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Diameter Distribution of Spherical Primary Grains in the boolean model from small‐angle scattering
Author(s) -
Gille Wilfried
Publication year - 1995
Publication title -
particle and particle systems characterization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.877
H-Index - 56
eISSN - 1521-4117
pISSN - 0934-0866
DOI - 10.1002/ppsc.19950120304
Subject(s) - scattering , small angle scattering , spheres , boolean model , covariance , distribution (mathematics) , isotropy , volume fraction , representation (politics) , hard spheres , mathematical analysis , mathematics , statistical physics , physics , optics , statistics , quantum mechanics , thermodynamics , astronomy , politics , political science , law
A method for determining the size‐distribution density of small spheres which are arranged, without any interaction between them, at random positions in space and form an isotropic twophase system is presented. In the case of higher volume fractions, frequent overlapping between the spheres is a logical consequence. This effect is an essential feature of the model itself and is well considered and observed. Stereological information, which contains all the necessary data about the unknown size distribution, is obtained from the angular intensity distribution (small‐angle scattering experiment) of the particle system concerned. The resulting formula still includes, in a first representation, the volume fraction p as a free parameter. In a second step, a general analytical method for the determination of the volume fraction p from the set covariance of the considered random closed set is derived. Therefore, the unknown diameter distribution can be obtained in every detail, starting from the scattering curve of the sample, by way of two independent working steps.