The effect of the shape function on small-angle scattering analysis by the maximum-entropy method

Analysis of small-angle scattering data to obtain a particle-size distribution is dependent upon the shape function used to model the scattering. From a maximum-entropy analysis of small-angle scattering data, the effect of shape-function selection on the obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two alloys. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly noninteracting irregular ellipsoidal precipitates. A comparison is made between the different forms of the shape function. The effect of an incident-wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.