Rietveld refinement of site-occupancy parameters of Mg2-xMnxSiO4 using a new weight function in least-squares fitting

The crystal structures of olivine-type Mg2-xMnxSiO4 (x = 0, 1, 1.4 and 2) were refined using high-resolution synchrotron radiation data and the Rietveld method, adopting the new weight function with the form 1/Y-o(e)(e similar or equal to 2) (Y-o is the observed profile intensity) [Toraya (1998). J. Appl. Cryst. 31, 333-343]. Positional parameters were accurately determined by optimizing e in 1/Y-o(e). Derived structures were in accordance with observations on olivine structures, having a constant tetrahedral Si-O distance and octahedral metal-oxygen distances which increase linearly on substitution of octahedral atoms with those having larger atomic radii. Site-occupancy parameters of octahedral atoms were refined under various refinement conditions and could be determined within +/-1.2% under the constraint of chemical composition. Deviations of x from assumed chemical compositions, when the site-occupancy parameters were refined without the constraint, were 1.0-3.5% using the new weight function; they are comparable with values obtained in single-crystal studies on Mg-Fe olivine (0.5-2.7%). The use of atomic scattering factors for fully ionized atoms gave better site-occupancy parameters, by 0.1-2.5%, than those for neutral atoms in the present analysis.