Theoretical Study of the Flexoelectric Effect Based on a Simple Model of Ferroelectric Material

Abstract

By the flexoelectric effect is called a linear relation between polarization and gradient of deformation. The aim of the present work is to estimate the flexoelectric coefficient of ferroelelectrics on the basis of a microscopic model. The well known model is used: the ion of charge e spaced in potential double-wells interacts with the other ions of the same type in neighboring cells with “springs” whose spring constant is β. Limiting our consideration on the regime of the order-disorder mechanism we find that flexoelectric coefficient is the product of susceptibility ϵ₀χ _r (ϵ₀ vacuum permitivity) and the coefficient βa ²/e, where a is a lattice constant. It can be shown that our results are not in contradiction with Tagantsev's expression [Phys. Rev., B34, 5883, (1986)] for flexoelectric coefficient: χ a/e. However the latter result was deduced by the more phenomenological way or concerns the displacement type of ferroelectrics only.

Keywords:

• Ferroelectrics
• piezoelectricity
• electrostriction

ACKNOWLEDGEMENTS

This work was supported by the grants No's 202/00/1187 and 202/02/0238 of Czech grant agency and by Research program MSM 113 200001 from Ministry of Education of Czech Republic. Our thanks belong to Prof. J. Fousek for discussions and Dr. Vera Marvanova for drawing the pictures.