Deconvolution of X-ray diffraction profiles by using series expansion

The deconvolution of X-ray diffraction profiles is a basic step in order to obtain reliable results on the microstructure of crystalline powder (crystallite size, lattice microstrain, etc.). A procedure for unfolding the linear integral equation h = g f involved in the kinematical theory of X-ray diffraction is proposed. This technique is based on the series expansion of the `pure' profile, f. The method has been tested with a simulated instrument-broadened profile overlaid with random noise by using Hermite polynomials and Fourier series, and applied to the deconvolution of the (111) peak of a sample of 9-YSZ. In both cases, the effects of the `ill-posed' nature of this deconvolution problem were minimized, especially when using the zero-order regularization combined with the series expansion.