Abstract
An effective Hamiltonian for the ferroelectric transition in PbTiO 3 is constructed from first principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ‘lattice Wannier functions’. Preliminary results of Monte Carlo simulations for this system show a first-order cubic-tetragonal transition at 660 K. The involvement of the Pb atom in the lattice instability and the coupling of local distortions to strain are found to be particularly important in producing the behavior characteristics of the PbTiO 3 transition. Factors affecting the distribution of local distortions above T c are discussed. Further applications of this method to a variety of systems and structures are proposed for the first principles study of finite temperature structural properties in individual materials.
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