Models for X-ray scattering from random systems

A new class of models is proposed for interpretation of the small-angle X-ray scattering from catalyst-like systems, which consist of a random arrangement of two or more phases, in each of which the electron density is uniform. By considering a grid formed of identical cells, each of which is filled with one phase or another, the calculation of the correlation function, and hence the scattering intensity, is reduced to a counting process and evaluation of P0(r), the probability that a line segment of length r lies wholly within one cell. Results for simple two-dimensional grids are considered in detail, with P0 calculated by several methods. The Fourier transform of the correlation function is calculated for the cubic lattice, and properties of the scattering intensity curve discussed. Extensions of the model discussed here, the simplest of the cell models, are indicated.