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

Abstract

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.

Critical Roles of Impurities and Imperfections in Various Phases of Materials

“…It has been suggested that the observed high dielectric constants are explained by flexoelectric polarization inside BaTiO 3 nanocubes [ 166 , 167 ]. Flexoelectric polarization is electric polarization induced by strain gradient in dielectric crystals regardless of the crystal symmetry [ 168 , 169 , 170 , 171 , 172 ].…”

“…Due to the presence of defects and dislocations (imperfections), the magnitude of compressive strain decreases as the distance from the interface increases toward the center of a nanocube [ 166 , 167 ]. This means that a strain gradient appears that induces flexoelectric polarization.…”

“…This means that a strain gradient appears that induces flexoelectric polarization. The magnitude of the flexoelectric polarization ( ) is estimated as follows [ 166 , 167 ]. where is the flexoelectric coefficient (10 μC m −1 ), is the strain gradient, is the width of the strain region ( is assumed, where is the size of a nanocube (15 nm)), and ° is assumed in Equation (3) because the tilt angle was experimentally estimated to be less than 10° [ 158 ].…”

“…Accordingly, there are six vectors of flexoelectric polarization inside a nanocube because there are six interfaces ( Figure 9 ) [ 166 ]. The flexoelectric polarization parallel to the applied alternating electric field, however, could not respond to the applied electric field because there is a mismatch of strain at the interface as the changes of strain at the interface are different between the two attaching nanocubes (the left of Figure 10 a) [ 167 ]. In other words, the flexoelectric polarization parallel to the applied alternating electric field does not contribute to the dielectric constant.…”

Production of O Radicals from Cavitation Bubbles under Ultrasound

“…In general, ODE modelling is sometimes superior to PDE modelling in that it is computationally more economical and that the important factors are more easily traced [ 34 ]. Examples of other ODE modellings are described in References [ 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 ]. With regard to bubble dynamics models for chemical reactions inside a bubble, there are several other theoretical models [ 74 , 86 , 87 , 88 , 89 , 90 , 91 , 92 ].…”