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Using exploratory factor analysis to examine consecutive in-situ X-ray diffraction measurements

Published online by Cambridge University Press:  11 November 2015

Torsten Westphal*
Affiliation:
Institut für Keramik, Glas-und Baustofftechnik, TU Bergakademie Freiberg, Germany
Thomas A. Bier
Affiliation:
Institut für Keramik, Glas-und Baustofftechnik, TU Bergakademie Freiberg, Germany
Keisuke Takahashi
Affiliation:
UBE Industries Ltd., Seavans North Bldg, 1-2-1, Shibaura, Minato-Ku, Tokyo 105-8449, Japan
Mirco Wahab
Affiliation:
Institut für physikalische Chemie, TU Bergakademie Freiberg, Germany
*
a)Author to whom correspondence should be addressed. Electronic mail: [email protected]

Abstract

A method is presented to examine consecutive in-situ X-ray diffraction (XRD) diffractograms using exploratory factor analysis. Systematic changes in the diffractograms are described numerically by score values that could be used to correlate diffraction data with other non-stationary sample properties. Phase and structure evolution in a reacting material can be studied by in-situ XRD. The consecutively collected data can be considered a time series of datasets. Time series are non-stationary data. Such non-stationary data are often hard to examine fully by conventional evaluation methods including applications of the Rietveld method. Here a method is presented to avoid shortcomings of conventional evaluation methods. The new method helps to identify and describe significant systematic changes in in-situ XRD datasets by numerical values. These systematic changes can represent structural changes as well as changes in phase composition. The method can be used to describe the development of the complex processes of compositional and structural changes. The method is demonstrated using the example of a hydrating Portland cement mortar. This hydration process involves at least 11 phases including non-crystalline phases. In the presented example factor analysis of in-situ XRD data results in three variables (factors) describing the observed changes numerically.

Type
Technical Articles
Copyright
Copyright © International Centre for Diffraction Data 2015 

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References

Anderson, T. W. (1963). “The use of factor analysis in the statistical analysis of multiple time series,” Psychometrika 28, 125.Google Scholar
Azari, H. (2010). Statistical Modeling of Cement Heat of Hydration Using Phase and Fineness Variables. NCHRP Web-Only Document 167, National Cooperative Highway Research Program, Transportation Research Board of the National Academies, available from http://www.trb.org/Main/Blurbs/164408.aspx (29th April 2015).Google Scholar
Evju, C. and Hansen, S. (2001). “Expansive properties of ettringite in a mixture of calcium aluminate cement, Portland cement and β-calcium sulfate hemihydrate,” Cem. Concr. Res. 31, 257261.CrossRefGoogle Scholar
Fuellmann, T., Meyer, R., and Witzke, T. (2012). Use of X-ray techniques to optimize the efficiency of cement and concrete characterization. Tagungsbericht Band 1 (Proc. part 1) of 18. Internationale Baustofftagung ibausil, edited by Ludwig, H.-M., Fischer, H.-B., Bode, K. A., and Beuthan, C., 12–15 September 2012, Weimar, Germany, pp. 185191.Google Scholar
Gemperline, P. J. (1989). “Mixture analysis using factor analysis I: calibration and quantification,” J. Chemometr. 3, 549568.Google Scholar
Hamilton, J. C. and Gemperline, P. J. (1990). “Mixture analysis using factor analysis II: self-modelling curve resolution,” J. Chemometr. 4, 113.Google Scholar
ICDD (2008). PDF-2 Release 2008, JCPDS – Int. Centre for Diffraction Data (ICDD), Newtown Square, USA.Google Scholar
Izenman, A. J. (2013). Modern Multivariate Statistical Techniques (Springer, New York, Heidelberg, Dordrecht, London), p. 584.Google Scholar
Kaiser, H. F. (1958). “The varimax criterion for analytic rotation in factor analysis,” Psychometrika 25, 187200.Google Scholar
Liao, B. and Chen, J. (1992). “The application of cluster analysis in X-ray diffraction phase analysis,” J. Appl. Crystallogr. 25, 336339.Google Scholar
Molenaar, P. C. M., de Gooijer, J. G., and Schmitz, B. (1992). “Dynamic factor analysis of nonstationary multivariate time series,” Psychometrika 57, 333349.Google Scholar
OriginLab (2007). Origin Pro 8G SR1 v.8.0773 (OriginLab Corporation, Northampton, USA).Google Scholar
Paine, M., König, U., and Staples, E. (2011). “Application of rapid X-ray diffraction (XRD) and cluster analysis to grade control of iron ores,” in Proc. 10th Int. Congress for Applied Mineralogy (ICAM), pp. 495502.Google Scholar
PANalytical (2008). X'Pert HighScore Plus Version 2.2d (PANalytical B.V., Almelo, The Netherlands).Google Scholar
Pöllmann, H. and Fylak, M. (2012). “Anfangshydratation von Portlandzement und Portlandkompositzement, Kryomikroskopie und Clusteranalyse. Tagungsbericht Band 1 (proceedings part one) of 18,” in Internationale Baustofftagung ibausil, edited by Ludwig, H.-M., Fischer, H.-B., Bode, K. A., and Beuthan, C., 12–15 September 2012, Weimar, Germany, pp. 103115.Google Scholar
Starks, T. H., Fang, J. H., and Zevin, L. S. (1984). “A standardless method of quantitative X-Ray diffractometry using target-transformation factor analysis,” Math. Geol. 16, 351367.CrossRefGoogle Scholar
Takahashi, K., Bier, Th. A., and Westphal, T. (2011). “Effects of mixing energy on technological properties and hydration kinetics of grouting mortars,” Cem. Concr. Res. 41, 11671176.Google Scholar
The R Core Team (2014). R: A Language and Environment for Statistical Computing – Reference Index. The R Foundation for Statistical Computing, Vienna University of Economics and Business, http://www.r-project.org Google Scholar
The R Foundation for Statistical Computing (2014). R version 3.0.3 (2014-03-06), Vienna University of Economics and Business, http://www.r-project.org Google Scholar
Tucker, L. R. and MacCallum, R. C. (1997). Exploratory Factor Analysis. unpublished manuscript, available from http://www.unc.edu/~rcm/book/factornew.htm (7th November 2014).Google Scholar
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