def get_vector_library(self, reciprocal_radius):
"""Calculates a library of diffraction vectors and pairwise inter-vector
angles for a library of crystal structures.
Parameters
----------
reciprocal_radius : float
The maximum g-vector magnitude to be included in the library.
Returns
-------
vector_library : :class:`DiffractionVectorLibrary`
Mapping of phase identifier to a numpy array with entries in the
form: [hkl1, hkl2, len1, len2, angle] ; lengths are in reciprocal
Angstroms and angles are in radians.
"""
# Define DiffractionVectorLibrary object to contain results
vector_library = DiffractionVectorLibrary()
# Get structures from structure library
structure_library = self.structures.struct_lib
# Iterate through phases in library.
for phase_name in structure_library.keys():
# Get diffpy.structure object associated with phase
structure = structure_library[phase_name][0]
# Get reciprocal lattice points within reciprocal_radius
recip_latt = structure.lattice.reciprocal()
indices, coordinates, distances = get_points_in_sphere(
recip_latt, reciprocal_radius)
# Iterate through all pairs calculating interplanar angle
phase_vector_pairs = []
for comb in itertools.combinations(np.arange(len(indices)), 2):
i, j = comb[0], comb[1]
# Specify hkls and lengths associated with the crystal structure.
# TODO: This should be updated to reflect systematic absences
if np.count_nonzero(coordinates[i]) == 0 or np.count_nonzero(
coordinates[j]) == 0:
continue # Ignore combinations including [000]
hkl1 = indices[i]
hkl2 = indices[j]
len1 = distances[i]
len2 = distances[j]
if len1 < len2: # Keep the longest first
hkl1, hkl2 = hkl2, hkl1
len1, len2 = len1, len2
angle = get_angle_cartesian(coordinates[i], coordinates[j])
phase_vector_pairs.append(
np.array([hkl1, hkl2, len1, len2, angle]))
vector_library[phase_name] = np.array(phase_vector_pairs)
# Pass attributes to diffraction library from structure library.
vector_library.identifiers = self.structures.identifiers
vector_library.structures = self.structures.structures
return vector_library
def get_vector_library(self,
reciprocal_radius):
"""Calculates a library of diffraction vectors and pairwise inter-vector
angles for a library of crystal structures.
Parameters
----------
reciprocal_radius : float
The maximum g-vector magnitude to be included in the library.
Returns
-------
vector_library : :class:`DiffractionVectorLibrary`
Mapping of phase identifier to phase information in dictionary
format.
"""
# Define DiffractionVectorLibrary object to contain results
vector_library = DiffractionVectorLibrary()
# Get structures from structure library
structure_library = self.structures.struct_lib
# Iterate through phases in library.
for phase_name in structure_library.keys():
# Get diffpy.structure object associated with phase
structure = structure_library[phase_name][0]
# Get reciprocal lattice points within reciprocal_radius
recip_latt = structure.lattice.reciprocal()
miller_indices, coordinates, distances = get_points_in_sphere(
recip_latt,
reciprocal_radius)
# Create pair_indices for selecting all point pair combinations
num_indices = len(miller_indices)
pair_a_indices, pair_b_indices = np.mgrid[:num_indices, :num_indices]
# Only select one of the permutations and don't pair an index with
# itself (select above diagonal)
upper_indices = np.triu_indices(num_indices, 1)
pair_a_indices = pair_a_indices[upper_indices].ravel()
pair_b_indices = pair_b_indices[upper_indices].ravel()
# Mask off origin (0, 0, 0)
origin_index = num_indices // 2
pair_a_indices = pair_a_indices[pair_a_indices != origin_index]
pair_b_indices = pair_b_indices[pair_b_indices != origin_index]
pair_indices = np.vstack([pair_a_indices, pair_b_indices])
# Create library entries
angles = get_angle_cartesian_vec(coordinates[pair_a_indices], coordinates[pair_b_indices])
pair_distances = distances[pair_indices.T]
# Ensure longest vector is first
len_sort = np.fliplr(pair_distances.argsort(axis=1))
# phase_index_pairs is a list of [hkl1, hkl2]
phase_index_pairs = np.take_along_axis(miller_indices[pair_indices.T], len_sort[:, :, np.newaxis], axis=1)
# phase_measurements is a list of [len1, len2, angle]
phase_measurements = np.column_stack((np.take_along_axis(pair_distances, len_sort, axis=1), angles))
# Only keep unique triplets
unique_measurements, unique_measurement_indices = np.unique(phase_measurements, axis=0, return_index=True)
vector_library[phase_name] = {
'indices': phase_index_pairs[unique_measurement_indices],
'measurements': unique_measurements
}
# Pass attributes to diffraction library from structure library.
vector_library.identifiers = self.structures.identifiers
vector_library.structures = self.structures.structures
vector_library.reciprocal_radius = reciprocal_radius
return vector_library
def calculate_ed_data(self,
structure,
reciprocal_radius,
with_direct_beam=True):
"""Calculates the Electron Diffraction data for a structure.
Parameters
----------
structure : Structure
The structure for which to derive the diffraction pattern. Note that
the structure must be rotated to the appropriate orientation and
that testing is conducted on unit cells (rather than supercells).
reciprocal_radius : float
The maximum radius of the sphere of reciprocal space to sample, in
reciprocal angstroms.
Returns
-------
pyxem.DiffractionSimulation
The data associated with this structure and diffraction setup.
"""
# Specify variables used in calculation
wavelength = self.wavelength
max_excitation_error = self.max_excitation_error
debye_waller_factors = self.debye_waller_factors
latt = structure.lattice
scattering_params = self.scattering_params
# Obtain crystallographic reciprocal lattice points within `max_r` and
# g-vector magnitudes for intensity calculations.
recip_latt = latt.reciprocal()
spot_indicies, cartesian_coordinates, spot_distances = get_points_in_sphere(
recip_latt, reciprocal_radius)
# Identify points intersecting the Ewald sphere within maximum
# excitation error and store the magnitude of their excitation error.
r_sphere = 1 / wavelength
r_spot = np.sqrt(np.sum(np.square(cartesian_coordinates[:, :2]), axis=1))
z_sphere = -np.sqrt(r_sphere**2 - r_spot**2) + r_sphere
proximity = np.absolute(z_sphere - cartesian_coordinates[:, 2])
intersection = proximity < max_excitation_error
# Mask parameters corresponding to excited reflections.
intersection_coordinates = cartesian_coordinates[intersection]
intersection_indices = spot_indicies[intersection]
proximity = proximity[intersection]
g_hkls = spot_distances[intersection]
# Calculate diffracted intensities based on a kinematical model.
intensities = get_kinematical_intensities(structure,
intersection_indices,
g_hkls,
proximity,
max_excitation_error,
debye_waller_factors,
scattering_params)
# Threshold peaks included in simulation based on minimum intensity.
peak_mask = intensities > 1e-20
intensities = intensities[peak_mask]
intersection_coordinates = intersection_coordinates[peak_mask]
intersection_indices = intersection_indices[peak_mask]
return DiffractionSimulation(coordinates=intersection_coordinates,
indices=intersection_indices,
intensities=intensities,
with_direct_beam=with_direct_beam)
def test_get_points_in_sphere():
latt = diffpy.structure.lattice.Lattice(0.5, 0.5, 0.5, 90, 90, 90)
ind, cord, dist = get_points_in_sphere(latt, 0.6)
assert len(ind) == len(cord)
assert len(ind) == len(dist)
assert len(dist) == 1 + 6
def calculate_profile_data(self, structure,
reciprocal_radius=1.0,
magnitude_tolerance=1e-5,
minimum_intensity=1e-3):
"""
Calculates a one dimensional diffraction profile for a structure.
Parameters
----------
structure : Structure
The structure for which to calculate the diffraction profile.
reciprocal_radius : float
The maximum radius of the sphere of reciprocal space to sample, in
reciprocal angstroms.
magnitude_tolerance : float
The minimum difference between diffraction magnitudes in reciprocal
angstroms for two peaks to be consdiered different.
minimum_intensity : float
The minimum intensity required for a diffraction peak to be
considered real. Deals with numerical precision issues.
Returns
-------
pyxem.ProfileSimulation
The diffraction profile corresponding to this structure and
experimental conditions.
"""
max_r = reciprocal_radius
wavelength = self.wavelength
scattering_params = self.scattering_params
latt = structure.lattice
is_hex = is_lattice_hexagonal(latt)
coeffs, fcoords, occus, dwfactors = get_vectorized_list_for_atomic_scattering_factors(structure, {
}, scattering_params=scattering_params)
# Obtain crystallographic reciprocal lattice points within range
recip_latt = latt.reciprocal()
spot_indicies, _, spot_distances = get_points_in_sphere(recip_latt, reciprocal_radius)
peaks = {}
mask = np.logical_not((np.any(spot_indicies, axis=1) == 0))
for hkl, g_hkl in zip(spot_indicies[mask], spot_distances[mask]):
# Force miller indices to be integers.
hkl = [int(round(i)) for i in hkl]
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.
fs = 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 * np.pi * g_dot_r)
* dw_correction)
# 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])
peaks[g_hkl] = [i_hkl, [tuple(hkl)], d_hkl]
# 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 > minimum_intensity:
x.append(k)
y.append(v[0])
hkls.append(fam)
d_hkls.append(v[2])
y = y / max(y) * 100
return ProfileSimulation(x, y, hkls)
