principia_materia.phonon_id.fourier_interpolation module

class principia_materia.phonon_id.fourier_interpolation.FourierInterpolation(structure, supa, order, pg='C1', tol=1e-06)

Bases: DynamicTensors

Generic Fourier interpolation of phonon interactions at arbitrary order.

Supports either dynamic tensors or force constants tensors as input, if dynamic tensors are provided, Fourier transform to force constants tensors and then perform WS cell packing; if force constants tensors are provided, skip the Fourier tranformation step.

Parameters:

structure (CrystalFTG object or a structure file of CrystalFTG) – The crystal structure.
supa (array of int, shape(dim, dim)) – The supercell matrix.
order (int) – Order of the dynamic tensor.
pg (str or PointGroup object) – The point group.
tol (float, optional, default to 1.0E-6) – Error tolerence.

analytic_derivative_dynamic_tensor(Qpoints)

Computes analytic derivatives of dynamic tensors with respect to Q-point.

The short range part is calculated as as following.

\[\frac{\partial\hat D_{\mathbf{K}}}{\partial K_\alpha} = \sum_{\mathbf{y}} \imag T_\alpha e^{\imag \mathbf{K} \cdot \mathbf{y}\hat a} \hat \Phi_{\mathbf{y}}\]

copy()

Make a copy

Returns:: new – A copy of the object.
Return type:: FourierInterpolation

fourier_transform(): Fourier transform dynamic tensors to real space force constants tensor.

classmethod from_dynamic_tensors(dynamic_tensors)

get_Phi(): Get force constants tensors of FTG.

get_Phi_WS_at_Tpoint(Tpoint): Get the force constants tensor at T-point that is shifted within the WS cell.

get_Phi_WS_dict()

Get all the force constants tensors that are shifted within the WS cell of the FTG.

Returns:: Phi_WS – The force constants tensors that are shifted within the WS cell of the FTG.
Return type:: OrderedDict with nested tuples of int as keys and array of complex as values

get_Tindex(Tpoints)

Similar to the indexing system of the Q-points, compute index of T-points

All T-points in a set FTG have consecutive indices from 0 to n_Tpoints - 1, thus we can create our own hash table for Phi.

Parameters:: Tpoints (array of int, shape(N, order, dim)) – An array of T-points to compute indices for.

get_Tpoints(): Get T-points of the FTG.

interpolate_Qpoint(Qpoints, q_direction=None)

Interpolate Phi to arbitrary Q-point(s) in reciprocal space.

Parameters:

Qpoints (array of float or Fraction, shape(dim, ) or shape(N, dim)) – The Q-point(s) to interpolate into.
q_direction (array of float or Fraction, shape(dim, ), optional, default to None) – The q-direction that’s used for dipole-dipole contribution for second order insulators.

prepend_hiden_t(Tpoints)

Prepend hidden t-point to T-points.

For a T-point at given order, the first t-point is always (0, 0, 0), this it can be omitted and referred to as the hidden t-point. This method prepend the hidden t-point back.

Parameters:: Tpoints (array of int, shape(N, order - 1, dim)) – T-points without the hidden t-point.

set_D(Qpoints, D)

Set dynamic tensors.

If force constants tensors are set, dynamic tensors cannot be set.

set_Phi(Tpoints, Phi)

Set force constants tensor.

If dynamic tensors are set, force constants tensors can only obtained by Fourier transform.

Parameters:

Tpoints (array of int, shape(N, order - 1, dim) or shape(N, order, dim)) – T-points of FTG. Can be the full T-points or the T-points without the hidden t-point.
Phi (array of real or complex, shape(N, ndof, ..., ndof), shape(N, ndof, ..., ndof, m)) – Force constants tensors in the same order as the Tpoints. Can be trivial force constants tensors or vectorized tensors with the last axis being the vector axis.

set_Wigner_Seitz_map(): Computes the WS map.

set_dipoledipole_contribution()

Set Dipole-Dipole contribution for Fourier Interpolation.

At second order, the dipole-dipole contribution for fourier interpolation is treated separately, the code computes the dipole-dipole terms on the FTG then transform to real space into a dummy Phi. It will be subtracted out of the regular fource constants when constructing Phi_WS.

set_irreducible_D(D): Set dynamic tensors of the irreducible Q-points.

principia_materia.phonon_id.fourier_interpolation.get_FourierInterpolation_from_hdf5(filename, tol=1e-06): Load FourierInterpolation from HDF5 file.

principia_materia.phonon_id.fourier_interpolation.get_FourierInterpolation_hdf5_wrapper(): HDF5 data wrapper for FourierInterpolation.

principia_materia.phonon_id.fourier_interpolation.save_FourierInterpolation_to_hdf5(obj, h5file='fourier_interpolation.hdf5', overwrite=False)

Save FourierInterpolation data into HDF5 file.

Parameters:

obj (FourierInterpolation) – A FourierInterpolation object.
h5file (str or h5py.File/h5py.Group obejct, optional, default to "fourier_interpolation.hdf5") – Path to a HDF5 file or a h5py.File/h5py.Group object.
overwrite (bool, optional, default to False) – When the file exists, whether to replace the content of the file with the content to be saved.