  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).
