Colloidal equilibrium in insulating crystals: Possible application to relaxor ferroelectrics.

Abstract

Decomposition in a multicomponent insulating compound with a considerable Coulomb interaction between ions is considered. A specific situation where decomposition occurs due to redistribution of ions of the same sign (either cations or anions) whereas all other atoms form an immobile frame is discussed. Such a situation may occur if a diffusivity of the ions of the same sign is much higher than that of atoms comprising the frame. It is shown that under these conditions the decomposition results in solid-state colloidal equilibrium. The colloidal state is formed by an array of coherent precipitate phase particles imbedded into a parent phase matrix. These particles are of the same stable size. This size, as well the volume fraction of a precipitate phase and the equilibrium compositions of precipitate and matrix phases, are determined by the balance between electrostatic and interfacial energies. The balance proves to be dependent on overall stoichiometry. This situation drastically differs from the conventional situation where the compositions of coexisting equilibrium phases do not depend on overall stoichiometry of a system (the lever rule is valid) and where the coarsening process always occurs. The proposed model is applied to relaxor ferroelectrics to explain occurrence of a mesoscopic inhomogeneous structure that does not undergo coarsening.