Engineering of atomic-scale flexoelectricity at grain boundaries

Flexoelectricity is a type of ubiquitous and prominent electromechanical coupling, pertaining to the electrical polarization response to mechanical strain gradients that is not restricted by the symmetry of materials. However, large elastic deformation is usually difficult to achieve in most solids, and the strain gradient at minuscule is challenging to control. Here, we exploit the exotic structural inhomogeneity of grain boundary to achieve a huge strain gradient (~1.2 nm−1) within 3–4-unit cells, and thus obtain atomic-scale flexoelectric polarization of up to ~38 μC cm−2 at a 24° LaAlO3 grain boundary. Accompanied by the generation of the nanoscale flexoelectricity, the electronic structures of grain boundaries also become different. Hence, the flexoelectric effect at grain boundaries is essential to understand the electrical activities of oxide ceramics. We further demonstrate that for different materials, altering the misorientation angles of grain boundaries enables tunable strain gradients at the atomic scale. The engineering of grain boundaries thus provides a general and feasible pathway to achieve tunable flexoelectricity.

Coexistence of Flexo- and Ferro-Electric Effects in an Ordered Assembly of BaTiO3 Nanocubes

It has been reported that the flexoelectric effect could be dominant in the nanoscale. The discrepancy between theory and experiments on the frequency dependence of the dielectric constant of an ordered assembly of BaTiO3 nanocubes is nearly resolved by assuming the coexistence of flexo- and ferro-electric effects. Although flexoelectric polarizations perpendicular to the applied alternating electric field contribute to the dielectric constant, those parallel to the electric field do not contribute because the magnitude of the flexoelectric polarization does not change due to the mismatch of strain at the interface of the nanocubes. On the other hand, some dielectric response is possible for the ferroelectric component of the polarization parallel to the electric field.

Analytical studies on Mode III fracture in flexoelectric solids

Due to the stress concentration near crack tips, strong flexoelectric effect would be observed there, which might lead to new applications of flexoelectricity in material science and devices. However, different from the flexoelectric effect in cantilever beams or truncated pyramids, at the crack tip, multiple components of strain gradients with nonuniform distribution contribute to the flexoelectric effect, which makes the problem extremely complex. In this paper, with the consideration of both direct and converse flexoelectricity, the electromechanical coupling effect around the tip of a Mode III crack is studied analytically. Based on the Williams' expansion method, the displacement field, polarization field, strain gradient field along with the actual physical stresses field are solved. A path independent J-integral for Mode III cracks in flexoelectric solids is presented. Our results indicate that the existence of flexoelectricity leads to a decrease of both the J-integral and the out-of-plane displacement in Mode III cracks, which means that the flexoelectric effect around the tip of Mode III cracks enhances the local strength of materials.

Flexoelectric properties of multilayer two-dimensional material MoS2

Two-dimensional (2D) materials exhibit a high strength and flexibility along with unique electrical-mechanical multiphysics properties. In this study, we experimentally demonstrated the electromechanical response of a multilayer 2D material, 2H-phase MoS2, by using a piezoresponse force microscope. In particular, the dominant physical quantity of the deformation response was determined by independently controlling the electric field and electric field gradient by changing the probe shape and material thickness (number of layers). The multilayer MoS2 exhibited an out-of-plane electrical-mechanical deformation response that followed and was inverted with respect to positive and negative voltages, respectively. Moreover, the relationships between the electric field gradient and strain were similar for all shapes of the probe tip and film thickness values. This result indicated that the electrical-mechanical response of this material was dominated by the electric field gradient, and the strain could be attributed to the converse flexoelectric effect. The findings can provide guidance for the realization of ultrathin electromechanical devices.

Influence of an electric field on flexopolarization induced by acoustic action on a liquid crystal

The work experimentally investigated the influence of an electric field on the direct flexoelectric effect that occurs under the influence of an acoustic field in liquid crystals. Thin layers of nematics 10-100 μm thick were studied. In this case, the liquid crystal sample was exposed to the piston method with an acoustic wave with a frequency of 1 kHz. The dependences of the first and second harmonics for different NLCs on the bias voltage value, shear amplitude, and crystal thickness were obtained. It was revealed that the flexosignal harmonics depend on the direction of the electric field; when a positive potential is applied to the movable plate, they take on smaller values than when negative. It was found that in low fields the magnitude of the flexosignal increases due to an increase in the amplitude of the director deviation, but at a critical value of the field it is suppressed, since the layer is stabilized by a constant electric field.

Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity

The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Kármán strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derived. Moreover, this nonlinear system is linearized for each load increment, where it is solved iteratively. For the vanishing flexoelectric coefficient, the governing equations lead to the classical Timoshenko beam model. Furthermore, the influence of the flexoelectricity coefficient and the microstructural length-scale parameter on the beam deflection and the induced electric intensity is investigated.

Nonlinear electromechanical analysis of axisymmetric thin circular plate based on flexoelectric theory

Flexoelectricity will dominate the electromechanical coupling of intelligent components in MEMS/NEMS due to its size-dependency. This paper focuses on investigating the flexoelectric responses of intelligent components of the circular plate type, which are commonly used in MEMS/NEMS. Utilizing Hamilton’s principle, the nonlinear flexoelectric circular plate model is presented by combining von Kármán plate theory and flexoelectric theory. The equilibrium equations and all boundary conditions are obtained and then discretized. The nonlinear static bending of the simply supported axisymmetric flexoelectric circular plate is investigated by combining DQM and iteration method. The distributions of dimensionless bending deflection and electric potential are analyzed under different loads. Moreover, the nonlinear free vibration behaviors are also investigated by combining the Galerkin method and Lindstedt–Poincaré Method. The flexoelectric effect and stiffening effect of strain gradient are revealed. This paper will be helpful to promote the application of flexoelectric intelligent components of the circular plate type, which are encountered commonly in engineering.

Large-scale Domain Engineering in Two-Dimensional Ferroelectric CuInP2S6 via Giant Flexoelectric Effect

Room-temperature ferroelectricity in two-dimensional materials offer a potential route for developing atomic-scale functional devices beyond Moore’s law. However, as a key for the technology implementations of ferroelectrics in electronics, the controllable generation of uniform domains remains challenging in two-dimensional ferroelectrics at current stage because domain engineering through an external electric field at 2D limit inevitably leads to large leakage current and material break-down. Here, we demonstrate a voltage-free method, the flexoelectric effect, to artificially generate large-scale stripe domains in two-dimensional ferroelectric CuInP2S6 with single domain lateral size at the scale of several hundred microns. With giant strain gradients (~106 m−1) at nanoscale, we mechanically switch the out-of-plane polarization in ultrathin CuInP2S6. The flexoelectric control of ferroelectric polarization is understood with a distorted Landau-Ginzburg-Devonshire double well model as evidenced by the shifted ferroelectric hysteresis loops and the first-principle calculations. Through substrate mechanical strain engineering, the stripe domain density is controllable. Our results not only highlight the potential of developing van der Waals ferroelectrics-based memories but also offer the opportunity to study ferroelectric domain physics in two-dimensional materials.

Flexoelectric effect on thickness-shear vibration of a rectangular piezoelectric crystal plate

Thickness-shear (TSh) vibration of a rectangular piezoelectric crystal plate is studied with the consideration of flexoelectric effect in this paper. The developed theoretical model is based on the assumed displacement function which includes the anti-symmetric mode through thickness and symmetric mode in length. The constitutive equation with flexoelectricity, governing equations and boundary conditions are derived from the Gibbs energy density function and variational principle. For the effect of flexoelectricity, we only consider the shear strain gradient in the thickness direction so as to simply the mathematical model. Thus, two flexoelectric coefficients are used in the present model. The electric potential functions are also obtained for different electric boundary conditions. The present results clearly show that the flexoelectric effect has significant effect on vibration frequencies of thickness-shear modes of thin piezoelectric crystal plate. It is also found that the flexoelectric coefficients and length to thickness ratio have influence on the thickness-shear modes. The results tell that flexoelectricity cannot be neglected for design of small size piezoelectric resonators.