In-situ neutron diffraction study of non-convergent cation ordering in the (Fe3O4)1-x(MgAl2O4)x spinel solid solution

Non-convergent cation ordering in the (Fe3O4)1-x(MgAl2O4)x solid solution was investigated using in-situ time-of-flight neutron powder diffraction. The approach to equilibrium in a sample with x = 0.75 was observed at 923 K by performing in-situ structure refinements at intervals of 5 min, and the ordering behavior was traced through the time-dependence of the lattice parameter, the cation-oxygen bond lengths, and the cation-site scattering lengths. The data are consistent with a two-stage kinetic process in which relatively rapid exchange of Fe with Mg and Fe between tetrahedral and octahedral sites was followed by slower exchange of Mg with Al. The Fe cations are shown to order onto tetrahedral sites, contrary to the predictions of thermodynamic models for the solid solution. Equilibrium cation distributions in samples with x = 0.4, 0.5, and 0.75 were determined between 1073 and 1273 K by combining the structure refinements with measurements of saturation magnetization in quenched material. The adopted cation distribution was a compromise between the normal and inverse distributions observed in the end-members. The conflict of site preference between these two ordering schemes resulted in a simple behavior in the middle of the solid solution in which Al occurred predominantly on octahedral sites and the Mg, Fe, and Fe cations were distributed randomly over the remaining sites. The ordering scheme adopted away from the middle of the solid solution was obtained by combining this pseudo-random scheme with a tetrahedral site preference of Fe relative to Mg and Fe. Comparison of the structure refinements with published thermodynamic models demonstrates that quantitative agreement was poor between calculated and observed behavior in this system. Qualitative agreement with the O’Neill-Navrotsky thermodynamic model was found near the middle of the solid solution. tween an ordered and a totally disordered spinel), such a completely random distribution would only be anticipated at infinite temperature and is approached asymptotically on increasing temperature. The end-members magnetite (Fe3O4) and spinel (MgAl2O4) adopt the inverse and normal cation distributions respectively at low temperature (Millard et al. 1992; Peterson et al. 1991; Wood et al. 1986; Wu and Mason 1981). Cation ordering in their solid solutions is expected to be a complex function of composition, due to the conflict of site preference displayed by Mg and Fe cations in the end-members (O’Neill and Navrotsky 1984). Experimental determination of the ordering is made difficult by several factors. First, the experiments have to be performed in situ, due to the unavoidable problem of cation redistribution during quenching from high temperature (Wood et al. 1986; Millard et al. 1992; Larsson et al. 1994; Harrison and Putnis 1996). This is especially a problem in spinels containing Fe and Fe cations, because these can exchange with each other relatively rapidly by the transfer of an electron. Second, the experiments have to be performed either under high vacuum or controlled oxygen fugacity to prevent oxidation of Fe to Fe. Finally, because of many independent variables needed to describe the cation distribution, a combination of several inde0003-004X/99/0004–0555$05.00 555 American Mineralogist, Volume 84, pages 555–563, 1999 *E-mail: [email protected] HARRISON ET AL.: ORDERING IN MAGNETITE-SPINEL SOLID SOLUTIONS 556 pendent experimental observations is required to obtain unique values for all the cation occupancies. The difficulty in determining cation distributions experimentally prompted several theoretical studies of cation ordering in this system (O’Neill and Navrotsky 1984; Lehmann and Roux 1984; Nell and Wood 1989; Sack and Ghiorso 1991). These models allow calculation of the cation distribution as a function of temperature and composition and are commonly used to ascertain oxygen fugacities in the upper mantle (O’Neill and Wall 1987; Woodland 1988; Wood 1990). To date, only one in-situ study exists with which to test these theoretical models: Nell et al. (1989) which measured in-situ cation distributions using the electrical conductivity/Seebeck-effect technique (Mason 1987). We demonstrate in this study, however, that inconsistencies exist between the experimental measurements of Nell et al. (1989) and the saturation magnetization measurements of Harrison and Putnis (1995) and Harrison (1997). This study aims to provide a new experimental constraint on the cation ordering in the (Fe3O4)1-x(MgAl2O4)x solid solution through in-situ structure refinements using time-of-flight neutron powder diffraction (Peterson et al. 1991; Redfern et al. 1996). Time-of-flight neutron scattering is an ideal probe of cation ordering in this mineral, due to the good contrast between the neutron scattering lengths of Fe, Mg, and Al (Table 1), the ability to perform the experiment in-situ under high vacuum, and the ability to record the entire diffraction pattern rapidly (hence reducing the amount of time the sample was annealed at high temperature, which lowers the probability of exsolution occurring at temperatures below 1000 °C). Although the data did not allow the specific distribution of Mg, Al, Fe, and Fe to be calculated uniquely, the high accuracy and precision of the results permitted evaluation of various thermodynamic theories of the cation ordering process. With appropriate assumptions, we propose a simple cation ordering scheme that is consistent with both the in-situ structure refinements and the measurements of saturation magnetization in quenched material. EXPERIMENTAL PROCEDURES