Skip to main content
×
×
Home

Routine (an)isotropic crystallite size analysis in the double-Voigt approximation done right?

  • D. Ectors (a1), F. Goetz-Neunhoeffer (a1) and J. Neubauer (a1)
Abstract

In this study, the application of (an)isotropic size determination using a recently proposed model for the double-Voigt approach is demonstrated and validated against line profile simulations using the Whole Powder Pattern Modelling approach. The fitting of simulated line profiles demonstrates that the attained crystallite sizes and morphologies are in very reasonable agreement with the simulated values and thus demonstrate that even in routine application scenarios credible size and morphology information can be obtained using the double-Voigt approximation. The aim of this contribution is to provide a comprehensive introduction to the problem, address the practical application of the developed model, and discuss the accuracy of the double-Voigt approach and derived size parameters. Mathematical formulations for the visualization of modeled morphologies, supporting the application of the recently developed macros, are additionally provided.

Copyright
Corresponding author
a) Author to whom correspondence should be addressed. Electronic mail: dominique.ectors@fau.de
References
Hide All
Balić Žunić, T. and Dohrup, J. (1999). “Use of an ellipsoid model for the determination of average crystallite shape and size in polycrystalline samples,” Powder Diffr. 14(3), 203207.
Balzar, D. and Ledbetter, H. (1993). “Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks,” J. Appl. Crystallogr. 26, 97103.
Barr, A. H. (1981). “Superquadrics and angle-preserving transformations,” IEEE Comput. Graph. 1(1), 1123.
Bertaut, E. (1949a). “Signification de la dimension crystalline mesurée d'après la largeur de raie Debye-Scherrer,” C. R. Acad. Sci. 228, 187189.
Bertaut, E. (1949b). “Étude aux rayons X de la répartition des dimensions des cristallites dans une poudre crystalline,” C. R. Acad. Sci. 228, 492494.
Cheary, R. and Coelho, A. (1992). “A fundamental parameters approach to X-ray line-profile fitting,” J. Appl. Crystallogr. 25, 109121.
Ectors, D. (2016). Advances in the analysis of cementitious reactions and hydrate phases (PhD thesis). University of Erlangen-Nuernberg (FAU), available online at: https://opus4.kobv.de/opus4-fau/frontdoor/index/index/docId/7174
Ectors, D., Goetz-Neunhoeffer, F., and Neubauer, J. (2015a). “A generalized geometric approach to anisotropic peak broadening due to domain morphology,” J. Appl. Crystallogr. 48, 189194.
Ectors, D., Goetz-Neunhoeffer, F., and Neubauer, J. (2015b). “Domain size anisotropy in the double-Voigt approach: an extended model,” J. Appl. Crystallogr. 48, 19982001. DOI: 10.1107/S1600576715018488/
Gielis, J. (2003). “A generic geometric transformation that unifies a wide range of natural and abstract shapes,” Am. J. Bot. 90(3), 333338.
Henderson, D. M. and Gutowsky, H. S. (1962). “A nuclear magnetic resonance determination of the hydrogen positions in Ca(OH)2 ,” Am. Mineral. 47, 12311251.
Hurle, K., Neubauer, J., and Goetz-Neunhoeffer, F. (2016). “Influence of Sr2+ on calcium-deficient hydroxyapatite formation kinetics and morphology in partially amorphized α-TCP,” J. Am. Ceram. Soc. 99(3), 10551063.
Langford, J. I. (1980). “Accuracy of crystallite size and strain determined from the integral breadth of powder diffraction lines,” Natl. Bur. Stand. Spec. Publ. 567, 255269.
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. 11, 102113.
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. 33, 964974.
Leonardi, A., Leoni, M., Siboni, S., and Scardi, P. (2012). “Common volume functions and diffraction line profiles of polyhedral domains,” J. Appl. Crystallogr. 45, 11621172.
Leoni, M., Confente, T., and Scardi, P. (2006). “PM2K: a flexible program implementing Whole Powder Pattern Modelling,” Z. Kristallogr. Suppl. 23, 249254.
Popa, N. C. and Balzar, D. (2002). “An analytical approximation for a size-broadened profile given by the lognormal and gamma distributions,” J. Appl. Crystallogr. 35, 338346.
Scardi, P. (2008). “Recent advances in whole powder pattern modelling,” Z. Kristallogr. Suppl. 27, 101111.
Scardi, P. and Leoni, M. (2002). “Whole powder pattern modelling,” Acta Crystallogr. A58, 190200.
Scherrer, P. (1918). “Bestimmung der Größe und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen,” Nachr. Göttinger Ges. 1918, 98100.
Stephens, P. W. (1999). “Phenomenological model of anisotropic peak broadening in powder diffraction,” J. Appl. Crystallogr. 32, 281289.
Stokes, A. R. (1948). “A numerical Fourier-analysis method for the correction of widths and shapes of lines on X-ray powder photographs,” Proc. Phys. Soc. Lond. 61(4), 382391.
Tournarie, M. (1956a). “Utilisation du deuxième moment comme critère d’élargissement des raies Debye Scherrer. Elimination de l'effet instrumental,” C. R. Acad. Sci. 242, 20162018.
Tournarie, M. (1956b). “Utilisation du deuxième moment comme critère d’élargissement des raies Debye Scherrer. Signification physique,” C. R. Acad. Sci. 242, 21612164.
von Laue, M. (1936). “Die äußere Form der Kristalle in ihrem Einfluß auf die Interferenzerscheinungen an Raumgittern,” Ann. Phys. (Leipzig) 26, 5568.
Wilson, A. J. C. (1962a). “Variance as a measure of line broadening,” Nature 193, 568569.
Wilson, A. J. C. (1962b). Chapter IV: Powder Patterns of Small Crystals in: X-Ray Optics (Methuen, London), 2nd ed.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Powder Diffraction
  • ISSN: 0885-7156
  • EISSN: 1945-7413
  • URL: /core/journals/powder-diffraction
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed