THERMODYNAMICS OF RHOMBOHEDRAL OXIDE SOLID SOLUTIONS AND A REVISION OF THE FE-TI TWO-OXIDE GEOTHERMOMETER AND OXYGEN-BAROMETER

A model for the thermodynamic properties of rhonibohedral oxide solid solutions in the system Fe2O3-FeTiO3-MgTiO3-MnTiO3 (containing minor amounts of Al2O3) is presented. The model accounts for temperature and compositionally dependent long-range cation-order and the related high to low symmetry structural phase transition. The model is calibrated from the cation-ordering data of Harrison and others (2000; Harrison and Redfern, 2001) and experimental data on Fe+2Ti double left right arrow (Fe+3)(2) exchange between rhombohedral oxide and spinel from Lattard and others (2005) and Evans and others (2006). Successful calibration require introduction of an energetic contribution attributed to short-range cation-order, which reduces the configurational entropy of the solid solution. The resultant thermodynamic model for the rhombohedral oxides is internally consistent with the model for spinel solid solutions of Sack and Ghiorso (1991a, 1991b) and with the endmember thermodynamic properties database of Berman (1988); a new model equation for the isobaric heat capacity of ulvospinel (cubic Fe2TiO4) is proposed and values of the enthalpy of formation, -1490.417 kj/mol, and third law entropy, 184.199 J/K-mol, at 298.15 K and 10(5) Pa are recommended. The new model forms the basis of a revised FeTi-oxide geothermometer/oxygen barometer, which is applied to a newly compiled dataset of natural two oxide pairs from silicic volcanic rocks. Results are compared to previous formulations with the general conclusion that the new model gives a better estimate of oxidation state for magmas that equilibrated tinder conditions more oxidizing than the nickel-nickel oxide buffer. Estimates of oxygen fugacity are fairly insensitive to analytical uncertainties in oxide compositions. By contrast, temperature estimates are especially sensitive to analytical error and to the abundances of minor constituents. Application of the geothermometer to oxide pairs that grew under conditions where the rhonibohedral phase was cation disordered (that is high temperature or at oxygen fugacities greater by about one log,,, unit than the nickel-nickel oxide buffer) results in an uncertainty due solely to analytical error of at least 50 degrees C and sometimes as high as 100 degrees C. Temperature estimates from the new geothermometer can be made using either the Fe+2Ti double left right arrow (Fe+3)(2) exchange or Fe+2 double left right arrow Mg exchange between the two oxides. Comparison of the two temperature estimates provides a means of evaluating the internal consistency of coexisting oxide compositions and assessing the extent of disequilibrium. Temperatures calculated from the new model are found to be consistent with experimental phase relations for the stability of cummingtonite in silicic volcanics. Other petrologic constraints on derived temperatures are examined including limits on the width of the miscibility gap and the development of self-reversed remanent magnetization in the rhombohedral series. Software that implements the new thermodynamic model and the two-oxide geothermometer/oxygen barometer is available from http://www.ofm-research.org/.