The beam diffusing properties of stacked layers of diffuser material were evaluated experimentally and compared to a Gaussian random phase screen model. The model was found to give promising accuracy in combination with a Lorentzian auto-correlation model. The tail behaviour of the angular scattering distribution as a function of number of diffusing layers was particularly well described by the model, and in the case of an amorphous carbon diffuser, the model could describe the whole of the scattering distribution convincingly.

We use dark-field x-ray microscopy to reveal evidence of subtle structural heterogeneity in BaTiO 3 single crystals at temperatures of 150 C-well above the Curie temperature of 125 C. The heterogeneity exhibits domain-like ordering on the scale of several micrometers, pronounced curvature, and a preference for h110i lattice directions. Complementary high-resolution x-ray reciprocal space measurements suggest that the features originate from point defects (most likely oxygen vacancies) that coalesce along pre-existing domain walls during aging. A simple thermodynamic model suggests that the weak elastic strains associated with the heterogeneity are likely to locally raise the Curie temperature in their vicinity, creating nucleation sites for the ferroelectric phase upon cooling through the ferroelectric phase transition.