High-temperature electrical measurements and thermodynamic properties of Fe₃O₄-FeCr₂O₄-MgCr₂O₄-FeAl₂O₄ spinels

Electrical conductivity and thermopower measurements have been made on Fe₃O₄-FeCr₂O₄, Fe₃O₄-MgCr₂O₄, and Fe₃O₄-FeCr₂O₄-FeAl₂O₄ spinel sotid solutions at 600 °C to 1400°C and 1 atm. Our analysis of the data indicates that these are n-type small polaron conductors with, as in Fe₃O₄, electron hopping confined to the octahedral sites. If Cr³⁺ is not involved in the conduction mechanism (i.e., Fe²⁺-Fe³⁺ hopping only) then, with octahedral site hopping, the combined thermopower-electrical conductivity technique enables high-temperature cation distributions to be obtained.

On the Fe₃O₄-FeCr₂O₄ join we have found, from measurements of the independent density of states, that hopping is octahedral and involves Fe²⁺ and Fe³⁺ only at compositions with 40% or more of Fe₃O₄, but that Cr³⁺ becomes involved in the conduction process at very FeCr₂O₄-rich compositions. We have therefore excluded data on very Crrich compositions, which also exhibit high activation energies, from our estimates of cation distributions.

The thermopower and electrical conductivity data were combined with earlier results on the joins Fe₃O₄-MgFe₂O₄, Fe₃O₄-FeAl₂O₄, and Fe₃O₄-MgAl₂O₄ to estimate cation distributions for compositions within the geologically important system (Mg²⁺,Fe²⁺)-(Fe³⁺,Al³⁺,Cr³⁺)₂O₄. The cation distributions were then combined with activity-composition relations and interphase partitioning data to derive a complete thermodynamic model for the complex system (Mg²⁺,Fe²⁺)(Fe³⁺,Al³⁺,Cr³⁺)₂O₄. The model, which takes explicit account oforder-disorder relations, produces and successfully predicts a wide range of macroscopic thermodynamic measurements that have been made on simple and complex spinels. A computer program to generate cation distributions and activities is available from B. J. Wood.