Logarithmic temperature variations of the elastic constant of barium titanate near the ferroelectric phase transition

The temperature variations of the elastic constant C11 and the corresponding acoustic attenuation coefficient of barium titanate single crystals grown by two different methods in the paraelectric phase were obtained in a wide temperature by means of Brillouin light scattering. Two phenomenological approaches were adopted to attempt to explain the anomalous change in C11 (denoted as ΔC11) in the paraelectric phase. ΔC11 exhibited a logarithmic variation as log[(T − T0)/T0] in a certain temperature range from Tc to about Tc + 80 °C instead of the other variation of (T − T0)ζ predicted by the mean-field approach. This temperature range was almost the same as the range where precursor dynamics were theoretically predicted to set in. The fact that the logarithmic variation was proposed for uniaxial systems might indicate that the correlated deformation of precursor polar clusters is tetragonal, as was suggested from nuclear magnetic resonance study [7].