Abstract
A two-dimensional phase field simulation of ferroelectric films is used that incorporates Landau-Devonshire energy, gradient energy and depolarization electrical energy. A new intermediate electrical boundary condition is firstly presented to study the effects on domain structures of ferroelectric films. Two-dimensional simulations of domain structures are carried out under the open circuit (OC), short circuit (SC) and intermediate (IM) electrical boundary conditions. The simulation results show that there are multi-vortices domains and 180° multi-stripes domains under OC and SC electrical boundary condition, respectively. And there is a transition from multi-vortices domains to 180° multi-stripes domains under the IM electrical boundary condition due to competition between the elastic energy and depolarization electrical energy in the films. The present IM electrical boundary condition can completely characterize different degrees of compensation for surface charges by the electrodes and further describe the effect on the depolarization electrical energy. It can also be reduced to OC and SC electrical boundary conditions. Hence, for nano-thin ferroelectric films, the IM electrical boundary condition plays an important role in the formation of domain structures.
Highlights
Ferroelectric materials are widely researched and used due to their excellent ferroelectric, dielectric, piezoelectric and pyroelectric properties
We mainly focus on the electrical boundary conditions
The new IM electrical boundary condition has been presented firstly to describe more reasonable electrical boundary condition, which can describe the degree of compensation for surface charges
Summary
Ferroelectric materials are widely researched and used due to their excellent ferroelectric, dielectric, piezoelectric and pyroelectric properties. A transition from single domain state to multidomain state is observed for PZT and PbTiO3 with electrodes as thickness is decreased.[11,12] These results are explained by the increasing presence of a strong depolarization field. Naumov et al.[13] performed ab initio simulations and presented unusual vortex phases associated with a new order parameter, namely, the toroid moment G of polarization in ferroelectric nanostructures. The requirement for the existence of most steady and equilibrium domain structure is to minimize the total free energy of nano-thin ferroelectric films. In this paper, based on the dielectric boundary condition of the crack in bipiezoelectrics, a new IM electrical boundary condition is presented firstly, which has the explicit physical meaning and physical background. The phase field method is applied to simulate the domain structures under different electrical boundary conditions. It should be noted that the IM electrical boundary condition could describe more general electrical boundary conditions
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