A model based on the presence of two-level systems identified with defect clusters is used to study different properties of superionic lead fluoride and calcium fluoride. The high degeneracy of the higher level indicates a liquid-like arrangement of anions within the cluster.

Recent experimental studies show that the dielectric constant of lead fluoride increases rapidly as the superionic transition temperatureT_c is approached. In this work the static dielectric constant (ε) is calculated theoretically for low and high temperature limits. Assuming conduction to take place through a percolation mechanism,ε is found to diverge at the threshold temperatureT_th where ionic conduction starts.

In the present paper, we report a theoretical calculation of temperature variation of the ultrasonic absorption coefficient of PbF₂. The absorption can be explained by the TLS model, with parameters which simultaneously reproduce the specific heat, thermal expansion, bulk modulus and ionic conductivity. Our results agree well with recent experimental reports of ultrasonic attenuation in PbF₂.