3D dependence of the dielectric dispersion in a BaTiO$_3$ single crystal

The 3D dependences $\varepsilon'(\lg f,T)$ and $\tan\delta(\lg f,T)$ of a perfect BaTiO$_3$ single crystal grown by the Remeika method have been studied in the ranges $f$ = 1–2 $\times$ 10$^7$ Hz and $T$ = -80–130$^\circ$C. These dependences characterize a transition from the paraelectric phase (121.5$^\circ$C) as a near-antiferroelectric transition followed by the transition to the tetragonal phase at $\sim$79.5$^\circ$C. According to a number of signs, the range 121.5–79.5$^\circ$C corresponds to a metastable phase typical of first-order phase transitions. The unexpected result of this work has been discussed with invoking the hypothesis on the BaTiO$_3$ structure in the paraelectric phase, according to which it consists of three antiferroelectric states oriented along the crystallographic axes. Using the dielectric properties of BaTiO$_3$ as an example, the method of direct correct determination of the temperatures of the structural transformations from the anomaly of $\tan\delta(\lg f,T)$ has also been demonstrated.