Merge pull request #720 from HEXRD/revert-crystallography-functions

Replace previously archived functions

hexrd/material/crystallography.py

@@ -27,6 +27,8 @@
 # =============================================================================
 import re
 import copy
+import csv
+import os
 from math import pi
 from typing import Optional, Union, Dict, List, Tuple
 
@@ -163,6 +165,32 @@ def processWavelength(arg: Union[valunits.valWUnit, float]) -> float:
             'wavelength', 'length', constants.keVToAngstrom(arg), 'angstrom'
         ).getVal(dUnit)
 
+def latticeParameters(lvec):
+    """
+    Generates direct and reciprocal lattice vector components in a
+    crystal-relative RHON basis, X. The convention for fixing X to the
+    lattice is such that a || x1 and c* || x3, where a and c* are
+    direct and reciprocal lattice vectors, respectively.
+    """
+    lnorm = np.sqrt(np.sum(lvec**2, 0))
+
+    a = lnorm[0]
+    b = lnorm[1]
+    c = lnorm[2]
+
+    ahat = lvec[:, 0] / a
+    bhat = lvec[:, 1] / b
+    chat = lvec[:, 2] / c
+
+    gama = np.arccos(np.dot(ahat, bhat))
+    beta = np.arccos(np.dot(ahat, chat))
+    alfa = np.arccos(np.dot(bhat, chat))
+    if outputDegrees:
+        gama = r2d * gama
+        beta = r2d * beta
+        alfa = r2d * alfa
+
+    return [a, b, c, alfa, beta, gama]
 
 def latticePlanes(
     hkls: np.ndarray,
@@ -540,6 +568,135 @@ def latticeVectors(
         'rparms': rparms,
     }
 
+def hexagonalIndicesFromRhombohedral(hkl):
+    """
+    converts rhombohedral hkl to hexagonal indices
+    """
+    HKL = np.zeros((3, hkl.shape[1]), dtype='int')
+
+    HKL[0, :] = hkl[0, :] - hkl[1, :]
+    HKL[1, :] = hkl[1, :] - hkl[2, :]
+    HKL[2, :] = hkl[0, :] + hkl[1, :] + hkl[2, :]
+
+    return HKL
+
+
+def rhombohedralIndicesFromHexagonal(HKL):
+    """
+    converts hexagonal hkl to rhombohedral indices
+    """
+    hkl = np.zeros((3, HKL.shape[1]), dtype='int')
+
+    hkl[0, :] = 2 * HKL[0, :] + HKL[1, :] + HKL[2, :]
+    hkl[1, :] = -HKL[0, :] + HKL[1, :] + HKL[2, :]
+    hkl[2, :] = -HKL[0, :] - 2 * HKL[1, :] + HKL[2, :]
+
+    hkl = hkl / 3.0
+    return hkl
+
+
+def rhombohedralParametersFromHexagonal(a_h, c_h):
+    """
+    converts hexagonal lattice parameters (a, c) to rhombohedral
+    lattice parameters (a, alpha)
+    """
+    a_r = np.sqrt(3 * a_h**2 + c_h**2) / 3.0
+    alfa_r = 2 * np.arcsin(3.0 / (2 * np.sqrt(3 + (c_h / a_h) ** 2)))
+    if outputDegrees:
+        alfa_r = r2d * alfa_r
+    return a_r, alfa_r
+
+
+def convert_Miller_direction_to_cartesian(uvw, a=1.0, c=1.0, normalize=False):
+    """
+    Converts 3-index hexagonal Miller direction indices to components in the
+    crystal reference frame.
+    Parameters
+    ----------
+    uvw : array_like
+        The (n, 3) array of 3-index hexagonal indices to convert.
+    a : scalar, optional
+        The `a` lattice parameter.  The default value is 1.
+    c : scalar, optional
+        The `c` lattice parameter.  The default value is 1.
+    normalize : bool, optional
+        Flag for whether or not to normalize output vectors
+    Returns
+    -------
+    numpy.ndarray
+        The (n, 3) array of cartesian components associated with the input
+        direction indices.
+    Notes
+    -----
+    1) The [uv.w] the Miller-Bravais convention is in the hexagonal basis
+       {a1, a2, a3, c}.  The basis for the output, {o1, o2, o3}, is
+       chosen such that
+       o1 || a1
+       o3 || c
+       o2 = o3 ^ o1
+    """
+    u, v, w = np.atleast_2d(uvw).T
+    retval = np.vstack([1.5 * u * a, sqrt3by2 * a * (2 * v + u), w * c])
+    if normalize:
+        return unitVector(retval).T
+    else:
+        return retval.T
+
+
+def convert_Miller_direction_to_MillerBravias(uvw, suppress_redundant=True):
+    """
+    Converts 3-index hexagonal Miller direction indices to 4-index
+    Miller-Bravais direction indices.
+    Parameters
+    ----------
+    uvw : array_like
+        The (n, 3) array of 3-index hexagonal Miller indices to convert.
+    suppress_redundant : bool, optional
+        Flag to suppress the redundant 3rd index.  The default is True.
+    Returns
+    -------
+    numpy.ndarray
+        The (n, 3) or (n, 4) array -- depending on kwarg -- of Miller-Bravis
+        components associated with the input Miller direction indices.
+    Notes
+    -----
+    * NOT for plane normals!!!
+    """
+    u, v, w = np.atleast_2d(uvw).T
+    retval = np.vstack([(2 * u - v) / 3, (2 * v - u) / 3, w]).T
+    rem = np.vstack([np.mod(np.tile(i[0], 2), i[1:]) for i in retval])
+    rem[abs(rem) < epsf] = np.nan
+    lcm = np.nanmin(rem, axis=1)
+    lcm[np.isnan(lcm)] = 1
+    retval = retval / np.tile(lcm, (3, 1)).T
+    if suppress_redundant:
+        return retval
+    else:
+        t = np.atleast_2d(1 - np.sum(retval[:2], axis=1)).T
+        return np.hstack([retval[:, :2], t, np.atleast_2d(retval[:, 2]).T])
+
+
+def convert_MillerBravias_direction_to_Miller(UVW):
+    """
+    Converts 4-index hexagonal Miller-Bravais direction indices to
+    3-index Miller direction indices.
+    Parameters
+    ----------
+    UVW : array_like
+        The (n, 3) array of **non-redundant** Miller-Bravais direction indices
+        to convert.
+    Returns
+    -------
+    numpy.ndarray
+        The (n, 3) array of Miller direction indices associated with the
+        input Miller-Bravais indices.
+    Notes
+    -----
+    * NOT for plane normals!!!
+    """
+    U, V, W = np.atleast_2d(UVW).T
+    return np.vstack([2 * U + V, 2 * V + U, W])
+
 
 class PlaneData(object):
     """
@@ -1618,6 +1775,68 @@ def _makeScatteringVectors(
 
         return Qs_vec, Qs_ang0, Qs_ang1
 
+    def calcStructFactor(self, atominfo):
+        """
+        Calculates unit cell structure factors as a function of hkl
+        USAGE:
+        FSquared = calcStructFactor(atominfo,hkls,B)
+        INPUTS:
+        1) atominfo (m x 1 float ndarray) the first threee columns of the
+        matrix contain fractional atom positions [uvw] of atoms in the unit
+        cell. The last column contains the number of electrons for a given atom
+        2) hkls (3 x n float ndarray) is the array of Miller indices for
+        the planes of interest.  The vectors are assumed to be
+        concatenated along the 1-axis (horizontal)
+        3) B (3 x 3 float ndarray) is a matrix of reciprocal lattice basis
+        vectors,where each column contains a reciprocal lattice basis vector
+        ({g}=[B]*{hkl})
+        OUTPUTS:
+        1) FSquared (n x 1 float ndarray) array of structure factors,
+        one for each hkl passed into the function
+        """
+        r = atominfo[:, 0:3]
+        elecNum = atominfo[:, 3]
+        hkls = self.hkls
+        B = self.latVecOps['B']
+        sinThOverLamdaList, ffDataList = LoadFormFactorData()
+        FSquared = np.zeros(hkls.shape[1])
+
+        for jj in np.arange(0, hkls.shape[1]):
+            # ???: probably have other functions for this
+            # Calculate G for each hkl
+            # Calculate magnitude of G for each hkl
+            G = (
+                hkls[0, jj] * B[:, 0]
+                + hkls[1, jj] * B[:, 1]
+                + hkls[2, jj] * B[:, 2]
+            )
+            magG = np.sqrt(G[0] ** 2 + G[1] ** 2 + G[2] ** 2)
+
+            # Begin calculating form factor
+            F = 0
+            for ii in np.arange(0, r.shape[0]):
+                ff = RetrieveAtomicFormFactor(
+                    elecNum[ii], magG, sinThOverLamdaList, ffDataList
+                )
+                exparg = complex(
+                    0.0,
+                    2.0
+                    * np.pi
+                    * (
+                        hkls[0, jj] * r[ii, 0]
+                        + hkls[1, jj] * r[ii, 1]
+                        + hkls[2, jj] * r[ii, 2]
+                    ),
+                )
+                F += ff * np.exp(exparg)
+
+            """
+            F = sum_atoms(ff(Q)*e^(2*pi*i(hu+kv+lw)))
+            """
+            FSquared[jj] = np.real(F * np.conj(F))
+
+        return FSquared
+
     # OLD DEPRECATED PLANE_DATA STUFF ====================================
     @deprecated(new_func="len(self.hkls.T)", removal_date="2025-08-01")
     def getNHKLs(self):
@@ -1910,6 +2129,70 @@ def getDparms(
     return latVecOps['dparms']
 
 
+def LoadFormFactorData():
+    """
+    Script to read in a csv file containing information relating the
+    magnitude of Q (sin(th)/lambda) to atomic form factor
+    Notes:
+    Atomic form factor data gathered from the International Tables of
+    Crystallography:
+     P. J. Brown, A. G. Fox,  E. N. Maslen, M. A. O'Keefec and B. T. M. Willis,
+    "Chapter 6.1. Intensity of diffracted intensities", International Tables
+     for Crystallography (2006). Vol. C, ch. 6.1, pp. 554-595
+    """
+
+    dir1 = os.path.split(valunits.__file__)
+    dataloc = os.path.join(dir1[0], 'data', 'FormFactorVsQ.csv')
+
+    data = np.zeros((62, 99), float)
+
+    # FIXME: marked broken by DP
+    jj = 0
+    with open(dataloc, 'rU') as csvfile:
+        datareader = csv.reader(csvfile, dialect=csv.excel)
+        for row in datareader:
+            ii = 0
+            for val in row:
+                data[jj, ii] = float(val)
+                ii += 1
+            jj += 1
+
+    sinThOverLamdaList = data[:, 0]
+    ffDataList = data[:, 1:]
+
+    return sinThOverLamdaList, ffDataList
+
+
+def RetrieveAtomicFormFactor(elecNum, magG, sinThOverLamdaList, ffDataList):
+    """Interpolates between tabulated data to find the atomic form factor
+    for an atom with elecNum electrons for a given magnitude of Q
+    USAGE:
+    ff = RetrieveAtomicFormFactor(elecNum,magG,sinThOverLamdaList,ffDataList)
+    INPUTS:
+    1) elecNum, (1 x 1 float) number of electrons for atom of interest
+    2) magG (1 x 1 float) magnitude of G
+    3) sinThOverLamdaList (n x 1 float ndarray) form factor data is tabulated
+       in terms of sin(theta)/lambda (A^-1).
+    3) ffDataList (n x m float ndarray) form factor data is tabulated in terms
+       of sin(theta)/lambda (A^-1). Each column corresponds to a different
+       number of electrons
+    OUTPUTS:
+    1) ff (n x 1 float) atomic form factor for atom and hkl of interest
+    NOTES:
+    Data should be calculated in terms of G at some point
+    """
+    sinThOverLambda = 0.5 * magG
+    # lambda=2*d*sin(th)
+    # lambda=2*sin(th)/G
+    # 1/2*G=sin(th)/lambda
+
+    ff = np.interp(
+        sinThOverLambda, sinThOverLamdaList, ffDataList[:, (elecNum - 1)]
+    )
+
+    return ff
+
+
 def lorentz_factor(tth: np.ndarray) -> np.ndarray:
     """
     05/26/2022 SS adding lorentz factor computation