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The dislocations contrast factors of cubic crystals in the Zener constant range between zero and unity

Published online by Cambridge University Press:  05 March 2012

I. C. Dragomir  and
T. Ungár
I. C. Dragomir
Affiliation:
Department of General Physics, Eötvös University Budapest, Pázmány Péter sétány 1/A, H-1518, P.O.B. 32, Budapest, Hungary
T. Ungár
Affiliation:
Department of General Physics, Eötvös University Budapest, Pázmány Péter sétány 1/A, H-1518, P.O.B. 32, Budapest, Hungary
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Abstract

Diffraction peak profiles broaden due to the smallness of crystallites and the presence of lattice defects. Strain broadening of powders of polycrystalline materials is often anisotropic in terms of the hkl indices. This kind of strain anisotropy has been shown to be well interpreted assuming dislocations as one of the major sources of lattice distortions. The knowledge of the dislocation contrast factors are inevitable for this interoperation. In a previous work the theoretical contrast factors were evaluated for cubic crystals for elastic constants in the Zener constant range 0.5≤Az≤8. A large number of ionic crystals and many refractory metals have elastic anisotropy, Az, well below 0.5. In the present work the contrast factors for this lower anisotropy-constant range are investigated. The calculations and the corresponding peak profile analysis are tested on ball milled PbS and Nb and nanocrystalline CeO2.

Keywords

contrast factorsdislocationspowder diffractionmicrostructureelastic anisotropy
Type
Technical Articles
Information
Powder Diffraction , Volume 17 , Issue 2 , June 2002 , pp. 104 - 111
Copyright
Copyright © Cambridge University Press 2005

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References

Audebrand, N., Auffrédic, J.-P., and Loue¨r, D. (2000). “An X-ray powder diffraction study of the microstructure and growth kinetics of nanoscale crystallites obtained from hydrated cerium oxides” Chem. Mater. CMATEX 12, 1791–1799. cma, CMATEX CrossRefGoogle Scholar
Bhagavantam, S., and Seshagiri Rao, T. (1951). “Elastic constants of galena” Nature (London) NATUAS 168, 42. nat, NATUAS CrossRefGoogle Scholar
Cerny, R., Joubert, J-L., Latroche, M., Percheron-Guégan, A., and Yvon, K. (2000). “Anisotropic diffraction line broadening and dislocation substructure in hydrogen cycled LaNi5 and substituted compounds,” J. Appl. Crystallogr. JACGAR 33, 997–1005. acr, JACGAR CrossRefGoogle Scholar
Cheary, R. W., Dooryhee, E., Lynch, P., Armstrong, N., and Dligatch, S. (2000). “X-ray diffraction line broadening from thermally deposited gold films,” J. Appl. Crystallogr. JACGAR 33, 1271–1283. acr, JACGAR CrossRefGoogle Scholar
Groma, I., Ungár, T., and Wilkens, M. (1988). “Asymmetric X-ray line broadening of plastically deformed crystals. Part I: Theory,” J. Appl. Crystallogr. JACGAR 21, 47–53. acr, JACGAR CrossRefGoogle Scholar
Hearmon, R. F. S. (1966). Landolt-Börnstein, Vol. 1.Google Scholar
Honeycombe, R. W. K. (1984). The Plastic Deformation of Metals (Edward Arnold Publ. Ltd., London), 106 pp.Google Scholar
Kim, S., and Ledbetter, H. (2001). “Elastic coefficients of monocrystal galena (PbS),” J. Appl. Phys. (submitted).Google Scholar
Kuzel, R., and Klimanek, P. (1988). “X-ray diffraction line broadening due to dislocations in non-cubic materials. II. The case of elastic anisotropy applied to hexagonal crystals,” J. Appl. Crystallogr. JACGAR 21, 363–368. acr, JACGAR CrossRefGoogle Scholar
Kuzel, R., and Klimanek, P. (1989). “X-ray diffraction line broadening due to dislocations in non-cubic materials. III. Experimental results for plastically deformed zirconium,” J. Appl. Crystallogr. JACGAR 22, 299–307. acr, JACGAR CrossRefGoogle Scholar
Ledbetter, H. (2001). Handbook of Elastic Properties of Solids, Liquids, and Gases (Academic, New York), Vol. 2.Google Scholar
Martinetto, P. (2000). Ph.D. thesis, Université de Grenoble, 260 pp.Google Scholar
Martinetto, P., Anne, M., Dooryhee, E., and Walter, P. (2000). “Les formulations cosmétiques de l’Egypte ancienne retrouvées gra⁁ce a` la diffraction des rayons X,” J. Phys. IV JPICEI 10, 465–472. jpv, JPICEI Google Scholar
Ramachandran, G. N., and Wooster, W. A. (1949). “Determination of elastic constants from diffuse reflexion of X-rays,” Nature (London) NATUAS 164, 839–840. nat, NATUAS CrossRefGoogle ScholarPubMed
Ramachandran, G. N., and Wooster, W. A. (1951). “Determination of elastic constants of crystals from diffuse reflexions of X-rays. II. Application to some cubic crystals,” Acta Crystallogr. ACCRA9 4, 431–440. acc, ACCRA9 CrossRefGoogle Scholar
Scardi, P., and Leoni, M. (1999). “Fourier modelling of the anisotropic line broadening of X-ray diffraction profiles due to line and plane lattice defects,” J. Appl. Crystallogr. JACGAR 32, 671–682. acr, JACGAR CrossRefGoogle Scholar
Seeger, A. (1968). Work Hardening, edited by J. P. Hirth and J. Weertman (Gordon and Breach, New York), 27 pp.Google Scholar
Steeds, J. W. (1973). Introduction to Anisotropic Theory of Dislocations (Clarendon, Oxford).Google Scholar
Taylor, G., and Christian, J. W. (1967). “Experiments on the deformation of niobium single crystals. II. Electron microscope study of dislocation structure” Philos. Mag. PHMAA4 15, 893–929. phm, PHMAA4 CrossRefGoogle 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. apl, APPLAB CrossRefGoogle Scholar
Ungár, T., and Tichy, Gy. (1999). “The effect of dislocation contrast on X-ray line profiles in untextured polycrystals,” Phys. Status Solidi A PSSABA 171, 425–434. psa, PSSABA 3.0.CO;2-W>CrossRefGoogle Scholar
Ungár, T., Dragomir, I., Révész, Á., and Borbély, A. (1999). “The contrast factors of dislocations in cubic crystals: the dislocation model of strain anisotropy in practice” J. Appl. Crystallogr. JACGAR 32, 992–1002. acr, JACGAR CrossRefGoogle Scholar
Ungár, T., Dragomir-Cernatescu, I., Loue¨r, D., and Audebrand, N. (2001a). “Dislocations and crystallite size distribution in nanocrystalline CeO2 obtained from an ammonium-cerium (IV)-nitrate solution,” J. Phys. Chem. Solids JPCSAW 62, 1935–1941. jpx, JPCSAW CrossRefGoogle Scholar
Ungár, T., Martinetto, P., Ribárik, G., Dooryhée, E., Walter, Ph., and Anne, M. (2001b). “Revealing the powdering methods of black make-up in Ancient Egypt by fitting microstructure based Fourier coefficients to the whole X-ray diffraction profiles of galena,” J. Appl. Phys. JAPIAU 91, 2455–2465. jap, JAPIAU CrossRefGoogle Scholar
Walter, Ph., Martinetto, P., Tsoucaris, G., Bréniaux, R., Lefebvre, M-A., Richard, G., Talabot, J., and Dooryhée, E. (1999). “Making make-up in Ancient Egypt,” Nature (London) NATUAS 397, 483–484. nat, NATUAS CrossRefGoogle Scholar
Wilkens, M., and Eckert, H. Z. (1964). “Röntgenographische Untersuchungen ueber die Versetzungsanordnung in Plastisch Verformten Kupfereinkristallen,” Z. Naturforsch. A ZENAAU 19a, 459–470. zen, ZENAAU CrossRefGoogle 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. psa, PSSABA CrossRefGoogle Scholar
Williamson, G. K., and Hall, W. H. (1953). “X-Ray line broadening from filed aluminium and wolfram,” Acta Metall. AMETAR 1, 22–31. ado, AMETAR CrossRefGoogle Scholar
Wu, E. et al. (1998). “Modelling dislocation-induced anisotropic line broadening in Rietveld refinements using a Voigt function. II. Application to neutron powder diffraction data,” J. Appl. Crystallogr. JACGAR 31, 363–368. acr, JACGAR CrossRefGoogle Scholar