On the polarization dynamics in the presence of flexoelectricity and morphotropic phase boundary in ferroelectrics
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ICAL PROPERTIES OF CRYSTALS
On the Polarization Dynamics in the Presence of Flexoelectricity and Morphotropic Phase Boundary in Ferroelectrics S. A. Pikin* Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of Sciences, Moscow, 119933 Russia *e-mail: [email protected] Received November 8, 2016
Abstract—It is shown that anomalous piezoelectric properties of epitaxial nanostructures arise on the morphotropic phase boundary (MPB) due to the strong flexoelectric effect on dislocation walls. The MPB (typical of many materials) exhibits a coexistence of various phases and partition of these phases to minimum sizes. This minimum size lс (nanoscale) is found using the dislocation theory; it coincides with the distance between individual dislocations in dislocation walls, which is much larger than the Burgers vector b, regardless of the type of crystalline material. The flexoelectric coefficients f are estimated taking into account dimensional relations and experimental data on the rotations of ferroelectric nanodomains in multiferroics. These estimates coincide with classical values. The critical value lс ∼ 10b specifies the measured dependence on the dielectric susceptibility χ e , f ~ χ1/2 e . The quantity χ e depends on the frequency ω of the ac electric field applied to a sample and on the dislocation density. The Ba0.6Sr0.4TiO3/Ni0.8Zn0.2Fe2O4 ceramic composite shows typical frequency dispersion of χ e in a wide frequency range. The frequency dependence of flexoelecric coefficients is shown to reproduce the frequency dependence of permittivity at high frequencies. DOI: 10.1134/S1063774517020213
INTRODUCTION It has been known for a long time that, in the absence of thermodynamic equilibrium, the mechanical deformation in nanofilms of various materials may be significant when the regions in which the nonequilibrium deformation changes (grains or nanodomains) are very small at the interfaces, which have an elevated energy due to the presence of dislocations. [1, 2]. An interest in multiferroic nanofilms has increased recently, when it became clear that the multilayer films of these materials may exhibit a large magnetoelectric effect and significant piezoelectric coefficient. It was demonstrated in [3] that, at high dislocation density and disclination power, the lattice deformation can significantly enhance the piezoelectric effect in these materials as a consequence of magnetostriction. This is especially pronounced in the formation of morphotropic phase boundary (MPB) in epitaxial films, when a gradual change in the properties (composition, ratio of atomic sizes, etc.) in a number of compounds of the same type (in stoichiometry) results in a stepwise change in the structure and leads to the occurrence of a phase boundary, at which different structures (both new and previous ones) are in contact [4–6]. In particular, perovskite structures form MPB during epitaxy. In this case, the structures may be in contact on the nanodomain scale. In epitax
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