Calculation of the Intensity of Small-Angle X-Ray Scattering at Relatively Large Scattering Angles

Abstract

Since the small‐angle x‐ray scattering intensity can be expressed as a Fourier integral, the techniques of asymptotic expansion of Fourier integrals can be used to calculate the small‐angle x‐ray scattering at relatively large scattering angles. Some asymptotic expansion techniques which are often useful are described. The relation between the scattered intensity at relatively large angles and the characteristic function and its derivatives is discussed. The scattered intensity for both prolate and oblate ellipsoids of revolution is calculated to provide examples of asymptotic expansion methods, and the resulting expressions are evaluated numerically. The behavior of the scattered intensity at relatively large scattering angles for platelet particles of negligible thickness is described.