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 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2062-2066 |
| Number of pages | 5 |
| Journal | Journal of the American Ceramic Society |
| Volume | 83 |
| Issue number | 8 |
| State | Published - Aug 1 2000 |
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All Science Journal Classification (ASJC) codes
- Ceramics and Composites
- Materials Chemistry
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Analysis of X-ray powder diffraction data using the maximum likelihood estimation method. / Tsur, Yoed; Randall, Clive A.
In: Journal of the American Ceramic Society, Vol. 83, No. 8, 01.08.2000, p. 2062-2066.Research output: Contribution to journal › Article
TY - JOUR
T1 - Analysis of X-ray powder diffraction data using the maximum likelihood estimation method
AU - Tsur, Yoed
AU - Randall, Clive A.
PY - 2000/8/1
Y1 - 2000/8/1
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 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.
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 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.
UR - http://www.scopus.com/inward/record.url?scp=0034247562&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034247562&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0034247562
VL - 83
SP - 2062
EP - 2066
JO - Journal of the American Ceramic Society
JF - Journal of the American Ceramic Society
SN - 0002-7820
IS - 8
ER -