Study Of Flexoelectric Effect On Phase Transition And Physical Properties In Ferroelectric Films

Ferroelectric materials can be broadly used in micro/nano devices such as information memories, nano-sensors, tunable resonator and nano-generators due to their superior piezoelectric, pyroelectric, acousto-optic, dielectric and nonlinear optoelectronic properties. In addition to the conventional piezoelectric effect, the ferroelectric thin films also have a coupling relationship between the polarization and the strain gradient, namely flexoelectric effect. With the miniaturization of electronic devices, the decreasing of material size can easily lead to larger strain gradient when compared to the bulk materials. And the flexoelectric effect becomes more remarkable, which can not be ignored. Though the regulation to the phase change, electric polarization, piezoelectric and pyroelectric properties of ferroelectric thin films by strain engineering is very mature, the research on the properties controlling of ferroelectric films by the strain gradient engineering is still quite scarce.In this paper, the nonlinear Landau thermodynamic theory and elastic theory are combined for the establishing of effective energy expression for film/substrate system with the flexoelectric effect items added. The Euler-Lagrange variational method is also used to obtain the controlling equation of polarization in steady state and the corresponding boundary conditions. The influence of the flexoelectric effect, induced by the strain gradient of films, on the coupling of stress, electricity and magnetism is analyzed.（1） For substrate-constrained ultrathin BaTiO₃（BTO） ferroelectric thin films, the flexoelectric effect on the ferroelectric properties of thin films（including the polarization of the critical thickness, the phase transition temperature, hysteresis loop, phase diagram, dielectric properties and piezoelectric properties） are analyzed by regulating the film strain gradient. The pyroelectric coefficient and adiabatic temperature of ferroelectric films are also effectively regulated by applying an external electric field and changing the electrode work function.（2） The phase transition properties of Ba_1-xSr_xTiO₃ graded ferroelectric films are studied by considering flexoelectric effect. It is found that external electric field can enhance the equivalent piezoelectric coefficients of graded ferroelectric films clamped by asymmetric electrode. Moreover, the appropriate thickness is important to obtain giant piezoelectric responses. At last, our theory can well explain the special hysteresis loop imprint reported in the experiment related to the graded ferroelectric films.（3） For monolayer BTO ferroelectric films under bending loads, the strain field distribution of the films is deduced by mechanical equilibrium condition. In order to adjust the flexoelectric effect, various strain gradients are obtained by applying different bending loads on BTO films. Therefore, applying bending loads can effectively modulate the equivalent piezoelectric coefficients of BTO films of different thickness.（4） Flexoelectric effect of bilayer composite films, which are subjected to bending loads, is regulated by changing the thickness ratios between two different material layers or applying prestrains. The equivalent piezoelectric coefficients of BTO/PDMS composite films are analyzed in different thickness ratios and prestrains. For BTO/CoFe₂O₄ composite films, magnetoelectric coupling coefficients are calculated in different bending load situations and magnetic fields.In summary, flexoelectric effect will enhance the polarization of ferroelectric thin films and thus affect a series of physical properties. And the strain engineering can provide a new method for the design of new intelligent materials. Therefore, our results provide the significant theoretical guide for the construction and performance optimizing of new micro/nano devices.