Models of Phase Transitions in Superionic Conductors.

The effect of the transfer term in the lattice gas Hamiltonian in the statistical mechanical treatment of phase transitions in some superionic conductors (or ionic solids with high ionic conductivity) was examined. The periodic cell cluster method was applied to the triangular lattice, choosing a 3-cell cluster of 4-site cells which maintain the sublattice structure of the lattice. No evidence of a sharp phase transition for any value of the applied field was found, in contrast to mean field theory. This explains the non-existence of a sharp transition in the super-lattice of beta-alumina observed experimentally. The renormalization method was used to obtain the impurity contribution to the free energy of a square Ising lattice with a single impurity. A comparison of the cumulant expansion result with the exact result, shows that the second order cumulant leads to irregular behavior.