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.
|Number of pages
|Published - Aug 2000
All Science Journal Classification (ASJC) codes
- Ceramics and Composites
- Materials Chemistry