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atomic_scattering_params.py
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# These two table of scattering parameters are taken from
# the "Structure of Materials" book by
# Marc de Graef and Michele E. McHenry.
# Text below is from the table captions in the book.
#
#
# Neutron scatering lengths (in femtometer, fm) for all naturally occurring elements, thermal neutrons are assumed.
# The list is taken from a longer list including all iscopes, at the NIST web site,
# URL: htp:/www.ncnr.nist.gov/resources/n-lengths/list.html). The values in the list are averages over all isotopes,
# weighted by the natural isotope abundances. There are elements for which the scatering lengths have not ben determined.
# Imaginary parts (for some) indicate a non-negligible probability for the neutron capture.
#
NEUTRON_SCATTERING_PARAMS = {"H":-3.739, "He":3.26, "Li": -1.9, "Be":7.79, "B":5.30-0.213j, "C":6.6460, "N":9.36, "O":5.803, "F":5.654, "Ne":4.566, "Na":3.63, "Mg":5.375, "Al":3.449, "Si":4.1491, "P":5.13, "S":2.847, "Cl":9.577, "Ar":1.909, "K":3.67, "Ca":4.7, "Sc":12.29, "Ti":-3.438, "V":-0.3824, "Cr":3.635, "Mn":-3.73, "Fe":9.45, "Co":2.49, "Ni":10.3, "Cu":7.718, "Zn":5.68, "Ga":7.288, "Ge":8.185, "As":6.58, "Se":7.97, "Br":6.795, "Kr":7.81, "Rb":7.09, "Sr":7.02, "Y":7.75, "Zr":7.16, "Nb":7.054, "Mo":6.715, "Tc":6.8, "Ru":7.03, "Rh":5.88, "Pd":5.91, "Ag":5.922, "Cd":4.87-0.7j, "In":4.065-0.0539j, "Sn":6.225, "Sb":5.57, "Te":5.8, "I":5.28, "Xe":4.92, "Cs":5.42, "Ba":5.07, "La":8.24, "Ce":4.84, "Pr":4.58, "Nd":7.69, "Pm":12.6, "Sm":0.8-1.65j, "Eu":7.22-1.26j, "Gd":6.5-13.82j, "Tb":7.38, "Dy":16.9-0.276j, "Ho":8.01, "Er":7.79, "Tm":7.07, "Yb":12.43, "Lu":7.21, "Hf":7.7, "Ta":6.91, "W":4.86, "Re":9.2, "Os":10.7, "Ir":10.6, "Pt":9.6, "Au":7.63, "Hg":12.692, "Tl":8.776, "Pb":9.405, "Bi":8.532, "Ra":10, "Th":10.31, "Pa":9.1, "U":8.417}
#
# Atomic scattering parameters for all elements Z=1-98.
# This table assumes that s (Q/4*pi) is expressed in 1/AA;
# if it is expressed ni 1/nm, then all entries must be multiplied by 0.01.
#
ATOMIC_SCATTERING_PARAMS = {"Ru": [[4.358, 27.881], [3.298, 5.179], [1.323, 0.594], [0, 0]], "Re": [[5.695, 28.968], [4.74, 5.156], [2.064, 0.575], [0, 0]], "Ra": [[6.215, 28.382], [5.17, 5.002], [2.316, 0.562], [0, 0]], "Rb": [[4.776, 140.782], [3.859, 18.991], [2.234, 3.701], [0.868, 0.419]], "Rn": [[4.078, 38.406], [4.978, 11.02], [3.096, 2.355], [1.326, 0.299]], "Rh": [[4.431, 27.911], [3.343, 5.153], [1.345, 0.592], [0, 0]], "Be": [[1.25, 60.804], [1.334, 18.591], [0.36, 3.653], [0.106, 0.416]], "Ba": [[7.821, 117.657], [6.004, 18.778], [3.28, 3.263], [1.103, 0.376]], "Bi": [[3.841, 50.261], [4.679, 11.999], [3.192, 2.56], [1.363, 0.318]], "Bk": [[6.502, 28.375], [5.478, 4.975], [2.51, 0.561], [0, 0]], "Br": [[2.166, 33.899], [2.904, 10.497], [1.395, 2.041], [0.589, 0.307]], "H": [[0.202, 30.868], [0.244, 8.544], [0.082, 1.273], [0, 0]], "P": [[1.888, 44.876], [2.469, 13.538], [0.805, 2.642], [0.32, 0.361]], "Os": [[5.75, 28.933], [4.773, 5.139], [2.079, 0.573], [0, 0]], "Ge": [[2.447, 55.893], [2.702, 14.393], [1.616, 2.446], [0.601, 0.342]], "Gd": [[5.225, 29.158], [4.314, 5.259], [1.827, 0.586], [0, 0]], "Ga": [[2.321, 65.602], [2.486, 15.458], [1.688, 2.581], [0.599, 0.351]], "Pr": [[5.085, 28.588], [4.043, 5.143], [1.684, 0.581], [0, 0]], "Pt": [[5.803, 29.016], [4.87, 5.15], [2.127, 0.572], [0, 0]], "Pu": [[6.415, 28.836], [5.419, 5.022], [2.449, 0.561], [0, 0]], "C": [[0.731, 36.995], [1.195, 11.297], [0.456, 2.814], [0.125, 0.346]], "Pb": [[3.51, 52.914], [4.552, 11.884], [3.154, 2.571], [1.359, 0.321]], "Pa": [[6.306, 28.688], [5.303, 5.026], [2.386, 0.561], [0, 0]], "Pd": [[4.436, 28.67], [3.454, 5.269], [1.383, 0.595], [0, 0]], "Cd": [[2.574, 55.675], [3.259, 11.838], [2.547, 2.784], [0.838, 0.322]], "Po": [[6.07, 28.075], [4.997, 4.999], [2.232, 0.563], [0, 0]], "Pm": [[5.201, 28.079], [4.094, 5.081], [1.719, 0.576], [0, 0]], "Ho": [[5.376, 28.773], [4.403, 5.174], [1.884, 0.582], [0, 0]], "Hf": [[5.588, 29.001], [4.619, 5.164], [1.997, 0.579], [0, 0]], "Hg": [[2.682, 42.822], [4.241, 9.856], [2.755, 2.295], [1.27, 0.307]], "He": [[0.091, 18.183], [0.181, 6.212], [0.11, 1.803], [0.036, 0.284]], "Mg": [[2.268, 73.67], [1.803, 20.175], [0.839, 3.013], [0.289, 0.405]], "K": [[3.951, 137.075], [2.545, 22.402], [1.98, 4.532], [0.482, 0.434]], "Mn": [[2.747, 67.786], [2.456, 15.674], [1.792, 3.0], [0.498, 0.357]], "O": [[0.455, 23.78], [0.917, 7.622], [0.472, 2.144], [0.138, 0.296]], "S": [[1.659, 36.65], [2.386, 11.488], [0.79, 2.469], [0.321, 0.34]], "W": [[5.709, 28.782], [4.677, 5.084], [2.019, 0.572], [0, 0]], "Zn": [[1.942, 54.162], [1.95, 12.518], [1.619, 2.416], [0.543, 0.33]], "Eu": [[6.267, 100.298], [4.844, 16.066], [3.202, 2.98], [1.2, 0.367]], "Zr": [[4.105, 28.492], [3.144, 5.277], [1.229, 0.601], [0, 0]], "Er": [[5.436, 28.655], [4.437, 5.117], [1.891, 0.577], [0, 0]], "Ni": [[2.21, 58.727], [2.134, 13.553], [1.689, 2.609], [0.524, 0.339]], "Na": [[2.241, 108.004], [1.333, 24.505], [0.907, 3.391], [0.286, 0.435]], "Nb": [[4.237, 27.415], [3.105, 5.074], [1.234, 0.593], [0, 0]], "Nd": [[5.151, 28.304], [4.075, 5.073], [1.683, 0.571], [0, 0]], "Ne": [[0.303, 17.64], [0.72, 5.86], [0.475, 1.762], [0.153, 0.266]], "Np": [[6.323, 29.142], [5.414, 5.096], [2.453, 0.568], [0, 0]], "Fr": [[6.201, 28.2], [5.121, 4.954], [2.275, 0.556], [0, 0]], "Fe": [[2.544, 64.424], [2.343, 14.88], [1.759, 2.854], [0.506, 0.35]], "B": [[0.945, 46.444], [1.312, 14.178], [0.419, 3.223], [0.116, 0.377]], "F": [[0.387, 20.239], [0.811, 6.609], [0.475, 1.931], [0.146, 0.279]], "Sr": [[5.848, 104.972], [4.003, 19.367], [2.342, 3.737], [0.88, 0.414]], "N": [[0.572, 28.847], [1.043, 9.054], [0.465, 2.421], [0.131, 0.317]], "Kr": [[2.034, 29.999], [2.927, 9.598], [1.342, 1.952], [0.589, 0.299]], "Si": [[2.129, 57.775], [2.533, 16.476], [0.835, 2.88], [0.322, 0.386]], "Sn": [[3.45, 59.104], [3.735, 14.179], [2.118, 2.855], [0.877, 0.327]], "Sm": [[5.255, 28.016], [4.113, 5.037], [1.743, 0.577], [0, 0]], "V": [[3.245, 76.379], [2.698, 17.726], [1.86, 3.363], [0.486, 0.374]], "Sc": [[3.966, 88.96], [2.917, 20.606], [1.925, 3.856], [0.48, 0.399]], "Sb": [[3.564, 50.487], [3.844, 13.316], [2.687, 2.691], [0.864, 0.316]], "Se": [[2.298, 38.83], [2.854, 11.536], [1.456, 2.146], [0.59, 0.316]], "Co": [[2.367, 61.431], [2.236, 14.18], [1.724, 2.725], [0.515, 0.344]], "Cm": [[6.46, 28.396], [5.469, 4.97], [2.471, 0.554], [0, 0]], "Cl": [[1.452, 30.935], [2.292, 9.98], [0.787, 2.234], [0.322, 0.323]], "Ca": [[4.47, 99.523], [2.971, 22.696], [1.97, 4.195], [0.482, 0.417]], "Cf": [[6.548, 28.461], [5.526, 4.965], [2.52, 0.557], [0, 0]], "Ce": [[5.007, 28.283], [3.98, 5.183], [1.678, 0.589], [0, 0]], "Xe": [[3.366, 35.509], [4.147, 11.117], [2.443, 2.294], [0.829, 0.289]], "Tm": [[5.441, 29.149], [4.51, 5.264], [1.956, 0.59], [0, 0]], "Cs": [[6.062, 155.837], [5.986, 19.695], [3.303, 3.335], [1.096, 0.379]], "Cr": [[2.307, 78.405], [2.334, 15.785], [1.823, 3.157], [0.49, 0.364]], "Cu": [[1.579, 62.94], [1.82, 12.453], [1.658, 2.504], [0.532, 0.333]], "La": [[4.94, 28.716], [3.968, 5.245], [1.663, 0.594], [0, 0]], "Li": [[1.611, 107.638], [1.246, 30.48], [0.326, 4.533], [0.099, 0.495]], "Tl": [[5.932, 29.086], [4.972, 5.126], [2.195, 0.572], [0, 0]], "Lu": [[5.553, 28.907], [4.58, 5.16], [1.969, 0.577], [0, 0]], "Th": [[6.264, 28.651], [5.263, 5.03], [2.367, 0.563], [0, 0]], "Ti": [[3.565, 81.982], [2.818, 19.049], [1.893, 3.59], [0.483, 0.386]], "Te": [[4.785, 27.999], [3.688, 5.083], [1.5, 0.581], [0, 0]], "Tb": [[5.272, 29.046], [4.347, 5.226], [1.844, 0.585], [0, 0]], "Tc": [[4.318, 28.246], [3.27, 5.148], [1.287, 0.59], [0, 0]], "Ta": [[5.659, 28.807], [4.63, 5.114], [2.014, 0.578], [0, 0]], "Yb": [[5.529, 28.927], [4.533, 5.144], [1.945, 0.578], [0, 0]], "Dy": [[5.332, 28.888], [4.37, 5.198], [1.863, 0.581], [0, 0]], "I": [[3.473, 39.441], [4.06, 11.816], [2.522, 2.415], [0.84, 0.298]], "U": [[6.767, 85.951], [6.729, 15.642], [4.014, 2.936], [1.561, 0.335]], "Y": [[4.129, 27.548], [3.012, 5.088], [1.179, 0.591], [0, 0]], "Ac": [[6.278, 28.323], [5.195, 4.949], [2.321, 0.557], [0, 0]], "Ag": [[2.036, 61.497], [3.272, 11.824], [2.511, 2.846], [0.837, 0.327]], "Ir": [[5.754, 29.159], [4.851, 5.152], [2.096, 0.57], [0, 0]], "Am": [[6.378, 29.156], [5.495, 5.102], [2.495, 0.565], [0, 0]], "Al": [[2.276, 72.322], [2.428, 19.773], [0.858, 3.08], [0.317, 0.408]], "As": [[2.399, 45.718], [2.79, 12.817], [1.529, 2.28], [0.594, 0.328]], "Ar": [[1.274, 26.682], [2.19, 8.813], [0.793, 2.219], [0.326, 0.307]], "Au": [[2.388, 42.866], [4.226, 9.743], [2.689, 2.264], [1.255, 0.307]], "At": [[6.133, 28.047], [5.031, 4.957], [2.239, 0.558], [0, 0]], "In": [[3.153, 66.649], [3.557, 14.449], [2.818, 2.976], [0.884, 0.335]], "Mo": [[3.12, 72.464], [3.906, 14.642], [2.361, 3.237], [0.85, 0.366]]}
####################
def ff(q,atom_type):
"""
Function that calculates the value of the X-ray atomic
scattering paramters for a given q value and
a given atom type
param q: real (>=0)
param atom_type: str (chemical symbol)
"""
from pylada.periodic_table import find as find_specie
import numpy as np
zz = find_specie(name=atom_type).atomic_number
coeffs = np.array(ATOMIC_SCATTERING_PARAMS[atom_type])
s = q / (4*np.pi)
s2 = s**2
ff = zz - 41.78214 * s2 * np.sum(coeffs[:, 0] * np.exp(-coeffs[:, 1] * s2))
return ff
####################
def bb(atom_type):
"""
Function that calculates the value of the neutron atomic
scattering paramters for a given atom type
param atom_type: str (chemical symbol)
"""
from pylada.periodic_table import find as find_specie
zz = find_specie(name=atom_type).atomic_number
bb = NEUTRON_SCATTERING_PARAMS[atom_type]
return bb
####################