# pymatgen.analysis.diffraction.xrd module

This module implements an XRD pattern calculator.

class XRDCalculator(wavelength='CuKa', symprec=0, debye_waller_factors=None)

  Bases: `pymatgen.analysis.diffraction.core.AbstractDiffractionPatternCalculator`

  Computes the XRD pattern of a crystal structure.

  This code is implemented by Shyue Ping Ong as part of UCSD’s NANO106 - Crystallography of Materials. The formalism for this code is based on that given in Chapters 11 and 12 of Structure of Materials by Marc De Graef and Michael E. McHenry. This takes into account the atomic scattering factors and the Lorentz polarization factor, but not the Debye-Waller (temperature) factor (for which data is typically not available). Note that the multiplicity correction is not needed since this code simply goes through all reciprocal points within the limiting sphere, which includes all symmetrically equivalent facets. The algorithm is as follows

  1. Calculate reciprocal lattice of structure. Find all reciprocal points within the limiting sphere given by \(\\frac{2}{\\lambda}\).

  2. For each reciprocal point \(\\mathbf{g_{hkl}}\) corresponding to lattice plane \((hkl)\), compute the Bragg condition \(\\sin(\\theta) = \\frac{\\lambda}{2d_{hkl}}\)

  3. Compute the structure factor as the sum of the atomic scattering factors. The atomic scattering factors are given by

     \[\begin{split}f(s) = Z - 41.78214 \\times s^2 \\times \\sum\\limits_{i=1}^n a_i \ \\exp(-b_is^2)\end{split}\]

     where \(s = \\frac{\\sin(\\theta)}{\\lambda}\) and \(a_i\) and \(b_i\) are the fitted parameters for each element. The structure factor is then given by

     \[\begin{split}F_{hkl} = \\sum\\limits_{j=1}^N f_j \\exp(2\\pi i \\mathbf{g_{hkl}} \\cdot \\mathbf{r})\end{split}\]

  4. The intensity is then given by the modulus square of the structure factor.

     \[I_{hkl} = F_{hkl}F_{hkl}^*\]

  5. Finally, the Lorentz polarization correction factor is applied. This factor is given by:

     \[\begin{split}P(\\theta) = \\frac{1 + \\cos^2(2\\theta)} {\\sin^2(\\theta)\\cos(\\theta)}\end{split}\]

  Initializes the XRD calculator with a given radiation.

  Parameters

    - wavelength (str/float) – The wavelength can be specified as either a float or a string. If it is a string, it must be one of the supported definitions in the AVAILABLE_RADIATION class variable, which provides useful commonly used wavelengths. If it is a float, it is interpreted as a wavelength in angstroms. Defaults to “CuKa”, i.e, Cu K_alpha 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.

    - symbol (debye_waller_factors ({element) – float}): Allows the specification of Debye-Waller factors. Note that these factors are temperature dependent.

  AVAILABLE_RADIATION = ('CuKa', 'CuKa2', 'CuKa1', 'CuKb1', 'MoKa', 'MoKa2', 'MoKa1', 'MoKb1', 'CrKa', 'CrKa2', 'CrKa1', 'CrKb1', 'FeKa', 'FeKa2', 'FeKa1', 'FeKb1', 'CoKa', 'CoKa2', 'CoKa1', 'CoKb1', 'AgKa', 'AgKa2', 'AgKa1', 'AgKb1')
  get_pattern(structure, scaled=True, two_theta_range=(0, 90))

    Calculates the diffraction pattern for a structure.

    Parameters

      - 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

      (XRDPattern)