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Reflection splitting-induced microstrain broadening

Published online by Cambridge University Press:  19 July 2017

Andreas Leineweber
Affiliation:
Institute of Materials Science, Gustav-Zeuner-Straße 5, TU Bergakademie Freiberg, 09599 Freiberg, Germany
Corresponding

Abstract

Crystal structure determination on the basis of powder diffraction data frequently involves the question how the given diffraction data with some appreciably hkl-dependent line broadening should be interpreted. In many cases, such line broadening may either: (i) reasonably well be reconciled with a certain high-symmetry structure model or (ii) with a variant of the former with lower symmetry crystal family, which frequently will give a somewhat better fit in Rietveld refinement. In this work, it is shown mathematically that symmetry reduction induced reflection spitting masked by other line broadening contributions, thus leading to some reflection splitting-induced line broadening, shows a similar hkl dependence as typically adopted for anisotropic microstrain broadening with respect to the high-symmetry structure. This implies that Rietveld refinement on the basis of the low-symmetry model (including typically isotropic line broadening) and on the basis of the high-symmetry model with anisotropic microstrain broadening can both lead to similar qualities of the fit. Hence, the refinement results for both possibilities should be carefully considered in combination with possibly available additional information (e.g. results of first-principles calculations) to arrive at adequate conclusions concerning the true symmetry of the material under investigation.

Type
Technical Articles
Copyright
Copyright © International Centre for Diffraction Data 2017 

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References

Aizu, K. (1970). “Determination of the state parameters and formulation of spontaneous strain for ferroelastics,” J. Phys. Soc. Japan 28, 706716.CrossRefGoogle Scholar
Boysen, H. (2007). “Coherence effects in the scattering from domain structures,” J. Phys.: Condens. Matter. 19, Article No. 275206.Google Scholar
Carpenter, M. A., Salje, E. K. H., and Grame-Barber, A. (1998). “Spontaneous strain as a determinant of thermodynamic properties for phase transitions in minerals,” Eur. J. Mineral. 10, 621691.CrossRefGoogle Scholar
Cowley, J. M. and Au, A. Y. (1978). “Diffraction by crystals with planar faults. III. Structure analyses using microtwins,” Acta Crystallogr. A 34, 738743.CrossRefGoogle Scholar
Fabrykiewicz, P. and Przenioslo, R. (2016). “Distortion of the crystal structure of MnO at ambient conditions,” Phys. B 489, 5662.CrossRefGoogle Scholar
Hayward, S. A. and Salje, E. K. H. (2005). “Diffuse scattering from microstructures and mesostructures,” Z. Kristallogr. 220, 9941001.CrossRefGoogle Scholar
Janovec, V. and Privratska, J. (2003). “Chapter 3.4 domain structures,” in International Tables for Crystallography Vol. D, Physical Properties of Crystals, edited by Authier, A. (Kluwer, Dordrecht/Boston/London), pp. 449505.Google Scholar
Leineweber, A. (2006). “Anisotropic diffraction-line broadening due to microstrain distribution; parametrization opportunities,” J. Appl. Crystallogr. 39, 509518.CrossRefGoogle Scholar
Leineweber, A. (2009). “Description of anisotropically microstrain-broadened line profiles by Edgeworth series,” Z. Kristallogr. 224, 432445.CrossRefGoogle Scholar
Leineweber, A. (2011). “Understanding anisotropic microstrain broadening in Rietveld refinement,” Z. Kristallogr. 226, 905923.CrossRefGoogle Scholar
Leineweber, A. (2012a). “Parabolic microstrain-like line broadening induced by random twin faulting,” Philos. Mag. 92, 18441864.CrossRefGoogle Scholar
Leineweber, A. (2012b). “Anisotropic microstrain broadening in cementite, Fe3C, caused by thermal microstress: comparison between prediction and results from diffraction-line profile analysis,” J. Appl. Crystallogr. 45, 944949.CrossRefGoogle Scholar
Leineweber, A. (2016). “Thermal expansion anisotropy as source for microstrain broadening of polycrystalline cementite, Fe3C,” J. Appl. Crystallogr. 49, 16321644.CrossRefGoogle Scholar
Leineweber, A. and Krumeich, F. (2013). “Broadening and shifting of Bragg reflections of nanoscale-microtwinned LT-Ni3Sn2 ,” Philos. Mag. 93, 44404468.CrossRefGoogle Scholar
Leineweber, A., Shang, S. L., Liu, Z. K., Widenmeyer, M., and Niewa, R. (2012). “Crystal structure determination of Hägg carbide, χ-Fe5C2 by first-principles calculations and Rietveld refinement,” Z. Kristallogr. 227, 207220.CrossRefGoogle Scholar
Popa, N. C. (1998). “The (hkl) dependence of diffraction-line broadening caused by strain and size for all Laue groups in Rietveld refinement,” J. Appl. Crystallogr. 31, 176180.CrossRefGoogle Scholar
Stephens, P. W. (1999). “Phenomenological model of anisotropic peak broadening in powder diffraction,” J. Appl. Crystallogr. 32, 281289.CrossRefGoogle Scholar
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