Domain Structures and Phase Diagram in 2D Ferroelectrics Under Applied Biaxial Strains - Phase Field Simulations and The
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Domain Structures and Phase Diagram in 2D Ferroelectrics under Applied Biaxial Strains - Phase Field Simulations and Thermodynamic Calculations Jie Wang,1 Yulan Li,2 Long-Qing Chen,2 and Tong-Yi Zhang1,* 1 Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 2 Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
ABSRACT The microscopic domain structures in 2D ferroelectrics under applied biaxial strains are investigated using a phase field model based on the time-dependent Ginzburg-Landau equation that takes both long-range electric and -elastic interactions into account. The stable polarization patterns are simulated at different temperatures and applied inequiaxial strains. The results show that the ferroelectrics transfer from multi-domain state to single-domain state when temperature surpasses a critical value. On the other hand, the macroscopic equilibrium polarization states are also studied through a nonlinear thermodynamic theory. The corresponding transition from a1a2 state ( P1 ≠ 0, P2 ≠ 0 ) to a1 state ( P1 ≠ 0, P2 = 0 ) or a 2 state ( P2 ≠ 0, P1 = 0 ) is also found from the “strain-straintemperature” phase diagram, which is constructed by minimizing Helmholtz free energy.
INTRODUCTION Ferroelectric materials have attracted much attention due to their pronounced dielectric, piezoelectric, and pyroelectric properties. In applications, ferroelectric devices usually undergo external mechanical loading, such as the mismatch strain between a ferroelectric thin film and its associated substrate, hydrostatic pressure in deep-water environments, etc. Mechanical loads and/or constraints may cause lattice distortion, domain wall motion, and changes in the domain structure [1] and thus shift the paraelectric/ferroelectric phase transition temperature and vary the ferroelectric and dielectric properties. These effects induced by mechanical loads and/or constraints may enhance or damage the performance of devices made of ferroelectric materials. Therefore, it is of great importance to understand and predict the effects of applied mechanical strains on the paraelectric/ferroelectric phase transition and on the ferroelectric and dielectric properties of ferroelectric materials. In the study of the effects of temperature, external mechanical loads and/or constraints on the phase diagram, the macroscopic polarization state and the microscopic domain structure of ferroelectrics, thermodynamic theories [2-8] and phase field models [9-12] are widely employed. Phase field models are based on thermodynamic theories and kinetics and take into account the gradient energy, i.e., the domain wall energy, and the multiple-dipole-dipole-electric and -elastic interaction energies, which play important *
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roles in the formation of domain structures and in the arrangements of dipol
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