There is considerable interest in the low-temperature growth of the stable α-phase of alumina, α-Al 2O 3, due to its superior chemical and mechanical properties compared to the other forms of alumina. Conventional methods for achieving this phase (such as chemical vapour deposition) utilise high temperatures which limits the range of substrate materials that can be beneficially coated. Recently, it has been reported that α-Al 2O 3 can be grown on α-Cr 2O 3 templates at a much lower substrate temperature (around 400 °C) by the RF magnetron sputtering deposition technique. Previous studies showed that both α-Al 2O 3 and α-Cr 2O 3 (0001) free surfaces relax considerably in comparison with the corresponding bulk structures. From the experimental point of view, a knowledge of the surface structure and stability of both materials will be of great help in determining the facet of α-Cr 2O 3 which best facilitates the growth of α-Al 2O 3. Here we present the results of first-principles Hartree–Fock calculations on the surface energy of the low-index planes of both α-alumina and α-chromia. The suitability of possible α-Cr 2O 3 facets as templates for the growth of α-Al 2O 3 is discusssed.