Truncation-rod scattering: Analysis by the dynamical theory of x-ray diffraction.

Abstract

The concept of truncation-rod scattering is analyzed in terms of standard dynamical theory, and specifically applied to grazing-incidence experiments on unreconstructed surfaces in which diffraction peaks are observed in the neighborhood of ``anti-Bragg'' points. A computer simulation of the (001) peak from the (110) surface of copper, based on a version of dynamical theory without approximations, is indeed able to reproduce the observed peak. The calculated penetration depth turns out to be 2700 \AA{}. It is found that the intensity along a truncation rod is a slow function of the angle of incidence, except when the scattered beam becomes evanescent. At this point the reflectivity has a sharp peak of asymmetric shape. For any given incident beam several scattered beams are simultaneously excited, with reflectivities in the range of ${10}^{\mathrm{\ensuremath{-}}5}$\char21{}${10}^{\mathrm{\ensuremath{-}}9}$. It is shown how n-beam dynamical theory leads to a description of truncation-rod scattering in terms of diffraction from a two-dimensional lattice, and how the intensities of the scattered beams are obtained from first principles.