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 $C{T}^{\ensuremath{-}3}$, and excellent fits to experimental data are obtained with single Einstein frequencies. The Einstein frequencies vary from 19 ${\mathrm{cm}}^{\ensuremath{-}1}$ for TlCl to 99 ${\mathrm{cm}}^{\ensuremath{-}1}$ for BaTi${\mathrm{O}}_{3}$. The frequencies in LiNb${\mathrm{O}}_{3}$ (79 ${\mathrm{cm}}^{\ensuremath{-}1}$) and LiTa${\mathrm{O}}_{3}$ (61 ${\mathrm{cm}}^{\ensuremath{-}1}$) 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 ${\mathrm{cm}}^{\ensuremath{-}1}$) agrees well with the lowest phonon anomaly determined from neutron data, and the KTa${\mathrm{O}}_{3}$ frequency (26 ${\mathrm{cm}}^{\ensuremath{-}1}$) 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 ${\mathrm{cm}}^{\ensuremath{-}1}$ (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.