Structural#
The structural module contains functions for working with both site and occupancies and atomic displacements required for setting up a general structural refinement.
- intensity(U_k, A_k, Q_k, coeffs, cond, p, i_dft, factors, subtract=True)[source]#
Structural scattering intensity.
- Parameters:
- U_k1d array
Fourier transform of Taylor expansion displacement products.
- A_k1d array
Fourier transform of relative site occupancies.
- Q_k1d array
Fourier transform of Taylor expansion wavevector products.
- coeffs1d array
Taylor expansion coefficients.
- cond1d array
Array indices corresponding to nuclear Bragg peaks.
- pint
Order of Taylor expansion.
- 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].
- structure(U_k, A_k, Q_k, coeffs, cond, p, i_dft, factors)[source]#
Partial displacive structure factor.
- Parameters:
- U_k1d array
Fourier transform of Taylor expansion displacement products.
- A_k1d array
Fourier transform of relative site occupancies times Taylor expansion displacement products.
- Q_k1d array
Fourier transform of Taylor expansion wavevector products.
- coeffs1d array
Taylor expansion coefficients.
- cond1d array
Array indices corresponding to nuclear Bragg peaks.
- pint
Order of Taylor expansion.
- 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].- F_nuc1d array
Bragg structure factor. Array has a flattened shape of size
cond.sum()*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.- prod_nuc1d array
Partial Bragg structure factor.Array has a flattened shape of size
coeffs.sum()*i_dft.shape[0]*n_atm.- V_k1d array
Structural parameter. Array has a flattened shape of size
coeffs.shape[0]*i_dft.shape[0]*n_atm.- V_k_nuc1d array
Bragg Structural parameter. Array has a flattened shape of size
coeffs.sum()*i_dft.shape[0]*n_atm.- even1d array, int
Array indices of the even Taylor expandion coefficients.
- bragg1d array, int
Indices of integer reciprocal coordinates. Array has a flattened shape of size
coeffs.sum().
- transform(U_r, A_r, H, K, L, nu, nv, nw, n_atm)[source]#
Discrete Fourier transform of Taylor expansion displacement products and relative occupancy parameter.
- Parameters:
- U_r1d array
Displacement parameter \(U\) (in Cartesian coordinates).
- A_r1d array
Relative occupancy parameter \(A\).
- 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:
- U_k1d array
Fourier transform of displacement paramter. Array has a flattened shape of size
nu*nw*nv*n_atm.- A_k1d array
Fourier transform of relative 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.