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

The temperature variations of the elastic constant C-11 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 C-11 ( denoted as Delta C-11) in the paraelectric phase. Delta C-11 exhibited a logarithmic variation as log[(T - T-0)/T-0] in a certain temperature range from T-c to about T-c + 80 degrees C instead of the other variation of (T - T0)(zeta) 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]. (c) 2012 Elsevier B.V. All rights reserved.