Analysis of X-ray powder diffraction data using the maximum likelihood estimation method

The details of substitutional chemistries can be deduced with the associate d relaxation of the crystal structure. This paper demonstrates the use of t he maximum likelihood estimation method (MLE) for X-ray powder diffraction (XRD) analysis, Detailed calculations are performed for cubic and tetragona l systems, Analysis of yittrium-doped BaTiO3 prepared under different condi tions is shown as an example. The methodology outlined here gives rise to a correct evaluation of the standard deviations of the lattice parameters. I n addition, MLE approaches asymptotically the Cramer-Rao lower bound (CRLB) and, therefore, has an advantage over other estimation methods. A link bet ween the output of a commercial software and the standard deviation in the peak position is also suggested.