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Determination of depth profiles from X-ray diffraction data

A direct method is described for determining depth profiles (z-profiles) of diffraction data from experimentally determined τ-profiles, where z is the depth beneath the sample surface and τ is the 1/e penetration depth of the X-ray beam. With certain assumptions, the relation between these two profile functions can be expressed in the form of a Laplace transform. The criteria for fitting experimental τ-data to functions which can be utilized by the method are described. The method was applied to two τ-data sets taken from the literature: (1) of residual strain in an A1 thin film and (2) of residual stress in a surface ground A12O3/5vol% TiC composite. For each data set, it was found that the z-profiles obtained were of two types: oscillatory and nonoscillatory. The nonoscillatory profiles appeared to be qualitatively consistent for a given data set. The oscillatory profiles were considered to be not physically realistic. For the data sets considered, the nonoscillatory z-profiles were found to lie consistently above the corresponding τ-profiles, and to approach the τ-profiles at large z, as expected from the relation between the two.