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Dislocations, crystallite size, and planar faults in nanocrystalline ceria

Published online by Cambridge University Press:  29 February 2012

S. R. Aghdaee and
V. Soleimanian
S. R. Aghdaee*
Affiliation:
Department of Physics, Iran University of Science and Technology, Narmak, 716844 Tehran, Iran
V. Soleimanian
Affiliation:
Department of Physics, Iran University of Science and Technology, Narmak, 716844 Tehran, Iran
*
a)Author to whom correspondence should be addressed. Electronic mail: aghdaee@iust.ac.ir
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Abstract

The modified Williamson–Hall and Warren–Averbach methods were used successfully for analyzing experimentally observed anisotropic X-ray diffraction line broadening and for determining reliable values of crystallite size and dislocation density in cerium oxide. The modified Williamson–Hall plot gives 22.3(2) nm for volume-weighted crystallite size, while the modified Warren–Averbach produces 18.0(2) nm for area-weighted grain size. The dislocation density and effective outer cut-off radius of dislocations obtained from the modified Warren–Averbach method are 1.8(3)×1015 m−2 and 15.5(1) nm, respectively.

Keywords

anisotropic line broadeningcrystallite sizedislocation density

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Type
Technical Articles
Information
Powder Diffraction , Volume 24 , Issue 3 , September 2009, pp. 228 - 233
Copyright
Copyright © Cambridge University Press 2009

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References

Armstrong, N., Kalceff, W., Cline, J. P., and Bonevich, J. (2004). Diffraction Analysis of Materials Microstructure, Springer Series in Materials Science edited by Mittemeijer, E. J. and Scardi, P. (Springer-Verlag, Berlin), pp. 249–268.CrossRefGoogle Scholar
Balzar, D., Audebrand, N., Daymond, M. R., Fitch, A., Hewat, A., Langford, J. I., Le Bail, A., Louër, D., Masson, O., McCowan, C. N., Popa, N. C., Stephens, P. W., and Toby, B. H. (2004). “Size-strain line-broadening analysis of the ceria round-robin sample,” J. Appl. Crystallogr. JACGAR 37, 911–924. 10.1107/S0021889804022551CrossRefGoogle Scholar
Borbély, A. and Groma, I. (2001). “Variance method for the evaluation of particle size and dislocation density from X-ray Bragg peaks,” Appl. Phys. Lett. APPLAB 79, 1772–1774. 10.1063/1.1404134CrossRefGoogle Scholar
Borbély, A., Dragomir-Cernatescu, J., Ribárik, G., and Ungár, T. (2003). “Computer program ANIZC for the calculation of diffraction contrast factors of dislocations in elastically anisotropic cubic, hexagonal and trigonal crystals,” J. Appl. Crystallogr. JACGAR 36, 160–162. 10.1107/S0021889802021581CrossRefGoogle Scholar
Dong, Y. H. and Scardi, P. (2000). “MARQX: A new program for whole-powder-pattern fitting,” J. Appl. Crystallogr. JACGAR 33, 184–189. 10.1107/S002188989901434XCrossRefGoogle Scholar
Groma, I., Ungár, T., and Wilkens, M. (1988). “Asymmetric X-ray line broadening of plastically deformed crystals. I. Theory,” J. Appl. Crystallogr. JACGAR 21, 47–53. 10.1107/S0021889887009178CrossRefGoogle 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
Krivoglaz, M. A. (1969). Theory of X-ray and Thermal Neutron Scattering by Real Crystals (Plenum, New York).Google Scholar
Krivoglaz, M. A. (1996). X-ray and Neutron Diffraction in Nonideal Crystals (Springer-Verlag, Berlin), p. 357.CrossRefGoogle Scholar
Kuzel, R. Jr. and Klimanek, P. (1988). “X-ray diffraction line broadening due to dislocations in noncubic crystalline materials. III. Experimental results for plastically deformed zirconium,” J. Appl. Crystallogr. JACGAR 21, 363–368. 10.1107/S002188988800336XCrossRefGoogle Scholar
Louer, D. and Langford, J. I. (1988). “Peak shape and resolution in conventional diffractometry with monochromatic X-rays,” J. Appl. Crystallogr. JACGAR 21, 430–437. 10.1107/S002188988800411XCrossRefGoogle Scholar
Ribárik, G. (2008). “Modeling of diffraction patterns based on microstructural properties,” Ph.D. thesis, Eötvös Loránd University.Google Scholar
Scardi, P., Leoni, M., and Delhez, R. (2004). “Line broadening analysis using integral breadth methods: A critical review,” J. Appl. Crystallogr. JACGAR 37, 381–390. 10.1107/S0021889804004583CrossRefGoogle Scholar
Scherrer, P. (1918). “Bestimmung der Gröss und der inner Struktur von Kolloidteilchen mittels Röntgenstrahlen,” Nachr. Gött. 2, 98–100.Google Scholar
Soleimanian, V. and Aghdaee, S. R. (2008). “Comparison methods of variance and line profile analysis for the evaluation of microstructures of materials,” Powder Diffr. PODIE2 23, 41–51. 10.1154/1.2888763CrossRefGoogle Scholar
Stokes, A. R. and Wilson, A. J. C. (1944). “The diffraction of X-rays by distorted crystal aggregates–I,” Proc. Phys. Soc. London PPSOAU 56, 174–181. 10.1088/0959-5309/56/3/303CrossRefGoogle Scholar
Ungár, T. and Borbély, A. (1996). “The effect of dislocation contrast on X-ray line broadening: A new approach to line profile analysis,” Appl. Phys. Lett. APPLAB 69, 3173–3175. 10.1063/1.117951CrossRefGoogle Scholar
Ungár, T. and Tichy, G. (1999). “The effect of dislocation contrast on X-ray line profiles in untextured polycrystals,” Phys. Status Solidi A PSSABA 147, 425–434.3.0.CO;2-W>CrossRefGoogle Scholar
Ungár, T., Groma, I., and Wilkens, M. (1989). “Asymmetric X-ray line broadening of plastically deformed crystals. II. Evaluation procedure and application to [001]-Cu crystals,” J. Appl. Crystallogr. JACGAR 22, 26–34. 10.1107/S0021889888009720CrossRefGoogle Scholar
Ungár, T., Leoni, M., and Scardi, P. (1999). “The dislocation model of strain anisotropy in whole powder-pattern fitting: The case of an Li–Mn cubic spinel,” J. Appl. Crystallogr. JACGAR 32, 290–295. 10.1107/S0021889898012710CrossRefGoogle Scholar
Warren, B. E. (1959). “X-ray studies of deformed metals,” Prog. Met. Phys. PMPHA7 8, 147–202. 10.1016/0502-8205(59)90015-2CrossRefGoogle Scholar
Warren, B. E. (1990). X-ray Diffraction (Addison-Wesley, Reading).Google Scholar
Wilkens, M. (1969). “Das mittlere Spannungsquadrat 〈σ2〉 begrenzt regellos verteilter Versetzungen in einem zylinderförmigen Körper,” Acta Metall. AMETAR 17, 1155–1159. 10.1016/0001-6160(69)90092-3CrossRefGoogle Scholar
Wilkens, M. (1970). “The determination of density and distribution of dislocations in deformed single crystals from broadened X-ray diffraction profiles,” Phys. Status Solidi A PSSABA 2, 359–370. 10.1002/pssa.19700020224CrossRefGoogle Scholar
Wilkens, M. (1987). “X-ray line broadening and mean square strains of straight dislocations in elastically anisotropic crystals of cubic symmetry,” Phys. Status Solidi A PSSABA 104, K1–K6. 10.1002/pssa.2211040137CrossRefGoogle Scholar
Williamson, G. K. and Hall, W. H. (1953). “X-ray line broadening from filed aluminium and wolfram,” Acta Metall. AMETAR 1, 22–31. 10.1016/0001-6160(53)90006-6CrossRefGoogle Scholar
Wilson, A. J. C. (1962). X-ray Optics, 2nd ed. (Methuen, London).Google Scholar