Theory and computer simulation of relaxor ferroelectrics doped by off-center impurities

A family of ferroelectric materials have relaxation type dynamics. These materials, called relaxor ferroelectrics, show remarkable dielectric and electromechanical properties important for many practical applications that are different from those of normal ferroelectrics. Despite of the engineering importance of relaxor ferroelectrics, the physical origin of the relaxor behavior is not fully understood. A purpose of this thesis is to advance the theory of relaxor ferroelectrics and to develop the model, which could be used for a computer simulation of the static dielectric and dynamic properties and their relation to the concentration of dopant ions. In this thesis, a Ginzburg-Landau type theory of interaction of randomly distributed local dipoles immersed in a paraelectric crystal is developed. The interaction is caused by the polarization of the host lattice generated by these dipoles. It is long-ranged and decays proportionally to the inverse distance between the local dipoles. The obtained effective Hamiltonian of the dipole-dipole interaction is employed for both the Monte Carlo and the Master Equation simulations of the dielectric and ferroelectric properties of a system with off-center dopant ions producing local dipoles. The computer simulation shows that at low concentration of dopant ions the paraelectric state transforms into a macroscopically paraelectric state consisting of randomly oriented polar clusters. The behavior of the system is similar to that of a spin-glass system. The polar clusters amplify the effective dipole moment and significantly increase the dielectric constant. It is shown that the interaction between the clusters results in a spectrum of relaxation times and the transition to the relaxor state. The real and imaginary parts of the susceptibility of this state are calculated. The slim hysteresis loop in the polarization, which usually appears in the high temperature non-polarized relaxor ferroelectrics, is also obtained for our doped system under similar physical conditions. At intermediate dopant concentration, the material undergoes a diffuse phase transition smeared within a temperature range to a ferroelectric state. A further increase in the dopant concentration makes the transition sharper and closer to the conventional ferroelectric transition. The results obtained are compared with the behavior of the K_1−xLi_xTaO ₃ relaxor ferroelectric.