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)