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Asymptotic analysis of small‐angle scattering intensities of plane columnar layers
Author(s) -
Ciccariello Salvino
Publication year - 2010
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/s0021889810034369
Subject(s) - scattering , isotropy , curvature , plane (geometry) , small angle scattering , radius , radius of curvature , small angle x ray scattering , physics , optics , reciprocal lattice , reciprocal , mathematical analysis , molecular physics , geometry , mathematics , mean curvature , diffraction , linguistics , computer security , philosophy , mean curvature flow , computer science
The asymptotic behaviour, at large scattering vector q , of the small‐angle scattering intensities of isotropic plane samples is similar to that of three‐dimensional samples. In fact, its expression, limited to the first two leading terms, is c 1 γ (1) (0)/ q 3 + c 3 γ (3) (0)/ q 5 , where c 1 and c 3 are appropriate numerical constants, and γ (1) (0) and γ (3) (0) the values, at the origin, of the first and third derivatives, respectively, of the two‐dimensional correlation function. These values are proportional to the specific length and to the mean square reciprocal curvature radius of the interface curve. The angularity of the latter can also be determined, while the presence of oscillations in the appropriate Porod plot is related to a parallelism condition obeyed by the interface curve. These results are useful for analysing the small‐angle scattering intensities collected under grazing incidence and diffused by film samples that are a collection of homogeneous cylinders of arbitrary right sections.