title: Determination of depth-dependent diffraction data: a new approach.
abstract: 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.
authors.affiliation: Centre for Materials Science and Engineering, Cranfield University, RMCS, Shrivenham, Swindon, Wilts SN6 8LA, England. a.broadhurst@rmcs.cranifield.ac.uk
authors.forename: A
authors.initials: A
authors.lastname: Broadhurst
authors.forename: K D
authors.initials: KD
authors.lastname: Rogers
authors.forename: T W
authors.initials: TW
authors.lastname: Lowe
authors.forename: D W
authors.initials: DW
authors.lastname: Lane