Abstract
An effective Hamiltonian for Zr-Ti cation ordering in PbZrxTi1−xO3 solid solutions is written out. To determine the parameters of the effective Hamiltonian, a nonempirical calculation is performed within an ionic-crystal model taking into account the deformation and dipole and quadrupole polarizabilities of ions. The thermodynamic properties of cation ordering are studied using the Monte Carlo method. The calculated phase transition temperatures (180 and 250 K for the concentrations x=1/3 and 1/2, respectively) are much lower than the melting temperature of the compound under study. At such temperatures, the ordering kinetics is frozen and, in reality, the phase transition to the ordered phase does not occur, in agreement with experimental observations. Within the same ionic-crystal model, we calculated the high-frequency permittivity, Born dynamic charges, and the lattice vibration spectrum for a completely disordered phase and certain ordered phases. It is shown that soft vibration modes, including ferroelectric ones, exist in the lattice vibration spectrum of both the completely disordered and the ordered phases.
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