crystal

Crystallography-related utilities and functions.

Functions

B_matrix(lattice_parameters)	Compute the B matrix of a lattice in float64 (from anri.crystal.lpars_to_B(), no 2 pi).
B_to_rmt(B)	Convert the B matrix to the reciprocal metric tensor.
UBI_to_mt(UBI)	Convert from (U.B)^-1 matrix to metric tensor.
allowed_hkls(hkls, sym_matrices[, tol])	Mark the reflections that are not systematically absent in a space group.
cubic_grid_misorientation(step_deg)	Largest misorientation (degrees) from any orientation to its nearest point of the cubic Rodrigues grid.
cubochoric_quaternions(semi_edge_steps)	Quaternions of the cubochoric grid of rotations, uniform in volume (Rosca et al., 2014; Singh & De Graef, 2016).
disorientation(Ua, Ub, ops)	Smallest misorientation angle between orientations over a Laue group.
float64()	Evaluate JAX in float64 inside a with block, without changing the global setting.
lattice_parameters(structure)	Return the lattice parameters of a Dans_Diffraction.Crystal.
laue_rotations(sym_ops, B)	Proper rotations of a crystal's Laue group, as Cartesian matrices S in the crystal frame.
lpars_rlpars_to_B(lpars, rlpars)	Get the Busing-Levy B matrix from the direct and reciprocal lattice parameters.
lpars_to_B(lpars)	Convert lattice parameters to B matrix (cross-transform).
lpars_to_mt(lpars)	Convert lattice parameters to metric tensor.
mat_to_quat(U)	Convert rotation matrices to unit quaternions (w, x, y, z) with w >= 0.
mat_to_rod(U)	Convert rotation matrices (rotation angle below 180 degrees) to Rodrigues vectors.
metric_to_volume(metric)	Get the volume of the (direct or reciprocal space) unit cell from the (direct or reciprocal space) metric tensor.
mt_to_lpars(metric)	Convert (direct or reciprocal) metric tensor back to (direct or reciprocal) lattice parameters.
mt_to_rmt(mt)	Convert metric tensor to reciprocal metric tensor.
orientation_grid(step_deg, ops)	Orientations covering one fundamental zone of a Laue group, and their worst-case spacing.
quat_mul(a, b)	Multiply quaternions (w, x, y, z): the rotation b followed by a.
quat_to_mat(q)	Convert unit quaternions (w, x, y, z) to rotation matrices.
reflections(lattice_parameters, ...)	List every reflection of a crystal up to a d* (and that diffracts at this wavelength), without absences.
rings(ds[, tol])	Group reflections into rings of equal d*.
rmt_to_mt(rmt)	Convert reciprocal metric tensor to metric tensor.
rod_to_mat(r)	Convert Rodrigues vectors r = tan(t / 2) n to rotation matrices.
space_group(structure_or_name)	Return the space-group number of a Dans_Diffraction.Crystal, or of a Hermann-Mauguin symbol.
structure_factors(structure, hkl, wavelength)	Compute |F|^2 of reflections of a structure, with Debye-Waller factors and anomalous dispersion.
symmetry_matrices(space_group_number)	Return a space group's operations as 4 x 4 matrices acting on fractional coordinates.
to_fundamental_zone(U, ops)	Replace each orientation by its equivalent U S with the smallest rotation angle.