Small-angle scattering intensity behaviours of cylindrical, spherical and planar lamellae

Abstract

Analytical asymptotic expressions for the small-angle scattering intensities of cylindrical, spherical and planar lamellar grains are determined. Denoting the lamellar spacing byDand the number of lamellae byN, it is found that in the corresponding Porod plots, the positions of the main peaks, whatever the shape, are nearly given by 2k\pi/D, wherekis a positive integer. At a fixed number of lamellar grains, the heights of the main peaks in the three cases increase withNasN3,N4andN2, 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 h\ge 2\pi/ND.