pymatgen.analysis.diffraction.core — pymatgen 2020.7.3 documentation

# 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

    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

    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

        @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

        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

        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()

        @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

    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