2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85288A single and self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. We have shown that the crystallite-size distribution can be determined without assuming a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO$_{2}$ data. The results demonstrate that the proposed method can determine size distributions, while making the least number of assumptions. The comparison of the Bayesian/MaxEnt results from experimental CeO$_2$ with TEM results is favorable43 pages, 13 Figures, 5 TablesData Analysis, Statistics and Probabilitytext