Dynamical diffraction of x rays at grazing angle

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Abstract
We present details of the theory and experimental observation of dynamical diffraction of x rays at grazing angle from crystal planes normal to a surface. We are able to associate different features of the specularly reflected and diffracted-reflected beam fluxes with the contributions from the α and β branches of the dispersion surfaces. The theory predicts surface propagation modes to which internal and external beams can couple only through the diffraction process. An experiment is described in which the specularly reflected and reflected-diffracted beams were simultaneously observed for 8-keV x rays incident on germanium. The agreement with first-order theory is good, but we observe systematic deviations. We present calculations that illustrate how eigenstates of the wave fields, which are x-ray standing waves with nodal planes normal to the surface of the crystal, can be used to obtain atomic registration at a surface or interface.