Correction of dipole field due to lattice deformation of a perovskite-type crystal

Abstract

Correction of Lorentz field coefficients in a Perovskite-type crystal is discussed by considering orthorhombic deformation of a simple cubic lattice. If one considers the deformation of crystal structure from the simple cubic lattice a 3 to the orthorhombic lattice a(1 + Δ 1) × a(1 + Δ 2) × a(1 + Δ 3), a change of the internal field at some respective points caused by the dipole interaction is calculated as follows. The internal electric fields at (000), ( 1 2 1 2 1 2 ) etc. are given by the equations E n(000) = { 4 3 π + S n(000) + 2.1563 (Δ 1 + Δ 2) − 16.8793Δ 3} p a 3 E n( 1 2 1 2 1 2 ) = { 4 3 π + S n( 1 2 1 2 1 2 ) − 10.0622(Δ 1 + Δ 2) + 7.5578Δ 3} p a 3 etc. where S' n s represent the Lorentz correction terms and p is the dipole moment placed at the lattice points. By applying the results the quantitative discussions are possible for many phenomena accompanied by the lattice deformation, namely, ferroelectricity, piezoelectricity, photoelasticity and so on. As an example calculations are made to estimate the birefringences of the BaTiO 3 and WO 3 crystals.