Thermodynamics of the R3 to R3c phase transition in the ilmenite-hematite solid solution

The thermodynamics of cation ordering in the ilmenite-hematite solid solution (FeTiO₃)_x(Fe₂O₃)_1-x were re-examined in view of a recent in-situ neutron diffraction study of the R3 to R3c phase transition. A macroscopic thermodynamic model is developed, in which the excess enthalpy of ordering is described by a fourth-order polynomial function of the long-range order parameter, Q, and the excess entropy is described by the configurational point entropy. The enthalpy coefficients are determined as a function of composition by fitting to the neutron diffraction data. The fourth-order energy coefficient increases smoothly with increasing Ti-content, indicating a change in the character of the transition from second-order (x < 0.87) to first-order (x > 0.87). Monte Carlo simulations confirm that the excess enthalpy is well described by a fourth-order polynomial, and demonstrate that the reduction in configurational entropy due to short-range ordering can be described by simply scaling the point entropy. This allows the enthalpy coefficients in the macroscopic model to be corrected for the effects of short-range ordering, yielding a revised estimate of x = 0.92 for the position of the tricritical point. Monte Carlo simulations are used to study both ordering and exsolution in the solid solution, allowing the paramagnetic portion of the equilibrium phase diagram to be derived. The changing character of the phase transition is reproduced successfully by treating Fe²⁺-Ti and Fe³⁺-Ti interactions separately in the simulations. Intralayer Fe²⁺-Ti interactions are negative (i.e., ordering of Fe²⁺ and Ti within the 001 layers is favored) whereas Fe³⁺-Ti intralayer interactions are positive (i.e., separation of Fe³⁺ and Ti is favored). The λ-line for the R3 to R3c phase transition intersects the low-temperature miscibility gap at a tricritical point near x = 0.6 and T = 800 °C, in reasonable agreement with previous thermodynamic models of the solid solution.