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The Determination of Direction-Dependent Crystallite Size and Strain by X-Ray Whole-Powder-Pattern Fitting

Published online by Cambridge University Press:  10 January 2013

H. Toraya
H. Toraya
Affiliation:
Ceramic Engineering Research Laboratory, Nagoya Institute of Technology, Asahigaoka, Tajimi 507, Japan
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Abstract

The procedure of whole-powder-pattern fitting without reference to a structural model has been applied to the determination of direction-dependent crystallite size and strain. The fitting function used is defined as the sum of (1) background intensity and (2) contributions from individual reflections given as the convolution of the observed instrumental function with the true data function in analytical form. Crystallite size and strain parameters are adjustable, together with unit-cell parameters and the integrated intensities of all reflections, during the whole-powder-pattern fitting. The procedure requires neither structural parameters nor intensity correction for preferred orientation in calculating profile intensity. The two models are incorporated for line broadening, one for isotropic size and strain effects and the other for the anisotropic size effect of cylindrical shape. The procedure has been tested for these two models using the observed data of 4 mole % Y2O3-doped tetragonal ZrO2 and hydroxyapatite, Ca5(PO4)3OH, respectively, and been shown to be effective for determining crystallite size and strain from the powder pattern with a relatively high peak density.

Type
Research Article
Information
Powder Diffraction , Volume 4 , Issue 3 , September 1989 , pp. 130 - 136
Copyright
Copyright © Cambridge University Press 1989

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References

Attfield, J.P., Sleight, A.W. & Cheetham, A.K. (1986). Nature (London) 322, 620–622.Google Scholar
Cox, D.E. (1984). Acta Crystallogr., Sect. A 40S, C369Google Scholar
Keijser, Th. H., de Langford, J.I., Mittemeijer, E.J. & Vogels, A.B.P. (1982). J. Appl. Crystallogr. 15, 308–314.Google Scholar
Keijser, Th. H., de Mittemeijer, E.J. & Rozendaal, H.C.F. (1983). J. Appl. Crystallogr. 16, 309–316.Google Scholar
Hall, M.M. Jr., Veeraraghavan, V.G., Rubin, H. & Winchell, P.G. (1977). J. Appl. Crystallogr. 10, 66–68.CrossRefGoogle Scholar
Hepp, A. & Baerlocher, CH. (1988). Aust. J. Phys. 41, 229–236.CrossRefGoogle Scholar
Hill, R.J. & Howard, C.J. (1985). J. Appl. Crystallogr. 18, 173–180.Google Scholar
Howard, S.A. & Snyder, R.L. (1984). Acta Crystallogr., Sect. A 40S, C369.Google Scholar
Langford, J.I. (1978). J. Appl. Crystallogr. 11, 10–14.CrossRefGoogle Scholar
Langford, J.I. & Louër, D. (1982). J. Appl. Crystallogr. 15, 20–26.Google Scholar
Langford, J.I. & Louër, D., Sonneveld, E.J. & Visser, J.W. (1986). Applications of Total Pattern Fitting to a Study of Crystallite Size and Strain in Zinc Oxide Powder. Pow. Diff. 1, 211–221.CrossRefGoogle Scholar
Louër, D., Auffrédic, J.P., Langford, J.I., Ciosmak, D. & Niepce, J.C. (1983). J. Appl. Crystallogr. 16, 183–191.Google Scholar
Louër, D., Weigel, D. & Louboutin, R. (1969). Acta Crystallogr., Sect. A 25, 335–338CrossRefGoogle Scholar
Moraweck, B., De Montgolfier, Ph. & Renouprez, A.J. (1977). J. Appl. Crystallogr. 10, 184–190.Google Scholar
Parrish, W., Huang, T.C. & Ayers, G.L. (1976). Trans. Am. Crystallogr. Assoc. 12, 55–73.Google Scholar
Paterson, M.S. (1950). Proc. Phys. Soc. London, Sect. A 63, 477–482.CrossRefGoogle Scholar
Pawley, G.S. (1980). J. Appl. Crystallogr. 13, 630–633.Google Scholar
Pawley, G.S. (1981). J. Appl. Crystallogr. 14, 357–361.Google Scholar
Rierveld, H.M. (1969). J. Appl. Crystallogr. 2, 65–71.CrossRefGoogle Scholar
Toraya, H. (1986). J. Appl. Crystallogr. 19, 440–447.CrossRefGoogle Scholar
Toraya, H. (1988). J. Appl. Crystallogr. 21, 192–196.Google Scholar
Toraya, H., Yoshimura, M. & Somiya, S. (1983). J. Appl. Crystallogr. 16, 653–657.Google Scholar
Young, R.A., Mackie, P.E. & Von Dreele, R.B. (1977). J. Appl. Crystallogr. 10, 262–269.Google Scholar
Young, R.A., Prince, E. & Sparks, R.A. (1982). J. Appl. Crystallogr. 15, 357–359.Google Scholar
Voigt, W. (1912). Sitzungsber. K. Bayer. Akad. Wiss. 42, 603–620.Google Scholar
Warren, B.E. & Averbach, B.L. (1950). Effect of Cold-Work Distortion on X-Ray Patterns. J. Appl. Phys. 21, 595–599.Google Scholar
Warren, B.E. & Averbach, B.L. (1952). J. Appl. Phys. 23, 497.Google Scholar
Wertheim, G.K., Butler, M.A., West, K.W. & Buchanan, D.N.E. (1974). Rev. Sci. Instrum. 45, 1369–1371.CrossRefGoogle Scholar
Williamson, G.K. & Hall, W.H. (1953). Acta Metall. 1, 22–31.CrossRefGoogle Scholar
Wilson, A.J.C. (1962). X-ray Optics. London: Methuen.Google Scholar
Wilson, A.J.C. (1963). Mathematical Theory of X-ray Powder Diffractometry. New York: Gordon and Breach, Science Publishers.Google Scholar