The Direct Determination of X-ray Diffraction Data from Specific Depths

A direct method for determining powder diffraction data from a range of depths is described, where the linear absorption coefficient may vary with depth. A series of traditional data collections with varying angles of incidence are required, and the X-ray diffraction data arising from specific depths will be calculated by the transformation of these measured, angle-dependent spectra. These may then be analysed using any conventional method in order to gain information about characteristics of the sample in question at specific depths. Regularisation techniques have been used to solve the governing Fredholm integral equation to determine the depth-dependent diffractograms. The method has been validated by the use of simulated data having known model profiles, and has also been applied to experimental data from polycrystalline thin film samples. INTRODUCTION Knowledge of structural characteristics of polycrystalline thin films may aid in the optimisation of manufacturing processes and in the understanding of thin film behaviour, making the ability to determine X-ray diffractograms from specific depths in a non-destructive manner a very useful and powerful tool. By reducing the angle made between the sample surface and the incident analysing probe, the effective depth of analysis is also reduced. For a given incident angle, the diffraction data obtained is an average of information from various depths over the depth of penetration, weighted towards the uppermost layers [1-3]. Until now, it has not been possible to directly determine information from a specific depth from the observed diffraction data [3]. Here, we introduce a method of transforming experimental data collected over a range of incident angles into diffraction data from specific depths beneath the sample surface. The method outlined here will yield diffraction data on a direct-depth scale as opposed to the absorption depth scale as outlined in other work [3, 4]. In this work, samples with discontinuities will be analysed, overcoming a limitation of previous works [4, 5]. No assumptions about the form of the depth-dependent diffraction data will be made, which is in contrast to work performed by other groups where assumed functions of quantity profiles with depth are assumed [2, 6]. Determination of layer thicknesses using the technique outlined here may have a higher spatial resolution than using the Rietveld specimen displacement coefficients to do the same, and also Copyright ©JCPDS International Centre for Diffraction Data 2005, Advances in X-ray Analysis, Volume 48. 183