This paper reviews the crystal structure of compounds with the general formula AB 2 X 4 , which crystallize with the same atomic structure as the mineral spinel, MgAl 2 O 4 . Three degrees of freedom associated with the detailed atomic arrangements of spinels are considered here: (i) the lattice parameter, a; (ii) the anion parameter, u; and (iii) the cation inversion parameter, i. Oxide spinels are used as examples to explore the interrelationships between these parameters.

Structure of Spinel

Electrocatalytic properties of transition metal oxides for oxygen evolution reaction

Calculation of oxygen isotope fractionation in metal oxides

Structural, magnetic and electrical properties of Co1- xZnxFe2O4 synthesized by co-precipitation method

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).

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

Thermoelectric coefficient measurements in the system Fe3O4-Fe2TiO4 were used to determine the cation distributions from 600° to 1300°C. The cation distributions obeyed the relation

-RT In K=-9.61+2(-0.0154T)b+0.0256T (kJ/mol)

where KFecd is the iron distribution constant and b is the tetrahedral Fe3+ concentration. Low-temperature extrapolations agreed with experimental magnetometry and lattice parameter results. With the incorporation of a subregular size-mismatch term, agreement with high-temperature thermodynamic data was achieved. A solvus at intermediate temperatures was correctly predicted by the model.

Thermoelectric Determination of Cation Distributions in

Thermoelectric coefficient measurements in the system Fe304-MgFe204 were used to determine the cation distributions from 600° to 1300°C. The cation distributions obeyed the relationship:

−RT ln KMgCD= 17.4 + 2(−16.4)b (kJ/mol)

where KMgCD is the magnesium distribution constant and b is the tetrahedral Fe3+ concentration. Low-temperature distributions are consistent with electrical behavior in the system. High-temperature thermodynamic activities calculated from our distributions agree with experimental values.

Thermoelectric Determination of Cation Distributions in Fe304-MgFe204

The influence of point-defect gradients on thermoelectric coefficient measurements in oxides is quantified. This permits corrections to be made for data collected by conventional means and suggests alternative techniques of thermopower measurements which maintain the average sample temperature while imposing thermal gradients. Experimental results on CoO, Fe/sub 3/O/sub 4/, and FeO in equilibrium with various atmospheres are considered.

A. Trestman-Matts

Papers

Thermoelectric Determination of Cation Distributions in

Thermoelectric Determination of Cation Distributions in Fe304-MgFe204

Measurement and Interpretation of Thermopower in Oxides

Thermoelectric determination of cation distributions in iron oxide-iron magnesium oxide (fe3o4-mgfe2o4)

Thermoelectric determination of cation distributions in iron oxide-iron titanate (fe3o4-fe2tio4)