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 u.sfit 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.

A method is derived, using information theory and the maximum entropy principle, for treating deconvolution problems. The approach is particularly suitable for the determination of instrumental effects in spectral lines. The technique is illustrated by recourse to numerical examples. A comparison is made with alternative methods. Although realistic situations are restricted to the correction of x-ray diffraction profiles (instrumental width), the formalism applies for any spectral technique.