| Summary: | 碩士 === 臺灣大學 === 應用力學研究所 === 98 === The phase field approach has been employed extensively to study the evolution of microstructure and patterns of domains. There are two phase field models in current literature: conventional and unconventional methods. The main difference between these two approaches is the different choice of field variables and the representation of anisotropic energy. Taking the example of ferroelectrics, the conventional phase field method choose the spontaneous polarization as the field variable and it needs an expansion of polynomials at high orders to construct the anisotropic energy density. Instead, the unconventional phase field method adopts the volume fraction of spontaneous polarization as field variable and the construction of anisotropic energy density is simple and concise. In spite of many advantages of using the unconventional phase field approach, this method is not able to handle the multi-phase problem yet, such as the coexistence of rhombohedral of tetragonal phases in the strained epitaxial bismuth ferrite films (BiFeO3). As a result, we choose the conventional phase field model to simulate this phenomenon. The result shows that the existing anisotropic energy density in the conventional phase field models is not able to simulate the problem of phase coexistence due to the saddle structure in the high energy phase. To resolve it, we develop a new anisotropic energy density taking into account the relative minimum structure of both R- and T-phase. The result satisfactorily demonstrates the coexistence of these two phases.
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