Specific heats of lead and cadmium niobates at low temperatures

Specific-heat data (2-25 K) are reported on the ferroelectrics Pb${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$ (orthorhombic), ${\mathrm{Cd}}_2$ ${\mathrm{Nb}}_2$ ${\mathrm{O}}_7$, and ${\mathrm{Cd}}_{1.6}$ ${\mathrm{Pb}}_{0.4}$ ${\mathrm{Nb}}_2$ ${\mathrm{O}}_7$, and on the nonferroelectrics Pb${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$ (rhombohedral), ${\mathrm{Pb}}_2$ ${\mathrm{Nb}}_2$ ${\mathrm{O}}_7$, and Cd${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$. All materials display maxima in $C{T}^{-3\mathrm{}}$, and excellent fits to experimental data are obtained with a single Einstein term added to the Debye background. The Einstein frequencies vary from 9 ${\mathrm{cm}}^{-1\mathrm{}}$ for Pb${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$ (rhombohedral) to 76 ${\mathrm{cm}}^{-1\mathrm{}}$ for Cd${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$, and the Debye temperatures from 171 K for Pb${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$ (rhombohedral) to 408 K for Cd${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$. The ferroelectric form of Pb${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$ varies dramatically from the nonferroelectric form: Einstein frequency, 37.6 ${\mathrm{cm}}^{-1\mathrm{}}$, and Debye temperature 224 K. The 20-mole%-Pb substitution on the Cd site in ${\mathrm{Cd}}_2$ ${\mathrm{Nb}}_2$ ${\mathrm{O}}_7$ lowers both the Einstein frequency and Debye temperature: 53 to 43 ${\mathrm{cm}}^{-1\mathrm{}}$ and 393 to 315 K, respectively. For all materials except Cd${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$, the Debye contribution is smaller than the Einstein contribution. Below 4 K, the ferroelectric niobates and Cd${\mathrm{Nb}}_2$ ${\mathrm{O}}_6$ have a Schottky contribution with an energy separation ∼50 mK (assumed two level). It is suggested that this term is due to the electric-quadrupole moment of Nb in an electric-field gradient. Published data on LiNb${\mathrm{O}}_3$ and LiTa${\mathrm{O}}_3$ support this interpretation.