TY - JOUR
T1 - Analysis of X-ray powder diffraction data using the maximum likelihood estimation method
AU - Tsur, Yoed
AU - Randall, Clive A.
PY - 2000/8
Y1 - 2000/8
N2 - 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.
AB - 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.
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U2 - 10.1111/j.1151-2916.2000.tb01512.x
DO - 10.1111/j.1151-2916.2000.tb01512.x
M3 - Article
AN - SCOPUS:0034247562
VL - 83
SP - 2062
EP - 2066
JO - [No source information available]
JF - [No source information available]
SN - 0042-1215
IS - 8
ER -