Dynamics of crystals with correlated defect positions

We present a treatment of crystals containing point defects in which deviations from random defect distributions are taken into account. Known averaging procedures which presuppose randomness of atomic disorder are generalized in order to deal with defect site correlations. The quasicrystalline-approximation-type theory obtained if the pure host crystal is taken as the reference system (which is applicable only to the case of low defect concentrations) is generalized by taking a (random) defect crystal as reference system. This allows a treatment of site-correlation effects also in materials with high defect concentrations. The method is applicable to solid solutions with an arbitrary number of components. For crystals with correlated defect sites, average Green's functions (no atom type specified at any lattice site), and conditionally averaged Green's functions (atom of a specific type—host or defect—at a certain site) are calculated. These two types of Green's functions are then used to determine scattering functions, dispersion curves, and fluctuations at host and defect sites. As a direct application to experiment the method is used to calculate explicitly the change of the polarization of a displacive ferroelectric due to defect site correlations. Realistic correlations are shown to lead to considerable $T_c$ shifts.