Low-temperature heat capacities of orthorhombic and cubic PbF2

Heat capacities of orthorhombic ($\alpha$) and cubic ($\beta$) lead fluoride (Pb${\mathrm{F}}_2$) have been measured between 3 and 22 K. For both structures the data can be well fitted to the sum of a Debye term and an Einstein term with exponential temperature dependence. The latter may be attributed to the existence of low-lying vibrational modes in the paraelectric compound. The observed Einstein frequency of 35 ${\mathrm{cm}}^{-1\mathrm{}}$ for the orthorhombic structure agrees with that of a Raman-active mode in Pb${\mathrm{Cl}}_2$ and Pb${\mathrm{Br}}_2$ of the same structure, which involves the movement of Pb atoms only.