StructureFactor

The StructureFactor object contains the structure factor at every q-point and mode, and optionally a temperature if temperature-dependent effects such as the Debye-Waller factor were used in the calculation.

Calculating Scattering Intensities

The structure factors can be used to create a \(S(Q, \omega)\) map with Q on the x-axis and energy on the y-axis using StructureFactor.calculate_sqw_map (see docstring for algorithm details). This requires an array of energy bin edges as a pint.Quantity. Calculating the Bose population factor is optional, but if calc_bose=True the temperature stored in StructureFactor is used. If there is no temperature in StructureFactor, then it must be provided in the function arguments. This function returns a generic Spectrum2D object.

from euphonic import ureg, StructureFactor

sf = StructureFactor.from_json_file('sf_100K.json')
energy_bins = np.arange(-100, 101, 1)*ureg('meV')
sqw_map = sf.calculate_sqw_map(energy_bins calc_bose=True)

Docstring

class StructureFactor(crystal, qpts, frequencies, structure_factors, temperature=None)

Stores the structure factor calculated per q-point and per phonon mode

Variables:
  • crystal (Crystal) – Lattice and atom information
  • n_qpts (int) – Number of q-points in the object
  • qpts ((n_qpts, 3) float ndarray) – Q-point coordinates, in fractional coordinates of the reciprocal lattice
  • frequencies ((n_qpts, 3*crystal.n_atoms) float Quantity) – Phonon frequencies per q-point and mode
  • structure_factors ((n_qpts, 3*crystal.n_atoms) float Quantity) – Structure factor per q-point and mode
  • temperature (float Quantity or None) – The temperature used to calculate any temperature-dependent parts of the structure factor (e.g. Debye-Waller, Bose population factor). None if no temperature-dependent effects have been applied
__init__(crystal, qpts, frequencies, structure_factors, temperature=None)
Parameters:
  • crystal (Crystal) – Lattice and atom information
  • qpts ((n_qpts, 3) float ndarray) – Q-point coordinates, in fractional coordinates of the reciprocal lattice
  • frequencies ((n_qpts, 3*crystal.n_atoms) float Quantity) – Phonon frequencies per q-point and mode
  • structure_factors ((n_qpts, 3*crystal.n_atoms) float Quantity) – Structure factor per q-point and mode
  • temperature (float Quantity or None) – The temperature used to calculate any temperature-dependent parts of the structure factor (e.g. Debye-Waller, Bose population factor). None if no temperature-dependent effects have been applied
calculate_sqw_map(e_bins, calc_bose=True, temperature=None)

Bin the structure factor in energy and apply the Bose population factor to produce a a S(Q,w) map

Parameters:
  • e_bins ((n_e_bins + 1,) float Quantity) – The energy bin edges
  • calc_bose (boolean, optional) – Whether to calculate and apply the Bose population factor
  • temperature (float Quantity, optional) – The temperature to use to calculate the Bose factor. Is only required if StructureFactor.temperature = None, otherwise the temperature stored in StructureFactor will be used
Returns:

sqw_map – A spectrum containing the q-point bins on the x-axis, energy bins on the y-axis and scattering intensities on the z-axis
Return type:

Spectrum2D
Raises:

ValueError – If a temperature is provided and isn’t consistent with the temperature in the StructureFactor object

Notes

StructureFactor.structure_factors is defined as \(|F(Q, \nu)|\) per unit cell. To create an \(S(Q,\omega)\) map, it is binned in energy and the Bose factor is applied [1]:

\[S(Q, \omega) = |F(Q, \nu)|^2 (n_\nu+\frac{1}{2}\pm\frac{1}{2}) \delta(\omega\mp\omega_{q\nu})\]

\(n_\nu\) is the Bose-Einstein distribution:

\[n_\nu = \frac{1}{e^{\frac{\hbar\omega_\nu}{k_{B}T}} - 1}\]
[1]M.T. Dove, Structure and Dynamics, Oxford University Press, Oxford, 2003, 225-226
to_dict()

Convert to a dictionary. See StructureFactor.from_dict for details on keys/values

Returns:
Return type:dict
to_json_file(filename)

Write to a JSON file. JSON fields are equivalent to StructureFactor.from_dict keys

Parameters:filename (str) – Name of the JSON file to write to
classmethod from_dict(d)

Convert a dictionary to a StructureFactor object

Parameters:d (dict) –

A dictionary with the following keys/values:

  • ’crystal’: dict, see Crystal.from_dict
  • ’qpts’: (n_qpts, 3) float ndarray
  • ’frequencies’: (n_qpts, 3*crystal.n_atoms) float ndarray
  • ’frequencies_unit’: str
  • ’structure_factors’: (n_qpts, 3*crystal.n_atoms) float ndarray
  • ’structure_factors_unit’: str

There are also the following optional keys:

  • ’temperature’: float
  • ’temperature_unit’: str
Returns:
Return type:StructureFactor
classmethod from_json_file(filename)

Read from a JSON file. See StructureFactor.from_dict for required fields

Parameters:filename (str) – The file to read from
Returns:
Return type:StructureFactor