Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-19T17:24:52.919Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffraction line profile from a disperse system: A simple alternative to Voigtian profiles

Published online by Cambridge University Press:  01 March 2012

P. Scardi ,
M. Leoni  and
J. Faber
P. Scardi
Affiliation:
Department of Materials Engineering and Industrial Technologies, University of Trento, 38050 via Mesiano 77, Trento, Italy
M. Leoni
Affiliation:
Department of Materials Engineering and Industrial Technologies, University of Trento, 38050 via Mesiano 77, Trento, Italy
J. Faber
Affiliation:
International Centre for Diffraction Data, 12 Campus Boulevard, Newtown Square, Pennsylvania 19073-3273
Get access Rights & Permissions [Opens in a new window]

Abstract

A general expression is proposed for the peak profile produced by a system of simple-shape crystalline domains (sphere, cube, tetrahedron, octahedron) whose size is dispersed according to a gamma distribution. The analytical expression obtained is particularly suited to “on the fly” pattern simulation or profile fitting for nanocrystalline materials. An advantage of using the proposed profile expression is that it always corresponds to a physically meaningful, though a priori fixed, size distribution, whereas the traditionally employed Voigtian profiles can produce unphysical negative size distributions for certain combinations of profile parameters. The peak profile depends on the distribution mean and variance instead of the more common empirical parameters of peak width and shape.

Keywords

profile fittingline profile analysisdomain size distributionnanocrystalline materialspowder diffraction
Type
Technical Articles
Information
Powder Diffraction , Volume 21 , Issue 4 , December 2006 , pp. 270 - 277
Copyright
Copyright © Cambridge University Press 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bertaut, E. F. (1949). “Etude aux rayons X de la repartition des dimensions des crystallites dans une poudre crystalline,” Acad. Sci., Paris, C. R. COREAF 228, 492–494.Google Scholar
ICDD (2006a). “DDView+,” International Centre for Diffraction Data, edited by McClune, Frank, 12 Campus Boulevard, Newtown Square, PA, 19073-3272.Google Scholar
ICDD (2006b). “Powder Diffraction File,” International Centre for Diffraction Data, edited by McClune, Frank, 12 Campus Boulevard, Newtown Square, PA, 19073–3272.Google Scholar
Klug, H. P. and Alexander, L. E. (1974). X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials, 2nd ed. (Wiley, New York).Google Scholar
Langford, J. I. (1978). “A rapid method for analysing the breadths of diffraction and spectral lines using the Voigt function,” J. Appl. Crystallogr. JACGAR 10.1107/S0021889878012601 11, 10–14.CrossRefGoogle Scholar
Langford, J. I., Louër, D., and Scardi, P. (2000). “Effect of a crystallite size distribution on X-ray diffraction line profiles and whole-powder-pattern fitting,” J. Appl. Crystallogr. JACGAR 10.1107/S002188980000460X 33, 964–974.CrossRefGoogle Scholar
Langford, J. I. and Wilson, A. J. C. (1978). “Scherrer after sixty years: a survey and some new results in the determination of crystallite size,” J. Appl. Crystallogr. JACGAR 10.1107/S0021889878012844 11, 102–113.CrossRefGoogle Scholar
Leoni, M. and Scardi, P. (2004). “Nanocrystalline domain size distributions from powder diffraction data,” J. Appl. Crystallogr. JACGAR 10.1107/S0021889804013366 37, 629–634.CrossRefGoogle Scholar
Leoni, M., Di Maggio, R., Polizzi, S., and Scardi, P. (2004). “X-ray diffraction methodology for the microstructural analysis of nanocrystalline powders: application to cerium oxide,” J. Am. Ceram. Soc. JACTAW 87, 1133–1140.CrossRefGoogle Scholar
Mittemeijer, E. J. and Scardi, P. (Eds.) (2004). Diffraction Analysis of the Microstructure of Materials (Springer-Verlag, Berlin).CrossRefGoogle Scholar
Pielaszek, R. (2004). “Analytical expression for diffraction line profile for polydispersive powders,” in Applied Crystallography, Proceedings of the XIX Conference, edited by Morawiec, H. and Stróż, D. (World Scientific, Singapore), pp. 43–50.CrossRefGoogle Scholar
Scardi, P. and Leoni, M. (2001). “Diffraction line profiles from polydisperse crystalline systems,” Acta Crystallogr. ACACEQ 10.1107/S0108767301008881 A57, 604–613.CrossRefGoogle Scholar
Scardi, P. and Leoni, M. (2002). “Whole powder pattern modeling,” Acta Crystallogr. ACACEQ 10.1107/S0108767301021298 58, 190–200.CrossRefGoogle Scholar
Scardi, P. and Leoni, M. (2004). “Whole Powder Pattern Modelling: theory and applications,” in Diffraction Analysis of the Microstructure of Materials, edited by Mittemeijer, E. J. and Scardi, P., Springer Series in Materials Science, Vol. 68 (Springer-Verlag, Berlin), pp. 51–92.CrossRefGoogle Scholar
Scardi, P., Leoni, M., and Delhez, R. (2004). “Line broadening analysis using integral breadth methods: a critical review,” J. Appl. Crystallogr. JACGAR 10.1107/S0021889804004583 37, 381–390.CrossRefGoogle Scholar
Scardi, P. and Leoni, M. (2006). “Line profile analysis: pattern modelling versus profile fitting,” J. Appl. Crystallogr. JACGAR 39, 24–31.CrossRefGoogle Scholar
Vargas, R., Louër, D., and Langford, J. I. (1983). “Diffraction line profiles and Scherrer constants for materials with hexagonal crystallites,” J. Appl. Crystallogr. JACGAR 10.1107/S0021889883010924 16, 512–518.CrossRefGoogle Scholar
Warren, B. E. (1969). X-ray Diffraction (Addison-Wesley, Reading, MA).Google Scholar
Wertheim, G. K., Butler, M. A., West, K. W., and Buchanan, D. N. E. (1974). “Determination of the Gaussian and Lorentzian content of experimental line shapes,” Rev. Sci. Instrum. RSINAK 11, 1369–1371.CrossRefGoogle Scholar
Wilson, A. J. C. (1949). X-ray Optics (Methuen, London).Google Scholar
Young, R. A., (Ed.). (1993). The Rietveld Method (Oxford U.P., Oxford).CrossRefGoogle Scholar
Young, R. A. and Wiles, D. B. (1982). “Profile shape functions in Rietveld refinements,” J. Appl. Crystallogr. JACGAR 10.1107/S002188988201231X 15, 430–438.CrossRefGoogle Scholar