CPA theory for mixed ferroelectric crystals

The excitations and dielectric properties of substitutionally disordered ferroelectrics have been considered using a simple model which assumes that the different constituents have different polarizability. The dipoles are taken to interact via an unperturbed Coulomb potential. The effective dielectric constant is calculated using the coherent potential approximation. If we neglect dispersion in the Coulomb eigenvalues the results are equivalent to those obtained for randomly located spheres in a medium.1 This is clearly the result appropriate for composites of macroscopic particles such as are found in a ceramic. For the microscopic disorder in a substitutionally mixed crystal somewhat different results are obtained. These may be extended to a dynamical treatment of the behaviour of the soft T.O. mode if this is assumed to be dominated by the electric forces. Calculations of T c and other properties show that improvements to the model are necessary to make a realistic comparison with experiment and these are being undertaken.