Analysis of X-Ray Powder Diffraction Data Using the Maximum Likelihood Estimation Method

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

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