The conductivity anomaly in PbF2: a numerical investigation by classical MD and MC simulations

Recently Hainovsky and Maier (N. Hainovsky, J. Maier, Phys. Rev. B 51 (1995) 15789) showed that for the Frenkel disordered material PbF2 as well as for AgI, AgCl and AgBr, the anomalous conductivity increase at high temperature can be described by a cube root term in the chemical potential of the defects, which reflects their mutual interaction in a mean field sense. For PbF2 it has been assumed that only one charge carrier is responsible for the conduction. In the case of PbF2, which undergoes a higher order phase transition, the description also includes conductivity behaviour at and above the phase transition. In this work we investigate the above model by molecular dynamics and Monte Carlo simulations. The defect concentrations and the defect energies, including excess energies, are computed as a function of temperature based on a classical semi-empirical potential that was successfully developed and applied to PbF2 by Walker et al. [A.B. Walker, M. Dixon, M.J. Gillan, J. Phys. C: Solid State Phys. 15 (1982) 4061] in an earlier work. We compute the concentration of fluoride defects as a function of temperature and investigate the mechanism of conduction. We estimate the mobility of the fluoride ions by comparing the defect concentrations with the experimental conductivity data. The results show that the conductivity anomaly is indeed essentially caused by an anomalous increase in defect concentrations and the cube-root approximation is reasonably well fulfilled. The computation also indicates a perceptible contribution of the interstitial defect conductivity for T>600 K.