Determination of the Thickness Distribution for Randomly Oriented, Independently Scattering Polydisperse Systems of Platelets

A method has been developed for using small-angle X-ray scattering data to compute the thickness distribution function for systems of randomly oriented, independently scattering platelets with constant electron density and with different thicknesses. Each platelet is assumed to have a uniform thickness. The dimensions defining the faces of the platelet are assumed to be large compared to the platelet thickness. Under these conditions, if the thickness distribution function &ro(a) is defined so that &ro(a)da is the probability that the platelet thickness lies in the interval between a and a + da, &ro(a) is found to be given by the Fourier transform of a quantity which can be evaluated from the experimental scattering curve. Some differently weighted average thicknesses can be calculated from the scattering curve without evaluating the Fourier transform. The function p(a) and the average thickness have been evaluated from the experimental scattering curves for two charcoal samples in which the voids are assumed to have the form of platelets.