The phase stability of rhodium oxides formed during the aging of model alpha-alumina supported rhodium in air at temperatures of 500, 850, and 1000 degrees C is investigated using high resolution transmission electron microscopy. The observed phases of rhodium oxides are similar to those predicted by bulk thermodynamics, with the RhO2 phase formed at 500 degrees C and the orthorhombic III-Rh2O3 phase formed at 1000 degrees C. However, in some instances, the epitaxy of the rhodium oxide particles with the underlying a-alumina support appears to influence the phases formed, causing the presence of the hexagonal I-Rh2O3 phase at 500 and 850 degrees C. Epitaxial stabilization of rhodium oxide phases is examined from the perspective of lattice matching at the oxide-support interface and minimization of the total oxide particle free energy.