X-ray scattering from stepped and kinked surfaces: An approach with the paracrystal model

A general formalism of X-ray scattering from different kinds of surface morphologies is described. Based on a description of the surface morphology at the atomic scale through the use of the paracrystal model and discrete distributions of distances, the scattered intensity by non-periodic surfaces is calculated over the whole reciprocal space. In one dimension, the scattered intensity by a vicinal surface, the two-level model, the N-level model, the faceted surface and the rough surface are addressed. In two dimensions, the previous results are generalized to the kinked vicinal surface, the two-level vicinal surface and the step meandering on a vicinal surface. The concept of crystal truncation rod is generalized considering also the truncation of a terrace by a step (yielding a terrace truncation rod) and a step by a kink (yielding a step truncation rod).