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A theory has been developed which relates the intensity of the non-specular scattering of X-rays from thin films to the correlation function for the local deviation of the dielectric constant of the film from its average value. The theory predicts the positions and intensities of the maxima and minima in the distribution of the non-specularly scattered radiation as well as the existence of the non-specular `anomalous surface reflection' first reported by Yoneda. The results of an experimental study with thin copper films were in good agreement with the theory.