords.append(site.frac_coords)
occus.append(occu)
zs = np.array(zs)
coeffs = np.array(coeffs)
fcoords = np.array(fcoords)
occus = np.array(occus)
dwfactors = np.array(dwfactors)
peaks = {}
two_thetas = []
for hkl, g_hkl, ind, _ in sorted(
recip_pts, key=lambda i: (i[1], -i[0][0], -i[0][1], -i[0][2])):
# Force miller indices to be integers.
hkl = [int(round(i)) for i in hkl]
if g_hkl != 0:
d_hkl = 1 / g_hkl
# Bragg condition
theta = asin(wavelength * g_hkl / 2)
# s = sin(theta) / wavelength = 1 / 2d = |ghkl| / 2 (d =
# 1/|ghkl|)
s = g_hkl / 2
# Store s^2 since we are using it a few times.
s2 = s ** 2
# Vectorized computation of g.r for all fractional coords and
# hkl.
g_dot_r = np.dot(fcoords, np.transpose([hkl])).T[0]
# Highly vectorized computation of atomic scattering factors.
# Equivalent non-vectorized code is::
#
# for site in structure:
# el = site.specie
# coeff = ATOMIC_SCATTERING_PARAMS[el.symbol]
# fs = el.Z - 41.78214 * s2 * sum(
# [d[0] * exp(-d[1] * s2) for d in coeff])
fs = zs - 41.78214 * s2 * np.sum(
coeffs[:, :, 0] * np.exp(-coeffs[:, :, 1] * s2), axis=1)
dw_correction = np.exp(-dwfactors * s2)
# Structure factor = sum of atomic scattering factors (with
# position factor exp(2j * pi * g.r and occupancies).
# Vectorized computation.
f_hkl = np.sum(fs * occus * np.exp(2j * pi * g_dot_r)
* dw_correction)
# Lorentz polarization correction for hkl
lorentz_factor = (1 + cos(2 * theta) ** 2) / \
(sin(theta) ** 2 * cos(theta))
# Intensity for hkl is modulus square of structure factor.
i_hkl = (f_hkl * f_hkl.conjugate()).real
two_theta = degrees(2 * theta)
if is_hex:
# Use Miller-Bravais indices for hexagonal lattices.
hkl = (hkl[0], hkl[1], - hkl[0] - hkl[1], hkl[2])
# Deal with floating point precision issues.
ind = np.where(np.abs(np.subtract(two_thetas, two_theta)) <
AbstractDiffractionPatternCalculator.TWO_THETA_TOL)
if len(ind[0]) > 0:
peaks[two_thetas[ind[0][0]]][0] += i_hkl * lorentz_factor
peaks[two_thetas[ind[0][0]]][1].append(tuple(hkl))
else:
peaks[two_theta] = [i_hkl * lorentz_factor, [tuple(hkl)],
d_hkl]
two_thetas.append(two_theta)
# Scale intensities so that the max intensity is 100.
max_intensity = max([v[0] for v in peaks.values()])
x = []
y = []
hkls = []
d_hkls = []
for k in sorted(peaks.keys()):
v = peaks[k]
fam = get_unique_families(v[1])
if v[0] / max_intensity * 100 > AbstractDiffractionPatternCalculator.SCALED_INTENSITY_TOL:
x.append(k)
y.append(v[0])
hkls.append([{"hkl": hkl, "multiplicity": mult}
for hkl, mult in fam.items()])
d_hkls.append(v[2])
xrd = DiffractionPattern(x, y, hkls, d_hkls)
if scaled:
xrd.normalize(mode="max", value=100)
return xrd
def apply_transformation(self, structure, return_ranked_list=False):
"""
Return either a single ordered structure or a sequence of all ordered
structures.
Args:
structure: Structure to order.
return_ranked_list (bool): Whether or not multiple structures are
returned. If return_ranked_list is a number, that number of
structures is returned.
Returns:
Depending on returned_ranked list, either a transformed structure
or a list of dictionaries, where each dictionary is of the form
{"structure" = .... , "other_arguments"}
The list of ordered structures is ranked by ewald energy / atom, if
the input structure is an oxidation state decorated structure.
Otherwise, it is ranked by number of sites, with smallest number of
sites first.
"""
try:
num_to_return = int(return_ranked_list)
except ValueError:
num_to_return = 1
if structure.is_ordered:
raise ValueError("Enumeration can be carried out only on "
"disordered structures!")
if self.refine_structure:
finder = SpacegroupAnalyzer(structure, self.symm_prec)
structure = finder.get_refined_structure()
contains_oxidation_state = all([
hasattr(sp, "oxi_state") and sp.oxi_state != 0
for sp in structure.composition.elements
])
adaptor = EnumlibAdaptor(
structure,
min_cell_size=self.min_cell_size,
max_cell_size=self.max_cell_size,
symm_prec=self.symm_prec,
refine_structure=False,
enum_precision_parameter=self.enum_precision_parameter,
check_ordered_symmetry=self.check_ordered_symmetry)
adaptor.run()
structures = adaptor.structures
original_latt = structure.lattice
inv_latt = np.linalg.inv(original_latt.matrix)
ewald_matrices = {}
all_structures = []
for s in structures:
new_latt = s.lattice
transformation = np.dot(new_latt.matrix, inv_latt)
transformation = tuple([
tuple([int(round(cell)) for cell in row])
for row in transformation
])
if contains_oxidation_state:
if transformation not in ewald_matrices:
s_supercell = Structure.from_sites(structure.sites)
s_supercell.make_supercell(transformation)
ewald = EwaldSummation(s_supercell)
ewald_matrices[transformation] = ewald
else:
ewald = ewald_matrices[transformation]
energy = ewald.compute_sub_structure(s)
all_structures.append({
"num_sites": len(s),
"energy": energy,
"structure": s
})
else:
all_structures.append({"num_sites": len(s), "structure": s})
def sort_func(s):
return s["energy"] / s["num_sites"] if contains_oxidation_state \
else s["num_sites"]
self._all_structures = sorted(all_structures, key=sort_func)
if return_ranked_list:
return self._all_structures[0:num_to_return]
else:
return self._all_structures[0]["structure"]
def apply_transformation(self, structure, return_ranked_list=False):
"""
Return either a single ordered structure or a sequence of all ordered
structures.
Args:
structure: Structure to order.
return_ranked_list (bool): Whether or not multiple structures are
returned. If return_ranked_list is a number, that number of
structures is returned.
Returns:
Depending on returned_ranked list, either a transformed structure
or a list of dictionaries, where each dictionary is of the form
{"structure" = .... , "other_arguments"}
The list of ordered structures is ranked by ewald energy / atom, if
the input structure is an oxidation state decorated structure.
Otherwise, it is ranked by number of sites, with smallest number of
sites first.
"""
try:
num_to_return = int(return_ranked_list)
except ValueError:
num_to_return = 1
if self.refine_structure:
finder = SpacegroupAnalyzer(structure, self.symm_prec)
structure = finder.get_refined_structure()
contains_oxidation_state = all([
hasattr(sp, "oxi_state") and sp.oxi_state != 0
for sp in structure.composition.elements
])
structures = None
if structure.is_ordered:
warn("Enumeration skipped for structure with composition {} "
"because it is ordered".format(structure.composition))
structures = [structure.copy()]
if self.max_disordered_sites:
ndisordered = sum([1 for site in structure if not site.is_ordered])
if ndisordered > self.max_disordered_sites:
raise ValueError("Too many disordered sites! ({} > {})".format(
ndisordered, self.max_disordered_sites))
max_cell_sizes = range(
self.min_cell_size,
int(math.floor(self.max_disordered_sites / ndisordered)) + 1)
else:
max_cell_sizes = [self.max_cell_size]
for max_cell_size in max_cell_sizes:
adaptor = EnumlibAdaptor(
structure,
min_cell_size=self.min_cell_size,
max_cell_size=max_cell_size,
symm_prec=self.symm_prec,
refine_structure=False,
enum_precision_parameter=self.enum_precision_parameter,
check_ordered_symmetry=self.check_ordered_symmetry,
timeout=self.timeout)
try:
adaptor.run()
except EnumError:
warn("Unable to enumerate for max_cell_size = %d".format(
max_cell_size))
structures = adaptor.structures
if structures:
break
if structures is None:
raise ValueError("Unable to enumerate")
original_latt = structure.lattice
inv_latt = np.linalg.inv(original_latt.matrix)
ewald_matrices = {}
all_structures = []
for s in structures:
new_latt = s.lattice
transformation = np.dot(new_latt.matrix, inv_latt)
transformation = tuple([
tuple([int(round(cell)) for cell in row])
for row in transformation
])
if contains_oxidation_state and self.sort_criteria == "ewald":
if transformation not in ewald_matrices:
s_supercell = structure * transformation
ewald = EwaldSummation(s_supercell)
ewald_matrices[transformation] = ewald
else:
ewald = ewald_matrices[transformation]
energy = ewald.compute_sub_structure(s)
all_structures.append({
"num_sites": len(s),
"energy": energy,
"structure": s
})
else:
all_structures.append({"num_sites": len(s), "structure": s})
def sort_func(s):
return s["energy"] / s["num_sites"] \
if contains_oxidation_state and self.sort_criteria == "ewald" \
else s["num_sites"]
self._all_structures = sorted(all_structures, key=sort_func)
if return_ranked_list:
return self._all_structures[0:num_to_return]
else:
return self._all_structures[0]["structure"]
def __init__(self, struct, symprec=None, write_magmoms=False):
"""
A wrapper around CifFile to write CIF files from pymatgen structures.
Args:
struct (Structure): structure to write
symprec (float): If not none, finds the symmetry of the structure
and writes the cif with symmetry information. Passes symprec
to the SpacegroupAnalyzer
write_magmoms (bool): If True, will write magCIF file. Incompatible
with symprec
"""
if write_magmoms and symprec:
warnings.warn(
"Magnetic symmetry cannot currently be detected by pymatgen.")
symprec = None
format_str = "{:.8f}"
block = OrderedDict()
loops = []
spacegroup = ("P 1", 1)
if symprec is not None:
sf = SpacegroupAnalyzer(struct, symprec)
spacegroup = (sf.get_space_group_symbol(),
sf.get_space_group_number())
# Needs the refined struture when using symprec. This converts
# primitive to conventional structures, the standard for CIF.
struct = sf.get_refined_structure()
latt = struct.lattice
comp = struct.composition
no_oxi_comp = comp.element_composition
block["_symmetry_space_group_name_H-M"] = spacegroup[0]
for cell_attr in ['a', 'b', 'c']:
block["_cell_length_" + cell_attr] = format_str.format(
getattr(latt, cell_attr))
for cell_attr in ['alpha', 'beta', 'gamma']:
block["_cell_angle_" + cell_attr] = format_str.format(
getattr(latt, cell_attr))
block["_symmetry_Int_Tables_number"] = spacegroup[1]
block["_chemical_formula_structural"] = no_oxi_comp.reduced_formula
block["_chemical_formula_sum"] = no_oxi_comp.formula
block["_cell_volume"] = latt.volume.__str__()
reduced_comp, fu = no_oxi_comp.get_reduced_composition_and_factor()
block["_cell_formula_units_Z"] = str(int(fu))
if symprec is None:
block["_symmetry_equiv_pos_site_id"] = ["1"]
block["_symmetry_equiv_pos_as_xyz"] = ["x, y, z"]
else:
sf = SpacegroupAnalyzer(struct, symprec)
symmops = []
for op in sf.get_symmetry_operations():
v = op.translation_vector
symmops.append(
SymmOp.from_rotation_and_translation(
op.rotation_matrix, v))
ops = [op.as_xyz_string() for op in symmops]
block["_symmetry_equiv_pos_site_id"] = \
["%d" % i for i in range(1, len(ops) + 1)]
block["_symmetry_equiv_pos_as_xyz"] = ops
loops.append(
["_symmetry_equiv_pos_site_id", "_symmetry_equiv_pos_as_xyz"])
contains_oxidation = True
try:
symbol_to_oxinum = OrderedDict([(el.__str__(), float(el.oxi_state))
for el in sorted(comp.elements)])
except AttributeError:
symbol_to_oxinum = OrderedDict([(el.symbol, 0)
for el in sorted(comp.elements)])
contains_oxidation = False
if contains_oxidation:
block["_atom_type_symbol"] = symbol_to_oxinum.keys()
block["_atom_type_oxidation_number"] = symbol_to_oxinum.values()
loops.append(["_atom_type_symbol", "_atom_type_oxidation_number"])
atom_site_type_symbol = []
atom_site_symmetry_multiplicity = []
atom_site_fract_x = []
atom_site_fract_y = []
atom_site_fract_z = []
atom_site_label = []
atom_site_occupancy = []
atom_site_moment_label = []
atom_site_moment_crystalaxis_x = []
atom_site_moment_crystalaxis_y = []
atom_site_moment_crystalaxis_z = []
count = 1
if symprec is None:
for site in struct:
for sp, occu in sorted(site.species_and_occu.items()):
atom_site_type_symbol.append(sp.__str__())
atom_site_symmetry_multiplicity.append("1")
atom_site_fract_x.append("{0:f}".format(site.a))
atom_site_fract_y.append("{0:f}".format(site.b))
atom_site_fract_z.append("{0:f}".format(site.c))
atom_site_label.append("{}{}".format(sp.symbol, count))
atom_site_occupancy.append(occu.__str__())
magmom = site.properties.get('magmom', Magmom(0))
moment = Magmom.get_moment_relative_to_crystal_axes(
magmom, latt)
if write_magmoms and abs(magmom) > 0:
atom_site_moment_label.append("{}{}".format(
sp.symbol, count))
atom_site_moment_crystalaxis_x.append(moment[0])
atom_site_moment_crystalaxis_y.append(moment[1])
atom_site_moment_crystalaxis_z.append(moment[2])
count += 1
else:
# The following just presents a deterministic ordering.
unique_sites = [
(sorted(sites,
key=lambda s: tuple([abs(x)
for x in s.frac_coords]))[0],
len(sites))
for sites in sf.get_symmetrized_structure().equivalent_sites
]
for site, mult in sorted(unique_sites,
key=lambda t:
(t[0].species_and_occu.average_electroneg,
-t[1], t[0].a, t[0].b, t[0].c)):
for sp, occu in site.species_and_occu.items():
atom_site_type_symbol.append(sp.__str__())
atom_site_symmetry_multiplicity.append("%d" % mult)
atom_site_fract_x.append("{0:f}".format(site.a))
atom_site_fract_y.append("{0:f}".format(site.b))
atom_site_fract_z.append("{0:f}".format(site.c))
atom_site_label.append("{}{}".format(sp.symbol, count))
atom_site_occupancy.append(occu.__str__())
count += 1
block["_atom_site_type_symbol"] = atom_site_type_symbol
block["_atom_site_label"] = atom_site_label
block["_atom_site_symmetry_multiplicity"] = \
atom_site_symmetry_multiplicity
block["_atom_site_fract_x"] = atom_site_fract_x
block["_atom_site_fract_y"] = atom_site_fract_y
block["_atom_site_fract_z"] = atom_site_fract_z
block["_atom_site_occupancy"] = atom_site_occupancy
loops.append([
"_atom_site_type_symbol", "_atom_site_label",
"_atom_site_symmetry_multiplicity", "_atom_site_fract_x",
"_atom_site_fract_y", "_atom_site_fract_z", "_atom_site_occupancy"
])
if write_magmoms:
block["_atom_site_moment_label"] = atom_site_moment_label
block[
"_atom_site_moment_crystalaxis_x"] = atom_site_moment_crystalaxis_x
block[
"_atom_site_moment_crystalaxis_y"] = atom_site_moment_crystalaxis_y
block[
"_atom_site_moment_crystalaxis_z"] = atom_site_moment_crystalaxis_z
loops.append([
"_atom_site_moment_label", "_atom_site_moment_crystalaxis_x",
"_atom_site_moment_crystalaxis_y",
"_atom_site_moment_crystalaxis_z"
])
d = OrderedDict()
d[comp.reduced_formula] = CifBlock(block, loops, comp.reduced_formula)
self._cf = CifFile(d)
class SpacegroupAnalyzerTest(PymatgenTest):
def setUp(self):
p = Poscar.from_file(
os.path.join(PymatgenTest.TEST_FILES_DIR, "POSCAR"))
self.structure = p.structure
self.sg = SpacegroupAnalyzer(self.structure, 0.001)
self.disordered_structure = self.get_structure("Li10GeP2S12")
self.disordered_sg = SpacegroupAnalyzer(self.disordered_structure,
0.001)
s = p.structure.copy()
site = s[0]
del s[0]
s.append(site.species, site.frac_coords)
self.sg3 = SpacegroupAnalyzer(s, 0.001)
graphite = self.get_structure("Graphite")
graphite.add_site_property("magmom", [0.1] * len(graphite))
self.sg4 = SpacegroupAnalyzer(graphite, 0.001)
self.structure4 = graphite
def test_primitive(self):
s = Structure.from_spacegroup("Fm-3m",
np.eye(3) * 3, ["Cu"], [[0, 0, 0]])
a = SpacegroupAnalyzer(s)
self.assertEqual(len(s), 4)
self.assertEqual(len(a.find_primitive()), 1)
def test_is_laue(self):
s = Structure.from_spacegroup("Fm-3m",
np.eye(3) * 3, ["Cu"], [[0, 0, 0]])
a = SpacegroupAnalyzer(s)
self.assertTrue(a.is_laue())
def test_magnetic(self):
lfp = PymatgenTest.get_structure("LiFePO4")
sg = SpacegroupAnalyzer(lfp, 0.1)
self.assertEqual(sg.get_space_group_symbol(), "Pnma")
magmoms = [0] * len(lfp)
magmoms[4] = 1
magmoms[5] = -1
magmoms[6] = 1
magmoms[7] = -1
lfp.add_site_property("magmom", magmoms)
sg = SpacegroupAnalyzer(lfp, 0.1)
self.assertEqual(sg.get_space_group_symbol(), "Pnma")
def test_get_space_symbol(self):
self.assertEqual(self.sg.get_space_group_symbol(), "Pnma")
self.assertEqual(self.disordered_sg.get_space_group_symbol(),
"P4_2/nmc")
self.assertEqual(self.sg3.get_space_group_symbol(), "Pnma")
self.assertEqual(self.sg4.get_space_group_symbol(), "P6_3/mmc")
def test_get_space_number(self):
self.assertEqual(self.sg.get_space_group_number(), 62)
self.assertEqual(self.disordered_sg.get_space_group_number(), 137)
self.assertEqual(self.sg4.get_space_group_number(), 194)
def test_get_hall(self):
self.assertEqual(self.sg.get_hall(), "-P 2ac 2n")
self.assertEqual(self.disordered_sg.get_hall(), "P 4n 2n -1n")
def test_get_pointgroup(self):
self.assertEqual(self.sg.get_point_group_symbol(), "mmm")
self.assertEqual(self.disordered_sg.get_point_group_symbol(), "4/mmm")
def test_get_symmetry_operations(self):
for sg, structure in [(self.sg, self.structure),
(self.sg4, self.structure4)]:
pgops = sg.get_point_group_operations()
fracsymmops = sg.get_symmetry_operations()
symmops = sg.get_symmetry_operations(True)
latt = structure.lattice
for fop, op, pgop in zip(fracsymmops, symmops, pgops):
# translation vector values should all be 0 or 0.5
t = fop.translation_vector * 2
self.assertArrayAlmostEqual(t - np.round(t), 0)
self.assertArrayAlmostEqual(fop.rotation_matrix,
pgop.rotation_matrix)
for site in structure:
newfrac = fop.operate(site.frac_coords)
newcart = op.operate(site.coords)
self.assertTrue(
np.allclose(latt.get_fractional_coords(newcart),
newfrac))
found = False
newsite = PeriodicSite(site.species,
newcart,
latt,
coords_are_cartesian=True)
for testsite in structure:
if newsite.is_periodic_image(testsite, 1e-3):
found = True
break
self.assertTrue(found)
# Make sure this works for any position, not just the atomic
# ones.
random_fcoord = np.random.uniform(size=(3))
random_ccoord = latt.get_cartesian_coords(random_fcoord)
newfrac = fop.operate(random_fcoord)
newcart = op.operate(random_ccoord)
self.assertTrue(
np.allclose(latt.get_fractional_coords(newcart), newfrac))
def test_get_symmetry_dataset(self):
ds = self.sg.get_symmetry_dataset()
self.assertEqual(ds["international"], "Pnma")
def test_get_crystal_system(self):
crystal_system = self.sg.get_crystal_system()
self.assertEqual("orthorhombic", crystal_system)
self.assertEqual("tetragonal", self.disordered_sg.get_crystal_system())
orig_spg = self.sg._space_group_data["number"]
self.sg._space_group_data["number"] = 0
try:
crystal_system = self.sg.get_crystal_system()
except ValueError as exc:
self.assertEqual(str(exc), "Received invalid space group 0")
finally:
self.sg._space_group_data["number"] = orig_spg
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
structure = self.get_structure("Li2O")
structure.add_site_property("magmom", [1.0] * len(structure))
sg = SpacegroupAnalyzer(structure, 0.01)
refined_struct = sg.get_refined_structure(keep_site_properties=True)
self.assertEqual(refined_struct.site_properties["magmom"],
[1.0] * len(refined_struct))
structure = self.get_structure("Li2O")
structure.add_site_property("magmom", [1.0] * len(structure))
sg = SpacegroupAnalyzer(structure, 0.01)
refined_struct = sg.get_refined_structure(keep_site_properties=False)
self.assertEqual(refined_struct.site_properties.get("magmom", None),
None)
def test_get_symmetrized_structure(self):
symm_struct = self.sg.get_symmetrized_structure()
for a in symm_struct.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(len(symm_struct.equivalent_sites), 5)
symm_struct = self.disordered_sg.get_symmetrized_structure()
self.assertEqual(len(symm_struct.equivalent_sites), 8)
self.assertEqual([len(i) for i in symm_struct.equivalent_sites],
[16, 4, 8, 4, 2, 8, 8, 8])
s1 = symm_struct.equivalent_sites[1][1]
s2 = symm_struct[symm_struct.equivalent_indices[1][1]]
self.assertEqual(s1, s2)
self.assertEqual(self.sg4.get_symmetrized_structure()[0].magmom, 0.1)
self.assertEqual(symm_struct.wyckoff_symbols[0], "16h")
# self.assertEqual(symm_struct[0].wyckoff, "16h")
# Check copying
self.assertEqual(symm_struct.copy(), symm_struct)
d = symm_struct.as_dict()
from pymatgen.symmetry.structure import SymmetrizedStructure
ss = SymmetrizedStructure.from_dict(d)
self.assertEqual(ss.wyckoff_symbols[0], "16h")
self.assertIn("SymmetrizedStructure", ss.__str__())
def test_find_primitive(self):
"""
F m -3 m Li2O testing of converting to primitive cell
"""
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "Li2O.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive()
self.assertEqual(primitive_structure.formula, "Li2 O1")
self.assertTrue(
primitive_structure.site_properties.get("magmom", None) is None)
# This isn't what is expected. All the angles should be 60
self.assertAlmostEqual(primitive_structure.lattice.alpha, 60)
self.assertAlmostEqual(primitive_structure.lattice.beta, 60)
self.assertAlmostEqual(primitive_structure.lattice.gamma, 60)
self.assertAlmostEqual(primitive_structure.lattice.volume,
structure.lattice.volume / 4.0)
structure = parser.get_structures(False)[0]
structure.add_site_property("magmom", [1.0] * len(structure))
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive(keep_site_properties=True)
self.assertEqual(primitive_structure.site_properties["magmom"],
[1.0] * len(primitive_structure))
structure = parser.get_structures(False)[0]
structure.add_site_property("magmom", [1.0] * len(structure))
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive(keep_site_properties=False)
self.assertEqual(
primitive_structure.site_properties.get("magmom", None), None)
def test_get_ir_reciprocal_mesh(self):
grid = self.sg.get_ir_reciprocal_mesh()
self.assertEqual(len(grid), 216)
self.assertAlmostEqual(grid[1][0][0], 0.1)
self.assertAlmostEqual(grid[1][0][1], 0.0)
self.assertAlmostEqual(grid[1][0][2], 0.0)
self.assertAlmostEqual(grid[1][1], 2)
def test_get_conventional_standard_structure(self):
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "bcc_1927.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.b, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.c, 9.1980270633769461)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "btet_1915.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.b, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.c, 4.2327080177761687)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "orci_1010.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 2.9542233922299999)
self.assertAlmostEqual(conv.lattice.b, 4.6330325651443296)
self.assertAlmostEqual(conv.lattice.c, 5.373703587040775)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "orcc_1003.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 4.1430033493799998)
self.assertAlmostEqual(conv.lattice.b, 31.437979757624728)
self.assertAlmostEqual(conv.lattice.c, 3.99648651)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "orac_632475.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 3.1790663399999999)
self.assertAlmostEqual(conv.lattice.b, 9.9032878699999998)
self.assertAlmostEqual(conv.lattice.c, 3.5372412099999999)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "monoc_1028.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 117.53832420192903)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 14.033435583000625)
self.assertAlmostEqual(conv.lattice.b, 3.96052850731)
self.assertAlmostEqual(conv.lattice.c, 6.8743926325200002)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "hex_1170.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 120)
self.assertAlmostEqual(conv.lattice.a, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.b, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.c, 6.9779585500000003)
structure = Structure.from_file(
os.path.join(PymatgenTest.TEST_FILES_DIR, "tric_684654.json"))
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 74.09581916308757)
self.assertAlmostEqual(conv.lattice.beta, 75.72817279281173)
self.assertAlmostEqual(conv.lattice.gamma, 63.63234318667333)
self.assertAlmostEqual(conv.lattice.a, 3.741372924048738)
self.assertAlmostEqual(conv.lattice.b, 3.9883228679270686)
self.assertAlmostEqual(conv.lattice.c, 7.288495840048958)
structure = Structure.from_file(
os.path.join(PymatgenTest.TEST_FILES_DIR, "tric_684654.json"))
structure.add_site_property("magmom", [1.0] * len(structure))
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure(keep_site_properties=True)
self.assertEqual(conv.site_properties["magmom"], [1.0] * len(conv))
structure = Structure.from_file(
os.path.join(PymatgenTest.TEST_FILES_DIR, "tric_684654.json"))
structure.add_site_property("magmom", [1.0] * len(structure))
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure(
keep_site_properties=False)
self.assertEqual(conv.site_properties.get("magmom", None), None)
def test_get_primitive_standard_structure(self):
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "bcc_1927.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.beta, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.gamma, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.a, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.b, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.c, 7.9657251015812145)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "btet_1915.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 105.015053349)
self.assertAlmostEqual(prim.lattice.beta, 105.015053349)
self.assertAlmostEqual(prim.lattice.gamma, 118.80658411899999)
self.assertAlmostEqual(prim.lattice.a, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.b, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.c, 4.1579321075608791)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "orci_1010.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 134.78923546600001)
self.assertAlmostEqual(prim.lattice.beta, 105.856239333)
self.assertAlmostEqual(prim.lattice.gamma, 91.276341676000001)
self.assertAlmostEqual(prim.lattice.a, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.b, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.c, 3.8428217771014852)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "orcc_1003.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 164.985257335)
self.assertAlmostEqual(prim.lattice.a, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.b, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.c, 3.99648651)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "orac_632475.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 144.40557588533386)
self.assertAlmostEqual(prim.lattice.a, 5.2005185662155391)
self.assertAlmostEqual(prim.lattice.b, 5.2005185662155391)
self.assertAlmostEqual(prim.lattice.c, 3.5372412099999999)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "monoc_1028.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 63.579155761999999)
self.assertAlmostEqual(prim.lattice.beta, 116.42084423747779)
self.assertAlmostEqual(prim.lattice.gamma, 148.47965136208569)
self.assertAlmostEqual(prim.lattice.a, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.b, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.c, 6.8743926325200002)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "hex_1170.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 120)
self.assertAlmostEqual(prim.lattice.a, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.b, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.c, 6.9779585500000003)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "rhomb_3478_conv.cif"))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.beta, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.gamma, 28.049186140546812)
self.assertAlmostEqual(prim.lattice.a, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.b, 5.9352627428399982)
self.assertAlmostEqual(prim.lattice.c, 5.9352627428399982)
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "rhomb_3478_conv.cif"))
structure = parser.get_structures(False)[0]
structure.add_site_property("magmom", [1.0] * len(structure))
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure(keep_site_properties=True)
self.assertEqual(prim.site_properties["magmom"], [1.0] * len(prim))
parser = CifParser(
os.path.join(PymatgenTest.TEST_FILES_DIR, "rhomb_3478_conv.cif"))
structure = parser.get_structures(False)[0]
structure.add_site_property("magmom", [1.0] * len(structure))
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure(keep_site_properties=False)
self.assertEqual(prim.site_properties.get("magmom", None), None)
def test_tricky_structure(self):
# for some reason this structure kills spglib1.9
# 1.7 can't find symmetry either, but at least doesn't kill python
s = Structure.from_file(
os.path.join(PymatgenTest.TEST_FILES_DIR,
"POSCAR.tricky_symmetry"))
sa = SpacegroupAnalyzer(s, 0.1)
sa.get_space_group_symbol()
sa.get_space_group_number()
sa.get_point_group_symbol()
sa.get_crystal_system()
sa.get_hall()
def apply_transformation(self, structure, return_ranked_list=False):
"""
Return either a single ordered structure or a sequence of all ordered
structures.
Args:
structure: Structure to order.
return_ranked_list (bool): Whether or not multiple structures are
returned. If return_ranked_list is a number, that number of
structures is returned.
Returns:
Depending on returned_ranked list, either a transformed structure
or a list of dictionaries, where each dictionary is of the form
{"structure" = .... , "other_arguments"}
The list of ordered structures is ranked by ewald energy / atom, if
the input structure is an oxidation state decorated structure.
Otherwise, it is ranked by number of sites, with smallest number of
sites first.
"""
try:
num_to_return = int(return_ranked_list)
except ValueError:
num_to_return = 1
if self.occu_tol:
species = [dict(d) for d in structure.species_and_occu]
# Here, we rescale all occupancies such that they meet the frac
# limit.
for sp in species:
for k, v in sp.items():
sp[k] = float(Fraction(v).limit_denominator(self.occu_tol))
structure = Structure(structure.lattice, species,
structure.frac_coords)
if self.refine_structure:
finder = SpacegroupAnalyzer(structure, self.symm_prec)
structure = finder.get_refined_structure()
contains_oxidation_state = all(
[hasattr(sp, "oxi_state") and sp.oxi_state != 0 for sp in
structure.composition.elements]
)
if structure.is_ordered:
warn("Enumeration skipped for structure with composition {} "
"because it is ordered".format(structure.composition))
structures = [structure.copy()]
else:
adaptor = EnumlibAdaptor(
structure, min_cell_size=self.min_cell_size,
max_cell_size=self.max_cell_size,
symm_prec=self.symm_prec, refine_structure=False,
enum_precision_parameter=self.enum_precision_parameter,
check_ordered_symmetry=self.check_ordered_symmetry)
adaptor.run()
structures = adaptor.structures
original_latt = structure.lattice
inv_latt = np.linalg.inv(original_latt.matrix)
ewald_matrices = {}
all_structures = []
for s in structures:
new_latt = s.lattice
transformation = np.dot(new_latt.matrix, inv_latt)
transformation = tuple([tuple([int(round(cell)) for cell in row])
for row in transformation])
if contains_oxidation_state:
if transformation not in ewald_matrices:
s_supercell = structure * transformation
ewald = EwaldSummation(s_supercell)
ewald_matrices[transformation] = ewald
else:
ewald = ewald_matrices[transformation]
energy = ewald.compute_sub_structure(s)
all_structures.append({"num_sites": len(s), "energy": energy,
"structure": s})
else:
all_structures.append({"num_sites": len(s), "structure": s})
def sort_func(s):
return s["energy"] / s["num_sites"] if contains_oxidation_state \
else s["num_sites"]
self._all_structures = sorted(all_structures, key=sort_func)
if return_ranked_list:
return self._all_structures[0:num_to_return]
else:
return self._all_structures[0]["structure"]
def convert_to_ieee(self, structure, atol = 0.1, ltol = 0.05):
"""
Given a structure associated with a tensor, attempts a
calculation of the tensor in IEEE format according to
the 1987 IEEE standards.
Args:
structure (Structure): a structure associated with the
tensor to be converted to the IEEE standard
atol (float): angle tolerance for conversion routines
ltol (float): length tolerance for conversion routines
"""
def get_uvec(vec):
""" Gets a unit vector parallel to input vector"""
return vec / np.linalg.norm(vec)
vecs = structure.lattice.matrix
lengths = np.array(structure.lattice.abc)
angles = np.array(structure.lattice.angles)
# Check conventional setting:
sga = SpacegroupAnalyzer(structure)
xtal_sys = sga.get_crystal_system()
conv_struct = sga.get_refined_structure()
conv_lengths = np.array(conv_struct.lattice.abc)
conv_angles = np.array(conv_struct.lattice.angles)
rhombohedral = xtal_sys == "trigonal" and \
(angles - angles[0] < atol).all()
if ((np.sort(lengths) - np.sort(conv_lengths) > ltol).any() \
or (np.sort(angles) - np.sort(conv_angles) > atol).any() \
or len(structure.sites) != len(conv_struct.sites)) \
and not rhombohedral:
raise ValueError("{} structure not in conventional cell, IEEE "\
"conversion from non-conventional settings "\
"is not yet supported.".format(xtal_sys))
a = b = c = None
rotation = np.zeros((3,3))
# IEEE rules: a,b,c || x1,x2,x3
if xtal_sys == "cubic":
rotation = [vecs[i]/lengths[i] for i in range(3)]
# IEEE rules: a=b in length; c,a || x3, x1
elif xtal_sys == "tetragonal":
rotation = np.array([vec/mag for (mag, vec) in
sorted(zip(lengths, vecs))])
if abs(lengths[2] - lengths[1]) < ltol:
rotation[0], rotation[2] = rotation[2], rotation[0].copy()
rotation[1] = get_uvec(np.cross(rotation[2], rotation[0]))
# IEEE rules: c<a<b; c,a || x3,x1
elif xtal_sys == "orthorhombic":
rotation = [vec/mag for (mag, vec) in sorted(zip(lengths, vecs))]
rotation = np.roll(rotation, 2, axis = 0)
# IEEE rules: c,a || x3,x1, c is threefold axis
elif xtal_sys in ("trigonal", "hexagonal"):
# Rhombohedral lattice
if rhombohedral:
rotation[0] = get_uvec(vecs[2] - vecs[0])
rotation[2] = get_uvec(np.sum(vecs, axis=0))
rotation[1] = get_uvec(np.cross(rotation[2], rotation[0]))
# Standard hexagonal lattice
else:
# find threefold axis:
tf_mask = np.where(abs(angles-120.0) < atol)
non_tf_mask = np.logical_not(tf_mask)
rotation[2] = get_uvec(vecs[tf_mask])
rotation[0] = get_uvec(vecs[non_tf_mask][0])
rotation[1] = get_uvec(np.cross(rotation[2], rotation[0]))
# IEEE rules: b,c || x2,x3; alpha=beta=90, c<a
elif xtal_sys == "monoclinic":
# Find unique axis
umask = abs(angles - 90.0) > atol
n_umask = np.logical_not(umask)
rotation[1] = get_uvec(vecs[umask])
# Shorter of remaining lattice vectors for c axis
c = [vec/mag for (mag, vec) in
sorted(zip(lengths[n_umask], vecs[n_umask]))][0]
rotation[2] = np.array(c)
rotation[0] = np.cross(rotation[1], rotation[2])
# IEEE rules: c || x3
elif xtal_sys == "triclinic":
rotation = [vec/mag for (mag, vec) in sorted(zip(lengths, vecs))]
rotation = np.roll(rotation, 2, axis = 0)
rotation[1] = get_uvec(np.cross(rotation[2], rotation[1]))
rotation[0] = np.cross(rotation[1], rotation[2])
return self.rotate(rotation)
def apply_transformation(self, structure, return_ranked_list=False):
"""
Return either a single ordered structure or a sequence of all ordered
structures.
Args:
structure: Structure to order.
return_ranked_list (bool): Whether or not multiple structures are
returned. If return_ranked_list is a number, that number of
structures is returned.
Returns:
Depending on returned_ranked list, either a transformed structure
or a list of dictionaries, where each dictionary is of the form
{"structure" = .... , "other_arguments"}
The list of ordered structures is ranked by ewald energy / atom, if
the input structure is an oxidation state decorated structure.
Otherwise, it is ranked by number of sites, with smallest number of
sites first.
"""
try:
num_to_return = int(return_ranked_list)
except ValueError:
num_to_return = 1
if self.refine_structure:
finder = SpacegroupAnalyzer(structure, self.symm_prec)
structure = finder.get_refined_structure()
contains_oxidation_state = all(
[hasattr(sp, "oxi_state") and sp.oxi_state != 0 for sp in
structure.composition.elements]
)
structures = None
if structure.is_ordered:
warn("Enumeration skipped for structure with composition {} "
"because it is ordered".format(structure.composition))
structures = [structure.copy()]
if self.max_disordered_sites:
ndisordered = sum([1 for site in structure if not site.is_ordered])
if ndisordered > self.max_disordered_sites:
raise ValueError(
"Too many disordered sites! ({} > {})".format(
ndisordered, self.max_disordered_sites))
max_cell_sizes = range(self.min_cell_size, int(
math.floor(self.max_disordered_sites / ndisordered)) + 1)
else:
max_cell_sizes = [self.max_cell_size]
for max_cell_size in max_cell_sizes:
adaptor = EnumlibAdaptor(
structure, min_cell_size=self.min_cell_size,
max_cell_size=max_cell_size,
symm_prec=self.symm_prec, refine_structure=False,
enum_precision_parameter=self.enum_precision_parameter,
check_ordered_symmetry=self.check_ordered_symmetry,
timeout=self.timeout)
try:
adaptor.run()
except EnumError:
warn("Unable to enumerate for max_cell_size = %d".format(
max_cell_size))
structures = adaptor.structures
if structures:
break
if structures is None:
raise ValueError("Unable to enumerate")
original_latt = structure.lattice
inv_latt = np.linalg.inv(original_latt.matrix)
ewald_matrices = {}
all_structures = []
for s in structures:
new_latt = s.lattice
transformation = np.dot(new_latt.matrix, inv_latt)
transformation = tuple([tuple([int(round(cell)) for cell in row])
for row in transformation])
if contains_oxidation_state and self.sort_criteria == "ewald":
if transformation not in ewald_matrices:
s_supercell = structure * transformation
ewald = EwaldSummation(s_supercell)
ewald_matrices[transformation] = ewald
else:
ewald = ewald_matrices[transformation]
energy = ewald.compute_sub_structure(s)
all_structures.append({"num_sites": len(s), "energy": energy,
"structure": s})
else:
all_structures.append({"num_sites": len(s), "structure": s})
def sort_func(s):
return s["energy"] / s["num_sites"] \
if contains_oxidation_state and self.sort_criteria == "ewald" \
else s["num_sites"]
self._all_structures = sorted(all_structures, key=sort_func)
if return_ranked_list:
return self._all_structures[0:num_to_return]
else:
return self._all_structures[0]["structure"]
def get_pattern(self, structure, scale_intensity=True, two_theta_range=None):
"""
Calculates the diffraction pattern for a structure.
Args:
structure (Structure): Input structure
scale_intensity (bool): Whether to return scaled intensities. The maximum
peak is set to a value of 100. Defaults to True. Use False if
you need the absolute values to combine XRD plots.
two_theta_range ([float of length 2]): Tuple for range of
two_thetas to calculate in degrees. Defaults to (0, 90). Set to
None if you want all diffracted beams within the limiting
sphere of radius 2 / wavelength.
Returns:
XRDPattern,
list of features for point cloud representation,
recip_latt
"""
try:
assert(self.symprec == 0)
except:
print('symprec is not zero, terminate the process and check your input..')
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
latt = structure.lattice
volume = structure.volume
is_hex = latt.is_hexagonal()
# Obtained from Bragg condition. Note that reciprocal lattice
# vector length is 1 / d_hkl.
try:
assert(two_theta_range == None)
except:
print('two theta range is not None, terminate the process and check your input..')
min_r, max_r = (0., 2. / self.wavelength) if two_theta_range is None else \
[2 * math.sin(math.radians(t / 2)) / self.wavelength for t in two_theta_range]
# Obtain crystallographic reciprocal lattice points within range
# recip_pts entry: [coord, distance, index, image]
recip_latt = latt.reciprocal_lattice_crystallographic
recip_pts = recip_latt.get_points_in_sphere(
[[0, 0, 0]], [0, 0, 0], max_r)
if min_r:
recip_pts = [pt for pt in recip_pts if pt[1] >= min_r]
# Create a flattened array of zs, coeffs, fcoords and occus. This is
# used to perform vectorized computation of atomic scattering factors
# later. Note that these are not necessarily the same size as the
# structure as each partially occupied specie occupies its own
# position in the flattened array.
zs = []
coeffs = []
fcoords = []
occus = []
for site in structure:
# do not consider mixed species at the same site
try:
assert(len(site.species.items()) == 1)
except:
print('mixed species at the same site detected, abort..')
for sp, occu in site.species.items():
zs.append(sp.Z)
try:
c = ATOMIC_SCATTERING_PARAMS[sp.symbol]
except KeyError:
raise ValueError("Unable to calculate XRD pattern as "
"there is no scattering coefficients for"
" %s." % sp.symbol)
coeffs.append(c)
fcoords.append(site.frac_coords)
occus.append(occu)
zs = np.array(zs)
coeffs = np.array(coeffs)
fcoords = np.array(fcoords)
occus = np.array(occus)
try:
assert(np.max(occus) == np.min(occus) == 1) # all sites should be singly occupied
except:
print('check occupancy values...')
peaks = {}
two_thetas = []
total_electrons = sum(zs)
features = [[0, 0, 0, float(total_electrons/volume)**2]]
for hkl, g_hkl, _, _ in sorted(recip_pts,
key=lambda i: (i[1], -i[0][0], -i[0][1], -i[0][2])):
# skip origin and points on the limiting sphere to avoid precision problems
if (g_hkl < 1e-4) or (g_hkl > 2./self.wavelength): continue
d_hkl = 1. / g_hkl
# Bragg condition
theta = math.asin(self.wavelength * g_hkl / 2)
# s = sin(theta) / wavelength = 1 / 2d = |ghkl| / 2 (d =
# 1/|ghkl|)
s = g_hkl / 2
# Store s^2 since we are using it a few times.
s2 = s ** 2
# Vectorized computation of g.r for all fractional coords and
# hkl. Output size is N_atom
g_dot_r = np.dot(fcoords, np.transpose([hkl])).T[0]
# Highly vectorized computation of atomic scattering factors.
# Equivalent non-vectorized code is::
#
# for site in structure:
# el = site.specie
# coeff = ATOMIC_SCATTERING_PARAMS[el.symbol]
# fs = el.Z - 41.78214 * s2 * sum(
# [d[0] * exp(-d[1] * s2) for d in coeff])
fs = zs - 41.78214 * s2 * np.sum(
coeffs[:, :, 0] * np.exp(-coeffs[:, :, 1] * s2), axis=1)
# Structure factor = sum of atomic scattering factors (with
# position factor exp(2j * pi * g.r and occupancies).
# Vectorized computation.
f_hkl = np.sum(fs * occus * np.exp(2j * math.pi * g_dot_r))
# Lorentz polarization correction for hkl
lorentz_factor = (1 + math.cos(2 * theta) ** 2) / \
(math.sin(theta) ** 2 * math.cos(theta))
# Intensity for hkl is modulus square of structure factor.
i_hkl = (f_hkl * f_hkl.conjugate()).real
try:
assert(i_hkl < total_electrons**2)
except:
print('assertion failed, check I_hkl values..')
i_hkl_out = i_hkl / volume**2
# add to features
features.append([hkl[0], hkl[1], hkl[2], i_hkl_out])
### for diffractin pattern plotting only
two_theta = math.degrees(2 * theta)
if is_hex:
# Use Miller-Bravais indices for hexagonal lattices.
hkl = (hkl[0], hkl[1], - hkl[0] - hkl[1], hkl[2])
# Deal with floating point precision issues.
ind = np.where(np.abs(np.subtract(two_thetas, two_theta)) <
AbstractDiffractionPatternCalculator.TWO_THETA_TOL)
if len(ind[0]) > 0:
peaks[two_thetas[ind[0][0]]][0] += i_hkl * lorentz_factor
peaks[two_thetas[ind[0][0]]][1].append(tuple(hkl))
else:
peaks[two_theta] = [i_hkl * lorentz_factor, [tuple(hkl)],
d_hkl]
two_thetas.append(two_theta)
# Scale intensities so that the max intensity is 100.
max_intensity = max([v[0] for v in peaks.values()])
x = []
y = []
hkls = []
d_hkls = []
for k in sorted(peaks.keys()):
v = peaks[k]
fam = get_unique_families(v[1])
if v[0] / max_intensity * 100 > AbstractDiffractionPatternCalculator.SCALED_INTENSITY_TOL:
x.append(k)
y.append(v[0])
hkls.append([{"hkl": hkl, "multiplicity": mult}
for hkl, mult in fam.items()])
d_hkls.append(v[2])
xrd = DiffractionPattern(x, y, hkls, d_hkls)
if scale_intensity:
xrd.normalize(mode="max", value=100)
return xrd, recip_latt.matrix, features
class SpacegroupAnalyzerTest(PymatgenTest):
def setUp(self):
p = Poscar.from_file(os.path.join(test_dir, 'POSCAR'))
self.structure = p.structure
self.sg = SpacegroupAnalyzer(self.structure, 0.001)
self.disordered_structure = self.get_structure('Li10GeP2S12')
self.disordered_sg = SpacegroupAnalyzer(self.disordered_structure, 0.001)
s = p.structure.copy()
site = s[0]
del s[0]
s.append(site.species_and_occu, site.frac_coords)
self.sg3 = SpacegroupAnalyzer(s, 0.001)
graphite = self.get_structure('Graphite')
graphite.add_site_property("magmom", [0.1] * len(graphite))
self.sg4 = SpacegroupAnalyzer(graphite, 0.001)
def test_get_space_symbol(self):
self.assertEqual(self.sg.get_spacegroup_symbol(), "Pnma")
self.assertEqual(self.disordered_sg.get_spacegroup_symbol(),
"P4_2/nmc")
self.assertEqual(self.sg3.get_spacegroup_symbol(), "Pnma")
self.assertEqual(self.sg4.get_spacegroup_symbol(), "R-3m")
def test_get_space_number(self):
self.assertEqual(self.sg.get_spacegroup_number(), 62)
self.assertEqual(self.disordered_sg.get_spacegroup_number(), 137)
self.assertEqual(self.sg4.get_spacegroup_number(), 166)
def test_get_hall(self):
self.assertEqual(self.sg.get_hall(), '-P 2ac 2n')
self.assertEqual(self.disordered_sg.get_hall(), 'P 4n 2n -1n')
def test_get_pointgroup(self):
self.assertEqual(self.sg.get_point_group(), 'mmm')
self.assertEqual(self.disordered_sg.get_point_group(), '4/mmm')
def test_get_symmetry_dataset(self):
ds = self.sg.get_symmetry_dataset()
self.assertEqual(ds['international'], 'Pnma')
def test_get_crystal_system(self):
crystal_system = self.sg.get_crystal_system()
self.assertEqual('orthorhombic', crystal_system)
self.assertEqual('tetragonal', self.disordered_sg.get_crystal_system())
def test_get_symmetry_operations(self):
fracsymmops = self.sg.get_symmetry_operations()
symmops = self.sg.get_symmetry_operations(True)
self.assertEqual(len(symmops), 8)
latt = self.structure.lattice
for fop, op in zip(fracsymmops, symmops):
for site in self.structure:
newfrac = fop.operate(site.frac_coords)
newcart = op.operate(site.coords)
self.assertTrue(np.allclose(latt.get_fractional_coords(newcart),
newfrac))
found = False
newsite = PeriodicSite(site.species_and_occu, newcart, latt,
coords_are_cartesian=True)
for testsite in self.structure:
if newsite.is_periodic_image(testsite, 1e-3):
found = True
break
self.assertTrue(found)
def test_get_refined_structure(self):
for a in self.sg.get_refined_structure().lattice.angles:
self.assertEqual(a, 90)
refined = self.disordered_sg.get_refined_structure()
for a in refined.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(refined.lattice.a, refined.lattice.b)
s = self.get_structure('Li2O')
sg = SpacegroupAnalyzer(s, 0.001)
self.assertEqual(sg.get_refined_structure().num_sites, 4 * s.num_sites)
def test_get_symmetrized_structure(self):
symm_struct = self.sg.get_symmetrized_structure()
for a in symm_struct.lattice.angles:
self.assertEqual(a, 90)
self.assertEqual(len(symm_struct.equivalent_sites), 5)
symm_struct = self.disordered_sg.get_symmetrized_structure()
self.assertEqual(len(symm_struct.equivalent_sites), 8)
self.assertEqual([len(i) for i in symm_struct.equivalent_sites],
[16,4,8,4,2,8,8,8])
s1 = symm_struct.equivalent_sites[1][1]
s2 = symm_struct[symm_struct.equivalent_indices[1][1]]
self.assertEqual(s1, s2)
self.assertEqual(self.sg4.get_symmetrized_structure()[0].magmom, 0.1)
def test_find_primitive(self):
"""
F m -3 m Li2O testing of converting to primitive cell
"""
parser = CifParser(os.path.join(test_dir, 'Li2O.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure)
primitive_structure = s.find_primitive()
self.assertEqual(primitive_structure.formula, "Li2 O1")
# This isn't what is expected. All the angles should be 60
self.assertAlmostEqual(primitive_structure.lattice.alpha, 60)
self.assertAlmostEqual(primitive_structure.lattice.beta, 60)
self.assertAlmostEqual(primitive_structure.lattice.gamma, 60)
self.assertAlmostEqual(primitive_structure.lattice.volume,
structure.lattice.volume / 4.0)
def test_get_ir_reciprocal_mesh(self):
grid=self.sg.get_ir_reciprocal_mesh()
self.assertEqual(len(grid), 216)
self.assertAlmostEquals(grid[1][0][0], 0.1)
self.assertAlmostEquals(grid[1][0][1], 0.0)
self.assertAlmostEquals(grid[1][0][2], 0.0)
self.assertEqual(grid[1][1], 2)
def test_get_conventional_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.b, 9.1980270633769461)
self.assertAlmostEqual(conv.lattice.c, 9.1980270633769461)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.b, 5.0615106678044235)
self.assertAlmostEqual(conv.lattice.c, 4.2327080177761687)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 2.9542233922299999)
self.assertAlmostEqual(conv.lattice.b, 4.6330325651443296)
self.assertAlmostEqual(conv.lattice.c, 5.373703587040775)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 4.1430033493799998)
self.assertAlmostEqual(conv.lattice.b, 31.437979757624728)
self.assertAlmostEqual(conv.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 117.53832420192903)
self.assertAlmostEqual(conv.lattice.gamma, 90)
self.assertAlmostEqual(conv.lattice.a, 14.033435583000625)
self.assertAlmostEqual(conv.lattice.b, 3.96052850731)
self.assertAlmostEqual(conv.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'rhomb_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
conv = s.get_conventional_standard_structure()
self.assertAlmostEqual(conv.lattice.alpha, 90)
self.assertAlmostEqual(conv.lattice.beta, 90)
self.assertAlmostEqual(conv.lattice.gamma, 120)
self.assertAlmostEqual(conv.lattice.a, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.b, 3.699919902005897)
self.assertAlmostEqual(conv.lattice.c, 6.9779585500000003)
def test_get_primitive_standard_structure(self):
parser = CifParser(os.path.join(test_dir, 'bcc_1927.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.beta, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.gamma, 109.47122063400001)
self.assertAlmostEqual(prim.lattice.a, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.b, 7.9657251015812145)
self.assertAlmostEqual(prim.lattice.c, 7.9657251015812145)
parser = CifParser(os.path.join(test_dir, 'btet_1915.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 105.015053349)
self.assertAlmostEqual(prim.lattice.beta, 105.015053349)
self.assertAlmostEqual(prim.lattice.gamma, 118.80658411899999)
self.assertAlmostEqual(prim.lattice.a, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.b, 4.1579321075608791)
self.assertAlmostEqual(prim.lattice.c, 4.1579321075608791)
parser = CifParser(os.path.join(test_dir, 'orci_1010.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 134.78923546600001)
self.assertAlmostEqual(prim.lattice.beta, 105.856239333)
self.assertAlmostEqual(prim.lattice.gamma, 91.276341676000001)
self.assertAlmostEqual(prim.lattice.a, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.b, 3.8428217771014852)
self.assertAlmostEqual(prim.lattice.c, 3.8428217771014852)
parser = CifParser(os.path.join(test_dir, 'orcc_1003.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 164.985257335)
self.assertAlmostEqual(prim.lattice.a, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.b, 15.854897098324196)
self.assertAlmostEqual(prim.lattice.c, 3.99648651)
parser = CifParser(os.path.join(test_dir, 'monoc_1028.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 63.579155761999999)
self.assertAlmostEqual(prim.lattice.beta, 116.42084423747779)
self.assertAlmostEqual(prim.lattice.gamma, 148.47965136208569)
self.assertAlmostEqual(prim.lattice.a, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.b, 7.2908007159612325)
self.assertAlmostEqual(prim.lattice.c, 6.8743926325200002)
parser = CifParser(os.path.join(test_dir, 'rhomb_1170.cif'))
structure = parser.get_structures(False)[0]
s = SpacegroupAnalyzer(structure, symprec=1e-2)
prim = s.get_primitive_standard_structure()
self.assertAlmostEqual(prim.lattice.alpha, 90)
self.assertAlmostEqual(prim.lattice.beta, 90)
self.assertAlmostEqual(prim.lattice.gamma, 120)
self.assertAlmostEqual(prim.lattice.a, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.b, 3.699919902005897)
self.assertAlmostEqual(prim.lattice.c, 6.9779585500000003)
def get_pattern(self, structure, scaled=True, two_theta_range=(0, 90)):
"""
Calculates the diffraction pattern for a structure.
Args:
structure (Structure): Input structure
scaled (bool): Whether to return scaled intensities. The maximum
peak is set to a value of 100. Defaults to True. Use False if
you need the absolute values to combine XRD plots.
two_theta_range ([float of length 2]): Tuple for range of
two_thetas to calculate in degrees. Defaults to (0, 90). Set to
None if you want all diffracted beams within the limiting
sphere of radius 2 / wavelength.
Returns:
(XRDPattern)
"""
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
wavelength = self.wavelength
latt = structure.lattice
is_hex = latt.is_hexagonal()
# Obtained from Bragg condition. Note that reciprocal lattice
# vector length is 1 / d_hkl.
min_r, max_r = ((0, 2 / wavelength) if two_theta_range is None else [
2 * sin(radians(t / 2)) / wavelength for t in two_theta_range
])
# Obtain crystallographic reciprocal lattice points within range
recip_latt = latt.reciprocal_lattice_crystallographic
recip_pts = recip_latt.get_points_in_sphere([[0, 0, 0]], [0, 0, 0],
max_r)
if min_r:
recip_pts = [pt for pt in recip_pts if pt[1] >= min_r]
# Create a flattened array of zs, coeffs, fcoords and occus. This is
# used to perform vectorized computation of atomic scattering factors
# later. Note that these are not necessarily the same size as the
# structure as each partially occupied specie occupies its own
# position in the flattened array.
zs = []
coeffs = []
fcoords = []
occus = []
dwfactors = []
for site in structure:
for sp, occu in site.species.items():
zs.append(sp.Z)
try:
c = ATOMIC_SCATTERING_PARAMS[sp.symbol]
except KeyError:
raise ValueError("Unable to calculate XRD pattern as "
"there is no scattering coefficients for"
" %s." % sp.symbol)
coeffs.append(c)
dwfactors.append(self.debye_waller_factors.get(sp.symbol, 0))
fcoords.append(site.frac_coords)
occus.append(occu)
zs = np.array(zs)
coeffs = np.array(coeffs)
fcoords = np.array(fcoords)
occus = np.array(occus)
dwfactors = np.array(dwfactors)
peaks = {}
two_thetas = []
for hkl, g_hkl, ind, _ in sorted(recip_pts,
key=lambda i:
(i[1], -i[0][0], -i[0][1], -i[0][2])):
# Force miller indices to be integers.
hkl = [int(round(i)) for i in hkl]
if g_hkl != 0:
d_hkl = 1 / g_hkl
# Bragg condition
theta = asin(wavelength * g_hkl / 2)
# s = sin(theta) / wavelength = 1 / 2d = |ghkl| / 2 (d =
# 1/|ghkl|)
s = g_hkl / 2
# Store s^2 since we are using it a few times.
s2 = s**2
# Vectorized computation of g.r for all fractional coords and
# hkl.
g_dot_r = np.dot(fcoords, np.transpose([hkl])).T[0]
# Highly vectorized computation of atomic scattering factors.
# Equivalent non-vectorized code is::
#
# for site in structure:
# el = site.specie
# coeff = ATOMIC_SCATTERING_PARAMS[el.symbol]
# fs = el.Z - 41.78214 * s2 * sum(
# [d[0] * exp(-d[1] * s2) for d in coeff])
fs = zs - 41.78214 * s2 * np.sum(
coeffs[:, :, 0] * np.exp(-coeffs[:, :, 1] * s2), axis=1)
dw_correction = np.exp(-dwfactors * s2)
# Structure factor = sum of atomic scattering factors (with
# position factor exp(2j * pi * g.r and occupancies).
# Vectorized computation.
f_hkl = np.sum(fs * occus * np.exp(2j * pi * g_dot_r) *
dw_correction)
# Lorentz polarization correction for hkl
lorentz_factor = (1 + cos(2 * theta)**2) / (sin(theta)**2 *
cos(theta))
# Intensity for hkl is modulus square of structure factor.
i_hkl = (f_hkl * f_hkl.conjugate()).real
two_theta = degrees(2 * theta)
if is_hex:
# Use Miller-Bravais indices for hexagonal lattices.
hkl = (hkl[0], hkl[1], -hkl[0] - hkl[1], hkl[2])
# Deal with floating point precision issues.
ind = np.where(
np.abs(np.subtract(two_thetas, two_theta)) <
AbstractDiffractionPatternCalculator.TWO_THETA_TOL)
if len(ind[0]) > 0:
peaks[two_thetas[ind[0][0]]][0] += i_hkl * lorentz_factor
peaks[two_thetas[ind[0][0]]][1].append(tuple(hkl))
else:
peaks[two_theta] = [
i_hkl * lorentz_factor, [tuple(hkl)], d_hkl
]
two_thetas.append(two_theta)
# Scale intensities so that the max intensity is 100.
max_intensity = max(v[0] for v in peaks.values())
x = []
y = []
hkls = []
d_hkls = []
for k in sorted(peaks.keys()):
v = peaks[k]
fam = get_unique_families(v[1])
if v[0] / max_intensity * 100 > AbstractDiffractionPatternCalculator.SCALED_INTENSITY_TOL:
x.append(k)
y.append(v[0])
hkls.append([{
"hkl": hkl,
"multiplicity": mult
} for hkl, mult in fam.items()])
d_hkls.append(v[2])
xrd = DiffractionPattern(x, y, hkls, d_hkls)
if scaled:
xrd.normalize(mode="max", value=100)
return xrd
def get_pattern(self, structure, scaled=True, two_theta_range=None):
"""
Calculates the powder neutron diffraction pattern for a structure.
Args:
structure (Structure): Input structure
scaled (bool): Whether to return scaled intensities. The maximum
peak is set to a value of 100. Defaults to True. Use False if
you need the absolute values to combine ND plots.
two_theta_range ([float of length 2]): Tuple for range of
two_thetas to calculate in degrees. Defaults to (0, 90). Set to
None if you want all diffracted beams within the limiting
sphere of radius 2 / wavelength.
Returns:
(NDPattern)
"""
try:
assert(self.symprec == 0)
except:
print('symprec is not zero, terminate the process and check your input..')
if self.symprec:
finder = SpacegroupAnalyzer(structure, symprec=self.symprec)
structure = finder.get_refined_structure()
skip = False # in case element does not have neutron scattering length
wavelength = self.wavelength
latt = structure.lattice
volume = structure.volume
is_hex = latt.is_hexagonal()
# Obtained from Bragg condition. Note that reciprocal lattice
# vector length is 1 / d_hkl.
try:
assert(two_theta_range == None)
except:
print('two theta range is not None, terminate the process and check your input..')
min_r, max_r = (
(0, 2 / wavelength)
if two_theta_range is None
else [2 * math.sin(radians(t / 2)) / wavelength for t in two_theta_range]
)
# Obtain crystallographic reciprocal lattice points within range
recip_latt = latt.reciprocal_lattice_crystallographic
recip_pts = recip_latt.get_points_in_sphere([[0, 0, 0]], [0, 0, 0], max_r)
if min_r:
recip_pts = [pt for pt in recip_pts if pt[1] >= min_r]
# Create a flattened array of coeffs, fcoords and occus. This is
# used to perform vectorized computation of atomic scattering factors
# later. Note that these are not necessarily the same size as the
# structure as each partially occupied specie occupies its own
# position in the flattened array.
coeffs = []
fcoords = []
occus = []
dwfactors = []
for site in structure:
# do not consider mixed species at the same site
try:
assert(len(site.species.items()) == 1)
except:
print('mixed species at the same site detected, abort..')
for sp, occu in site.species.items():
try:
c = ATOMIC_SCATTERING_LEN[sp.symbol]
except KeyError:
print("Unable to calculate ND pattern as "
"there is no scattering coefficients for"
" {}.".format(sp.symbol))
# quick return
return None, None, None
coeffs.append(c)
fcoords.append(site.frac_coords)
occus.append(occu)
dwfactors.append(self.debye_waller_factors.get(sp.symbol, 0))
coeffs = np.array(coeffs)
fcoords = np.array(fcoords)
occus = np.array(occus)
try:
assert(np.max(occus) == np.min(occus) == 1) # all sites should be singly occupied
except:
print('check occupancy values...')
dwfactors = np.array(dwfactors)
peaks = {}
two_thetas = []
total_coeffs = sum(coeffs)
features = [[0, 0, 0, float(total_coeffs/volume)**2]]
for hkl, g_hkl, ind, _ in sorted(recip_pts,
key=lambda i: (i[1], -i[0][0], -i[0][1], -i[0][2])):
# skip origin and points on the limiting sphere to avoid precision problems
if (g_hkl < 1e-4) or (g_hkl > 2./self.wavelength): continue
# Force miller indices to be integers.
hkl = [int(round(i)) for i in hkl]
d_hkl = 1 / g_hkl
# Bragg condition
theta = math.asin(wavelength * g_hkl / 2)
# s = sin(theta) / wavelength = 1 / 2d = |ghkl| / 2 (d =
# 1/|ghkl|)
s = g_hkl / 2
# Calculate Debye-Waller factor
dw_correction = np.exp(-dwfactors * (s ** 2))
# Vectorized computation of g.r for all fractional coords and
# hkl.
g_dot_r = np.dot(fcoords, np.transpose([hkl])).T[0]
# Structure factor = sum of atomic scattering factors (with
# position factor exp(2j * pi * g.r and occupancies).
# Vectorized computation.
f_hkl = np.sum(
#coeffs * occus * np.exp(2j * math.pi * g_dot_r) * dw_correction
coeffs * occus * np.exp(2j * math.pi * g_dot_r)
)
# Lorentz polarization correction for hkl
lorentz_factor = 1 / (math.sin(theta) ** 2 * math.cos(theta))
# Intensity for hkl is modulus square of structure factor.
i_hkl = (f_hkl * f_hkl.conjugate()).real
i_hkl_out = i_hkl / volume**2
# add to features
features.append([hkl[0], hkl[1], hkl[2], i_hkl_out])
two_theta = math.degrees(2 * theta)
if is_hex:
# Use Miller-Bravais indices for hexagonal lattices.
hkl = (hkl[0], hkl[1], -hkl[0] - hkl[1], hkl[2])
# Deal with floating point precision issues.
ind = np.where(
np.abs(np.subtract(two_thetas, two_theta)) < self.TWO_THETA_TOL
)
if len(ind[0]) > 0:
peaks[two_thetas[ind[0][0]]][0] += i_hkl * lorentz_factor
peaks[two_thetas[ind[0][0]]][1].append(tuple(hkl))
else:
peaks[two_theta] = [i_hkl * lorentz_factor, [tuple(hkl)], d_hkl]
two_thetas.append(two_theta)
# Scale intensities so that the max intensity is 100.
max_intensity = max([v[0] for v in peaks.values()])
x = []
y = []
hkls = []
d_hkls = []
for k in sorted(peaks.keys()):
v = peaks[k]
fam = get_unique_families(v[1])
if v[0] / max_intensity * 100 > self.SCALED_INTENSITY_TOL:
x.append(k)
y.append(v[0])
hkls.append(
[{"hkl": hkl, "multiplicity": mult} for hkl, mult in fam.items()]
)
d_hkls.append(v[2])
nd = DiffractionPattern(x, y, hkls, d_hkls)
if scaled:
nd.normalize(mode="max", value=100)
return nd, recip_latt.matrix, features
