API reference¶
This reference manual details the public classes, modules and functions in diffsims as generated from their docstrings. Some of the docstrings contain examples.
Caution
diffsims is in an alpha stage, and there will likely be breaking changes with each release.
crystallography¶
Generation of reciprocal lattice points (crystal plane, reflector, g, hkl) for a crystal structure.

class
diffsims.crystallography.
ReciprocalLatticePoint
(phase, hkl)[source]¶ Bases:
object
Reciprocal lattice point (or crystal plane, reflector, g, etc.) with Miller indices, length of the reciprocal lattice vectors and other relevant structure_factor parameters.

property
allowed
¶ Return whether planes diffract according to structure_factor selection rules assuming kinematical scattering theory.

calculate_structure_factor
(method=None, voltage=None)[source]¶ Populate self.structure_factor with the structure factor F for each plane.
 Parameters
method (str, optional) – Either “kinematical” for kinematical Xray structure factors or “doyleturner” for structure factors using DoyleTurner atomic scattering factors. If None (default), kinematical structure factors are calculated.
voltage (float, optional) – Beam energy in V used when method=doyleturner.

calculate_theta
(voltage)[source]¶ Populate self.theta with the Bragg angle \(theta_B\) for each plane.
 Parameters
voltage (float) – Beam energy in V.

property
dspacing
¶ Return
np.ndarray
of direct lattice interplanar spacings.

classmethod
from_highest_hkl
(phase, highest_hkl)[source]¶ Create a CrystalPlane object populated by unique Miller indices below, but including, a set of higher indices.
 Parameters
phase (orix.crystal_map.phase_list.Phase) – A phase container with a crystal structure and a space and point group describing the allowed symmetry operations.
highest_hkl (np.ndarray, list, or tuple of int) – Highest Miller indices to consider (including).

classmethod
from_min_dspacing
(phase, min_dspacing=0.5)[source]¶ Create a CrystalPlane object populated by unique Miller indices with a direct space interplanar spacing greater than a lower threshold.
 Parameters
phase (orix.crystal_map.phase_list.Phase) – A phase container with a crystal structure and a space and point group describing the allowed symmetry operations.
min_dspacing (float, optional) – Smallest interplanar spacing to consider. Default is 0.5 Å.

property
gspacing
¶ Return
np.ndarray
of reciprocal lattice point spacings.

property
h
¶ Return
np.ndarray
of Miller index h.

property
hkl
¶ Return
Vector3d
of Miller indices.

property
k
¶ Return
np.ndarray
of Miller index k.

property
l
¶ Return
np.ndarray
of Miller index l.

property
multiplicity
¶ Return either int or
np.ndarray
of int.

property
scattering_parameter
¶ Return
np.ndarray
of scattering parameters s.

property
shape
¶ Return tuple.

property
size
¶ Return int.

property
structure_factor
¶ Return
np.ndarray
of structure factors F or None.

symmetrise
(antipodal=True, unique=True, return_multiplicity=False)[source]¶ Return planes with symmetrically equivalent Miller indices.
 Parameters
antipodal (bool, optional) – Whether to include antipodal symmetry operations. Default is True.
unique (bool, optional) – Whether to return only distinct indices. Default is True. If True, zeroentries, which are assumed to be degenerate, are removed.
return_multiplicity (bool, optional) – Whether to return the multiplicity of indices. This option is only available if unique is True. Default is False.
 Returns
ReciprocalLatticePoint – Planes with Miller indices symmetrically equivalent to the original planes.
multiplicity (np.ndarray) – Multiplicity of the original Miller indices. Only returned if return_multiplicity is True.
Notes
Should be the same as EMsoft’s CalcFamily in their symmetry.f90 module, although not entirely sure. Use with care.

property
theta
¶ Return
np.ndarray
of twice the Bragg angle.

property

diffsims.crystallography.
get_equivalent_hkl
(hkl, operations, unique=False, return_multiplicity=False)[source]¶ Return symmetrically equivalent Miller indices.
 Parameters
hkl (orix.vector.Vector3d, np.ndarray, list or tuple of int) – Miller indices.
operations (orix.quaternion.symmetry.Symmetry) – Point group describing allowed symmetry operations.
unique (bool, optional) – Whether to return only unique Miller indices. Default is False.
return_multiplicity (bool, optional) – Whether to return the multiplicity of the input indices. Default is False.
 Returns
new_hkl (orix.vector.Vector3d) – The symmetrically equivalent Miller indices.
multiplicity (np.ndarray) – Number of symmetrically equivalent indices. Only returned if return_multiplicity is True.

diffsims.crystallography.
get_highest_hkl
(lattice, min_dspacing=0.5)[source]¶ Return the highest Miller indices hkl of the plane with a direct space interplanar spacing greater than but closest to a lower threshold.
 Parameters
lattice (diffpy.structure.Lattice) – Crystal lattice.
min_dspacing (float, optional) – Smallest interplanar spacing to consider. Default is 0.5 Å.
 Returns
highest_hkl – Highest Miller indices.
 Return type
np.ndarray

diffsims.crystallography.
get_hkl
(highest_hkl)[source]¶ Return a list of planes from a set of highest Miller indices.
 Parameters
highest_hkl (orix.vector.Vector3d, np.ndarray, list, or tuple of int) – Highest Miller indices to consider.
 Returns
hkl – An array of Miller indices.
 Return type
np.ndarray
generators¶
Generation of diffraction simulations and libraries, and lists of rotations.
diffraction_generator¶
Electron diffraction pattern simulation.

class
diffsims.generators.diffraction_generator.
AtomicDiffractionGenerator
(accelerating_voltage, detector, reciprocal_mesh=False)[source]¶ Bases:
object
Computes electron diffraction patterns for an atomic lattice.
 Parameters
accelerating_voltage (float, 'inf') – The accelerating voltage of the microscope in kV
detector (list of 1D floattype arrays) – List of mesh vectors defining the (flat) detector size and sensor positions
reciprocal_mesh (bool, optional) – If True then detector is assumed to be a reciprocal grid, else (default) it is assumed to be a real grid.

calculate_ed_data
(structure, probe, slice_thickness, probe_centre=None, z_range=200, precessed=False, dtype='float64', ZERO=1e14, mode='kinematic', **kwargs)[source]¶ Calculates single electron diffraction image for particular atomic structure and probe.
 Parameters
structure (Structure) – The structure for upon which to perform the calculation
probe (instance of probeFunction) – Function representing 3D shape of beam
slice_thickness (float) – Discretisation thickness in the zaxis
probe_centre (ndarray (or iterable), shape [3] or [2]) – Translation vector for the probe. Either of the same dimension of the space or the dimension of the detector. default=None focusses the probe at [0,0,0]
zrange (float) – zthickness to discretise. Only required if sample is not thick enough to fully resolve the Ewaldsphere. Default value is 200.
precessed (bool, float, or (float, int)) – Dictates whether beam precession is simulated. If False or the float is 0 then no precession is computed. If <precessed> = (alpha, n) then the precession arc of tilt alpha (in degrees) is discretised into n projections. If n is not provided then default of 30 is used.
dtype (str or numpy.dtype) – Defines the precision to use whilst computing diffraction image.
ZERO (float > 0) – Rounding error permitted in computation of atomic density. This value is the smallest value rounded to 0. Default is 1e14.
mode (str) – Only <mode>=’kinematic’ is currently supported.
kwargs (dictionary) – Extra keyword arguments to pass to child simulator. For kinematic: GPU (bool): Flag to use GPU if available, default is True. pointwise (bool): Flag to evaluate charge pointwise on voxels rather than average, default is False.
 Returns
Diffraction data to be interpreted as a discretisation on the original detector mesh.
 Return type
ndarray

class
diffsims.generators.diffraction_generator.
DiffractionGenerator
(accelerating_voltage, scattering_params='lobato', precession_angle=0, shape_factor_model='lorentzian', approximate_precession=True, minimum_intensity=1e20, **kwargs)[source]¶ Bases:
object
Computes electron diffraction patterns for a crystal structure.
Calculate reciprocal lattice of structure. Find all reciprocal points within the limiting sphere given by \(\frac{2}{\lambda}\).
For each reciprocal point \(\mathbf{g_{hkl}}\) corresponding to lattice plane \((hkl)\), compute the Bragg condition \(\sin(\theta) = \frac{\lambda}{2d_{hkl}}\)
The intensity of each reflection is then given in the kinematic approximation as the modulus square of the structure factor. \(I_{hkl} = F_{hkl}F_{hkl}^*\)
 Parameters
accelerating_voltage (float) – The accelerating voltage of the microscope in kV.
scattering_params (str) – “lobato” or “xtables”
minimum_intensity (float) – Minimum intensity for a peak to be considered visible in the pattern
precession_angle (float) – Angle about which the beam is precessed. Default is no precession.
approximate_precession (boolean) – When using precession, whether to precisely calculate average excitation errors and intensities or use an approximation. See notes.
shape_factor_model (function or string) – A function that takes excitation_error and max_excitation_error (and potentially kwargs) and returns an intensity scaling factor. If None defaults to shape_factor_models.linear. A number of preprogrammed functions are available via strings.
kwargs – Keyword arguments passed to shape_factor_model.
Notes
A full calculation is much slower and is not recommended for calculating a diffraction library for precession diffraction patterns.
When using precession and approximate_precession=True, the shape factor
model defaults to Lorentzian; shape_factor_model is ignored. Only with approximate_precession=False the custom shape_factor_model is used.

calculate_ed_data
(structure, reciprocal_radius, rotation=(0, 0, 0), with_direct_beam=True, max_excitation_error=0.01, debye_waller_factors={})[source]¶ Calculates the Electron Diffraction data for a structure.
 Parameters
structure (diffpy.structure.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.
rotation (tuple) – Euler angles, in degrees, in the rzxz convention. Default is (0, 0, 0) which aligns ‘z’ with the electron beam.
with_direct_beam (bool) – If True, the direct beam is included in the simulated diffraction pattern. If False, it is not.
max_excitation_error (float) – The extinction distance for reflections, in reciprocal Angstroms. Roughly equal to 1/thickness.
debye_waller_factors (dict of str:value pairs) – Maps element names to their temperaturedependent DebyeWaller factors.
 Returns
The data associated with this structure and diffraction setup.
 Return type

calculate_profile_data
(structure, reciprocal_radius=1.0, minimum_intensity=0.001, debye_waller_factors={})[source]¶ Calculates a one dimensional diffraction profile for a structure.
 Parameters
structure (diffpy.structure.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.
minimum_intensity (float) – The minimum intensity required for a diffraction peak to be considered real. Deals with numerical precision issues.
debye_waller_factors (dict of str:value pairs) – Maps element names to their temperaturedependent DebyeWaller factors.
 Returns
The diffraction profile corresponding to this structure and experimental conditions.
 Return type
library_generator¶
Diffraction pattern library generator and associated tools.

class
diffsims.generators.library_generator.
DiffractionLibraryGenerator
(electron_diffraction_calculator)[source]¶ Bases:
object
Computes a library of electron diffraction patterns for specified atomic structures and orientations.

get_diffraction_library
(structure_library, calibration, reciprocal_radius, half_shape, with_direct_beam=True, max_excitation_error=0.01, debye_waller_factors={})[source]¶ Calculates a dictionary of diffraction data for a library of crystal structures and orientations.
Each structure in the structure library is rotated to each associated orientation and the diffraction pattern is calculated each time.
Angles must be in the Euler representation (Z,X,Z) and in degrees
 Parameters
structure_library (difffsims:StructureLibrary Object) – Dictionary of structures and associated orientations for which electron diffraction is to be simulated.
calibration (float) – The calibration of experimental data to be correlated with the library, in reciprocal Angstroms per pixel.
reciprocal_radius (float) – The maximum gvector magnitude to be included in the simulations.
half_shape (tuple) – The half shape of the target patterns, for 144x144 use (72,72) etc
with_direct_beam (bool) – Include the direct beam in the library.
max_excitation_error (float) – The extinction distance for reflections, in reciprocal Angstroms.
debye_waller_factors (dict of str:value pairs) – Maps element names to their temperaturedependent DebyeWaller factors.
 Returns
diffraction_library – Mapping of crystal structure and orientation to diffraction data objects.
 Return type
DiffractionLibrary


class
diffsims.generators.library_generator.
VectorLibraryGenerator
(structure_library)[source]¶ Bases:
object
Computes a library of diffraction vectors and pairwise intervector angles for a specified StructureLibrary.

get_vector_library
(reciprocal_radius)[source]¶ Calculates a library of diffraction vectors and pairwise intervector angles for a library of crystal structures.
 Parameters
reciprocal_radius (float) – The maximum gvector magnitude to be included in the library.
 Returns
vector_library – Mapping of phase identifier to phase information in dictionary format.
 Return type
DiffractionVectorLibrary

rotation_list_generators¶
Provides users with a range of gridding functions

diffsims.generators.rotation_list_generators.
get_beam_directions_grid
(crystal_system, resolution, mesh='spherified_cube_corner')[source]¶ Produces an array of beam directions, within the stereographic triangle of the relevant crystal system. The way the array is constructed is based on different methods of meshing the sphere [Cajaravelli2015] and can be specified through the mesh argument.
 Parameters
crystal_system (str) – Allowed are: ‘cubic’,’hexagonal’,’trigonal’,’tetragonal’, ‘orthorhombic’,’monoclinic’,’triclinic’
resolution (float) – An angle in degrees representing the worstcase angular distance to a first nearest neighbor grid point.
mesh (str) – Type of meshing of the sphere that defines how the grid is created. Options are: uv_sphere, normalized_cube, spherified_cube_corner (default), spherified_cube_edge, icosahedral, random.
 Returns
rotation_list
 Return type
list of tuples

diffsims.generators.rotation_list_generators.
get_fundamental_zone_grid
(resolution=2, point_group=None, space_group=None)[source]¶ Generates an equispaced grid of rotations within a fundamental zone.
 Parameters
resolution (float, optional) – The characteristic distance between a rotation and its neighbour (degrees)
point_group (orix.quaternion.symmetry.Symmetry, optional) – One of the 11 proper point groups, defaults to None
space_group (int, optional) – Between 1 and 231, defaults to None
 Returns
rotation_list – Grid of rotations lying within the specified fundamental zone
 Return type
list of tuples

diffsims.generators.rotation_list_generators.
get_grid_around_beam_direction
(beam_rotation, resolution, angular_range=(0, 360))[source]¶ Creates a rotation list of rotations for which the rotation is about given beam direction.
 Parameters
beam_rotation (tuple) – A desired beam direction as a rotation (rzxz eulers), usually found via get_rotation_from_z_to_direction.
resolution (float) – The resolution of the grid (degrees).
angular_range (tuple) – The minimum (included) and maximum (excluded) rotation around the beam direction to be included.
 Returns
rotation_list
 Return type
list of tuples
Examples
>>> from diffsims.generators.zap_map_generator import get_rotation_from_z_to_direction >>> beam_rotation = get_rotation_from_z_to_direction(structure,[1,1,1]) >>> grid = get_grid_around_beam_direction(beam_rotation,1)

diffsims.generators.rotation_list_generators.
get_list_from_orix
(grid, rounding=2)[source]¶ Converts an orix sample to a rotation list
 Parameters
grid (orix.quaternion.rotation.Rotation) – A grid of rotations
rounding (int, optional) – The number of decimal places to retain, defaults to 2
 Returns
rotation_list – A rotation list
 Return type
list of tuples

diffsims.generators.rotation_list_generators.
get_local_grid
(resolution=2, center=None, grid_width=10)[source]¶ Generates a grid of rotations about a given rotation
 Parameters
resolution (float, optional) – The characteristic distance between a rotation and its neighbour (degrees)
center (euler angle tuple or orix.quaternion.rotation.Rotation, optional) – The rotation at which the grid is centered. If None (default) uses the identity
grid_width (float, optional) – The largest angle of rotation away from center that is acceptable (degrees)
 Returns
rotation_list
 Return type
list of tuples
sphere_mesh_generators¶

diffsims.generators.sphere_mesh_generators.
beam_directions_grid_to_euler
(vectors)[source]¶ Convert list of vectors representing zones to a list of Euler angles in the bunge convention with the constraint that phi1=0.
 Parameters
vectors (numpy.ndarray (N, 3)) – N 3dimensional vectors to convert to Euler angles
 Returns
grid – Euler angles in bunge convention corresponding to each vector in degrees.
 Return type
numpy.ndarray (N, 3)
Notes
The Euler angles represent the orientation of the crystal if that particular vector were parallel to the beam direction [001]. The additional constraint of phi1=0 means that this orientation is uniquely defined for most vectors. phi1 represents the rotation of the crystal around the beam direction and can be interpreted as the rotation of a particular diffraction pattern.

diffsims.generators.sphere_mesh_generators.
get_cube_mesh_vertices
(resolution, grid_type='spherified_corner')[source]¶ Return the (x, y, z) coordinates of the vertices of a cube mesh on a sphere. To generate the mesh, a cube is made to surround the sphere. The surfaces of the cube are subdivided into a grid. The vectors from the origin to these grid points are normalized to unit length. The grid on the cube can be generated in three ways, see grid_type and reference [Cajaravelli2015].
 Parameters
 Returns
points_in_cartesian – Rows are x, y, z where z is the 001 pole direction
 Return type
numpy.ndarray (N,3)
Notes
The resolution determines the maximum angle between first nearest neighbor grid points, but to get an integer number of points between the cube face center and the edges, the number of grid points is rounded up. In practice this means that resolution is always an upper limit. Additionally, where on the grid this maximum angle will be will depend on the type of grid chosen. Resolution says something about the maximum angle but nothing about the distribution of nearest neighbor angles or the minimum angle  also this is fixed by the chosen grid.
In the normalized grid, the grid on the surface of the cube is linear. The maximum angle between nearest neighbors is found between the <001> directions and the first grid point towards the <011> directions. Points approaching the edges and corners of the cube will have a smaller angular deviation, so orientation space will be oversampled there compared to the cube faces <001>.
In the spherified_edge grid, the grid is constructed so that there are still two sets of perpendicular grid lines parallel to the {100} directions on each cube face, but the spacing of the grid lines is chosen so that the angles between the grid points on the line connecting the face centers (<001>) to the edges (<011>) are equal. The maximum angle is also between the <001> directions and the first grid point towards the <011> edges. This grid slightly oversamples the directions between <011> and <111>
The spherified_corner case is similar to the spherified_edge case, but the spacing of the grid lines is chosen so that the angles between the grid points on the line connecting the face centers to the cube corners (<111>) is equal. The maximum angle in this grid is from the corners to the first grid point towards the cube face centers.
References
 Cajaravelli2015(1,2,3,4)
O. S. Cajaravelli, “Four Ways to Create a Mesh for a Sphere,” https://medium.com/gamedevdaily/fourwaystocreateameshforasphered7956b825db4.

diffsims.generators.sphere_mesh_generators.
get_icosahedral_mesh_vertices
(resolution)[source]¶ Return the (x, y, z) coordinates of the vertices of an icosahedral mesh of a cube, see [Cajaravelli2015]. Method was adapted from meshzoo [Meshzoo].
 Parameters
resolution (float) – The maximum angle in degrees between neighboring grid points. Since the mesh is generated iteratively, the actual maximum angle in the mesh can be slightly smaller.
 Returns
points_in_cartesian – Rows are x, y, z where z is the 001 pole direction
 Return type
numpy.ndarray (N,3)
References
 Meshzoo
The meshzoo.sphere module, https://github.com/nschloe/meshzoo/blob/master/meshzoo/sphere.py.

diffsims.generators.sphere_mesh_generators.
get_random_sphere_vertices
(resolution, seed=None)[source]¶ Create a mesh that randomly samples the surface of a sphere
 Parameters
 Returns
points_in_cartesian – Rows are x, y, z where z is the 001 pole direction
 Return type
numpy.ndarray (N,3)
References

diffsims.generators.sphere_mesh_generators.
get_uv_sphere_mesh_vertices
(resolution)[source]¶ Return the vertices of a UV (spherical coordinate) mesh on a unit sphere [Cajaravelli2015]. The mesh vertices are defined by the parametrization:
\[ \begin{align}\begin{aligned}x = sin(u)cos(v)\\y = sin(u)sin(v)\\z = cos(u)\end{aligned}\end{align} \] Parameters
resolution (float) – An angle in degrees. The maximum angle between nearest neighbor grid points. In this mesh this occurs on the equator of the sphere. All elevation grid lines are separated by at most resolution. The step size of u and v are rounded up to get an integer number of elevation and azimuthal grid lines with equal spacing.
 Returns
points_in_cartesian – Rows are x, y, z where z is the 001 pole direction
 Return type
numpy.ndarray (N,3)
zap_map_generator¶

diffsims.generators.zap_map_generator.
corners_to_centroid_and_edge_centers
(corners)[source]¶ Produces the midpoints and center of a trio of corners
 Parameters
corners (list of lists) – Three corners of a streographic triangle
 Returns
list_of_corners – Length 7, elements ca, cb, cc, mean, cab, cbc, cac where naming is such that ca is the first corner of the input, and cab is the midpoint between corner a and corner b.
 Return type

diffsims.generators.zap_map_generator.
generate_directional_simulations
(structure, simulator, direction_list, reciprocal_radius=1, **kwargs)[source]¶ Produces simulation of a structure aligned with certain axes
 Parameters
structure (diffpy.structure.structure.Structure) – The structure from which simulations need to be produced.
simulator (DiffractionGenerator) – The diffraction generator object used to produce the simulations
direction_list (list of lists) – A list of [UVW] indices, eg. [[1,0,0],[1,1,0]]
reciprocal_radius (float) – Default to 1
 Returns
direction_dictionary – Keys are zone axes, values are simulations
 Return type

diffsims.generators.zap_map_generator.
generate_zap_map
(structure, simulator, system='cubic', reciprocal_radius=1, density='7', **kwargs)[source]¶ Produces a number of zone axis patterns for a structure
 Parameters
structure (diffpy.structure.structure.Structure) – The structure to be simulated.
simulator (DiffractionGenerator) – The simulator used to generate the simulations
system (str) – ‘cubic’, ‘hexagonal’, ‘trigonal’, ‘tetragonal’, ‘orthorhombic’, ‘monoclinic’. Defaults to ‘cubic’.
reciprocal_radius (float) – The range of reciprocal lattice spots to be included. Default to 1.
density (str) – ‘3’ for the corners or ‘7’ (corners + midpoints + centroids). Defaults to 7.
kwargs – Keyword arguments to be passed to simulator.calculate_ed_data().
 Returns
zap_dictionary – Keys are zone axes, values are simulations
 Return type
Examples
Plot all of the patterns that you have generated
>>> zap_map = generate_zap_map(structure,simulator,'hexagonal',density='3') >>> for k in zap_map.keys(): >>> pattern = zap_map[k] >>> pattern.calibration = 4e3 >>> plt.figure() >>> plt.imshow(pattern.get_diffraction_pattern(),vmax=0.02)

diffsims.generators.zap_map_generator.
get_rotation_from_z_to_direction
(structure, direction)[source]¶ Finds the rotation that takes [001] to a given zone axis.
 Parameters
structure (diffpy.structure.structure.Structure) – The structure for which a rotation needs to be found.
direction (array like) – [UVW] direction that the ‘z’ axis should end up point down.
 Returns
euler_angles – ‘rzxz’ in degrees.
 Return type
Notes
This implementation works with an axis arrangement that has +x as left to right, +y as bottom to top and +z as out of the plane of a page. Rotations are counter clockwise as you look from the tip of the axis towards the origin
libraries¶
Diffraction, structure and vector libraries.
diffraction_library¶

class
diffsims.libraries.diffraction_library.
DiffractionLibrary
(*args, **kwargs)[source]¶ Bases:
dict
Maps crystal structure (phase) and orientation to simulated diffraction data.

identifiers
¶ A list of phase identifiers referring to different atomic structures.
 Type
list of strings/ints

structures
¶ A list of diffpy.structure.Structure objects describing the atomic structure associated with each phase in the library.
 Type
list of diffpy.structure.Structure objects.

diffraction_generator
¶ Diffraction generator used to generate this library.
 Type

get_library_entry
(phase=None, angle=None)[source]¶ Extracts a single DiffractionLibrary entry.
 Parameters
 Returns
library_entries – Dictionary containing the simulation associated with the specified phase and orientation with associated properties.
 Return type

structure_library¶

class
diffsims.libraries.structure_library.
StructureLibrary
(identifiers, structures, orientations)[source]¶ Bases:
object
A dictionary containing all the structures and their associated rotations in the .struct_lib attribute.

identifiers
¶ A list of phase identifiers referring to different atomic structures.
 Type
list of strings/ints

structures
¶ A list of diffpy.structure.Structure objects describing the atomic structure associated with each phase in the library.
 Type
list of diffpy.structure.Structure objects.

orientations
¶ A list over identifiers of lists of euler angles (as tuples) in the rzxz convention and in degrees.
 Type

classmethod
from_crystal_systems
(identifiers, structures, systems, resolution, equal='angle')[source]¶ Creates a structure library from crystal system derived orientation lists
 Parameters
identifiers (list of strings/ints) – A list of phase identifiers referring to different atomic structures.
structures (list of diffpy.structure.Structure objects.) – A list of diffpy.structure.Structure objects describing the atomic structure associated with each phase in the library.
systems (list) – A list over indentifiers of crystal systems
resolution (float) – resolution in degrees
equal (str) – Default is ‘angle’
 Raises
NotImplementedError: – “This function has been removed in version 0.3.0, in favour of creation from orientation lists”

classmethod
from_orientation_lists
(identifiers, structures, orientations)[source]¶ Creates a structure library from “manual” orientation lists
 Parameters
identifiers (list of strings/ints) – A list of phase identifiers referring to different atomic structures.
structures (list of diffpy.structure.Structure objects.) – A list of diffpy.structure.Structure objects describing the atomic structure associated with each phase in the library.
orientations (list of lists of tuples) – A list over identifiers of lists of euler angles (as tuples) in the rzxz convention and in degrees.
 Returns
 Return type

vector_library¶

class
diffsims.libraries.vector_library.
DiffractionVectorLibrary
(*args, **kwargs)[source]¶ Bases:
dict
Maps crystal structure (phase) to diffraction vectors.
The library is a dictionary mapping from a phase name to phase information. The phase information is stored as a dictionary with the following entries:
 ‘indices’np.array
List of peak indices [hkl1, hkl2] as a 2D array.
 ‘measurements’np.array
List of vector measurements [len1, len2, angle] in the same order as the indices. Lengths in reciprocal Angstrom and angles in radians.

identifiers
¶ A list of phase identifiers referring to different atomic structures.
 Type
list of strings/ints

structures
¶ A list of diffpy.structure.Structure objects describing the atomic structure associated with each phase in the library.
 Type
list of diffpy.structure.Structure objects.
sims¶
Diffraction simulations.
diffraction_simulation¶

class
diffsims.sims.diffraction_simulation.
DiffractionSimulation
(coordinates=None, indices=None, intensities=None, calibration=1.0, offset=(0.0, 0.0), with_direct_beam=False)[source]¶ Bases:
object
Holds the result of a kinematic diffraction pattern simulation.
 Parameters
coordinates (arraylike, shape [n_points, 2]) – The xy coordinates of points in reciprocal space.
indices (arraylike, shape [n_points, 3]) – The indices of the reciprocal lattice points that intersect the Ewald sphere.
intensities (arraylike, shape [n_points, ]) – The intensity of the reciprocal lattice points.
calibration (float or tuple of float, optional) – The x and yscales of the pattern, with respect to the original reciprocal angstrom coordinates.
offset (tuple of float, optional) – The xy offset of the pattern in reciprocal angstroms. Defaults to zero in each direction.

property
calibrated_coordinates
¶ Coordinates converted into pixel space.
 Type
ndarray

property
calibration
¶ The x and yscales of the pattern, with respect to the original reciprocal angstrom coordinates.
 Type
tuple of float

property
coordinates
¶ The coordinates of all unmasked points.
 Type
ndarray

property
direct_beam_mask
¶ If with_direct_beam is True, returns a True array for all points. If with_direct_beam is False, returns a True array with False in the position of the direct beam.
 Type
ndarray

get_diffraction_pattern
(size=512, sigma=10)[source]¶ Returns the diffraction data as a numpy array with twodimensional Gaussians representing each diffracted peak. Should only be used for qualitative work.
 Parameters
 Returns
diffractionpattern – The simulated electron diffraction pattern, normalised.
 Return type
numpy.array
Notes
If don’t know the exact calibration of your diffraction signal using 1e2 produces reasonably good patterns when the lattice parameters are on the order of 0.5nm and a the default size and sigma are used.

property
intensities
¶ The intensities of all unmasked points.
 Type
ndarray

class
diffsims.sims.diffraction_simulation.
ProfileSimulation
(magnitudes, intensities, hkls)[source]¶ Bases:
object
Holds the result of a given kinematic simulation of a diffraction profile.
 Parameters
magnitudes (arraylike, shape [n_peaks, 1]) – Magnitudes of scattering vectors.
intensities (arraylike, shape [n_peaks, 1]) – The kinematic intensity of the diffraction peaks.
hkls ([{(h, k, l): mult}] {(h, k, l): mult} is a dict of Miller) – indices for all diffracted lattice facets contributing to each intensity.

get_plot
(annotate_peaks=True, with_labels=True, fontsize=12)[source]¶  Plots the diffraction profile simulation for the
calculate_profile_data method in DiffractionGenerator.
 Parameters
annotate_peaks (boolean) – If True, peaks are annotaed with hkl information.
with_labels (boolean) – If True, xlabels and ylabels are added to the plot.
fontsize (integer) – Fontsize for peak labels.
structure_factor¶
Calculation of scattering factors and structure factors.

diffsims.structure_factor.
find_asymmetric_positions
(positions, space_group)[source]¶ Return the asymmetric atom positions among a set of positions when considering symmetry operations defined by a space group.
 Parameters
positions (list) – A list of cartesian atom positions.
space_group (diffpy.structure.spacegroupmod.SpaceGroup) – Space group describing the symmetry operations.
 Returns
Asymmetric atom positions.
 Return type

diffsims.structure_factor.
get_atomic_scattering_parameters
(element, unit=None)[source]¶ Return the eight atomic scattering parameters a_14, b_14 for elements with atomic numbers Z = 198 from Table 12.1 in [DeGraef2007], which are themselves from [Doyle1968] and [Smith1962].
 Parameters
 Returns
a (numpy.ndarray) – The four atomic scattering parameters a_14.
b (numpy.ndarray) – The four atomic scattering parameters b_14.
References
 DeGraef2007
De Graef, M. E. McHenry, “Structure of Materials,” Cambridge University Press (2007).
 Doyle1968(1,2,3)
P. A. Doyle, P. S. Turner, “Relativistic HartreeFock Xray and electron scattering factors,” Acta Cryst. 24 (1968), doi: https://doi.org/10.1107/S0567739468000756.
 Smith1962
G. Smith, R. Burge, “The analytical representation of atomic scattering amplitudes for electrons,” Acta Cryst. A15 (1962), doi: https://doi.org/10.1107/S0365110X62000481.

diffsims.structure_factor.
get_doyleturner_atomic_scattering_factor
(atom, scattering_parameter, unit_cell_volume)[source]¶ Return the atomic scattering factor f for a certain atom and scattering parameter using DoyleTurner atomic scattering parameters [Doyle1968].
Assumes structure’s DebyeWaller factors are expressed in Ångströms.
This function is adapted from EMsoft.
 Parameters
atom (diffpy.structure.atom.Atom) – Atom with element type, DebyeWaller factor and occupancy number.
scattering_parameter (float) – The scattering parameter s for these Miller indices describing the crystal plane in which the atom lies.
unit_cell_volume (float) – Volume of the unit cell.
 Returns
f – Scattering factor for this atom on this plane.
 Return type

diffsims.structure_factor.
get_doyleturner_structure_factor
(phase, hkl, scattering_parameter, voltage, return_parameters=False)[source]¶ Return the structure factor for a given family of Miller indices using DoyleTurner atomic scattering parameters [Doyle1968].
Assumes structure’s lattice parameters and DebyeWaller factors are expressed in Ångströms.
This function is adapted from EMsoft.
 Parameters
phase (orix.crystal_map.phase_list.Phase) – A phase container with a crystal structure and a space and point group describing the allowed symmetry operations.
hkl (numpy.ndarray or list) – Miller indices.
scattering_parameter (float) – Scattering parameter for these Miller indices.
voltage (float) – Beam energy in V.
return_parameters (bool, optional) – Whether to return a set of parameters derived from the calculation as a dictionary. Default is False.
 Returns
structure_factor (float) – Structure factor F.
params (dict) – A dictionary with (key, item) (str, float) of parameters derived from the calculation. Only returned if return_parameters=True.

diffsims.structure_factor.
get_element_id_from_string
(element_str)[source]¶ Get periodic element ID for elements Z = 198 from onetwo letter string.

diffsims.structure_factor.
get_kinematical_atomic_scattering_factor
(atom, scattering_parameter)[source]¶ Return the kinematical (Xray) atomic scattering factor f for a certain atom and scattering parameter.
Assumes structure’s DebyeWaller factors are expressed in Ångströms.
This function is adapted from EMsoft.
 Parameters
atom (diffpy.structure.atom.Atom) – Atom with element type, DebyeWaller factor and occupancy number.
scattering_parameter (float) – The scattering parameter s for these Miller indices describing the crystal plane in which the atom lies.
 Returns
f – Scattering factor for this atom on this plane.
 Return type

diffsims.structure_factor.
get_kinematical_structure_factor
(phase, hkl, scattering_parameter)[source]¶ Return the kinematical (Xray) structure factor for a given family of Miller indices.
Assumes structure’s lattice parameters and DebyeWaller factors are expressed in Ångströms.
This function is adapted from EMsoft.
 Parameters
phase (orix.crystal_map.phase_list.Phase) – A phase container with a crystal structure and a space and point group describing the allowed symmetry operations.
hkl (numpy.ndarray or list) – Miller indices.
scattering_parameter (float) – Scattering parameter for these Miller indices.
 Returns
structure_factor – Structure factor F.
 Return type

diffsims.structure_factor.
get_refraction_corrected_wavelength
(phase, voltage)[source]¶ Return the refraction corrected relativistic electron wavelength in Ångströms for a given crystal structure and beam energy in V.
This function is adapted from EMsoft.
 Parameters
phase (orix.crystal_map.phase_list.Phase) – A phase container with a crystal structure and a space and point group describing the allowed symmetry operations.
voltage (float) – Beam energy in V.
 Returns
wavelength – Refraction corrected relativistic electron wavelength in Ångströms.
 Return type
pattern¶
detector_functions¶

diffsims.pattern.detector_functions.
add_dead_pixels
(pattern, n=None, fraction=None, seed=None)[source]¶ Adds randomly placed dead pixels onto a pattern
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
n (int) – The number of dead pixels, defaults to None
fraction (float) – The fraction of dead pixels, defaults to None
seed (int or None) – seed value for the random number generator
 Returns
corrupted_pattern – The pattern, with dead pixels included
 Return type

diffsims.pattern.detector_functions.
add_detector_offset
(pattern, offset)[source]¶ Adds/subtracts a fixed offset value from a pattern
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
offset (float or numpy.ndarray) – Added through the pattern, broadcasting applies
 Returns
corrupted_pattern – The pattern, with offset applied, pixels that would have been negative are instead 0.
 Return type
np.ndarray

diffsims.pattern.detector_functions.
add_gaussian_noise
(pattern, sigma, seed=None)[source]¶ Applies gaussian noise at each pixel within the pattern
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
sigma (float) – The (absolute) deviation of the gaussian errors
seed (int or None) – seed value for the random number generator
 Returns
 Return type
corrupted_pattern

diffsims.pattern.detector_functions.
add_gaussian_point_spread
(pattern, sigma)[source]¶ Blurs intensities across space with a gaussian function
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
sigma (float) – The standard deviation of the gaussian blur, in pixels
 Returns
blurred_pattern – The blurred pattern (deterministic)
 Return type

diffsims.pattern.detector_functions.
add_linear_detector_gain
(pattern, gain)[source]¶ Multiplies the pattern by a gain (which is not a function of the pattern)
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
gain (float or numpy.ndarray) – Multiplied through the pattern, broadcasting applies
 Returns
corrupted_pattern – The pattern, with gain applied
 Return type

diffsims.pattern.detector_functions.
add_shot_and_point_spread
(pattern, sigma, shot_noise=True, seed=None)[source]¶ Adds shot noise (optional) and gaussian point spread (via a convolution) to a pattern
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
sigma (float) – The standard deviation of the gaussian blur, in pixels
shot_noise (bool) – Whether to include shot noise in the original signal, default True
seed (int or None) – seed value for the random number generator (effects the shot noise only)
 Returns
detector_pattern – A single sample of the pattern after accounting for detector properties
 Return type
See also
add_shot_noise
adds only shot noise
add_gaussian_point_spread
adds only point spread

diffsims.pattern.detector_functions.
add_shot_noise
(pattern, seed=None)[source]¶ Applies shot noise to a pattern
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector
seed (int or None) – seed value for the random number generator
 Returns
shotted_pattern – A single sample of the pattern after accounting for shot noise
 Return type
Notes
This function will (as it should) behave differently depending on the pattern intensity, so be mindful to put your intensities in physical units

diffsims.pattern.detector_functions.
constrain_to_dynamic_range
(pattern, detector_max=None)[source]¶ Force the values within pattern to lie between [0,detector_max]
 Parameters
pattern (numpy.ndarray) – The diffraction pattern at the detector after corruption
detector_max (float) – The maximum allowed value at the detector
 Returns
within_range_pattern – The pattern, with values >=0 and =< detector_max
 Return type
utils¶
Diffraction utilities used by the other modules.
atomic_diffraction_generator_utils¶
Back end for computing diffraction patterns with a kinematic model.

diffsims.utils.atomic_diffraction_generator_utils.
get_diffraction_image
(coordinates, species, probe, x, wavelength, precession, GPU=True, pointwise=False, **kwargs)[source]¶ Return kinematically simulated diffraction pattern
 Parameters
coordinates (numpy.ndarray [float], (n_atoms, 3)) – List of atomic coordinates
species (numpy.ndarray [int], (n_atoms,)) – List of atomic numbers
probe (diffsims.ProbeFunction) – Function representing 3D shape of beam
x (list [numpy.ndarray [float] ], of shapes [(nx,), (ny,), (nz,)]) – Mesh on which to compute the volume density
wavelength (float) – Wavelength of electron beam
precession (a pair (float, int)) – The float dictates the angle of precession and the int how many points are used to discretise the integration.
dtype ((str, str)) – tuple of floating/complex datatypes to cast outputs to
ZERO (float > 0, optional) – Rounding error permitted in computation of atomic density. This value is the smallest value rounded to 0.
GPU (bool, optional) – Flag whether to use GPU or CPU discretisation. Default (if available) is True
pointwise (bool, optional) – Optional parameter whether atomic intensities are computed pointwise at the centre of a voxel or an integral over the voxel. default=False
 Returns
DP – The twodimensional diffraction pattern evaluated on the reciprocal grid corresponding to the first two vectors of x.
 Return type
numpy.ndarray [dtype[0]], (nx, ny, nz)

diffsims.utils.atomic_diffraction_generator_utils.
grid2sphere
(arr, x, dx, C)[source]¶ Projects 3d array onto a sphere
 Parameters
arr (np.ndarray [float], (nx, ny, nz)) – Input function to be projected
x (list [np.ndarray [float]], of shapes [(nx,), (ny,), (nz,)]) – Vectors defining mesh of <arr>
dx (list [np.ndarray [float]], of shapes [(3,), (3,), (3,)]) – Basis in which to orient sphere. Centre of sphere will be at C*dx[2] and mesh of output array will be defined by the first two vectors
C (float) – Radius of sphere
 Returns
out – If y is the point on the line between i*dx[0]+j*dx[1] and C*dx[2] which also lies on the sphere of radius C from C*dx[2] then: out[i,j] = arr(y). Interpolation on arr is linear.
 Return type
np.ndarray [float], (nx, ny)

diffsims.utils.atomic_diffraction_generator_utils.
precess_mat
(alpha, theta)[source]¶ Generates rotation matrices for precession curves.
 Parameters
alpha (float) – Angle (in degrees) of precession tilt
theta (float) – Angle (in degrees) along precession curve
 Returns
R – Rotation matrix associated to the tilt of alpha away from the vertical axis and a rotation of theta about the vertical axis.
 Return type
numpy.ndarray [float], (3, 3)
atomic_scattering_params¶
discretise_utils¶
Utils for converting lists of atoms to a discretised volume

diffsims.utils.discretise_utils.
do_binning
(x, loc, Rmax, d, GPU)[source]¶ Utility function which takes in a mesh, atom locations, atom radius and minimal gridspacing and returns a binned array of atom indices.
 Parameters
x (list [np.ndarray [float]], of shape [(nx,), (ny,), ..]) – Dictates the range of the box over which to bin atoms.
loc (np.ndarray, (n, 3)) – Atoms to bin.
Rmax (float > 3) – Maximum radius of an atom (rounded up to 3).
d (list of float > 0) – The finest permitted binning.
GPU (bool) – If True then constrains to memory of GPU rather than RAM.
 Returns
subList (np.ndarray [int]) – subList[i0,i1,i2] is a list of indices [j0, j1, …, jn, 1,…] such that the only atoms which are contained in the box: [x[0].min()+i0*r,x[0].min(),+(i0+1)*r] x [x[1].min()+i1*r,x[1].min(),+(i1+1)*r]…
r (np.ndarray [float]) – Size of each bin.
mem (int) – Upper limit of memory in bytes.

diffsims.utils.discretise_utils.
get_atoms
(Z, returnFunc=True, dtype='f8')[source]¶ This function returns an approximation of the atom with atomic number Z using a list of Gaussians.
 Parameters
 Returns
obj1, obj2 – Continuous atom is represented by: .. math:: ymapsto sum_i a[i]*exp(b[i]*y^2)
 Return type
numpy.ndarray or function
This is data table 3 from ‘Robust Parameterization of Elastic and Absorptive Electron Atomic Scattering Factors’ by L.M. Peng, G. Ren, S. L. Dudarev and M. J. Whelan, 1996

diffsims.utils.discretise_utils.
get_discretisation
(loc, Z, x, GPU=False, ZERO=None, dtype=('f8', 'c16'), pointwise=False, FT=False, **kwargs)[source]¶  Parameters
loc (numpy.ndarray, (n, 3)) – Atoms to bin
Z (str, int, or numpy.ndarray [str or int], (n,)) – atom labels, either string or atomic masses.
x (list [numpy.ndarray [float]]) – Dictates mesh over which to discretise. Volume will be discretised at points [x[0][i],x[1][j],…]
GPU (bool, optional) – If True (default) then attempts to use the GPU.
ZERO (float > 0) – Approximation threshold
dtype ((str, str), optional) – Real and complex data precisions to use, default=(‘float64’, ‘complex128’)
pointwise (bool, optional) – If True (default) then computes pointwise atomic potentials on mesh points, else averages the potential over cube of same size as the discretisation.
FT (bool, optional) – If True then computes the Fourier transform directly on the reciprocal mesh, otherwise (default) computes the volume potential
 Returns
out – Discretisation of atoms defined by loc/Z on mesh defined by x.
 Return type
numpy.ndarray, (x[0].size, x[1].size, x[2].size)

diffsims.utils.discretise_utils.
rebin
(x, loc, r, k, mem)[source]¶ Bins each location into a grid subject to memory constraints.
 Parameters
x (list [np.ndarray [float]], of shape [(nx,), (ny,), ..]) – Dictates the range of the box over which to bin atoms.
loc (np.ndarray, (n, 3)) – Atoms to bin.
r (float or [float, float, float]) – Mesh size (in each direction).
k (int) – Integer such that the radius of the atom is <= k*r. Consequently, each atom will appear in approximately 8k^3 bins.
mem (int) – Upper limit of number of bytes permitted for mesh. If not possible then raises a MemoryError.
 Returns
subList – subList[i0,i1,i2] is a list of indices [j0, j1, …, jn, 1,…] such that the only atoms which are contained in the box: [x[0].min()+i0*r,x[0].min(),+(i0+1)*r] x [x[1].min()+i1*r,x[1].min(),+(i1+1)*r]… are the atoms with locations loc[j0], …, loc[jn].
 Return type
np.ndarray [int]
fourier_transform¶
Created on 31 Oct 2019
Module provides optimised fft and Fourier transform approximation.
@author: Rob Tovey

diffsims.utils.fourier_transform.
convolve
(arr1, arr2, dx=None, axes=None)[source]¶ Performs a centred convolution of input arrays
 Parameters
arr1 (numpy.ndarray) – Arrays to be convolved. If dimensions are not equal then 1s are appended to the lower dimensional array. Otherwise, arrays must be broadcastable.
arr2 (numpy.ndarray) – Arrays to be convolved. If dimensions are not equal then 1s are appended to the lower dimensional array. Otherwise, arrays must be broadcastable.
dx (float > 0, list of float, or None , optional) – Grid spacing of input arrays. Output is scaled by dx**max(arr1.ndim, arr2.ndim). default=`None` applies no scaling
axes (tuple of ints or None, optional) – Choice of axes to convolve. default=`None` convolves all axes

diffsims.utils.fourier_transform.
fast_abs
(x, y=None)[source]¶ Fast computation of abs of an array
 Parameters
x (numpy.ndarray) – Input
y (numpy.ndarray or None, optional) – If y is not None, used as preallocated output
 Returns
y – Array equal to abs(x)
 Return type
numpy.ndarray

diffsims.utils.fourier_transform.
fast_fft_len
(n)[source]¶ Returns the smallest integer greater than input such that the fft can be computed efficiently at this size
 Parameters
n (int) – minimum size
 Returns
N – smallest integer greater than n which permits efficient ffts.
 Return type
int

diffsims.utils.fourier_transform.
fftshift_phase
(x)[source]¶ Fast implementation of fft_shift: fft(fftshift_phase(x)) = fft_shift(fft(x))
Note two things:  this is an inplace manipulation of the (3D) input array  the input array must have even side lengths. This is softly guaranteed by fast_fft_len but will raise error if not true.

diffsims.utils.fourier_transform.
from_recip
(y)[source]¶ Converts Fourier frequencies to spatial coordinates.
 Parameters
y (list [numpy.ndarray [float]], of shape [(nx,), (ny,), …]) – List (or equivalent) of vectors which define a mesh in the dimension equal to the length of x
 Returns
x – List of vectors defining a mesh such that for a function, f, defined on the mesh given by y, ifft(f) is defined on the mesh given by x. 0 will be in the middle of x.
 Return type
list [numpy.ndarray [float]], of shape [(nx,), (ny,), …]

diffsims.utils.fourier_transform.
get_DFT
(X=None, Y=None)[source]¶ Returns discrete analogues for the Fourier/inverse Fourier transform pair defined from grid X to grid Y and back again.
 Parameters
X (list [numpy.ndarray [float]], of shape [(nx,), (ny,), …], optional) – Mesh on real space
Y (list [numpy.ndarray [float]], of shape [(nx,), (ny,), …], optional) – Corresponding mesh on Fourier space
either X or Y is None then it is inferred from the other (If) –
 Returns
DFT (function(f, axes=None)) – If f is a function on X then DFT(f) is the Fourier transform of f on Y. axes parameter can be used to specify which axes to transform.
iDFT (function(f, axes=None)) – If f is a function on Y then iDFT(f) is the inverse Fourier transform of f on X. axes parameter can be used to specify which axes to transform.

diffsims.utils.fourier_transform.
get_recip_points
(ndim, n=None, dX=inf, rX=0, dY=inf, rY=1e16)[source]¶ Returns a minimal pair of real and Fourier grids which satisfy each given requirement.
 Parameters
ndim (int) – Dimension of domain
n (int, list of length ndim, or None , optional) – Sugested number of pixels (per dimension). default=`None` infers this from other parameters. If enough other constraints are given to define a discretisation then this will be shrunk if possible.
dX (float > 0 or list of float of length ndim, optional) – Maximum grid spacing (per dimension). default=`numpy.inf` infers this from other parameters
rX (float > 0 or list of float of length ndim, optional) – Minimum grid range (per dimension). default=`None` infers this from other parameters. In this case, range is maximal span, i.e. diameter.
dY (float > 0 or list of float of length ndim) – Maximum grid spacing (per dimension) in Fourier domain. default=`None` infers this from other parameters
rY (float > 0 or list of float of length ndim) – Minimum grid range (per dimension) in Fourier domain. default=`None` infers this from other parameters. In this case, range is maximal span, i.e. diameter.
 Returns
x (list [numpy.ndarray [float]], of shape [(nx,), (ny,), …]) – Real mesh of points, centred at 0 with at least n pixels, resolution higher than dX, and range greater than rX.
y (list [numpy.ndarray [float]], of shape [(nx,), (ny,), …]) – Fourier mesh of points, centred at 0 with at least n pixels, resolution higher than dY, and range greater than rY.

diffsims.utils.fourier_transform.
plan_fft
(A, n=None, axis=None, norm=None, **_)[source]¶ Plans an fft for repeated use. Parameters are the same as for pyfftw’s fftn which are, where possible, the same as the numpy equivalents. Note that some functionality is only possible when using the pyfftw backend.
 Parameters
A (numpy.ndarray, of dimension d) – Array of same shape to be input for the fft
n (iterable or None, len(n) == d, optional) – The output shape of fft (default=`None` is same as A.shape)
axis (int, iterable length d, or None, optional) – The axis (or axes) to transform (default=`None` is all axes)
overwrite (bool, optional) – Whether the input array can be overwritten during computation (default=False)
planner ({0, 1, 2, 3}, optional) – Amount of effort put into optimising Fourier transform where 0 is low and 3 is high (default=`1`).
threads (int, None) – Number of threads to use (default=`None` is all threads)
auto_align_input (bool, optional) – If True then may realign input (default=`True`)
auto_contiguous (bool, optional) – If True then may reorder input (default=`True`)
avoid_copy (bool, optional) – If True then may overwrite initial input (default=`False`)
norm ({None, 'ortho'}, optional) – Indicate whether fft is normalised (default=`None`)
 Returns
plan (function) – Returns the Fourier transform of B, plan() == fftn(B)
B (numpy.ndarray, A.shape) – Array which should be modified inplace for fft to be computed. If possible, B is A.
Example
A = numpy.zeros((8,16)) plan, B = plan_fft(A)
B[:,:] = numpy.random.rand(8,16) numpy.fft.fftn(B) == plan()
B = numpy.random.rand(8,16) numpy.fft.fftn(B) != plan()

diffsims.utils.fourier_transform.
plan_ifft
(A, n=None, axis=None, norm=None, **_)[source]¶ Plans an ifft for repeated use. Parameters are the same as for pyfftw’s ifftn which are, where possible, the same as the numpy equivalents. Note that some functionality is only possible when using the pyfftw backend.
 Parameters
A (numpy.ndarray, of dimension d) – Array of same shape to be input for the ifft
n (iterable or None, len(n) == d, optional) – The output shape of ifft (default=`None` is same as A.shape)
axis (int, iterable length d, or None, optional) – The axis (or axes) to transform (default=`None` is all axes)
overwrite (bool, optional) – Whether the input array can be overwritten during computation (default=False)
planner ({0, 1, 2, 3}, optional) – Amount of effort put into optimising Fourier transform where 0 is low and 3 is high (default=`1`).
threads (int, None) – Number of threads to use (default=`None` is all threads)
auto_align_input (bool, optional) – If True then may realign input (default=`True`)
auto_contiguous (bool, optional) – If True then may reorder input (default=`True`)
avoid_copy (bool, optional) – If True then may overwrite initial input (default=`False`)
norm ({None, 'ortho'}, optional) – Indicate whether ifft is normalised (default=`None`)
 Returns
plan (function) – Returns the inverse Fourier transform of B, plan() == ifftn(B)
B (numpy.ndarray, A.shape) – Array which should be modified inplace for ifft to be computed. If possible, B is A.

diffsims.utils.fourier_transform.
to_recip
(x)[source]¶ Converts spatial coordinates to Fourier frequencies.
 Parameters
x (list [numpy.ndarray [float]], of shape [(nx,), (ny,), …]) – List (or equivalent) of vectors which define a mesh in the dimension equal to the length of x
 Returns
y – List of vectors defining a mesh such that for a function, f, defined on the mesh given by x, fft(f) is defined on the mesh given by y
 Return type
list [numpy.ndarray [float]], of shape [(nx,), (ny,), …]
generic_utils¶
Created on 31 Oct 2019
Generic tools for all areas of code.
@author: Rob Tovey

class
diffsims.utils.generic_utils.
GLOBAL_BOOL
(val)[source]¶ Bases:
object
An object which behaves like a bool but can be changed inplace by set or by calling as a function.

diffsims.utils.generic_utils.
to_mesh
(x, dx=None, dtype=None)[source]¶  Generates dense meshes from grid vectors, broadly:
to_mesh(x)[i,j,…] = (x[0][i], x[1][j], …)
 Parameters
x (list [numpy.ndarray], of shape [(nx,), (ny,), …]) – List of grid vectors
dx (list [numpy.ndarray] or None, optional) – Basis in which to expand mesh, default is the canonical basis
dtype (str or None, optional) – String representing the numpy type of output, default inherits from x
 Returns
X – X[i,j,…, k] = x[0][i]*dx[0][k] + x[1][j]*dx[1][k] + …
 Return type
numpy.ndarray [dtype], (x[0].size, x[1].size, …, len(x))
kinematic_simulation_utils¶
Created on 1 Nov 2019
Back end for computing diffraction patterns with a kinematic model.
@author: Rob Tovey

diffsims.utils.kinematic_simulation_utils.
get_diffraction_image
(coordinates, species, probe, x, wavelength, precession, GPU=True, pointwise=False, **kwargs)[source]¶ Return kinematically simulated diffraction pattern
 Parameters
coordinates (numpy.ndarray [float], (n_atoms, 3)) – List of atomic coordinates
species (numpy.ndarray [int], (n_atoms,)) – List of atomic numbers
probe (diffsims.ProbeFunction) – Function representing 3D shape of beam
x (list [numpy.ndarray [float] ], of shapes [(nx,), (ny,), (nz,)]) – Mesh on which to compute the volume density
wavelength (float) – Wavelength of electron beam
precession (a pair (float, int)) – The float dictates the angle of precession and the int how many points are used to discretise the integration.
dtype ((str, str)) – tuple of floating/complex datatypes to cast outputs to
ZERO (float > 0, optional) – Rounding error permitted in computation of atomic density. This value is the smallest value rounded to 0.
GPU (bool, optional) – Flag whether to use GPU or CPU discretisation. Default (if available) is True
pointwise (bool, optional) – Optional parameter whether atomic intensities are computed pointwise at the centre of a voxel or an integral over the voxel. default=False
 Returns
DP – The twodimensional diffraction pattern evaluated on the reciprocal grid corresponding to the first two vectors of x.
 Return type
numpy.ndarray [dtype[0]], (nx, ny, nz)

diffsims.utils.kinematic_simulation_utils.
grid2sphere
(arr, x, dx, C)[source]¶ Projects 3d array onto a sphere.
 Parameters
arr (np.ndarray [float], (nx, ny, nz)) – Input function to be projected
x (list [np.ndarray [float]], of shapes [(nx,), (ny,), (nz,)]) – Vectors defining mesh of <arr>
dx (list [np.ndarray [float]], of shapes [(3,), (3,), (3,)]) – Basis in which to orient sphere. Centre of sphere will be at C*dx[2] and mesh of output array will be defined by the first two vectors.
C (float) – Radius of sphere.
 Returns
out – If y is the point on the line between i*dx[0]+j*dx[1] and C*dx[2] which also lies on the sphere of radius C from C*dx[2] then: out[i,j] = arr(y). Interpolation on arr is linear.
 Return type
np.ndarray [float], (nx, ny)

diffsims.utils.kinematic_simulation_utils.
precess_mat
(alpha, theta)[source]¶ Generates rotation matrices for precession curves.
 Parameters
alpha (float) – Angle (in degrees) of precession tilt
theta (float) – Angle (in degrees) along precession curve
 Returns
R – Rotation matrix associated to the tilt of alpha away from the vertical axis and a rotation of theta about the vertical axis.
 Return type
numpy.ndarray [float], (3, 3)
lobato_scattering_params¶
probe_utils¶
Created on 5 Nov 2019
@author: Rob Tovey

class
diffsims.utils.probe_utils.
ProbeFunction
(func=None)[source]¶ Bases:
object
Object representing a probe function.
 Parameters
func (function) – Function which takes in an array, r, of shape [nx, ny, nz, 3] and returns an array of shape [nx, ny, nz]. r[…,0] corresponds to the x coordinate, r[…, 1] to y etc. If not provided (or None) then the __call__ and FT methods must be overrided.

__call__
(x, out=None, scale=None)[source]¶ Returns func(x)*scale. If out is provided then it is used as preallocated storage. If scale is not provided then it is assumed to be 1. If x is a list of arrays it is converted into a mesh first.
 Parameters
x (numpy.ndarray, (nx, ny, nz, 3) or list of arrays of shape) – [(nx,), (ny,), (nz,)] Mesh points at which to evaluate the probe density.
out (numpy.ndarray, (nx, ny, nz), optional) – If provided then computation is performed inplace.
scale (numpy.ndarray, (nx, ny, nz), optional) – If provided then the probe density is scaled by this before being returned.
 Returns
out – An array equal to probe(x)*scale.
 Return type
numpy.ndarray, (nx, ny, nz)

FT
(y, out=None)[source]¶ Returns the Fourier transform of func on the mesh y. Again, if out is provided then computation is inplace. If y is a list of arrays then it is converted into a mesh first. If this function is not overridden then an approximation is made using func and the fft.
 Parameters
y (numpy.ndarray, (nx, ny, nz, 3) or list of arrays of shape) – [(nx,), (ny,), (nz,)] Mesh of Fourier coordinates at which to evaluate the probe density.
out (numpy.ndarray, (nx, ny, nz), optional) – If provided then computation is performed inplace.
 Returns
out – An array equal to FourierTransform(probe)(y).
 Return type
numpy.ndarray, (nx, ny, nz)

class
diffsims.utils.probe_utils.
BesselProbe
(r)[source]¶ Bases:
diffsims.utils.probe_utils.ProbeFunction
Probe function given by a radially scaled Bessel function of the first kind.
 Parameters
r (float) – Width of probe at the surface of the sample. More specifically, the smallest 0 of the probe.

__call__
(x, out=None, scale=None)[source]¶ If X = sqrt(x[…,0]**2+x[…,1]**2)/r then returns J_1(X)/X*scale. If out is provided then this is computed inplace. If scale is not provided then it is assumed to be 1. If x is a list of arrays it is converted into a mesh first.
 Parameters
x (numpy.ndarray, (nx, ny, nz, 3) or list of arrays of shape) – [(nx,), (ny,), (nz,)] Mesh points at which to evaluate the probe density. As a plotting utility, if a lower dimensional mesh is provided then the remaining coordinates are assumed to be 0 and so only the respective 1D/2D slice of the probe is returned.
out (numpy.ndarray, (nx, ny, nz), optional) – If provided then computation is performed inplace.
scale (numpy.ndarray, (nx, ny, nz), optional) – If provided then the probe density is scaled by this before being returned.
 Returns
out – An array equal to probe(x)*scale. If ny=0 or nz=0 then array is of smaller dimension.
 Return type
numpy.ndarray, (nx, ny, nz)

FT
(y, out=None)[source]¶ If Y = sqrt(y[…,0]**2 + y[…,1]**2)*r then returns an indicator function on the disc Y < 1, y[2]==0. Again, if out is provided then computation is inplace. If y is a list of arrays then it is converted into a mesh first.
 Parameters
y (numpy.ndarray, (nx, ny, nz, 3) or list of arrays of shape) – [(nx,), (ny,), (nz,)] Mesh of Fourier coordinates at which to evaluate the probe density. As a plotting utility, if a lower dimensional mesh is provided then the remaining coordinates are assumed to be 0 and so only the respective 1D/2D slice of the probe is returned.
out (numpy.ndarray, (nx, ny, nz), optional) – If provided then computation is performed inplace.
 Returns
out – An array equal to FourierTransform(probe)(y). If ny=0 or nz=0 then array is of smaller dimension.
 Return type
numpy.ndarray, (nx, ny, nz)
scattering_params¶
Scattering Paramaters as Tabulated in “Advanced Computing in Electron Microscopy  Second Edition (2010)  Earl.J.Kirkland” ISBN 9781441965325 Pages 253260 Appendix C
This transcription comes from scikitued (MIT license)  https://pypi.python.org/pypi/scikitued
shape_factor_models¶

diffsims.utils.shape_factor_models.
atanc
(excitation_error, max_excitation_error, minima_number=5)[source]¶ Intensity with arctan(s)/s profile that closely follows sin(s)/s but is smooth for s!=0.
 Parameters
excitation_error (arraylike or float) – The distance (reciprocal) from a reflection to the Ewald sphere
max_excitation_error (float) – The distance at which a reflection becomes extinct
minima_number (int) – The minima_number’th minima in the corresponding sinx/x lies at max_excitation_error from 0
 Returns
intensity
 Return type
arraylike or float

diffsims.utils.shape_factor_models.
binary
(excitation_error, max_excitation_error)[source]¶ Returns a unit intensity for all reflections

diffsims.utils.shape_factor_models.
linear
(excitation_error, max_excitation_error)[source]¶ Returns an intensity linearly scaled with by the excitation error

diffsims.utils.shape_factor_models.
lorentzian
(excitation_error, max_excitation_error)[source]¶ Lorentzian intensity profile that should approximate the twobeam rocking curve. This is equation (6) in reference [1].
 Parameters
 Returns
intensity_factor – Vector representing the relrod factor for each reflection
 Return type
arraylike or float
References
[1] L. Palatinus, P. Brázda, M. Jelínek, J. Hrdá, G. Steciuk, M. Klementová, Specifics of the data processing of precession electron diffraction tomography data and their implementation in the program PETS2.0, Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater. 75 (2019) 512–522. doi:10.1107/S2052520619007534.

diffsims.utils.shape_factor_models.
lorentzian_precession
(excitation_error, max_excitation_error, r_spot, precession_angle)[source]¶ Intensity profile factor for a precessed beam assuming a Lorentzian intensity profile for the unprecessed beam. This is equation (10) in reference [1].
 Parameters
excitation_error (arraylike or float) – The distance (reciprocal) from a reflection to the Ewald sphere
max_excitation_error (float) – The distance at which a reflection becomes extinct
r_spot (arraylike or float) – The distance (reciprocal) from each reflection to the origin
precession_angle (float) – The beam precession angle in degrees; the angle the beam makes with the optical axis.
 Returns
intensity_factor – Vector representing the relrod factor for each reflection
 Return type
arraylike or float
References
[1] L. Palatinus, P. Brázda, M. Jelínek, J. Hrdá, G. Steciuk, M. Klementová, Specifics of the data processing of precession electron diffraction tomography data and their implementation in the program PETS2.0, Acta Crystallogr. Sect. B Struct. Sci. Cryst. Eng. Mater. 75 (2019) 512–522. doi:10.1107/S2052520619007534.

diffsims.utils.shape_factor_models.
sin2c
(excitation_error, max_excitation_error, minima_number=5)[source]¶ Intensity with sin^2(s)/s^2 profile, after HowieWhelan relrod
 Parameters
 Returns
intensity
 Return type
arraylike or float
sim_utils¶

diffsims.utils.sim_utils.
acceleration_voltage_to_relativistic_mass
(acceleration_voltage)[source]¶ Get relativistic mass of electron as function of acceleration voltage.
 Parameters
acceleration_voltage (float) – In Volt
 Returns
mr – Relativistic electron mass
 Return type
Example
>>> import diffsims.utils.sim_utils as sim_utils >>> mr = sim_utils.acceleration_voltage_to_relativistic_mass(200000) # 200 kV

diffsims.utils.sim_utils.
acceleration_voltage_to_velocity
(acceleration_voltage)[source]¶ Get relativistic velocity of electron from acceleration voltage.
Example
>>> import diffsims.utils.sim_utils as sim_utils >>> v = sim_utils.acceleration_voltage_to_velocity(200000) # 200 kV >>> round(v) 208450035

diffsims.utils.sim_utils.
acceleration_voltage_to_wavelength
(acceleration_voltage)[source]¶ Get electron wavelength from the acceleration voltage.

diffsims.utils.sim_utils.
beta_to_bst
(beam_deflection, acceleration_voltage)[source]¶ Calculate Bs * t values from beam deflection (beta).
 Parameters
beam_deflection (NumPy array) – In radians
acceleration_voltage (float) – In Volts
 Returns
bst – In Tesla * meter
 Return type
NumPy array
Examples
>>> import numpy as np >>> import diffsims.utils.sim_utils as sim_utils >>> data = np.random.random((100, 100)) # In radians >>> acceleration_voltage = 200000 # 200 kV (in Volt) >>> bst = sim_utils.beta_to_bst(data, 200000)

diffsims.utils.sim_utils.
bst_to_beta
(bst, acceleration_voltage)[source]¶ Calculate beam deflection (beta) values from Bs * t.
 Parameters
bst (NumPy array) – Saturation induction Bs times thickness t of the sample. In Tesla*meter
acceleration_voltage (float) – In Volts
 Returns
beta – Beam deflection in radians
 Return type
NumPy array
Examples
>>> import numpy as np >>> import diffsims.utils.sim_utils as sim_utils >>> data = np.random.random((100, 100)) # In Tesla*meter >>> acceleration_voltage = 200000 # 200 kV (in Volt) >>> beta = sim_utils.bst_to_beta(data, acceleration_voltage)

diffsims.utils.sim_utils.
diffraction_scattering_angle
(acceleration_voltage, lattice_size, miller_index)[source]¶ Get electron scattering angle from a crystal lattice.
Returns the total scattering angle, as measured from the middle of the direct beam (0, 0, 0) to the given Miller index.
Miller index: h, k, l = miller_index Interplanar distance: d = a / (h**2 + k**2 + l**2)**0.5 Bragg’s law: theta = arcsin(electron_wavelength / (2 * d)) Total scattering angle (phi): phi = 2 * theta

diffsims.utils.sim_utils.
et_to_beta
(et, acceleration_voltage)[source]¶ Calculate beam deflection (beta) values from E * t.
 Parameters
et (NumPy array) – Electric field times thickness t of the sample.
acceleration_voltage (float) – In Volts
 Returns
beta – Beam deflection in radians
 Return type
NumPy array
Examples
>>> import numpy as np >>> import diffsims.utils.sim_utils as sim_utils >>> data = np.random.random((100, 100)) >>> acceleration_voltage = 200000 # 200 kV (in Volt) >>> beta = sim_utils.et_to_beta(data, acceleration_voltage)

diffsims.utils.sim_utils.
get_atomic_scattering_factors
(g_hkl_sq, coeffs, scattering_params)[source]¶ Calculate atomic scattering factors for n atoms.
 Parameters
g_hkl_sq (ndarray) – Onedimensional array of gvector lengths squared.
coeffs (ndarray) – Threedimensional array [n, 5, 2] of coefficients corresponding to the n atoms.
scattering_params (string) – Type of scattering factor calculation to use. One of ‘lobato’, ‘xtables’.
 Returns
scattering_factors – The calculated atomic scattering parameters.
 Return type
ndarray

diffsims.utils.sim_utils.
get_electron_wavelength
(accelerating_voltage)[source]¶ Calculates the (relativistic) electron wavelength in Angstroms for a given accelerating voltage in kV.

diffsims.utils.sim_utils.
get_holz_angle
(electron_wavelength, lattice_parameter)[source]¶ Converts electron wavelength and lattice paramater to holz angle :param electron_wavelength: In nanometers :type electron_wavelength: scalar :param lattice_parameter: In nanometers :type lattice_parameter: scalar
 Returns
scattering_angle – Scattering angle in radians
 Return type
scalar
Examples
>>> import diffsims.utils.sim_utils as sim_utils >>> lattice_size = 0.3905 # STO(001) in nm >>> wavelength = 2.51/1000 # Electron wavelength for 200 kV >>> angle = sim_utils.get_holz_angle(wavelength, lattice_size)

diffsims.utils.sim_utils.
get_intensities_params
(reciprocal_lattice, reciprocal_radius)[source]¶ Calculates the variables needed for get_kinematical_intensities
 Parameters
reciprocal_lattice (diffpy.Structure.Lattice) – The reciprocal crystal lattice for the structure of interest.
reciprocal_radius (float) – The radius of the sphere in reciprocal space (units of reciprocal Angstroms) within which reciprocal lattice points are returned.
 Returns
unique_hkls (arraylike) – The unique plane families which lie in the given reciprocal sphere.
multiplicites (arraylike) – The multiplicites of the given unqiue planes in the sphere.
g_hkls (list) – The g vector length of the given hkl in the sphere.

diffsims.utils.sim_utils.
get_interaction_constant
(accelerating_voltage)[source]¶ Calculates the interaction constant, sigma, for a given acelerating voltage.

diffsims.utils.sim_utils.
get_kinematical_intensities
(structure, g_indices, g_hkls_array, debye_waller_factors={}, scattering_params='lobato', prefactor=1)[source]¶ Calculates peak intensities.
The peak intensity is a combination of the structure factor for a given peak and the position the Ewald sphere intersects the relrod. In this implementation, the intensity scales linearly with proximity.
 Parameters
structure (Structure) – The structure for which to derive the structure factors.
g_indices (arraylike) – Indicies of spots to be considered
g_hkls_array (arraylike) – coordinates of spots to be considered
debye_waller_factors (dict of str:value pairs) – Maps element names to their temperaturedependent DebyeWaller factors.
scattering_params (str) – “lobato” or “xtables”
prefactor (arraylike) – multiplciation factor for structure factor
 Returns
peak_intensities – The intensities of the peaks.
 Return type
arraylike

diffsims.utils.sim_utils.
get_points_in_sphere
(reciprocal_lattice, reciprocal_radius)[source]¶ Finds all reciprocal lattice points inside a given reciprocal sphere. Utilised within the DiffractionGenerator.
 Parameters
reciprocal_lattice (diffpy.Structure.Lattice) – The reciprocal crystal lattice for the structure of interest.
reciprocal_radius (float) – The radius of the sphere in reciprocal space (units of reciprocal Angstroms) within which reciprocal lattice points are returned.
 Returns
spot_indices (numpy.array) – Miller indices of reciprocal lattice points in sphere.
cartesian_coordinates (numpy.array) – Cartesian coordinates of reciprocal lattice points in sphere.
spot_distances (numpy.array) – Distance of reciprocal lattice points in sphere from the origin.

diffsims.utils.sim_utils.
get_scattering_params_dict
(scattering_params)[source]¶ Get scattering parameter dictionary from name.
 Parameters
scattering_params (string) – Name of scattering factors. One of ‘lobato’, ‘xtables’.
 Returns
scattering_params_dict – Dictionary of scattering parameters mapping from element name.
 Return type

diffsims.utils.sim_utils.
get_unique_families
(hkls)[source]¶ Returns unique families of Miller indices, which must be permutations of each other.
 Parameters
hkls (list) – List of Miller indices ([h, k, l])
 Returns
pretty_unique – A dict with unique hkl and multiplicity {hkl: multiplicity}.
 Return type
dictionary

diffsims.utils.sim_utils.
get_vectorized_list_for_atomic_scattering_factors
(structure, debye_waller_factors, scattering_params)[source]¶ Create a flattened array of coeffs, fcoords and occus for vectorized computation of atomic scattering factors.
Note: The dimensions of the returned objects are not necessarily the same size as the number of atoms in the structure as each partially occupied specie occupies its own position in the flattened array.
 Parameters
structure (diffpy.structure) – The atomic structure for which scattering factors are required.
debye_waller_factors (list) – List of DebyeWaller factors for atoms in structure.
 Returns
coeffs (np.array()) – Coefficients of atomic scattering factor parameterization for each atom.
fcoords (np.array()) – Fractional coordinates of each atom in structure.
occus (np.array()) – Occupancy of each atomic site.
dwfactors (np.array()) – DebyeWaller factors for each atom in the structure.

diffsims.utils.sim_utils.
is_lattice_hexagonal
(latt)[source]¶ Determines if a diffpy lattice is hexagonal or trigonal. :param latt: The diffpy lattice object to be determined as hexagonal or not. :type latt: diffpy.Structure.lattice
 Returns
is_true – True if hexagonal or trigonal.
 Return type

diffsims.utils.sim_utils.
scattering_angle_to_lattice_parameter
(electron_wavelength, angle)[source]¶ Convert scattering angle data to lattice parameter sizes.
 Parameters
electron_wavelength (float) – Wavelength of the electrons in the electron beam. In nm. For 200 kV electrons: 0.00251 (nm)
angle (NumPy array) – Scattering angle, in radians.
 Returns
lattice_parameter – Lattice parameter, in nanometers
 Return type
NumPy array
Examples
>>> import diffsims.utils.sim_utils as sim_utils >>> angle_list = [0.1, 0.1, 0.1, 0.1] # in radians >>> wavelength = 2.51/1000 # Electron wavelength for 200 kV >>> lattice_size = sim_utils.scattering_angle_to_lattice_parameter( ... wavelength, angle_list)

diffsims.utils.sim_utils.
simulate_kinematic_scattering
(atomic_coordinates, element, accelerating_voltage, simulation_size=256, max_k=1.5, illumination='plane_wave', sigma=20, scattering_params='lobato')[source]¶ Simulate electron scattering from arrangement of atoms comprising one elemental species.
 Parameters
atomic_coordinates (array) – Array specifying atomic coordinates in structure.
element (string) – Element symbol, e.g. “C”.
accelerating_voltage (float) – Accelerating voltage in keV.
simulation_size (int) – Simulation size, n, specifies the n x n array size for the simulation calculation.
max_k (float) – Maximum scattering vector magnitude in reciprocal angstroms.
illumination (string) – Either ‘plane_wave’ or ‘gaussian_probe’ illumination
sigma (float) – Gaussian probe standard deviation, used when illumination == ‘gaussian_probe’
scattering_params (string) – Type of scattering factor calculation to use. One of ‘lobato’, ‘xtables’.
 Returns
simulation – ElectronDiffraction simulation.
 Return type
ElectronDiffraction

diffsims.utils.sim_utils.
tesla_to_am
(data)[source]¶ Convert data from Tesla to A/m
 Parameters
data (NumPy array) – Data in Tesla
 Returns
output_data – In A/m
 Return type
NumPy array
Examples
>>> import numpy as np >>> import diffsims.utils.sim_utils as sim_utils >>> data_T = np.random.random((100, 100)) # In tesla >>> data_am = sim_utils.tesla_to_am(data_T)
vector_utils¶

diffsims.utils.vector_utils.
get_angle_cartesian
(a, b)[source]¶ Compute the angle between two vectors in a cartesian coordinate system.
 Parameters
a (arraylike with 3 floats) – The two directions to compute the angle between.
b (arraylike with 3 floats) – The two directions to compute the angle between.
 Returns
angle – Angle between a and b in radians.
 Return type

diffsims.utils.vector_utils.
get_angle_cartesian_vec
(a, b)[source]¶ Compute the angles between two lists of vectors in a cartesian coordinate system.
 Parameters
a (np.array()) – The two lists of directions to compute the angle between in Nx3 float arrays.
b (np.array()) – The two lists of directions to compute the angle between in Nx3 float arrays.
 Returns
angles – List of angles between a and b in radians.
 Return type
np.array()

diffsims.utils.vector_utils.
vectorised_spherical_polars_to_cartesians
(z)[source]¶ Converts an array of spherical polars into an array of (x,y,z) = r(cos(psi)sin(theta),sin(psi)sin(theta),cos(theta))
 Parameters
z (np.array) – With rows of r : the radius value, r = sqrt(x**2+y**2+z**2) psi : The azimuthal angle generally (0,2pi]) theta : The elevation angle generally (0,pi)
 Returns
xyz – With rows of x,y,z
 Return type
np.array