X-ray scattering in disordered superlattices: Theory and application to FeF2/ZnF2 superlattices.

We present a theory for the x-ray scattering of a two-component superlattice. We show that the statistical averages involved in the problem can be computed using the characteristic function formalism. Using this technique we obtain a closed, analytical formulation that includes discrete and continuous disorders. Also, a seed buffer layer is explicitly included in the theory. The model is applied to fit experimental results of x-ray scans of ${\mathrm{FeF}}_{2}$/${\mathrm{ZnF}}_{2}$ superlattices. In these samples we find that interatomic spacings relax to the bulk value with increasing layer thickness, interdiffusion seems to be limited to the layers nearest to the interfaces, and discrete disorder grows with the mean number of atomic layers. Our results indicate that correlated lateral roughness is important in determining the x-ray profile. \textcopyright{} 1996 The American Physical Society.