Simultaneous structure and size–strain refinement by the Rietveld method

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 ZrO₂ (P4₂/nmc, a = 3.5961, c = 5.1770 Å, V_c = 66.95 ų, Z = 2, R_wp = 0.077, M ≃100 Å, 〈[epsilon]²〉^1/2 ≃ 3 × 10⁻³); tetragonal Zr_0.82Ce_0.18O₂ (P4₂/nmc, a = 3.6419, c = 5.2440 Å, V_c = 69.556 ų, Z = 2, R_wp = 0.0654, M ≃1000 Å, 〈[epsilon]²〉^1/2 ≃8 × 10⁻⁴); α-Al₂O₃ (Rc, a = 4.7605, c = 12.9956 Å, V_c = 255.05 ų, Z = 6, R_wp = 0.0684, M ≃ 1400 Å, 〈[epsilon]²〉^1/2 ≃7 × 10⁻⁴).