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Generalization of the Fedorova–Schmidt method for determining particle size distributions
Author(s) -
Ciccariello Salvino
Publication year - 2014
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576714020378
Subject(s) - polynomial , generalization , particle (ecology) , function (biology) , particle size , mathematics , tetrahedron , correlation function (quantum field theory) , mathematical analysis , physics , geometry , chemistry , statistics , oceanography , spectral density , evolutionary biology , biology , geology
This article reports the integral transform that determines the particle size distribution of a given sample from the small‐angle scattering intensity under the assumption that the particle correlation function is a polynomial of degree M . The Fedorova–Schmidt solution [Fedorova & Schmidt (1978). J. Appl. Cryst. 11 , 405–411] corresponds to the case M = 3. The procedure for obtaining a polynomial approximation to a particle correlation function is discussed in the cases M = 3 and 4 and applied to the cases of polydisperse particles of tetrahedral, octahedral or cubic shape.