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

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

Low pressure phase equilibria for natural mafic systems may be calculated utilizing empirically derived single component distribution coefficients and the constraints placed upon mineral-melt equilibria by stoichiometry and mass balance, without any knowledge of thermochemical properties of melts (Langmuir and Hanson 1981). Variations in distribution coefficients caused by differences in melt composition may be largely eliminated by the application of a two-lattice melt model based upon the models of Nielsen and Drake (1979), Drake (1976b), and Bottinga and Weill (1972). In the two-lattice melt model, the melt is assumed to be made up of two independent quasi-lattices, the network formers, composed of the components SiO2, NaAlO2, and KAlO2, and the network modifiers, composed of the free oxides of Ca, Mg, Fe, Al, Ti, and Cr. Compositionally independent mineral-melt distribution coefficients were calculated for all the major and some minor components in olivine, plagioclase, high-Ca pyroxene, low-Ca pyroxene, spinel, and ilmenite. Regression constants were calculated from data from 1 atmosphere, anhydrous, equilibrium experiments on natural and synthetic mafic compositions including data obtained from the literature and from new synthetic spinel-melt experiments in the Fo-Ab-An system doped with Ti, Mn, Ni, and Fe. The distribution coefficients are internally consistent within 3 mole % (1σ) for all components. The effects of variable oxygen fugacity on mafic mineral-melt equilibria were calculated utilizing the relations of Sack et al. (1980) for the determination of the Fe+3/Fe+2 ratio, and the results of Schreiber and Haskin (1976) for Cr+3/Cr+2. A computer program, EQUIL.FOR, incorporating the derived mineral-melt distribution coefficients, calculates the sequence of mineral and melt compositions, and liquidus temperatures for mafic melt compositions undergoing equilibrium or fractional crystallization. This program reproduces, within 15° C, 52 experimentally determined crystallization sequences collected from the literature. These published crystallization sequences are for mafic systems not represented in the data set used to calculate the mineral-melt distribution coefficients.

Low pressure mineral-melt equilibria in natural anhydrous mafic systems

Magnesioferrite spinel, MgFe 2 O 4 , was synthesized at 900 °C from equimolar amounts of reagent-grade oxides, MgO and Fe 2 O 3 , and quenched in air. The structural behavior of magnesioferrite was determined from in situ synchrotron X-ray powder-diffraction data [λ = 0.92225(4) A] at room pressure and temperatures from 28 to 982 °C on heating and cooling. The a unit-cell parameter increases linearly on heating, but deviates to give a discontinuity at 581 °C. Above 581 °C and on cooling from 982 °C, the a parameter varies linearly. The a parameter at 28 °C before heating [8.39704(5) A] and after cooling to 47 °C [8.39514(4) A] is different because the cation order frozen in the structure is not the same. Cation order, analyzed in terms of the inversion parameter, x, { i v [Mg 1 - x Fe x ] v i [Mg x / 2 Fe 1 - x / 2 ] 2 O 4 }, and the order parameter, Q=1 - (3/2) x, show no change on heating until the temperature is high enough to cause exchange of Mg 2 + and Fe 3 + cations between the octahedral and tetrahedral sites. This activation barrier is overcome at 581 °C, where the sample achieves the maximum ordered state on heating [x m a x = 0.867(4)] and begins to move toward equilibrium. This relaxation is toward a more ordered configuration and is a kinetically controlled process. Above 581 °C, the cations continuously disorder along the equilibrium pathway to the maximum temperature studied [T m a x = 982 °C, x = 0.769(3)] and reverse along the equilibrium pathway on cooling. At T B , the maximum equilibrium order is frozen in, and maintained to room temperature, where x m a x = 0.895(4). O'Neill-Navrotsky, Landau, and Ginzburg-Landau models give good descriptions of the ordering process in MgFe 2 O 4 . Simultaneous differential scanning calorimetry (DSC) and thermogravimetry (TG) data were obtained using a Netzsch STA 449C simultaneous TG-DSC instrument. The DSC curve for MgFe 2 O 4 contains an irreversible exothermic peak at about 550 °C = T r e l a x in the first heating experiment, and the energy change associated with this peak is -162 J/g (= -32 KJ/mol), and corresponds to cation relaxation. From Rietveld refinements, T r e l a x 581 °C. The T C u r i e 360 °C was obtained from TG experiments carried out in a magnetic field.

/pdf/cation-ordering-in-magnesioferrite-mgfe2o4-to-982-c-using-in-1n81s4pnqt.pdf

Cation ordering in magnesioferrite, MgFe2O4, to 982 °C using in situ synchrotron X-ray powder diffraction

The temperature dependence of the cation‐distribution parameter η, the lattice constant a, and the oxygen‐position parameter u, for Mg1.06Fe1.94O3.97 has been established for quench temperatures between 410° and 1100°C. The fraction of magnesium ions on tetrahedral sites, η, increases from 0.12 to 0.28 in this temperature range and follows the formula η(2−y+ny)(1−η)(1−ηy)=exp[−(θ0−θ1η)yT], where the magnesium concentration, y, is 1.06, θ0=1850°K and θ1=4480°K. The lattice constant varies linearly with η from 8.385 A for the 410° quench to 8.398 A for the 1100°C quench, and the u parameter is 0.381, independent of quench temperature.

Cation Distributions in Nonstoichiometric Magnesium Ferrite

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Cation Distributions in Nonstoichiometric Magnesium Ferrite