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A general analytical method for calculating particle‐dimension distributions from scattering data
Author(s) -
Fedorova I. S.,
Schmidt P. W.
Publication year - 1978
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/s0021889878013503
Subject(s) - scattering , bessel function , dimension (graph theory) , intensity (physics) , physics , collimated light , function (biology) , particle (ecology) , computational physics , optics , distribution (mathematics) , distribution function , geometry , mathematical analysis , mathematics , quantum mechanics , laser , combinatorics , biology , oceanography , evolutionary biology , geology
A method has been developed for using the Titchmarsh transform to calculate the dimension distribution function Q ( a ) for particles with a characteristic dimension a (such as the length or the diameter) from the measured small‐angle X‐ray scattering intensity I ( h ) for a polydisperse system of independently scattering particles, where h = 4 πλ −1 sin ( θ /2), λ is the wavelength and θ is the scattering angle. This technique permits the dimension distribution to be calculated for any particle shape for which the intensity l a ( h ) for a single particle with characteristic dimension a is proportional to [ J v ( ha )] 2 where J v ( x ) is the Bessel function of the first kind and order v . Techniques for computing Q ( a ) from the characteristic function γ ( a ) are discussed, and a method is given for calculating Q ( a ) directly from the measured scattering intensity F ( h ) for collimating slits with arbitrary length and negligible width. This calculation avoids the errors which may be produced by collimation corrections. The behavior of I ( h ) and F ( h ) for large h is discussed.