principia_materia.phonon_id.phonon_tools module

principia_materia.phonon_id.phonon_tools.adjust_eigenvectors_subspace(mat, frequencies, eigenvectors, tol=0.0001)

Adjust eigenvectors in degerate subspace based on the input matrices.

It picks the eigenvectors in the frequency degenarete subspace so that the sub-matrix of mat can be diagonalized by the eigenvectors as well.

Parameters:

  • mat (array of complex, shape(nq, nband, nband)) – Matrices the adjustments of eigenvectors are based on. Renormalized with mass.

  • frequencies (array of float, shape(nq, nband)) – Phonon frequencies, the subspace of eigenvectors are based on the degenracy of the phonon frequencies.

  • eigenvectors (array of complex, shape(nq, nband, nband)) – Phonon eigenvectors.

  • tol (float, optional, default to 1.0E-4) – Tolerance threshold.

Returns:

adjusted_eigenvectors – Ajusted eigenvectors.

Return type:

array of complex, shape(nq, nband, nband)

principia_materia.phonon_id.phonon_tools.compute_eigenvalues(dq, mass_matrix, UPLO='L', decimal=8)

Just find the eigenvalues and eigenvectors of Dq with mass matrix.

Parameters:

  • dq (array of complex, shape (nband, nband) or (nq, nband, nband)) – Dynamic matrix or an array of dynamic matrices.

  • mass_matrix (array of float, shape (nband, ) or (nband, nband)) – Mass matrix. (either mass_matrix or structure need to be present to compute phonon)

  • UPLO ('L' or 'U', optional, default to 'L') – Use either lower or upper triangular of the Hermetian matrix.

  • decimal (int, optional, default to 8) – Decimal points of the precision.

Returns:

  • evals (array of float, shape (nband, ) or (nq, nband)) – Eigenvalues of dynamic matrices.

  • evecs (array of complex, shape (nband, nband) or (nq, nband, nband)) – Phonon eigenvectors.

principia_materia.phonon_id.phonon_tools.compute_phonon_frequencies_from_eigenvalues(evals, units='cm-1')

Compute phonon frequencies from eigenvalues.

Parameters:

  • evals (array of float, shape (nband, ) or (nq, nband)) – Eigenvalues of dynamic matrices.

  • units (str, optional, default to 'cm-1') – Unit of phonon frequencies

Returns:

freqs – Phonon frequencies.

Return type:

array of float, shape (nband, ) or (nq, nband)

principia_materia.phonon_id.phonon_tools.compute_phonons(dq, mass_matrix=None, structure=None, units='cm-1', UPLO='L', decimal=8)

Compute phonon and eigenvectors for given structure, dynamic matrices and units.

It is using the following formula:

\[\hat{M}^{-\frac{1}{2}} \hat{D_q} \hat{M}^{-\frac{1}{2}} \vec{S} = \omega^2 \vec{S}\]

This class also support diagonalization and unit adjustments for an array of dynamic matrices.

Parameters:

  • dq (array of complex, shape (nband, nband) or (nq, nband, nband)) – Dynamic matrix or an array of dynamic matrices.

  • mass_matrix (array of float, shape (nband, ) or (nband, nband)) – Mass matrix. (either mass_matrix or structure need to be present to compute phonon)

  • structure (str or CrystalFTG instance) – Path to the CrystalFTG structure file or a CrystalFTG instance.

  • units (str, optional, default to 'cm-1') – Unit of phonon frequencies

  • UPLO ('L' or 'U', optional, default to 'L') – Use either lower or upper triangular of the Hermetian matrix.

  • decimal (int, optional, default to 8) – Decimal points of the precision.

Returns:

  • freqs (array of float, shape (nband, ) or (nq, nband)) – Phonon frequencies.

  • evecs (array of complex, shape (nband, nband) or (nq, nband, nband)) – Phonon eigenvectors.

principia_materia.phonon_id.phonon_tools.find_degenerate_frequencies(frequencies, tol=0.0001)

Find degerate sets of frequencies.

Parameters:

  • frequencies (array of float, shape(nq, nband)) – Phonon frequencies.

  • tol (float, optional, default to 1.0E-4) – Tolerance threshold.

Returns:

degenerate_indicies – Index of degenerate indices of the frequencies grouped into list of lists.

Return type:

list of lists of integers

principia_materia.phonon_id.phonon_tools.get_mass_matrix(structure)

Compute mass matrix from given structure.

Parameters:

structure (str or CrystalFTG instance) – Path to the CrystalFTG structure file or a CrystalFTG instance.

Returns:

mass_matrix – Mass matrix.

Return type:

array of float, shape (nband, nband)

principia_materia.phonon_id.phonon_tools.multiply_mass_matrix(dq, mass_matrix)

Multiply mass matrix to dynamic matrices.

Parameters:

  • dq (array of complex, shape (nband, nband) or (nq, nband, nband)) – Dynamic matrices.

  • mass_matrix (array of float, shape (nband, ) or (nband, nband)) – Mass matrix. (either mass_matrix or structure need to be present to compute phonon)

Returns:

dq – Mass renormalized dynamic matrices.

Return type:

array of complex, shape (nband, nband) or (nq, nband, nband)