Theory of Spontaneous Deformation of Barium Titanate

Abstract

The spontaneous ferroelectric deformation of the BaTiO 3 , crystal to tetragonal form is calculated, taking account of the electrostatic energy and the short-range interaction of the type λ r -9 -µ r -6 , but neglecting the effect of thermal motion. It can be deduced that ionic shift causes the lattice spacing to extend a few percent to the same direction (i.e. the direction of spontaneous polarization). The result is sensitive to the choice of the “ effective charge ” of the Tin ion. However, for a certain range of this parameter, the dependence of the lattice constant on it shows a striking resemblance to the observed dependence of the lattice constant on temperature. Contraction perpendicular to the direction of polarization is a also calculated here considering the interaction among ions. we can show that the extension and contraction suddenly occur when the dipole interaction becomes stronger than some critical value. By taking a proper value for the dipole interaction energy the result can be made t...