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Automatic determination of phase transition points in in situ X-ray powder diffraction experiments

Published online by Cambridge University Press:  29 February 2012

P. Rajiv ,
R. E. Dinnebier  and
M. Jansen
P. Rajiv
Affiliation:
Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
R. E. Dinnebier*
Affiliation:
Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
M. Jansen
Affiliation:
Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
*
a)Author to whom correspondence should be addressed. Electronic mail: r.dinnebier@fkf.mpg.de
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Abstract

Powder diffraction experiments performed as a function of external variables like, e.g., temperature, pressure, or time open possibilities to gain additional information about the physical and chemical properties of the system under study. Sensible extraction of such information directly from in situ experiments requires the treatment of the dataset with methods like sequential and/or parametric refinements. We are progressing towards the development of the parametric refinement method, which performs simultaneous phase refinements of in situ powder patterns by imposing several rational physical models of the evolving parameters on the calculated powder diffraction profiles. One of the fundamental prerequisites for this method is that the powder patterns in the in situ dataset be grouped to their relevant phases. In this paper, we present an analytical method which uses the Pearson’s correlations coefficients of the powder patterns to automatically determine the phase transition points of the in situ powder dataset. The phase transition points determined are used to group the powder patterns belonging to identical phases and to prepare the patterns for automated sequential phase refinements. The proposed algorithm is implemented as an automated module in the multi powder diffraction pattern, data reduction software Powder 3D.

Keywords

sequential refinementparametric refinementPearson’s correlationsphase transitionin situ powder diffractionautomation

Information

Type
Technical Articles
Information
Powder Diffraction , Volume 24 , Issue 1 , March 2009 , pp. 8 - 16
Copyright
Copyright © Cambridge University Press 2009

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References

Abdullah, M. (1990). “On a robust correlation coefficient,” StatisticianSTTNAP 39, 455–460.CrossRefGoogle Scholar
Azzalini, A. (1985). “A class of distributions which includes the normal ones,” Scand. J. Stat.SJSADG 12, 171–178.Google Scholar
Barr, G., Dong, W., and Gilmore, C. J. (2004). “High-throughput powder diffraction. II. Applications of clustering methods and multivariate data analysis,” J. Appl. Crystallogr.JACGAR10.1107/S0021889804000391 37, 243–252.CrossRefGoogle Scholar
Brückner, S. (2000). “Estimation of the background in powder diffraction patterns through a robust smoothing procedure,” J. Appl. Crystallogr.JACGAR10.1107/S0021889800003617 33, 977–979.CrossRefGoogle Scholar
Bruker AXS (2000). TOPAS V2.0: “General profile and structure analysis software for powder diffraction data,” Karlsruhe, Germany.Google Scholar
Dinnebier, R. E., Kowalevsky, A., Reichert, H., and Jansen, M. (2007). “Polymorphism of Ag3VO4,” Z. Kristallogr.ZEKRDZ 222, 420–426.CrossRefGoogle Scholar
Dinnebier, R. E., Vensky, S., Jansen, M., and Hanson, J. C. (2005). “Crystal structures and topological aspects of the high-temperature phases and decomposition products of the alkali-metal oxalates M2[C2O4] (M=K,Rb,Cs),” Chem.-Eur. J.CEUJED 11(4), 1119–1129.CrossRefGoogle ScholarPubMed
Gilmore, C. J., Barr, G., and Paisley, J. (2004). “High-throughput powder diffraction. I. A new approach to qualitative and quantitative powder diffraction pattern analysis using full pattern profiles,” J. Appl. Crystallogr.JACGAR10.1107/S002188980400038X 37(2), 231–242.CrossRefGoogle Scholar
Hinrichsen, B., Dinnebier, R. E., and Jansen, M. (2006). “Powder3D: An easy to use program for data reduction and graphical presentation of large numbers of powder diffraction patterns,” Z. Kristallogr.ZEKRDZ10.1524/zksu.2006.suppl_23.231 2006(suppl. 23), 231–236.CrossRefGoogle Scholar
Horn, D. and Gottlieb, A. (2001). “Algorithm for data clustering in pattern recognition problems based on quantum mechanics,” Phys. Rev. Lett.PRLTAO 88, 0187021.CrossRefGoogle ScholarPubMed
Jain, A. K., Duin, R. P. W., and Mao, J. (2000). “Statistical pattern recognition: A review,” IEEE Trans. Pattern Anal. Mach. Intell.ITPIDJ10.1109/34.824819 22(1), 4–37.CrossRefGoogle Scholar
Jarque, C. M. and Bera, A. K. (1980). “Efficient tests for normality, homoscedasticity and serial independence of regression residuals,” Econ. Lett.ECLEDS10.1016/0165-1765(80)90024-5 6(3), 255–259.CrossRefGoogle Scholar
Öztuna, D., Elhan, A. H., and Tüccar, E. (2006). “Investigation of four different normality tests in terms of type 1 rrror rate and power under different distributions,” Turk. J. Med. Sci. 36(3), 171–176.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2002). Numerical Recipes in C (Cambridge U. P., New York).Google Scholar
Rajiv, P., Hinrichsen, B., Dinnebier, R. E., Joswig, M., and Jansen, M. (2007). “Automatic calibration of powder diffraction experiments using 2D-detectors,” Powder Diffr.PODIE210.1154/1.2486434 22(1), 3–19.CrossRefGoogle Scholar
Seul, M., O’Gorman, L., and Sammon, M. J. (2000). Practical Algorithms for Image Analysis—Description, Examples and Code (Cambridge U. P., New York).Google Scholar
Smith, S. W. (2003). Digital Signal Processing (Newnes, New York).Google Scholar
Stinton, G. W. and Evans, J. S. O. (2007). “Parametric Rietveld refinement,” J. Appl. Crystallogr.JACGAR10.1107/S0021889806043275 40, 87–95.CrossRefGoogle ScholarPubMed
Sugimoto, K., Dinnebier, R. E., and Hanson, J. C. (2007). “Structures of three dehydration products of bischofite from in situ synchrotron powder diffraction data (MgCl2.nH2O; n=1,2,4),” Acta Crystallogr., Sect. B: Struct. Sci.ASBSDK B63, 235–242.CrossRefGoogle Scholar
Xua, D. and Redman-Furey, N. (2007). “Statistical cluster analysis of pharmaceutical solvents,” Int. J. Pharm.IJPHDE 339(1–2), 175–188.CrossRefGoogle Scholar