Superionic phase transition of doped fluorites

In this paper we present new results of specific-heat experiments on superionic mixtures of cubic lead fluoride and some rare-earth fluorides. The results depend very strongly on the rare-earth ion; for samples doped with ${\mathrm{LaF}}_3$ we observe a peak in the specific heat as a function of T, which is located at an approximately fixed position. This peak, which is due to the superionic transition, increases in width with increasing concentrations of ${\mathrm{LaF}}_3$. If we add ${\mathrm{YbF}}_3$, however, the position of the peak varies. It appears that in samples doped with a few mol % ${\mathrm{YbF}}_3$ there are two peaks in the ‘‘specific-heat spectrum’’: one very similar to the peak observed in pure ${\mathrm{PbF}}_2$ and a second peak situated at significantly lower temperatures. The results are discussed in view of the experimental data on the clustering properties of the different solid solutions. In addition, we treat some of the specific-heat data with theoretical models, which have been proposed by Vlieg, den Hartog, and Winnink. This analysis suggests that due to the introduction of La impurities the formation of Frenkel pairs is more difficult. The introduction of Yb impurities, however, leads to additional Frenkel-pair formation, because ${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Yb}}_{\mathrm{x}}$ ${\mathrm{F}}_{2+\mathrm{x}}$ clusters, consisting of more than one Yb-F interstitial pair, trap extra interstitial ${\mathrm{F}}^{\mathrm{-}}$ ions. Because the energy of these extra trapped interstitial ${\mathrm{F}}^{\mathrm{-}}$ ions is lower than the energy of free anion interstitials, this leads to an enhancement of the formation of Frenkel pairs.