Lattice Instabilities, Anharmonicity and Phase Transitions in PbTiO 3 and PbZrO 3
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addition, we have established that strain coupling is crucial in producing the observed first-order cubic-tetragonal transition. If the parameters coupling the local polar distortion to strain are set to zero in the model, Monte Carlo calculations show a change in character to a second-order cubic-rhomobohedral transition at a significantly lower temperature of 400 K [15]. For PbZr0 3 , calculations of the phonon dispersion relation show that there are several unstable branches. Thus, even to obtain correct qualitative features of the low-energy surface, the form of the anharmonic terms is crucial. We include onsite and short-range intersite anharmonic interactions as well as coupling to strain, with parameters determined from first-principles calculations of uniform distortions and doubled supercells. Comparisons, where possible, with energies calculated using the LAPW method in Ref. 12 show good agreement. Exploration of low-energy distortions shows a local minimum corresponding to the observed ground state structure, with other local minima extremely close in energy. This puts stringent demands on the accuracy of the model, which can be achieved by selected additional first-principles calculations for overdetermination of the effective Hamiltonian parameters. Ongoing and future work using these effective Hamiltonians includes studies of the dynamical behavior of PbTi0 3 , made possible by the simple form of the kinetic energy obtained in the lattice Wannier function method, and Monte Carlo simulations to investigate the antiferroelectric transition and intermediate phase in PbZr0 3. ACKNOWLEDGEMENTS We thank M. C. Payne and V. Milman for the use of CASTEP 2.1. This work was supported by ONR Grant N00014-91-J-1247 and the Cornell Theory Center. In addition, K. M. R. acknowledges the support of the Clare Boothe Luce Fund and the Alfred P. Sloan Foundation.
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