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Simultaneous structure and size–strain refinement by the Rietveld method
Author(s) -
Lutterotti L.,
Scardi P.
Publication year - 1990
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889890002382
Subject(s) - crystallite , rietveld refinement , tetragonal crystal system , anisotropy , materials science , crystallography , diffraction , crystal structure , physics , chemistry , optics
A new procedure for simultaneous refinement of structural and microstructural disorder parameters for polycrystalline materials is proposed. It is based on the Rietveld method combined with Fourier analysis for broadened peaks. Crystallite size and shape and r.m.s. microstrain are regarded as fitting parameters, replacing the well known formula of Caglioti, Paoletti & Ricci [ Nucl. Instrum. Methods (1958), 3 , 223–228] for the angular dependence of the peak width. In particular, from these microstructural disorder parameters, by inverting the Warren–Averbach procedure [Warren & Averbach (1950). J. Appl. Phys. 21 , 595–599; (1952), 23 , 1059] for a single peak, it is possible to obtain the parameters of the pseudo‐Voigt (pV) functions employed to fit the experimental data. The anisotropy of the crystallite size and microstrain is also taken into account. The method has been tested on three materials with different degrees of crystallization: tetragonal ZrO 2 ( P 4 2 / nmc , a = 3.5961, c = 5.1770 Å, V c = 66.95 Å 3 , Z = 2, R wp = 0.077, M ≃100 Å, 〈 ɛ 2 〉 1/2 ≃ 3 × 10 −3 ); tetragonal Zr 0.82 Ce 0.18 O 2 ( P 4 2 / nmc , a = 3.6419, c = 5.2440 Å, V c = 69.556 Å 3 , Z = 2, R wp = 0.0654, M ≃1000 Å, 〈 ɛ 2 〉 1/2 ≃8 × 10 −4 ); α ‐Al 2 O 3 ( R c , a = 4.7605, c = 12.9956 Å, V c = 255.05 Å 3 , Z = 6, R wp = 0.0684, M ≃ 1400 Å, 〈 ɛ 2 〉 1/2 ≃7 × 10 −4 ).