Determination of depth-dependent diffraction data: a new approach

Broadhurst, A.; Rogers, K. D.; Lowe, T. W. and Lane, D. W. (2005). Determination of depth-dependent diffraction data: a new approach. Acta Crystallographica Section A: Foundations of Crystallography, A61 pp. 139–146.




A direct method for determining powder diffraction data at specific depths from angle-dependent diffraction data is described. The method is non-destructive and only traditional data collections, where the angle of incidence is varied, are required. These angle-dependent spectra are transformed to give diffraction data arising from different depths, which may then be exploited using any conventional method. This is a novel approach as traditional methods are forced to tolerate the inherent depth averaging of grazing-angle diffraction, or only examine specific structural characteristics. In order to obtain depth-dependent X-ray diffraction data, a Fredholm integral equation of the first kind is solved using regularization techniques. The method has been validated by the generation of pseudo-experimental data having known depth profiles and solving the Fredholm integral equation to recover the solution. The method has also been applied to experimental data from a number of thin film systems.

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