Space#
The space module contains functions for working with real and reciprocal-space maps.
- cell(nu, nv, nw, A)[source]#
Supercell lattice points.
- Parameters:
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- A2d array, 3x3
Transformation matrix from crystal to Cartesian coodinates in real space.
- Returns:
- ix, iy, iz1d array
Lattice points in Cartesian coordinates.
- condition(H, K, L, nu=1, nv=1, nw=1, centering=None)[source]#
Reflection condition.
Symbol
Reflection condition
P
Primitive
I
Body-centered
F
Face-centered
R(obv)
Rhombohedral, obverse
R(rev)
Rhombohedral, reverse
C
C-centered
A
A-centered
B
B-centered
- Parameters:
- H, K, L1d array, int
Supercell index along the \(a^*\), \(b^*\), and \(c^*\)-axis in reciprocal space.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell. Default is
1.- centeringstr
Lattice centering. The default is
None.
- Returns:
- h, k, l1d array
Supercell index where reflection condition is met.
- cond1d array, bool
Array indices where reflection condition is met.
- debye_waller(h_range, k_range, l_range, nh, nk, nl, U11, U22, U33, U23, U13, U12, a_, b_, c_, W=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]))[source]#
Debye-Waller factor.
- Parameters:
- h_range, k_range, l_range2-tuple or 2-list
Extents of \(h\), \(k\), and \(l\) (min, max) pairs
- nh, nk, nlint
Number of grid points along the axes of the reciprocal space volume.
- U11, U22, U33, U23, U13, U121d array
Atomic displacement parameters in crystal axis system.
- a_, b_, c_float
Reciprocal lattice costants \(a^*\), \(b^*\) and \(c^*\).
- W2d array, 3x3, optional
Transformation matrix from axis-aligned to nonaxis-aligned projection. Default is the identity matrix.
- Returns:
- T1d arry
Temperature factor.
- factor(nu, nv, nw)[source]#
Phase factor for discrete Fourier Transform.
- Parameters:
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- Returns:
- pf1d array
Spatial vector in Cartesian coordinates.
- indices(mask)[source]#
Masked and unmasked indices.
- Parameters:
- mask1d array, bool
Mask array.
- Returns:
- i_mask1d array, int
Indices of the masked values.
- i_unmask1d array, int
Indices of the unmask values.
- intensity(delta_k, i_dft, factors)[source]#
Average structural scattering intensity.
- Parameters:
- delta_k1d array
Fourier transform of occupancy parameter.
- i_dft1d array, int
Array indices of Fourier transform corresponding to reciprocal space.
- factors1d array
Prefactors of form factors, phase factors, and composition factors.
- Returns:
- I1d array
Intensity. Array has a flattened shape of size
i_dft.shape[0].
- mapping(h_range, k_range, l_range, nh, nk, nl, nu, nv, nw, W=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), laue=None)[source]#
Reciprocal space mapping.
- Parameters:
- h_range, k_range, l_range2-tuple or 2-list
Extents of \(h\), \(k\), and \(l\) (min, max) pairs
- nh, nk, nlint
Number of grid points along the axes of the reciprocal space volume.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- W2d array, 3x3, optional
Transformation matrix from axis-aligned to nonaxis-aligned projection. Default is the identity matrix.
- lauestr
Laue class to use for symmetrization. Default is
None.
- Returns:
- h, k, l1d array
Reciprocal space lattice units
- H, K, L1d array, int
Supercell index along the \(a^*\), \(b^*\), and \(c^*\)-axis in reciprocal space.
- index1d array, int
Index of reduced data.
- reverses1d array, int
Mapping of reduced data that reconstructs full volume.
- symops1d array, str
Symmetry operations correspoding to Laue class.
- prefactors(scattering_length, phase_factor, occupancy)[source]#
Scattering prefactors.
- Parameters:
- scattering_length1d array
Scattering length or form factors.
- phase_factor1d array
Phase factors
- occupancy1d array
Unit cell occupancies.
- Returns:
- factors1d array
Constant prefactors.
- real(ux, uy, uz, ix, iy, iz, atm)[source]#
Real space spatial vectors.
- Parameters:
- ux, uy, uz1d array
Unit cell atomic coordinates in Cartesian coordiantes.
- ix, iy, iz1d array
Supercell lattice points in Cartesian coordinates.
- atm1d array, str
Unit cell atomic, ions, or isotopes.
- Returns:
- rx, ry, rz1d array
Spatial vector in Cartesian coordinates.
- atms1d array, str
Supercell atomic, ions, or isotopes.
- reciprocal(h_range, k_range, l_range, mask, B, W=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]))[source]#
Reciprocal space wavevector.
- Parameters:
- h_range, k_range, l_range2-tuple or 2-list
Extents of \(h\), \(k\), and \(l\) (min, max) pairs.
- mask3d array, bool
Reciprocal space volume mask. Shape determines bin size.
- B2d array, 3x3
Transformation matrix from crystal to Cartesian coodinates in reciprocal space.
- W2d array, 3x3, optional
Transformation matrix from axis-aligned to nonaxis-aligned projection. Default is the identity matrix.
- Returns:
- Qh, Qk, Ql1d array
Wavevector in Cartesian coordinates.
- reduced(h_range, k_range, l_range, nh, nk, nl, nu, nv, nw, W=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), laue=None)[source]#
Reduced reciprocal space mapping with resolution constrained by supercell.
- Parameters:
- h_range, k_range, l_range2-tuple or 2-list
Extents of \(h\), \(k\), and \(l\) (min, max) pairs
- nh, nk, nlint
Number of grid points along the axes of the reciprocal space volume.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- W2d array, 3x3, optional
Transformation matrix from axis-aligned to nonaxis-aligned projection. Default is the identity matrix.
- lauestr
Laue class to use for symmetrization. Default is
None.
- Returns:
- index1d array, int
Index of reduced data.
- reverses1d array, int
Mapping of reduced data that reconstructs full volume.
- symops1d array, str
Symmetry operations correspoding to Laue class.
- Nu, Nv, Nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell corresponding to the resolution of reciprocal space.
- structure(delta_k, i_dft, factors)[source]#
Partial average structure factor.
- Parameters:
- delta_k1d array
Fourier transform of occupancy parameter.
- i_dft1d array, int
Array indices of Fourier transform corresponding to reciprocal space.
- factors1d array
Prefactors of scattering lengths, phase factors, and occupancies.
- Returns:
- F1d array
Structure factor. Array has a flattened shape of size
coeffs.shape[0]*i_dft.shape[0].- prod1d array
Partial structure factor. Array has a flattened shape of size
coeffs.shape[0]*i_dft.shape[0]*n_atm.
- transform(delta_r, H, K, L, nu, nv, nw, n_atm)[source]#
Discrete Fourier transform of occupancy parameter.
- Parameters:
- delta_r1d array
Occupancy parameter.
- H, K, L1d array, int
Supercell index along the \(a^*\), \(b^*\), and \(c^*\)-axis in reciprocal space.
- nu, nv, nwint
Number of grid points \(N_1\), \(N_2\), \(N_3\) along the \(a\), \(b\), and \(c\)-axis of the supercell.
- n_atmint
Number of atoms in the unit cell.
- Returns:
- delta_k1d array
Fourier transform of occupancy parameter. Array has a flattened shape of size
nu*nw*nv*n_atm.- i_dft1d array, int
Fourier transform indices. Array has a flattened shape of size
nu*nw*nv*n_atm.