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We carry out a completely first-principles study of the ferroelectric phase transitions in BaTiO 3 . Our approach takes advantage of two features of these transitions: the structural changes are small, and only low-energy distortions are important. Based on these observations, we make systematically improvable approximations which enable the parameterization of the complicated energy surface. The parameters are determined from first-principles totalenergy calculations using ultra-soft pseudopotentials and a preconditioned conjugate-gradient scheme. The resulting effective Hamiltonian is then solved by Monte Carlo simulation. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. We find the transitions to be intermediate between order-disorder and displacive character. We find all three phase transitions 1 to be of first order. The roles of different interactions are discussed.

We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds.We obtain an effective Hamiltonian which is fully specified by first-principles ultrasoft pseudopotential calculations.This approach is applied to BaTi03, and the resulting Hamiltonian is studied using Monte Carlo simulations.The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment.The order-disorder versus displacive character of the transitions and the roles played by different interactions are discussed.

We study the antiferrodistortive instability and its interaction with ferroelectricity in cubic perovskite compounds. Our first-principles calculations show that coexistence of both instabilities is very common. We develop a firstprinciples scheme to study the thermodynamics of these compounds when both instabilities are present, and apply it to SrTiO 3 . We find that increased pressure enhances the antiferrodistortive instability while suppressing the ferroelectric one. Moreover, the presence of one instability tends to suppress the other. A very rich P -T phase diagram results.Submitted to Phys. Rev. Lett.

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