Source code for dynasor.post_processing.x_ray_form_factors
import json
from importlib.resources import files
from typing import List, Dict
from warnings import warn
from numpy import exp, abs, pi
from pandas import DataFrame, concat
from .weights import Weights
[docs]class XRayFormFactors(Weights):
r"""This class generates sample weights corresponding to X-ray form factors,
specifically the non-dispersion corrected parametrized form factors.
In general, the form factor for may be written as
.. math::
f(q, \omega) = f_0(q) + f'(q, \omega) + if''(q, \omega)
where :math:`q` is a scalar, corresponding to the norm
of the desired reciprocal lattice point.
The weights generated by this class corresponds to :math:`f_0(q)`.
There are two possible parametrizations of :math:`f_0(q)`
to choose from, both based on a sum of exponentials of the form
.. math::
f_0(q) = \sum_{i=1}^k a_i \exp(-b_i q^2) + c.
Two parametrizations are available:
* ``'waasmaier-1995'`` corresponds to Table 1 from D. Waasmaier, A. Kirfel,
Acta Crystallographica Section A **51**, 416 (1995);
`doi: 10.1107/S0108767394013292 <https://doi.org/10.1107/S0108767394013292>`_.
This parametrization uses five exponentials (:math:`k=5`) and extends up to
:math:`6.0\,\mathrm{Å}^{-1}`.
* ``'itc-2006'`` corresponds to Table 6.1.1.4. from
*International Tables for Crystallography, Volume C: Mathematical, physical
and chemical tables* (2006);
`doi: 10.1107/97809553602060000103 <https://doi.org/10.1107/97809553602060000103>`_.
This parametrization use sfour exponentials (:math:`k=4`) and extends up to
:math:`2.0\,\mathrm{Å}^{-1}`.
In practice differences are expected to be insignificant. It is unlikely that
you have to deviate from the default, which is ``'waasmaier-1995'``.
Parameters
----------
atom_types
List of atomic species for which to retrieve scattering lengths.
source
Source to use for parametrization of the form factors :math:`f_0(q)`.
Allowed values are ``'waasmaier-1995'`` and ``'itc-2006'``
(see above).
"""
def __init__(
self,
atom_types: List[str],
source: str = 'waasmaier-1995'
):
self._source = source
form_factors = self._read_form_factors(source)
# Select the relevant species
form_factors = form_factors[form_factors.index.isin(atom_types)] # Atom species is index
self._form_factors = form_factors
# Check if any of the fetched form factors are missing,
# indicating that it is missing in the experimental database.
for s in atom_types:
row = form_factors[form_factors.index == s]
if row.empty:
if s == 'H':
# Manually insert values for H such that the form factor is
# zero and raise a warning, since it is such a common element.
warn('No parametrization for H. Setting form factor for H to zero.')
values = [['DUMMY', 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
form_factors = concat([DataFrame(data=values,
index=['H'],
columns=form_factors.columns),
form_factors])
continue
raise ValueError('Missing tabulated values '
f'for requested species {s}.')
weights_coh = form_factors.to_dict(orient='index')
supports_currents = False
super().__init__(weights_coh, None, supports_currents=supports_currents)
[docs] def get_weight_coh(self, atom_type, q_norm):
"""Get the coherent weight for a given atom type and q-vector norm."""
return self._compute_f0(self._weights_coh[atom_type], q_norm, self._source)
def _compute_f0(
self,
coefficients: Dict,
q_norm: float,
source: str):
r"""Compute :math:`f_0(q)` based on the chosen parametrization.
There are two possible parametrizations of :math:`f_0(q)` to choose from,
both based on a sum of exponentials of the form
.. math::
f_0(q) = \sum_{i=1}^k a_i * exp(-b_i * s**2) + c
where :math:`s = sin(theta) / lambda`.
Parameters
----------
coefficients
Parametrization parameters, read from the corresponding source file.
q_norm
The |q|-value at which to evaluate the form factor.
source
Either 'waasmaier-1995' or 'itc-2006',
corresponding to the two available sources for the
parametrization of the :math:`f_0(q)` term of the form factors.
"""
s = q_norm / (4 * pi) # q in dynasor is q = 4 pi sin(theta) / lambda.
s_squared = s*s # s = sin(theta) / lambda
if source == 'waasmaier-1995':
if abs(s) > 6.0:
warn('Waasmaier parametrization is not reliable for q '
'above 75.398 rad/Å (corresponding to s=6.0 1/Å)')
return self._get_f0(coefficients, s_squared, nmax=5)
elif source == 'itc-2006':
if abs(s) > 2.0:
warn('ITC.C parametrization is not reliable for q '
'above 25.132 rad/Å (corresponding to s=2.0 1/Å)')
return self._get_f0(coefficients, s_squared, nmax=4)
else:
raise ValueError(f'Unknown source {source}')
def _get_f0(self, coefficients, s_squared, nmax=5):
r"""
Compute parametrisations of :math:`f_0(q)` on the form
.. math::
f_0(q) = \sum_{i=1}^k a_i * exp(-b_i * s**2) + c
where :math:`s = sin(theta) / lambda`.
"""
f0 = coefficients['c']
for i in range(1, nmax+1):
f0 += coefficients[f'a{i}'] * exp(-coefficients[f'b{i}'] * s_squared)
return f0
def _read_form_factors(self, source: str) -> DataFrame:
r"""
Extracts the parametrization for the form factors :math:`f_0(q)`,
based on either of two sources.
Parameters
----------
source
Either 'waasmaier-1995' or 'itc-2006',
corresponding to the two available sources for the
parametrization of the :math:`f_0(q)` term of the form factors.
"""
if source == 'waasmaier-1995':
data_file = files(__package__) / \
'form-factors/x-ray-parameters-waasmaier-kirfel-1995.json'
with open(data_file) as fp:
coefficients = json.load(fp)
form_factors = DataFrame.from_dict(coefficients)
form_factors.index.names = ['species']
elif source == 'itc-2006':
data_file = files(__package__) / \
'form-factors/x-ray-parameters-itcc-2006.json'
with open(data_file) as fp:
coefficients = json.load(fp)
form_factors = DataFrame.from_dict(coefficients)
# There are two entries for H, one calculated using
# Hartree-Fock and one calculated with SDS.
# Both parametrizations are similar. We'll
# use HF since that has been used for the majority
# of species.
form_factors.drop(index='0', inplace=True) # H SDS is the first row
form_factors = form_factors.set_index('species')
else:
raise ValueError(f'Unknown source {source}')
return form_factors