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Analysis of X‐ray Powder Diffraction Data Using the Maximum Likelihood Estimation Method
Author(s) -
Tsur Yoed,
Randall Clive A.
Publication year - 2000
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.2000.tb01512.x
Subject(s) - tetragonal crystal system , diffraction , position (finance) , standard deviation , maximum likelihood , powder diffraction , upper and lower bounds , relative standard deviation , lattice (music) , crystal structure , materials science , relaxation (psychology) , mathematics , computational physics , statistics , crystallography , physics , mathematical analysis , optics , chemistry , psychology , social psychology , finance , detection limit , acoustics , economics
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 BaTiO 3 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.