Defractalization of films adsorbed on fractal surfaces

We report a calculation of small-angle x-ray and neutron scattering from films adsorbed on fractal surfaces. The film is shown to defractalize the substrate surface in the sense that the film thickness $d$ becomes the new lower limit of the length scale of fractality. Fractal behavior can be observed only in the range of the scattering wave vector $q\ll \frac{1}{d}$, while a smooth-surface result is expected in the limit $\mathrm{qd}\gg 1$. A scaling formula for the scattered intensity $I$ as a function of $\mathrm{qd}$ is derived. When applied to films in equilibrium with their vapor, it predicts the scattering curve as a function of pressure. The formula can also be applied to the scattering from "dry" samples (without films); the "thickness" $d$ then provides a natural definition of the lower limit of the fractal regime.