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<i>Ab initio</i>study of the phase diagram of epitaxial<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>BaTiO</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>
Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of ${\text{BaTiO}}_{3}$ 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, Zembilgotov, and Tagantsev [Phys. Rev. Lett. 80, …