Specific heats of paraelectrics, ferroelectrics, and antiferroelectrics at low temperatures

Abstract

Measurements of low-temperature specific heats (2-37 K) are reported for the first time on some common paraelectrics (thallous halides, Pb${\mathrm{F}}_2$, KTa${\mathrm{O}}_3$), ferroelectrics [BaTi${\mathrm{O}}_3$, potassium dihydrogen phosphate or KDP, triglycine sulfate or TGS, LiNb${\mathrm{O}}_3$, LiTa${\mathrm{O}}_3$, Pb(${\mathrm{Zr}}_{0.65}$ ${\mathrm{Ti}}_{0.35}$)${\mathrm{O}}_3$ or PZT 65/35], and antiferroelectrics [Pb(${\mathrm{Zr}}_{0.95}$ ${\mathrm{Ti}}_{0.05}$)${\mathrm{O}}_3$ or PZT 95/5, ${\mathrm{Pb}}_2$ ${\mathrm{Nb}}_2$ ${\mathrm{O}}_7$]. All materials display maxima in $C{T}^{-3\mathrm{}}$, and excellent fits to experimental data are obtained with single Einstein frequencies. The Einstein frequencies vary from 19 ${\mathrm{cm}}^{-1\mathrm{}}$ for TlCl to 99 ${\mathrm{cm}}^{-1\mathrm{}}$ for BaTi${\mathrm{O}}_3$. The frequencies in LiNb${\mathrm{O}}_3$ (79 ${\mathrm{cm}}^{-1\mathrm{}}$) and LiTa${\mathrm{O}}_3$ (61 ${\mathrm{cm}}^{-1\mathrm{}}$) agree reasonably well with earlier Raman data at 300 K on $E$-symmetry optic modes and with recent low-temperature pyroelectric data. The TlBr frequency (22 ${\mathrm{cm}}^{-1\mathrm{}}$) agrees well with the lowest phonon anomaly determined from neutron data, and the KTa${\mathrm{O}}_3$ frequency (26 ${\mathrm{cm}}^{-1\mathrm{}}$) is in good agreement with the average soft-mode frequency in this temperature range. No evidence is seen for the suggested phase transition in KTa${\mathrm{O}}_3$ at 10 K. The PZT materials, which are compositionally in a field inaccessible to powder Raman methods, have frequencies of 32 (65/35) and 38 ${\mathrm{cm}}^{-1\mathrm{}}$ (95/5), due probably to low-lying TA phonons. An unusual $T^{\frac{3}{2}}$ contribution to the specific heat of the ferroelectrics TGS, KDP, BaTi${\mathrm{O}}_3$, and LiNb${\mathrm{O}}_3$ was found at the lowest temperatures. Experimental data are in excellent agreement with $C=A{T}^3+B{T}^{\frac{3}{2}}$, and it is suggested that the $T^{\frac{3}{2}}$ term is the domain-wall contribution.