abinslib.almost_isotropic_incoherent

Semi-analytic powder averaging approximations in CLIMAX/AbINS lineage.

Functions

calculate_almost_isotropic_incoherent_fundamentals(...)

Calculate fundamental mode intensities in almost-isotropic approximation.

calculate_almost_isotropic_incoherent_combinations(...)

Calculate second-order mode intensities in almost-isotropic approximation.

calculate_almost_isotropic_incoherent_spectra(...)

Calculate INS intensities in almost-isotropic incoherent approximation.

calculate_almost_isotropic_incoherent_combination_spectra(...)

Calculate two-phonon intensities in almost-isotropic incoherent approximation.

q_scaling_almost_isotropic_incoherent_combination_spectra(...)

Calculate two-phonon intensities in almost-isotropic incoherent approximation.

mantid_like_combination_spectra(...)

Calculate two-phonon intensities with approximations from Abins-Mantid.

Module Contents

abinslib.almost_isotropic_incoherent.calculate_almost_isotropic_incoherent_fundamentals(mode_displacements: abinslib.displacements.Displacements, atomic_displacements: euphonic.Quantity, nominal_q2: euphonic.Quantity) → numpy.ndarray[source]

Calculate fundamental mode intensities in almost-isotropic approximation.

S = exp(-(Q^2 tr(A + 2 tr(A:B)/tr(B))/5)) Q^2 tr(B) / 3

  • Fundamentals only

  • Atomic cross sections not applied

  • Ignore actual q-points and use nominal Q^2 instead

Parameters:

  • mode_displacements – phonon mode displacement dataset

  • atomic_displacements – thermal average atomic displacements indexed (atom, direction, direction)

  • nominal_q2 – Scalar Q^2 values corresponding to modes; note that all q-points are used and this is typically related to the mode frequency by neutron instrument parameters.

Returns:

Dimensionless mode intensities with array indices (qpt, mode, atom)

abinslib.almost_isotropic_incoherent.calculate_almost_isotropic_incoherent_combinations(mode_displacements: abinslib.displacements.Displacements, atomic_displacements: euphonic.Quantity, nominal_q2: euphonic.Quantity, include_dw: bool = False) → numpy.ndarray[source]

Calculate second-order mode intensities in almost-isotropic approximation.

S(Q, ω_ν + ω_ν’) =

exp(-Q^2 tr(A/3)) Q^4 / 15C (tr(B_ν)tr(B_ν’) + B_ν:B_ν’ + B_ν’:B_ν)

for some atom, where C = 2 if ν=ν’ else 1

  • Atomic cross sections not applied

  • Ignore actual q-points and use nominal Q^2 instead

Note that this has cubic scaling with system size as n_modes ∝ n_atoms; while this reference implementation constructs the whole array, memory-efficient approaches need to reduce the data to binned spectra on-the-fly.

It is also possible to reduce the calculation effort by calculating at constant Q and rescaling the intensity based on post-binning Q values; this is implemented in q_scaling_almost_isotropic_incoherent_combination_spectra()

Parameters:

  • mode_displacements – phonon mode displacement dataset

  • atomic_displacements – thermal average atomic displacements indexed (atom, direction, direction)

  • nominal_q2 – Scalar Q^2 values corresponding to modes; note that all q-points are used and this is typically related to the mode frequency by neutron instrument parameters.

  • include_dw – Include mode-by-mode Debye-Waller intensity scaling

Returns:

Dimensionless combination mode intensities with array indices (qpt1, mode1, qpt2, mode2, atom)

abinslib.almost_isotropic_incoherent.calculate_almost_isotropic_incoherent_spectra(modes: euphonic.QpointPhononModes, mode_displacements: abinslib.displacements.Displacements, atomic_displacements: euphonic.Quantity, nominal_q2: euphonic.Quantity, bins: euphonic.Quantity, apply_cross_section: bool = True) → euphonic.spectra.Spectrum1DCollection[source]

Calculate INS intensities in almost-isotropic incoherent approximation.

Actual q-points of phonon modes will be disregarded; instead each mode intensity will be based on a separate array of nominal Q^2 values corresponding to modes. This is intended to approximate powder-averaging with kinematic constraints: for indirect geometry the energy-Q^2 relationship can be determined using abinslib.utils.calculate_indirect_q2.

Parameters:

  • modes – phonon frequency and eigenvector dataset

  • mode_displacements – phonon mode displacement dataset (This can be obtained using Displacements.from_modes(modes)().)

  • atomic_displacements – thermal average atomic displacements indexed (atom, direction, direction)

  • nominal_q2 – Scalar Q^2 values corresponding to modes; note that all q-points are used and this is typically related to the mode frequency by neutron instrument parameters.

  • bins – Energy or frequency bins used as x_data in resulting spectra

  • apply_cross_section – Multiply each atom/isotope spectrum by a corresponding total neutron scattering cross-section (σ_tot).

Returns:

binned spectra of contribution from each nucleus

abinslib.almost_isotropic_incoherent.calculate_almost_isotropic_incoherent_combination_spectra(modes: euphonic.QpointPhononModes, mode_displacements: abinslib.displacements.Displacements, atomic_displacements: euphonic.Quantity, nominal_q2: euphonic.Quantity, bins: euphonic.Quantity, apply_cross_section: bool = True) → euphonic.spectra.Spectrum1DCollection[source]

Calculate two-phonon intensities in almost-isotropic incoherent approximation.

Actual q-points of phonon modes will be disregarded; instead each mode intensity will be based on a separate array of nominal Q^2 values corresponding to modes. This is intended to approximate powder-averaging with kinematic constraints: for indirect geometry the energy-Q^2 relationship can be determined using abinslib.utils.calculate_indirect_q2.

These should be determined for each two-phonon combination

Parameters:

  • modes – phonon frequency and eigenvector dataset

  • mode_displacements – phonon mode displacement dataset (This can be obtained using Displacements.from_modes(modes)().)

  • atomic_displacements – thermal average atomic displacements indexed (atom, direction, direction)

  • nominal_q2 – Scalar Q^2 values for each combination of two fundamental modes, indexed by (q, band, q, band). This is typically related to the combination mode frequency by neutron instrument parameters.

  • bins – Energy or frequency bins used as x_data in resulting spectra

  • apply_cross_section – Multiply each atom/isotope spectrum by a corresponding total neutron scattering cross-section (σ_tot).

Returns:

binned spectra of contribution from each nucleus

abinslib.almost_isotropic_incoherent.q_scaling_almost_isotropic_incoherent_combination_spectra(modes: euphonic.QpointPhononModes, mode_displacements: abinslib.displacements.Displacements, atomic_displacements: euphonic.Quantity, nominal_q2: euphonic.Quantity, bins: euphonic.Quantity, apply_cross_section: bool = True) → euphonic.spectra.Spectrum1DCollection[source]

Calculate two-phonon intensities in almost-isotropic incoherent approximation.

Actual q-points of phonon modes will be disregarded; instead each mode intensity will be based on a separate array of nominal Q^2 values corresponding to modes. This is intended to approximate powder-averaging with kinematic constraints.

Here we also make the “optimisation” that intensities are initially calculated at Q=1 and then re-scaled after binning. (Not actually a big computational optimisation here as we still multiply a large Q2 array, but it imitates the Mantid implementation.)

Parameters:

  • modes – phonon frequency and eigenvector dataset

  • mode_displacements – phonon mode displacement dataset (This can be obtained using Displacements.from_modes(modes)().)

  • atomic_displacements – thermal average atomic displacements indexed (atom, direction, direction)

  • nominal_q2 – Scalar Q^2 values corresponding to bin centres. For indirect geometry the energy-Q^2 relationship can be determined using abinslib.utils.calculate_indirect_q2.

  • bins – Energy or frequency bins used as x_data in resulting spectra

  • apply_cross_section – Multiply each atom/isotope spectrum by a corresponding total neutron scattering cross-section (σ_tot).

Returns:

binned spectra of contribution from each nucleus

abinslib.almost_isotropic_incoherent.mantid_like_combination_spectra(modes: euphonic.QpointPhononModes, mode_displacements: abinslib.displacements.Displacements, atomic_displacements: euphonic.Quantity, nominal_q2: euphonic.Quantity, bins: euphonic.Quantity, apply_cross_section: bool = True) → euphonic.spectra.Spectrum1DCollection[source]

Calculate two-phonon intensities with approximations from Abins-Mantid.

Currently the emphasis is on reproducibility, not efficiency.

  • DOS-like almost-isotropic incoherent approximation (i.e. semi-analytic powder-averaging equations with traces and contractions)

  • Calculate at nominal Q=1, rescale for Q4 relation and apply Debye-Waller _after_ binning

  • Treat each input q-point independently: - only consider combination modes at each q - weight each of these spectra with the weight of corresponding q

  • Order-2 scale factor is 1/60 for overtones and 1/30 for combinations

  • DW factor is still correctly averaged over q-point contributions

Parameters:

  • modes – phonon frequency and eigenvector dataset

  • mode_displacements – phonon mode displacement dataset (This can be obtained using Displacements.from_modes(modes)().)

  • atomic_displacements – thermal average atomic displacements indexed (atom, direction, direction)

  • nominal_q2 – Scalar Q^2 values corresponding to bin centres. For indirect geometry the energy-Q^2 relationship can be determined using abinslib.utils.calculate_indirect_q2.

  • bins – Energy or frequency bins used as x_data in resulting spectra

  • apply_cross_section – Multiply each atom/isotope spectrum by a corresponding total neutron scattering cross-section (σ_tot).

Returns:

binned spectra of contribution from each nucleus