The acoustic-phonon velocities of a single crystal of BaTi03 have been measured as a function of pressure up to 8 GPa, including the transition pressure p c =2.35 GPa, by means of Brillouin scattering technique. Only one elastic eigenmode shows an anomalous decrease on approaching p c and the elastic anisotropy increases. The elastic anomaly of cubic BaTiC>3 is interpreted well by introducing a new tensorial order parameter which describes the anisotropy. The cubic-to-tetragonal phase transition in BaTiC>3 is shown to be triggered by the fluctuation of the anisotropy, not the polarization itself.PACS numbers: 77.80.Bh, 62.50.+p, 62.65.+k, 78.35,+c Studies on the cubic-to-tetragonal phase transition in BaTiC>3 have been extensively done, 1 ' 2 using a variety of experimental methods. The result of an infrared measurement by Luspin, Servoin, and Gervais showed that the frequency co s of the soft phonon mode varies from 1350 to 520 K as G)}azT-T c , but becomes independent of temperature below 520 K to T c , 3 and suggested the existence of a crossover from displacive to order-disorder type of transition. 4 The recent results of hyper-Ramanscattering measurements, which were done independently by Inoue and Akimoto 5 and by Vogt, Sanjurju, and Rossbroich, 6 were in conflict with each other as to the interpretation of the phase transition, i.e., whether the mechanism of the phase transition is of the orderdisorder type or of the displacive type. Thus the controversy on the mechanism of the phase transition is still unresolved.A measurement of inelastic neutron scattering showed the existence of a strong anisotropy in the spectra near the phase transition. 7 The anisotropy seems to be related to the elastic anisotropy. Although the elastic anomaly of BaTiC>3 was observed in the cubic phase near the phase transition, 8 the contribution of the elastic anisotropy to the phase transition was not elucidated since the experiments on the elastic properties were partly performed within the limited region close to the phase transition. Thus no systematic study of the elastic properties of BaTiC>3 has been hitherto performed in relation to the elastic anisotropy. If the anisotropy plays an important role in the phase transition, the studies on the elastic properties will give important information on the mechanism of the phase transition since the anisotropic fluctuation should be of relaxational type.By means of the Brillouin scattering technique in combination with a diamond anvil cell, we have performed the first systematic study of the elastic properties of BaTiOs for a wide region including the phase-transition point, as a function of pressure at room temperature. We have found that the elastic anisotropy increases anomalously on approaching the phase transition. The purpose of this paper is to give new insight into the phase-transition mechanism of BaTiC>3 on the basis of the elastic anomaly accompanying the phase transition.The 6-cut plates were prepared from a melt-grown BaTiOs single crystal (NEC Co. Ltd.) which has ...