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A Rietveld tutorial—Mullite

Published online by Cambridge University Press:  29 February 2012

James A. Kaduk
James A. Kaduk*
Affiliation:
Poly Crystallography Inc., 423 East Chicago Avenue, Naperville, Illinois 60540
*
a)Electronic mail: kaduk@polycrystallography.com
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Abstract

The crystal structure of the mullite in a commercial material was refined by the Rietveld method using laboratory X-ray powder diffraction data. In this one refinement, most of the common challenges—including variable stoichiometry (partially occupied sites), multiple impurity phases, amorphous material, constraints, restraints, correlation, anisotropic profiles, microabsorption, and contamination during grinding—are encountered and the thought processes during the refinement are described step-by-step. Interpretation of the refinements includes bulk chemical analysis, chemical composition of the mullite, assessment of the geometry, bond valence sums, the displacement coefficients, crystallite size and microstrain, comparison to similar structures to assess chemical reasonableness, and the nature of the amorphous phase.

Keywords

Rietveldmulliteconstraintsrestraintsmicroabsorptionamorphousquantitative phase analysis
Type
Crystallography Education
Information
Powder Diffraction , Volume 24 , Issue 4 , December 2009 , pp. 351 - 361
Copyright
Copyright © Cambridge University Press 2009

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References

Ban, T. and Okada, K. (1992). “Structure refinement of mullite by the Rietveld method and a new method for estimation of chemical composition,” J. Am. Ceram. Soc.JACTAW 75, 227–230; ICSD collection code 66451.10.1111/j.1151-2916.1992.tb05473.xCrossRefGoogle Scholar
Brindley, G. W. (1945). “The effect of grain or particle size on X-ray reflections from mixed powders and alloys, considered in relation to the quantitative determination of crystalline substances by X-ray methods,” Philos. Mag.PMHABF 36, 347–369.CrossRefGoogle Scholar
Brown, I. D. (2002). The Chemical Bond in Inorganic Chemistry (Oxford University, Oxford).Google Scholar
Buhrke, V. E., Jenkins, R., and Smith, D. K. (1998). A Practical Guide for the Preparation of Specimens for X-ray Fluorescence and X-ray Diffraction Analysis (Wiley-VCH, New York).Google Scholar
Chung, F. H. (1974). “Quantitative interpretation of X-ray diffraction patterns. II. Adiabatic principle of X-ray diffraction analysis of mixtures,” J. Appl. Crystallogr.JACGAR 7, 526–531.10.1107/S0021889874010387CrossRefGoogle Scholar
Deer, W. A., Howie, R. A., and Zussman, Y. (1982). Rock Forming Minerals, Volume 1A, Orthosilicates (Geological Society of London, Oxford), p. 745.Google Scholar
Dragoe, N. (2004). POWDER4, VERSION 1.2.Google Scholar
Hellenbrandt, M. (2004). “The Inorganic Crystal Structure Database (ICSD)—Present and future,” Crystallogr. Rev.CRRVEN 10, 17–22.10.1080/08893110410001664882CrossRefGoogle Scholar
Kaduk, J. A. (1998). “Chemical accuracy and precision in structure refinement from powder data,” Adv. X-Ray Anal.AXRAAA 40, 352–370.Google Scholar
Kaduk, J. A. (2007). “Chemical reasonableness in Rietveld analysis: Inorganics,” Powder Diffr.PODIE2 22, 268–278.10.1154/1.2770747CrossRefGoogle Scholar
Larson, A. C. and Von Dreele, R. B. (2004). General Structure Analysis System (GSAS) (Report LAUR 86–748) (Los Alamos National Laboratory, Los Alamos, New Mexico).Google Scholar
Li, J. F., Li, L., and Scott, F. H. (2004). “Crystallographic analysis of surface layers of refractory ceramics formed using combined flame spray and simultaneous laser treatment,” J. Eur. Ceram. Soc.JECSER 24, 3129–3138; ICSD collection code 99327.10.1016/j.jeurceramsoc.2003.11.002CrossRefGoogle Scholar
Madsen, I. C., Scarlett, N. V. Y., Cranswick, L. M. D., and Lwin, T. (2001). “Outcomes of the International Union of Crystallography Commission on Powder Diffraction round robin on quantitative phase analysis: Samples 1a to 1h,” J. Appl. Crystallogr.JACGAR 34, 409–426.10.1107/S0021889801007476CrossRefGoogle Scholar
Materials Data, Inc. (2007). Jade 8.0.Google Scholar
National Bureau of Standards (U.S.) (1964). Monograph 25, Part 3, p. 3.Google Scholar
See EPAPS Document No. http://dx.doi.org/10.1154/1.3257610 E-PODIE2-24-006904 for supplemental data. This step-by-step description of a complex Rietveld refinement illustrates many of the common challenges faced in inorganic materials, and provides guidance on how to decide what to do next and how to interpret the refined parameters. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.Google Scholar
Siggel, A. and Jansen, M. (1990). “Roentgenographische untersuchungen zur bestimmung der einbauposition von seltenen erden,” Z. Anorg. Allg. Chem.ZAACAB 583, 67–77; ICSD collection code 69645.10.1002/zaac.19905830109CrossRefGoogle Scholar
Stephens, P. W. (1999). “Phenomenological model of anisotropic peak broadening in powder diffraction,” J. Appl. Crystallogr.JACGAR 32, 281–289.10.1107/S0021889898006001CrossRefGoogle Scholar
Yang, H., Downs, R. T., Finer, L. W., Hazen, R. M., and Prewitt, C. T. (1997). “Compressibility and crystal structure of kyanite, Al2SiO5, at high pressure,” Am. Mineral.AMMIAY 82, 467–474; ICSD collection code 83450.CrossRefGoogle Scholar
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