An Unconventional Phase Field Method For Investigating Tetragonal And Orthorhombic Domain Structures Of Ferroelectric Materials

The macroscopic properties of ferroelectric materials almost depend on its microstructures and simulating microstructures of ferroelectric materials has an important significance for materials design. Conventional phase field method, as a powerful simulation method for ferroelectric material microstructures, requires much more material parameters, and the energy potential wells and symmetry is not obvious, which seriously hinder the investigation on the ferroelectric materials microstructures, especially in new ferroelectric materials. In order to overcome these difficulties, we have developed an unconventional phase field modeling for tetragonal and orthorhombic ferroelectrics in this thesis. We employ it to study the formation and evolution of domains under the stress and electric field loading in tetragonal and orthorhombic ferroelectric single crystals, as well as the energy, stress and strain distributions under different domain boundary energy. The main work are as follows:Firstly, we have developed an unconventional phase field method, which is suitable for tetragonal and orthorhombic ferroelectric crystals. Based on characteristic functions of ferroelectric variants, we construct the anisotropy energy of tetragonal variants, which is used instead of Landau-Devonshire potential in conventional phase field method, resulting in that much fewer parameters are needed for simulations. Moreover, the unconventional phase field approach has explicit symmetry and energy well structure, and involves much smaller number of parameters.Secondly, we employ unconventional phase field approach to study the formation and evolution of domains in tetragonal crystals, in which the effects of electromechanical loading and domain wall energy on the microstructures of tetragonal ferroelectric materials are analyzed. A multi-rank laminated ferroelectric domain pattern with 90 o domain wall along <110>, and 180 o domain wall along <010> are found. The good agreement between simulation results and experimental measurement is observed. We also observe that 90 o and 180 o switching occur under electric field loading, but only 90 o domain switching occur under stress loading. Also, the volume fraction of ferroelectric variants can be tuned by strain loading. The periodic closure domains can be obtained by increasing the domain wall energy, resulting in decreasing depolarization energy. And the maximum energy, externes stress σ11、σ22、σ12 and strain ε11、ε22、ε12 appear in the locations of domain walls, suggesting that the type and locations of domains can be determined by those features.Thirdly, we employ unconventional phase field approach to study microstructures of orthorhombic ferroelectric materials, in which 60°, 90°, 120° and 180° domains structures are observed, the good agreement between simulation results and experimental measurements is found. It shows that 60° domain wall do not have a fixed direction, 90° domain wall along the <010>, 120° domain wall along <110>, 180° domain wall along <110>. We obtain the periodic closure domains by increasing the domain boundary energy, which can decrease depolarization energy in ferroelectrics. The energy, stress and strain distributions under different domain boundary energy are also investigated, and these maximum values occur around the locations of domain walls, which allows us to identify the type and locations of domain structures.