  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 transitions. 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.
