Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of BaTiO3 under epitaxial constraints applicable to growth on perovskite substrates. We obtain a phase diagram in temperature and misfit strain that is qualitatively different from that reported by Pertsev et al. [Phys. Rev. Lett. 80, 1988 (1998)], who based their results on an empirical thermodynamic potential with parameters fitted at temperatures in the vicinity of the bulk phase

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... . In particular, we find a region of 'r phase' at low temperature where Pertsev et al. have reported an 'ac phase'. We expect our results to be relevant to thin epitaxial films of BaTiO3 at low temperatures and experimentally-achievable strains.