Source code for pymatgen.analysis.diffraction.core

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

"""
This module implements core classes for calculation of diffraction patterns.
"""

import collections
import abc
import numpy as np
from pymatgen.core.spectrum import Spectrum
from pymatgen.util.plotting import add_fig_kwargs


[docs]class DiffractionPattern(Spectrum): """ A representation of a diffraction pattern """ XLABEL = "$2\\Theta$" YLABEL = "Intensity" def __init__(self, x, y, hkls, d_hkls): """ Args: x: Two theta angles. y: Intensities hkls: [{"hkl": (h, k, l), "multiplicity": mult}], where {"hkl": (h, k, l), "multiplicity": mult} is a dict of Miller indices for all diffracted lattice facets contributing to each intensity. d_hkls: List of interplanar spacings. """ super().__init__(x, y, hkls, d_hkls) self.hkls = hkls self.d_hkls = d_hkls
[docs]class AbstractDiffractionPatternCalculator(abc.ABC): """ Abstract base class for computing the diffraction pattern of a crystal. """ # Tolerance in which to treat two peaks as having the same two theta. TWO_THETA_TOL = 1e-5 # Tolerance in which to treat a peak as effectively 0 if the scaled # intensity is less than this number. Since the max intensity is 100, # this means the peak must be less than 1e-5 of the peak intensity to be # considered as zero. This deals with numerical issues where systematic # absences do not cancel exactly to zero. SCALED_INTENSITY_TOL = 1e-3
[docs] @abc.abstractmethod def get_pattern(self, structure, scaled=True, two_theta_range=(0, 90)): """ Calculates the 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 XRD 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: (DiffractionPattern) """ pass
[docs] def get_plot(self, structure, two_theta_range=(0, 90), annotate_peaks=True, ax=None, with_labels=True, fontsize=16): """ Returns the diffraction plot as a matplotlib.pyplot. Args: structure: Input structure 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. annotate_peaks: Whether to annotate the peaks with plane information. ax: matplotlib :class:`Axes` or None if a new figure should be created. with_labels: True to add xlabels and ylabels to the plot. fontsize: (int) fontsize for peak labels. Returns: (matplotlib.pyplot) """ if ax is None: from pymatgen.util.plotting import pretty_plot plt = pretty_plot(16, 10) ax = plt.gca() else: # This to maintain the type of the return value. import matplotlib.pyplot as plt xrd = self.get_pattern(structure, two_theta_range=two_theta_range) for two_theta, i, hkls, d_hkl in zip(xrd.x, xrd.y, xrd.hkls, xrd.d_hkls): if two_theta_range[0] <= two_theta <= two_theta_range[1]: label = ", ".join([str(hkl["hkl"]) for hkl in hkls]) ax.plot([two_theta, two_theta], [0, i], color='k', linewidth=3, label=label) if annotate_peaks: ax.annotate(label, xy=[two_theta, i], xytext=[two_theta, i], fontsize=fontsize) if with_labels: ax.set_xlabel(r"$2\theta$ ($^\circ$)") ax.set_ylabel("Intensities (scaled)") if hasattr(ax, "tight_layout"): ax.tight_layout() return plt
[docs] def show_plot(self, structure, **kwargs): """ Shows the diffraction plot. Args: structure (Structure): Input structure 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. annotate_peaks (bool): Whether to annotate the peaks with plane information. """ self.get_plot(structure, **kwargs).show()
[docs] @add_fig_kwargs def plot_structures(self, structures, fontsize=6, **kwargs): """ Plot diffraction patterns for multiple structures on the same figure. Args: structures (Structure): List of structures 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. annotate_peaks (bool): Whether to annotate the peaks with plane information. fontsize: (int) fontsize for peak labels. """ import matplotlib.pyplot as plt nrows = len(structures) fig, axes = plt.subplots(nrows=nrows, ncols=1, sharex=True, squeeze=False) for i, (ax, structure) in enumerate(zip(axes.ravel(), structures)): self.get_plot(structure, fontsize=fontsize, ax=ax, with_labels=i == nrows - 1, **kwargs) spg_symbol, spg_number = structure.get_space_group_info() ax.set_title("{} {} ({}) ".format(structure.formula, spg_symbol, spg_number)) return fig
[docs]def get_unique_families(hkls): """ Returns unique families of Miller indices. Families must be permutations of each other. Args: hkls ([h, k, l]): List of Miller indices. Returns: {hkl: multiplicity}: A dict with unique hkl and multiplicity. """ # TODO: Definitely can be sped up. def is_perm(hkl1, hkl2): h1 = np.abs(hkl1) h2 = np.abs(hkl2) return all([i == j for i, j in zip(sorted(h1), sorted(h2))]) unique = collections.defaultdict(list) for hkl1 in hkls: found = False for hkl2 in unique.keys(): if is_perm(hkl1, hkl2): found = True unique[hkl2].append(hkl1) break if not found: unique[hkl1].append(hkl1) pretty_unique = {} for k, v in unique.items(): pretty_unique[sorted(v)[-1]] = len(v) return pretty_unique