Simple phenomenological approach to premelting and sublattice melting in Frenkel disordered ionic crystals

The occurrence of anomalously high ionic-defect concentrations in solids at temperatures approaching the transition to a molten or superionic (i.e., molten cation or anion sublattice) phase is a well-known phenomenon. We show that this premelting phenomenon can be quantitatively described by a cube-root law not only for the Frenkel disordered AgCl, AgBr, and AgI, but also for the anti-Frenkel disorderd PbF₂. In all cases, the computed defect-defect interaction leads to a phase instability of first order or of higher order at a temperature which is very close to the actual transition point. Moreover, the specific heat data can be consistently explained by the same effect. The validity of the cube-root law is discussed in particular regarding the unexpectedly good prediction of the transition temperatures. Implications for the melting behavior of ionic conductors and for doping effects are briefly touched upon.