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Cubic spline representation of the two‐variable cumulative distribution functions for coherent and incoherent x‐ray scattering
Author(s) -
Yacout A. M.,
Verghese K.,
Gardner R. P.
Publication year - 1986
Publication title -
x‐ray spectrometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 45
eISSN - 1097-4539
pISSN - 0049-8246
DOI - 10.1002/xrs.1300150408
Subject(s) - scattering , incoherent scatter , spline interpolation , monte carlo method , physics , computational physics , optics , mathematics , mathematical analysis , statistics , bilinear interpolation
In Monte Carlo simulation of energy‐dispersive x‐ray fluorescence analysers, one must account for both x‐ray scattering effects and photoelectric absorption. To access the required random values of differential coherent and incoherent scattering angles, two‐variable cubic spline representations of the appropriate cumulative distribution functions are developed and their use is demonstrated. In this approach the scattering angle is taken to be the dependent variable while the two independent variables are the x‐ray energy and the normalized cross‐sections. Cubic spline coefficients for the elements from sodium to nickel have been obtained for x‐ray energies from 1 to 150 keV for all scattering angles for both coherent and incoherent scattering. Compared with the commonly used method of numerically integrating tabular values of coherent and incoherent cross‐sections to produce a table of values for subsequent interpolation, use of cubic spline representations gives a 90% reduction in storage space and a 25–80% reduction in the amount of computer time required for equal accuracy.