Scattering by an Inhomogeneous Solid. II. The Correlation Function and Its Application

TLDR

The study measures the angular intensity distribution of x‑ray scattering from porous solids at small angles. The scattering follows an exponential correlation function, yielding a linear relation between the reciprocal square root of intensity and the square of the scattering angle, from which the specific surface can be extracted and compared with adsorption‑based measurements.

Abstract

Experiments on the angular intensity distribution of x-rays scattered by porous materials (hole structures) in the range of small angles are described. It is shown that the scattering can be characterized by an exponential correlation function in the case of a distribution of holes of random shape and size in solid; a theoretical derivation of the exponential function is given for this case. When the correlation function is an exponential, the rule holds that the reciprocal square root of the scattered intensity is a linear function of the square of the scattering angle. The specific surface of the material is determined by the slope of this straight line. Specific surfaces of a number of compositions are calculated from their experimental correlation functions and compared to surfaces based on adsorption measurements.