Source code for pymatgen.analysis.diffraction.neutron

# coding: utf-8
# Copyright (c) Pymatgen Development Team.
# Distributed under the terms of the MIT License.

"""
This module implements a neutron diffraction (ND) pattern calculator.
"""

from math import sin, cos, asin, pi, degrees, radians
import os

import numpy as np
import json

from .core import DiffractionPattern, AbstractDiffractionPatternCalculator, \
    get_unique_families
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer

__author__ = "Yuta Suzuki"
__copyright__ = "Copyright 2018, The Materials Project"
__version__ = "0.1"
__maintainer__ = "Yuta Suzuki"
__email__ = "resnant@outlook.jp"
__date__ = "4/19/18"

with open(os.path.join(os.path.dirname(__file__),
                       "neutron_scattering_length.json")) as f:
    # This table was cited from "Neutron Data Booklet" 2nd ed (Old City 2003).
    ATOMIC_SCATTERING_LEN = json.load(f)


[docs]class NDCalculator(AbstractDiffractionPatternCalculator): """ Computes the powder neutron diffraction pattern of a crystal structure. This code is a slight modification of XRDCalculator in pymatgen.analysis.diffraction.xrd. See it for details of the algorithm. Main changes by using neutron instead of X-ray are as follows: 1. Atomic scattering length is a constant. 2. Polarization correction term of Lorentz factor is unnecessary. Reference: Marc De Graef and Michael E. McHenry, Structure of Materials 2nd ed, Chapter13, Cambridge University Press 2003. """ def __init__(self, wavelength=1.54184, symprec=0, debye_waller_factors=None): """ Initializes the ND calculator with a given radiation. Args: wavelength (float): The wavelength of neutron in angstroms. Defaults to 1.54, corresponds to Cu K_alpha x-ray radiation. symprec (float): Symmetry precision for structure refinement. If set to 0, no refinement is done. Otherwise, refinement is performed using spglib with provided precision. debye_waller_factors ({element symbol: float}): Allows the specification of Debye-Waller factors. Note that these factors are temperature dependent. """ self.wavelength = wavelength self.symprec = symprec self.debye_waller_factors = debye_waller_factors or {}
[docs] def get_pattern(self, structure, scaled=True, two_theta_range=(0, 90)): """ Calculates the powder neutron diffraction pattern for a structure. Args: structure (Structure): Input structure scaled (bool): Whether to return scaled intensities. The maximum peak is set to a value of 100. Defaults to True. Use False if you need the absolute values to combine ND plots. two_theta_range ([float of length 2]): Tuple for range of two_thetas to calculate in degrees. Defaults to (0, 90). Set to None if you want all diffracted beams within the limiting sphere of radius 2 / wavelength. Returns: (NDPattern) """ if self.symprec: finder = SpacegroupAnalyzer(structure, symprec=self.symprec) structure = finder.get_refined_structure() wavelength = self.wavelength latt = structure.lattice is_hex = latt.is_hexagonal() # Obtained from Bragg condition. Note that reciprocal lattice # vector length is 1 / d_hkl. min_r, max_r = (0, 2 / wavelength) if two_theta_range is None else \ [2 * sin(radians(t / 2)) / wavelength for t in two_theta_range] # Obtain crystallographic reciprocal lattice points within range recip_latt = latt.reciprocal_lattice_crystallographic recip_pts = recip_latt.get_points_in_sphere( [[0, 0, 0]], [0, 0, 0], max_r) if min_r: recip_pts = [pt for pt in recip_pts if pt[1] >= min_r] # Create a flattened array of coeffs, fcoords and occus. This is # used to perform vectorized computation of atomic scattering factors # later. Note that these are not necessarily the same size as the # structure as each partially occupied specie occupies its own # position in the flattened array. coeffs = [] fcoords = [] occus = [] dwfactors = [] for site in structure: for sp, occu in site.species.items(): try: c = ATOMIC_SCATTERING_LEN[sp.symbol] except KeyError: raise ValueError("Unable to calculate ND pattern as " "there is no scattering coefficients for" " %s." % sp.symbol) coeffs.append(c) dwfactors.append(self.debye_waller_factors.get(sp.symbol, 0)) fcoords.append(site.frac_coords) occus.append(occu) coeffs = np.array(coeffs) fcoords = np.array(fcoords) occus = np.array(occus) dwfactors = np.array(dwfactors) peaks = {} two_thetas = [] for hkl, g_hkl, ind, _ in sorted( recip_pts, key=lambda i: (i[1], -i[0][0], -i[0][1], -i[0][2])): # Force miller indices to be integers. hkl = [int(round(i)) for i in hkl] if g_hkl != 0: d_hkl = 1 / g_hkl # Bragg condition theta = asin(wavelength * g_hkl / 2) # s = sin(theta) / wavelength = 1 / 2d = |ghkl| / 2 (d = # 1/|ghkl|) s = g_hkl / 2 # Calculate Debye-Waller factor dw_correction = np.exp(-dwfactors * (s ** 2)) # Vectorized computation of g.r for all fractional coords and # hkl. g_dot_r = np.dot(fcoords, np.transpose([hkl])).T[0] # Structure factor = sum of atomic scattering factors (with # position factor exp(2j * pi * g.r and occupancies). # Vectorized computation. f_hkl = np.sum(coeffs * occus * np.exp(2j * pi * g_dot_r) * dw_correction) # Lorentz polarization correction for hkl lorentz_factor = 1 / (sin(theta) ** 2 * cos(theta)) # Intensity for hkl is modulus square of structure factor. i_hkl = (f_hkl * f_hkl.conjugate()).real two_theta = degrees(2 * theta) if is_hex: # Use Miller-Bravais indices for hexagonal lattices. hkl = (hkl[0], hkl[1], - hkl[0] - hkl[1], hkl[2]) # Deal with floating point precision issues. ind = np.where(np.abs(np.subtract(two_thetas, two_theta)) < self.TWO_THETA_TOL) if len(ind[0]) > 0: peaks[two_thetas[ind[0][0]]][0] += i_hkl * lorentz_factor peaks[two_thetas[ind[0][0]]][1].append(tuple(hkl)) else: peaks[two_theta] = [i_hkl * lorentz_factor, [tuple(hkl)], d_hkl] two_thetas.append(two_theta) # Scale intensities so that the max intensity is 100. max_intensity = max([v[0] for v in peaks.values()]) x = [] y = [] hkls = [] d_hkls = [] for k in sorted(peaks.keys()): v = peaks[k] fam = get_unique_families(v[1]) if v[0] / max_intensity * 100 > self.SCALED_INTENSITY_TOL: x.append(k) y.append(v[0]) hkls.append(fam) d_hkls.append(v[2]) nd = DiffractionPattern(x, y, hkls, d_hkls) if scaled: nd.normalize(mode="max", value=100) return nd