Statistical Inference of Distribution of Crystal Size by X‐Ray Powder Diffraction

We describe a method to calculate the distribution of sizes of fine crystals from pure powder‐diffraction profile using a method of maximum entropy (MAXENT). We apply a Monte‐Carlo technique of simulated annealing to seek a global minimum of the error surface in fitting this diffraction profile. We consider pure diffraction profile (instrument de‐convoluted) of a powder specimen without lattice imperfection to a significant extent. Under these circumstances, the distribution of the pure diffraction profile can be attributed to the distribution of crystallite size. We applied this method to three cases of crystal sizes having a highly inhomogeneous distribution with certain noise‐tolerance. The results agree well with synthetic data of diffraction.