Modelling and experimental observation of ferrroelectric domains
Keywords: Barium Titanate
Ferroelectric
Needle domain

This thesis focuses on studying the interaction and evolution of the needle domains in barium titanate single crystal through the simulation and experimental methods. The results are expected to assist in the interpretation of the arrangement and evolution of the needle domains and improve the design of future material.
The existence of a needle domain gives rise to an internal stress field and electric field around the needle tip, which influences the polarization switching process and crack propagation in a single crystal. A model is established to study the interaction and evolution of the needle domains in barium titanate single crystals using the theory of dislocations. Considering the electrical and mechanical incompatibility at the needle tip, the fields produced by a needle domain are represented using the fields due to the equivalent edge dislocations and line charges distributed over the needle tip. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are used to analyse the stress and electric fields around the needle domains. The calculation of the modified Peach-Koehler force and the total energy due to the needle domains is used to study the interaction among the needle domains and the stability of the needle pattern. Through experimental observation, we further know about the microstructure and common pattern of needle domains. X-ray diffraction is used to map the shape of needle tip and detect the strain field around the needle tip.
The interaction of pairs of needle domains in an infinite piezoelectric body is studied. It is found that the needle tip interactions tend to be dominated by the electrostatic terms. Additionally, the stability of groups of needle domains is investigated. Stable configurations of needle domains in a herringbone pattern are identified, consistent with experimental evidence. However, comb-like arrays of needles are found to be unstable. This is contrary to experimental observations, where needle domains are observed in aligned arrays. This contradictory result leads to an analysis of the effect of charge produced by the polarization jump at a needle tip on domain interaction. The existence and position of stable equilibrium states are found to be sensitive to a change in the quantity of polarization charge. When the polarization charge is reduced to about 48% of its theoretical value, the modified model works well to interpret the stability of comb-like needle pattern and herringbone needle pattern.
A viscous model is proposed to further analyse the evolution of the needle domains under the external perturbation. Based on the superposition theory proposed by Van der Giessen, boundary value problems are discussed. Single needles and pairs of needle domains are selected to analyse the effect of boundary condition on the distribution and arrangement of the needle domains. After that, the evolution of the comb-like needle domains under the applied external loads is studied. During the process of analysis, a lattice friction model, and the viscous model are compared.