Statistical inference and crystallite size distributions

Abstract

An information theory approach is devised in order to obtain crystallite size distributions from X-ray line broadening. The method is shown to be superior to those based on Fourier expansions, as illustrated by numerical examples and a realistic situation. The powder model of Warren and Averbach is considered, in which the sample is thought of as a 'column-like' structure of unit cells perpendicular to the diffraction plane. Errors in excess of 100% arise as a result of truncating the diffraction peak. It is shown that, with the present approach, the corresponding figure is reduced to 5%, which confirms the power of information theory, and makes this method especially convenient in those cases in which there are large overlaps between the tails of two diffraction peaks.