Modeling the Ferroelectric Phase Transition in Perovskite Relaxors and New Corresponding Solving Method

TL;DR

This paper models the ferroelectric phase transition in perovskite relaxors using a 3D random-site Ising model with Glauber dynamics, introducing a new mean-field method to analyze subsystem interactions and phase behaviors.

Contribution

It applies the 3D-RSIM with Glauber dynamics to relaxor ferroelectrics and proposes a novel mean-field of PS-strings method for solving the model, revealing subsystem compositions and transition mechanisms.

Findings

Identification of three subsystems with varying dominance based on PS concentration

Observation of crossover from critical to Vogel-Fulcher to Arrhenius slowdown with increasing PS concentration

Proposal of a new mechanism for Burns transformation involving PS-lattice coupling

Abstract

Three-dimensional-random-site-Ising-model (3D-RSIM) along with Glauber dynamics of pseudo-spins (PSs) is applied for the first time to study the relaxion-ferroelectric-phase-transition (RFPT) of perovskite-relaxor-ferroelectrics (PRFEs) in detail. To solve this model, we proposed a new method, mean-field of PS-strings (MF-PSSs). We find: 1) 3D-RSIM is a mixed system consisting of permanent-paraelectric-subsystem (PPSS), low-transition-temperature ferroelectric-subsystem (LTT-FSS), and high-transition-temperature ferroelectric-subsystem (HTT-FSS). The contents of these three subsystems change with the PS concentration (phi) of the model; 2) When phi < phi_p (phi_p is the percolation threshold of the 3D-RSIM), HTT-FSS dominates the whole system. On cooling, the system undergoes an inhomogeneous-diffuse-ferroelectric-phase-transition (IDFPT), and as phi increases, it shows a crossover from the critical, gradually to Vogel-Fulcher, and to Arrehnius type slowdown. Specifically, we observe this crossover from the relationship between the peak temperature (Tm) of the real susceptibility of the correlated relaxation of PSs and angular frequency (omega); 3) When phi = phi_p, the three subsystems have comparable contents. However, as temperature decreases, the spontaneous polarization and specific heat of the whole system show an IDFPT, but Tm shifts to lower temperature with omega until 0K. Since the relaxation time of PPSS rapidly increases at lower temperature and diverges at 0K, during a cooling process at a limited rate, PPSS must be frozen at a certain temperature, i.e. PS glass transition occurs. In short, with the increase of phi, 3D-RSIGM gradually evolves from the IDFPT system to PS glass system, and phi_p is the characteristic concentration of this evolution. Moreover, based on the coupling between PSs and crystal lattice, we also give a new possible mechanism of Burns transformation.