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Kinematic theory of the effect of surface relaxation on X-ray diffraction peak shifts

Elsevier B.V.
Publication Date
DOI: 10.1016/0039-6028(73)90167-2


Abstract The effect of surface layer relaxations on the X-ray diffraction line peak position and the corresponding interplanar spacings obtained from thin crystalline films has been calculated on the basis of the kinematic theory of X-ray diffraction. The calculations were based upon a model in which only a few layers near a free surface were involved in the effective surface relaxation. The calculated diffraction line peak shift depends upon the total surface relaxation α and the manner in which the relaxation decays as one goes into the crystal from the surface. In the present work an exponentially decaying relaxation was assumed. Theoretically, it was found that the lattice parameter of thin films with two free surfaces varies approximately linearly with the square of the reciprocal of the film thickness. The theoretical calculations were applied to (111) oriented gold films with two free surfaces. The results were compared with earlier theoretical and experimental work. It was found that the total surface relaxation, α, was appreciably higher than that obtained from the earlier analysis.

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