Internal stresses and elastic energy in ferroelectric and ferroelastic ceramics: Calculations by the dislocation method

Abstract

A method is proposed for calculating the internal stresses in ferroelectric and ferroelastic ceramics which is based on the modelling of the mechanical sources of stress by fictitious dislocations continuously distributed on the grain and twin boundaries. For tetragonal and orthorhombic ceramics with a lamellar twin structure, the dislocation models of representative grain boundaries are worked out. On this basis the elastic energy is calculated which is associated with highly inhomogeneous stress fields concentrated near the boundaries of twinned grains. The part of the energy of long-range internal stress fields, which depends on the twin structure, is also estimated with the aid of the dislocation method. The results obtained are used to calculate the equilibrium parameters of the lamellar twin structures in ferroelectric BaTiO3 ceramic and ferroelastic high-Tc superconducting YBa2Cu3O7-δ ceramic.