Deconvolution of Powder Diffraction Spectra

An improved deconvolution theory is presented for the resolution enhancement in powder diffraction spectra. In powder patterns, diffracted intensity, which is conceptually located at a single 2θ position, is actually distributed over a range of 2θ because of instrumental factors, crystal defects, beam penetration, and sample flatness. The location of the peak is usually taken as the peak maximum or the peak centroid. However, when interpreting complex spectra these approaches to locating peaks are not straightforward and deconvolution can be a useful tool. The method presented herein enhances resolution without altering peak area or peak position. Comparisons are made with results of other methods, with emphasis on deconvoluting spectra that contain random error. The discussion includes treatment of discrete data and analysis of the properties of the solution.