The cause of high-temperature quantum paraelectricity in some perovskite titanates

Abstract

High-temperature quantum paraelectricity in perovskite titanate series (Ln 1/2Na 1/2)TiO 3 has been investigated in relation to their structural deformation for Ln 3+-substitutions, Ln=La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu. Except for Ln=La and Ce, (Ln 1/2Na 1/2)TiO 3 has an orthorhombic unit cell with space group Pnma. The essential deformation parameter which lowers the highest dielectric constant ε a at the quantum paraelectric state, is found to be the average tilt angle δ among the neighboring [TiO 6]-octahedra for (Ln 1/2Na 1/2)TiO 3. ε a decreases moderately as a function of cos( δ/2) for less than half-filled Ln 3+-range, however, it decreases sharply for more than half-filled Ln 3+-range. Supposing a virtual spontaneous polarization P s with a virtual ferroelectric transition temperature T 0, and a zero-point vibrational energy h v 0/2 of Ti 4+-oscillators in [TiO 6]-octahedra, a condition for the appearance of quantum paraelectricity in perovskite titanates is given by T 0< T*∼ h v 0/2 k, where T* is the cross-over temperature from classical to quantum regime. By analogy with the simple harmonic oscillator, the width of the potential on the Ti 4+ ions in [TiO 6]-octahedra determines their zero-point energy h v 0/2, which is considered as the quantum fluctuation energy, replaces the thermal fluctuation energy k T below the cross-over temperature T*. The fundamental frequency v 0 of the Ti 4+-oscillator is characteristic of the materials, that is, the narrower the potential is, the higher the v 0 is. Therefore, the structural deformations through the tilts or shrinks of the [TiO 6]-octahedra cause to the high-temperature quantum paraelectricity in the perovskite titanates via increase in v 0, T* and T a, the arrival temperature at the quantum paraelectric state.