The size of a cation is important in determining its site preference. In oxide spinels containing 2 (super +) and 3+) ions (2-3 spinels) there is a tendency for the larger ion to prefer the tetrahedral site; the reverse holds for 2-4 spinels. A set of cation radii optimized to best fit spinel lattice parameters is presented.--Modified journal abstract.

/pdf/simple-spinels-crystallographic-parameters-cation-radii-4g6ycpl79i.pdf

Simple spinels; crystallographic parameters, cation radii, lattice energies, and cation distribution

The thermodynamics of cation distributions in simple spinels

A general model is presented to enable the calculation of the cation distribution and thermodynamic properties of any binary solid solution between oxide spinels containing 2+,3+ and 4+ cations. The model includes the effect of disordering enthalpy which depends linearly on the degree of disorder. In addition there are important contributions to the thermodynamic properties from the size mismatch of the substituting cations, which may be accounted for adequately using the simplest possible approach, that of a strictly regular solution. The regular solution parameter, W, depends on the difference in volume of the substituting cations. The model has been tested against the extensive literature data on spinel solutions; in the great majority of cases agreement with experimental observation is good. The model may be used to explain a diverse array of phenomena associated with the cation distribution in spinel solutions, to discriminate among conflicting experimental data, to extrapolate experimental data to other temperatures and pressures, and to predict the properties of unstudied systems.

/pdf/cation-distributions-and-thermodynamic-properties-of-binary-376gjnvp2r.pdf

Cation distributions and thermodynamic properties of binary spinel solid solutions.

A model is developed for the thermodynamic properties of Fe2+−Mg2+-aluminate-titanate-ferrite spinels of space group Fd3m. The model incorporates an expression for the configurational entropy of mixing which accounts for long-range order over tetrahedral and octahedral sites. Short-range order or departures from cubic symmetry are not considered. The non-configurational Gibbs energy is formulated as a second degree Taylor expansion in six linearly independent composition and ordering variables. The model parameters are calibrated to reproduce miscibility gap constraints, order-disorder phenomena in MgAl2O4 and MgFe2O4, and Fe2+−Mg2+ partitioning data between olivine and: (1) aluminate spinels; (2) ferrite spinels; (3) titanate spinels; (4) mixed aluminate-ferrite spinels. This calibration is achieved without invoking non-configurational excess entropies of mixing. The model predicts that the ordering state of FeAl2O4 is more normal than that of MgAl2O4. It also successfully accounts for heat of solution measurements and activity-composition relations in the constituent binaries. Phase equilibrium constraints require that the structure of Fe3O4 is more inverse than random at all temperatures and that Mg2+ has a strong tetrahedral site preference with respect to that of Fe2+. The analysis suggests that in the titanates short range order on octahedral sites may be significant at temperatures as high as 1300° C. Constraints developed from calibrating the thermodynamic properties of Fe2+−Mg2+-aluminatetitanate-ferrite spinel solid solutions permit extension of the database of Berman (1988) to include estimates of the end-member properties of hercynite (FeAl2O4), ulvospinel (Fe2TiO4), MgFe2O4 and cubic Mg2TiO4. In constructing these estimates, provision is made for low-temperature magnetic entropy contributions and the energetic consequences of disordering the aluminates and the ferrites. These estimates are consistent with all of the available low-temperature adiabatic calorimetry, high-temperature heat content, and heat of solution measurements on the end-members. The analysis implies that there is a substantial heat capacity anomaly in the range 300°–900° C associated with disordering of the MgAl2O4 structure while that in FeAl2O4 becomes significant at temperatures above 700° C. The same heat capacity response in the ferrites indicates that the order/disorder transformation is coupled to the antiferromagnetic-paramagnetic transition in MgFe2O4 but takes place well above the ferrimagnetic-paramagnetic transition in magnetite. The proposed model is internally consistent with solution theory reported elsewhere for Fe2+−Mg2+ olivines and orthopyroxenes (Sack and Ghiorso 1989), rhombohedral oxides (Ghiorso 1990a) and the remaining end-member properties of Berman (1988).

/pdf/an-internally-consistent-model-for-the-thermodynamic-1dnjul63kz.pdf

An internally consistent model for the thermodynamic properties of Fe−Mg-titanomagnetite-aluminate spinels

Magnesioferrite (MgFe204 spinel) was synthesized in equilibrium with excess MgO using a flux method. Chemical analysis shows that the MgFe204 is stoichiometric, within analytical uncertainty. Samples were annealed at intervals of 50 °C between 450 and 1250 °C and quenched in H20. The time needed to reach equilibrium at low temperatures (450650 0C) was assessed by monitoring the change of lattice parameter (ao) with time. In addition, the changes in ao at 550-650 °C were reversed, using material annealed at 400 °C for 50 d. Some samples were further characterized by measuring their Neel temperatures, using DSC. The cation distributions in the quenched samples were determined using both powder X-ray diffraction and M6ssbauer spectroscopy. To increase the resolution in the latter, the samples were studied in an applied magnetic field of 4.5 T at 12-171 K. The cation distribution changes smoothly with temperature, with the cation inversion parameter (x) decreasing from 0.90 at 450 °C to 0.72 at 1100 0c. The precision with which x can be determined is ::to.004 from XRD and -::to.O! from the M6ssbauer spectroscopy. The two sets of measurements agree well with each other, the mean difference in x being 0.0056 ::t 0.0102. Thermodynamic modeling shows that the cation distribution can be described with a nonlinear enthalpy of disordering model, with aMg-Fe}+ = 26.6 ::t 0.4 and {1= - 21. 7 ::t 0.3 kJ/g-atom. Incorporation of a small excess (nonconfigurational) entropy term into the model gives a slightly better fit, however. The disordering in MgFe204 as a function of temperature is virtually identical to that found in Fe,04 from thermopower measurements. The present results differ to a greater or lesser extent from most of the previous work on MgFe204. This is most likely attributable to differences in stoichiometry. We also present some results on nonstoichiometric "MgFe204," i.e., solutions of MgFe204 and 1'-Fe20" which tend to confirm this hypothesis, at least for some of the earlier studies.

/pdf/the-temperature-dependence-of-the-cation-distribution-in-r6gmkkoyaq.pdf

The temperature dependence of the cation distribution in magnesioferrite (MgFe2O4) from powder XRD structural refinements and Mössbauer spectroscopy

A study has been made of the magnetic properties of the system of quenched magnesium ferrites (MgxIIFe1−xIII) · (Mg1−xIIFe1+xIII)O4, where x, the fraction of magnesium ions in tetrahedral sites, varies from 0.14 to 0.26. Included among the properties examined are: saturation moment, Curie point, initial permeability, and coercive force. A limited study of the kinetics of the cation redistribution has also been made. Samples quenched from 1100°C and then tempered at 600°C require somewhat less than 16 hours to attain an equilibrium cation distribution at the latter temperature. The approach to equilibrium is consistent with a model in which the rate of approach is proportional to exp(−θ0′+θ1′x)/T where θ0′ and θ1′ are activation constants.

Some Properties of Quenched Magnesium Ferrites

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Some Properties of Quenched Magnesium Ferrites