Magnetite activities across the MgAl₂O₄-Fe₃O₄ spinel join, with application to thermobarometric estimates of upper mantle oxygen fugacity

The activity of Fe₃O₄ component in MgAl₂O₄-Fe₃O₄ spinels has been measured at 900° and 1000° C and 1 atm total pressure using a zirconia oxygen electrolyte. As previously reported for the dilute Fe₃O₄ concentration region (Mattioli and Wood 1986a), magnetite activity at 1000° C is greater than at 900° C at constant Fe₃O₄ mole fraction, for compositions across the MgAl₂O₄-Fe₃O₄ join between 20 and 80 mol% Fe₃O₄ component. The 1-atm solvus crest lies between 900° and 1000° C and, at 900° C the limbs are at Fe₃O₄ mole fractions of 0.2 and 0.6 approximately. Application of the O'Neill and Navrotsky (1983, 1984) cation distribution model indicates that the unusual activity - composition behavior of Fe₃O₄ is caused by changes in the equilibrium state of disorder of mixed MgAl₂O₄-Fe₃O₄ spinels relative to the disordered Fe₃O₄ standard state. In addition, both stoichiometric volumes (Mattioli et al. 1987) and activities across the MgAl₂O₄-Fe₃O₄ join suggest that short range order is significant for this binary. Excess free energy terms must be added to "ideal" Fe₃O₄ activities formulated from equilibrium cation distributions in complex MgAl₂O₄-Fe₃O₄ spinels in order to increase Fe₃O₄ activities to values consistent with observation and to generate the apparent region of immiscibility at 900° C. We have applied our activity data to the estimation of upper mantle spinel-lherzolite oxygen fugacities. We calculated that minimum {Mathematical expression}'s are about 2 log units below the synthetic QFM buffer at 15 kbar total pressure for Fe₃O₄ concentration of 2 mol%, in a Cr-free spinel phase. If a preliminary calibration of an additional 25 mol% Fe²⁺-substitution as FeCr₂O₄ or FeAl₂O₄ component is incorporated into Fe₃O₄ activity, then olivine-orthopyroxene-spinel assemblages of depleted-Type 1-spinel-lherzolite xenoliths indicate {Mathematical expression}'s close to QFM at 15 kbar. This is in good agreement with previous thermobarometric {Mathematical expression} estimates and in sharp contrast to 1 atm intrinsic {Mathematical expression} measurements near IW.