Thermodynamic properties of hematite — ilmenite — geikielite solid solutions

AbstractA solution model is developed for rhombohedral oxide solid solutions having compositions within the ternary system ilmenite [(Fe2+sTi4+1−s)A (Fe2+1−sTi4+s)B O3]-geikielite [(Mg2+tTi4+1−t)A (Mg2+1−tTi4+t)B O3]-hematite [(Fe3+)A (Fe3+)B O3]. The model incorporates an expression for the configurational entropy of solution, which accounts for varying degrees of structural long-range order (0≤s, t≤1) and utilizes simple regular solution theory to characterize the excess Gibbs free energy of mixing within the five-dimensional composition-ordering space. The 13 model parameters are calibrated from available data on: (1) the degree of long-range order and the composition-temperature dependence of the $$R\bar 3c - R\bar 3$$ transition along the ilmenite-hematite binary join; (2) the compositions of coexisting olivine and rhombohedral oxide solid solutions close to the Mg−Fe2+ join; (3) the shape of the miscibility gap along the ilmenite-hematite join; (4) the compositions of coexisting spinel and rhombohedral oxide solid solutions along the Fe2+−Fe3+ join. In the course of calibration, estimates are obtained for the reference state enthalpy of formation of ulvöspinel and stoichiometric hematite (−1488.5 and −822.0 kJ/mol at 298 K and 1 bar, respectively). The model involves no excess entropies of mixing nor does it incorporate ternary interaction parameters. The formulation fits the available data and represents an internally consistent energetic model when used in conjuction with the standard state thermodynamic data set of Berman (1988) and the solution theory for orthopyroxenes, olivines and Fe−Mg titanomagnetite-aluminate-chromate spinels developed by Sack and Ghiorso (1989, 1990a, b). Calculated activity-composition relations for the end-members of the series, demonstrate the substantial degree of nonideality associated with interactions between the ordered and disordered structures and the dominant influence of the miscibility gap across much of the ternary system. The predicted shape of the miscibility gap, and the orientation of tie-lines relating the compositions of coexisting phases, display the effects of coupling between the excess enthalpy of solution and the degree of long-range order. One limb of the miscibility gap follows the composititiontemperature surface corresponding to the ternary $$R\bar 3 - R\bar 3c$$ second-order transition.