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|Title:||Theoretical studies on domain structures in ferroelectrics||Authors:||Tsang, Chun-ho||Keywords:||Hong Kong Polytechnic University -- Dissertations
Ferroelectricity -- Mathematical models
|Issue Date:||2006||Publisher:||The Hong Kong Polytechnic University||Abstract:||Common ferroelectric crystals, such as barium titanate (BaTiO₃), possess two or more possible spontaneous polarization orientations in the absence of electric field. It is well known that a ferroelectric crystal tends to split into many domains in which all of the electric dipoles have an identical spontaneous polarization direction. Many ferroelectrics are used in the form of ceramics which are polycrystals comprising a large number of differently oriented single crystal grains, each of which contains one or several domains. Domains play an important role in all phenomena of polarization and deformation of ferroelectrics. This project investigates ferroelectric domain structures in the absence of external field and evolution dynamics under the action of an alternating field, both in crystals and in ceramics. First, we focus on the formation of domain pattern in a single crystal. We develop a model to study two-dimensional domain structures using the time-dependent Landau theory. The effects of external electric field, inhomogeneity in polarization and electroelasticity have been considered. The elastic strains are subjected to the elastic compatibility constraint. Unlike previous models for two-dimensional domain formation, the depolarization effect is involved via the Poisson equation. Next, we attempt to model ceramics. In the study of ceramic domains, we use a model containing variously oriented grains. The behavior of each grain is described by our foregoing model for ferroelectric crystals. The grain boundary region is assumed to be in the paraelectric phase. Finally, we use the model to simulate the evolutions of domain structures in single crystals and ceramics under an A.C. electric field. Numerical computations are based on a 128 x 128 grid with periodic boundary conditions applied to the edges.
We use BaTiO₃ to perform model calculations. In our simulations for single crystal BaTiO₃, it is found that only head-to-tail dipole arrangements occur in the whole formation process. In particular, our simulations reproduce experimentally observed domain patterns, including 90° wedged domains, 180° antiparallel domains and 90° wedged domains with 180° sub-domains (for brevity, "90° -with-180" domains), the formation of the latter has not been reported in previous theoretical investigations. The results also indicate that 90° domains occur frequently and is most stable; 90° with-180° domains are rare. Electrostrictive energy and elastic energy are found to dominate the pattern formation process. During formation from initially random dipoles, "vortex" domains, like ferromagnetic vortices, appear in a short period. These findings offer insights into the roles of electroelasticity and the inhomogeneity in polarization in the formation process as well as provide an understanding of the mechanism for forming domain pattern and the relation among different domain configurations. For the studies on ceramics, our simulations report that the domain pattern in a grain can be influenced by the neighboring grains. In particular, a banded structure over many grains is obtained - this has been observed experimentally but not been reported in other theory work. Some cases illustrate that the domain pattern in a grain does not necessarily propagate to the surrounding grains. In general, our results show that grain size and grain boundary regions play crucial roles in the domain pattern. We are unaware of other systematic modeling of domain structures over many grains in the open literature. When an A.C. electric field is applied in the simulations, the results give quite a square P-E hysteresis loop for BaTiO₃ crystal which agrees with experiment. The domain pattern shows a single domain immediately after coercivity. In the case of BaTiO₃ ceramics, the domain pattern obtained differs from those in single crystals. Single domain pattern does not usually appear in the process. The simulations report that the P-E loops change with the thickness of grain boundary regions.
|Description:||137 leaves : ill. (some col.) ; 30 cm.
PolyU Library Call No.: [THS] LG51 .H577P AP 2006 Tsang
|URI:||http://hdl.handle.net/10397/2991||Rights:||All rights reserved.|
|Appears in Collections:||Thesis|
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