Analysis of Scattering Data for Mixtures of Amorphous Solids or Liquids

Abstract

Results are derived which show that in the analysis of x‐ray or neutron‐scattering data from mixtures of amorphous solids or liquids, a meaningful scattering function, $\mathrm{i(s),}$ can always be computed without recourse to simplifying assumptions regarding the atomic scattering functions. Fourier inversion of $\mathrm{i(s)}$ yields a distribution function, ${\mathrm{H(r)\hspace{0.17em}=\hspace{0.17em}\Sigma \Sigma x}}_i{x}_j{H}_{\mathrm{ij}}\mathrm{(r),}$ where $x_i$ is the atomic fraction of species $\mathrm{i,}$ and $H_{\mathrm{ij}}\mathrm{(r)}$ is the convolution of the true net radial‐distribution function, $h_{\mathrm{ij}}\mathrm{(r),}$ with a particular function of the atomic scattering factors. The much‐used assumption that all atomic‐scattering factors are proportional to the same function yields an $\mathrm{H(r)}$ that is a weighted sum of the $h_{\mathrm{ij}}\mathrm{(r),}$ but does not offer any means of ascertaining the individual $h_{\mathrm{ij}}\mathrm{(r)}$ terms if only one scattering experiment is performed.