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Small‐angle scattering intensity behaviours of cylindrical, spherical and planar lamellae
Author(s) -
Ciccariello Salvino,
Sobry Roger
Publication year - 1999
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/s0021889899005610
Subject(s) - lamellar structure , planar , scattering , intensity (physics) , small angle scattering , physics , range (aeronautics) , optics , momentum transfer , materials science , geometry , molecular physics , chemistry , crystallography , mathematics , composite material , computer graphics (images) , computer science
Analytical asymptotic expressions for the small‐angle scattering intensities of cylindrical, spherical and planar lamellar grains are determined. Denoting the lamellar spacing by D and the number of lamellae by N , it is found that in the corresponding Porod plots, the positions of the main peaks, whatever the shape, are nearly given by , where k is a positive integer. At a fixed number of lamellar grains, the heights of the main peaks in the three cases increase with N as N 3 , N 4 and N 2 , respectively. The satellite peaks are much more structured for cylindrical and spherical lamellae than for planar ones. The momentum‐transfer ( h ) range in which the asymptotic expressions turn out to be accurate is .