Numerical modeling of superlattice x-ray-scattering intensities

We describe a one-dimensional x-ray-scattering model that includes discrete layer-thickness fluctuations and interfacial diffusion in the kinematical approximation. We demonstrate the use of the model in an analysis of the out-of-plane scattering intensities of epitaxial Co-Au and Co-Cu superlattices. In the case of Co-Au superlattices, the experimental data show that interfacial diffusion is limited to a two-monolayer region, and that layer-thickness fluctuations are of order ±{}1 monolayer. The superlattice features in Co-Cu superlattice measurements are shown to arise from lattice-spacing modulations and are insensitive to composition modulation. The measured intensities are consistent with Co-Cu interfaces which are 2 monolayers thick. A dilation of the Co lattice in the direction of growth is observed for both Co-Au and Co-Cu superlattices. We speculate that the expansion is due to a slightly reduced density of atoms in an imperfectly stacked structure.