Experimental data by Navrotsky and co-workers show that the excess enthalpy of mixing, Delta H-xs(x), in the system (Fe-x(2+),Ti-x(4+),Fe-2-2x(3+))O-3 joining alpha-Fe2O3 (hematite) and FeTiO3 (ilmenite) changes in an unusual way from positive to negative with increasing x. Calculations using an ionic model supplemented by short-range repulsion and van der Waals terms allow excellent qualitative agreement with the experimental data and numerical agreement to within a factor of 3. The oscillating behavior of the excess enthalpy of mixing with x is shown to be associated with the specific substitution pattern of the Fe3+ ions for Fe2+ and Ti4+, which avoid the generation of close Fe3+/Fe3+ pairs at high x, but is random at low x.