Finite-Temperature Phase-Field Investigation of Switching Kinetics in Ferroelectric Ceramics

Abstract

Ferroelectric materials exhibit an atomic-level electric dipole moment, known as spontaneous polarization, which can be reoriented by an applied electric field. Furthermore, ferroelectrics tend to form a microstructure consisting of regions of identical polarization orientation, called domains, separated by domain walls. This thesis aims to enhance the predictability of ferroelectric material response at the macroscale by gradually refining our understanding of the kinetics of polarization switching at lower length scales. This is achieved by examining the intricate interaction between ferroelectric microstructure evolution, which occurs through the nucleation and growth of domains, and structural defects, such as pores and grain boundaries. In addition, finite-temperature effects play a crucial role in the formation and evolution of ferroelectric domain patterns. To accurately predict the effective material behavior at the device-level, it is essential to consider all of these factors in our models. The first part of this thesis details a novel finite-temperature constitutive model for ferroelectric lead zirconate titanate (PZT) ceramics that accounts for the temperature dependence of the first-principles-informed polarization potential and the effect of thermal lattice vibrations. Based on statistical mechanics, a temperature-dependent Gaussian noise is introduced to the evolution equation for the polarization, which mimics atomic-level lattice vibrations at the continuum scale. The theoretical derivation and Fourier-based implementation are discussed, along with numerical examples and experimental observations. Results show that thermal fluctuations can induce branching of existing domains and nucleation of new domains. These finite-temperature effects stimulate the effective switching kinetics and promote the formation of realistic domain patterns, reminiscent of ferroelectric microstructure observed in experiments. The second part of the thesis investigates the combined effect of porosity and temperature on porous, single-crystalline PZT by utilizing the developed finite-temperature model. Circular pores are modeled, and their impact on an approaching ferroelectric domain wall is investigated. The results show that larger pore sizes and higher densities impede the kinetics of domain walls, while an increase in temperature mitigates the pinning effect of pores, enhancing the mobility of domain walls. These findings are generally consistent with experimental reports and emphasize the importance of considering finite-temperature effects on effective switching kinetics. The third part of this thesis presents a high-resolution phase-field analysis of complex domain pattern formation in tetragonal PZT ceramics, showing well-known lamellar bands within grains and wedged-shaped domains near grain boundaries. The simulations of polycrystalline PZT, which combined more than 12,000 grain samples, revealed distinct correlations between grain orientation and the grain-averaged polarization, strain, and domain density that are consistent with experimental reports and theoretical models. In addition, we discuss novel computational techniques for domain wall identification and tracking, and demonstrate their ability to assess the domain wall density and effective switching mechanism of an evolving ferroelectric microstructure. In summary, the newly introduced models and findings help predict and understand domain switching mechanisms in ferroelectric materials by considering crucial effects of structural defects and temperature. The finite-temperature phase-field framework presents a powerful tool to efficiently studying the lower-scale mechanics of domain evolution, which play a key role in the macroscopic switching kinetics and are challenging to capture with experimental techniques in this detail.