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Interpretation of small‐angle scattering curves proportional to a negative power of the scattering vector
Author(s) -
Schmidt P. W.
Publication year - 1982
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/s002188988201259x
Subject(s) - scattering , physics , small angle scattering , particle (ecology) , intensity (physics) , biological small angle scattering , distribution (mathematics) , small angle neutron scattering , dimension (graph theory) , optics , computational physics , neutron scattering , mathematics , mathematical analysis , oceanography , pure mathematics , geology
The intensity of the small‐angle X‐ray and neutron scattering from a polydisperse system of randomly oriented independently scattering particles is shown to be proportional to h −α for all values of the scattering vector h when the distribution of particle dimensions is proportional to r −(2 d + 1 − α ) , where h = 4 πλ −1 sin( θ /2); θ is the scattering angle; λ is the wavelength; r is the maximum dimension of a particle; and d is the number of dimensions of the particles. The value of α lies in the interval 0 < α < ω , where ω = 4, 2, and 1 for d = 3, 2, and 1 respectively. This relationship between the scattered intensity and the particle‐dimension distribution does not depend on the shape of the particles in the polydisperse system, provided that the particle‐shape distribution is independent of the distribution of particle dimensions.