On the basis of a kinematic approximation for the analysis of spot profiles, a general closed-form solution was presented for the spot profiles of surfaces with randomly displaced domains. Both lateral and vertical displacements of the domains were considered. All of the atoms within one domain were arranged perfectly with respect to each other. The spot profiles depended only upon the distribution of displacements and domain sizes, on the assumption that they were not correlated. By analyzing spot profiles for various spot orders and vertical scattering conditions, it was possible to identify the defects, determine their distribution, and judge the distribution of domain sizes. Finally, a detailed analysis was made of the spot profiles for strongly distorted surfaces (where all of the atoms were displaced) and for surfaces with grain boundaries. In the case of strongly distorted surfaces, the spots vanished with increasing scattering vector. In the case of surfaces with grains under these scattering conditions, spot profiles could be obtained from incoherent interference of the grains.

J.Wollschläger: Surface Science, 1995, 328, 325-36