Microscopic approach to the statics and dynamics of solid electrolytes near the phase transition

Abstract

The statics and local dynamics of solid electrolytes near the transition temperature is investigated within mean field approach and Mori theory, starting from an Hamiltonian which takes into account the mutual interactions of the mobile ions and their coupling to the phonons of the cage. The Hamiltonian is written as function of the local density of the mobile ions on their available sites and as function of the displacements of the cage ions. The correlation functions of these variables are calculated within MFA. Those correlations which are connected with the order parameter diverge at the stability limits but they finite atTc. As a consequence, the sound velocities of those acoustic modes which are coupled to the mobile ions show a softening atTc only when the coupling strength is sufficient large. It is shown that this softening can be observed by ultrasonic methods, but not by neutron scattering, in agreement with experiments. The experimental relevance of aZ-branch, which may appear in the dispersion of the relaxational peak nearTc, is discussed. The coupling between optical modes and mobile ions is also considered. It is shown that a softening of optical modes nearTc is not expected in solid electrolytes, in agreement with the experimental situation.