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The small‐angle scattering of distorted lamellar structures
Author(s) -
Vonk C. G.
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/s0021889878013837
Subject(s) - lamellar structure , scattering , diffraction , molecular physics , radial distribution function , materials science , correlation function (quantum field theory) , small angle scattering , optics , function (biology) , condensed matter physics , crystallography , chemistry , physics , molecular dynamics , computational chemistry , optoelectronics , evolutionary biology , dielectric , biology
The effects of deviations from an ideal lamellar structure (infinite‐size clusters of parallel layers of alternating electron densities) on the small‐angle scattering curve are treated with the aid of the correlation function. If surrounded by a matrix of the average electron density, reduction of the size of the clusters in the direction of the layer normals leads to a simple modification of the one‐dimensional correlation function. Distortions giving rise to structures containing concentric layers have little effect on this function, whereas corrugation of the surfaces causes minor modifications. Second‐order defects are shown to reduce the three‐dimensional correlation function of the ideal structure γ °( r ) according to γ ( r ) = γ °( r ) exp (−2 r/d ), where d is the `distortion length'. This is the average length of the vectors for which the number of intersections with lamellar interfaces has changed by ±1 as a consequence of the distortions. Calculated diffraction curves show that the effects of reducing the cluster size and of increasing the width β of the lamellar thickness distribution function are very similar. However, changes in d and β affect the scattering curves in a different way, which, other conditions being favourable, may enable these parameters to be determined from observed scattering curves.