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

Yoed Tsur, Clive A. Randall

Research output: Contribution to journalArticle

7 Scopus citations

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 yttrium-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.

Original languageEnglish (US)
Pages (from-to)2062-2066
Number of pages5
JournalUnknown Journal
Volume83
Issue number8
DOIs
StatePublished - Aug 2000

All Science Journal Classification (ASJC) codes

  • Ceramics and Composites
  • Materials Chemistry

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