T Nakamura, YJ Shan, PH Sun, Y Inaguma, M Itoh
SOLID STATE IONICS 108(1-4) 53-58 1998年5月 査読有り
High-temperature quantum paraelectricity in perovskite titanate series (Ln(1/2)Na(1/2))TiO3 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(1/2)Na(1/2))TiO3 has an orthorhombic unit cell with space group Pnma. The essential deformation parameter which lowers the highest dielectric constant epsilon(a) at the quantum paraelectric state, is found to be the average tilt angle delta among the neighboring [TiO6]-octahedra for (Ln(1/2)Na(1/2))TiO3. epsilon(a) decreases moderately as a function of cos(delta/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-o, and a zero-point vibrational energy hvo/2 of Ti4+-oscillators in [TiO6]-octahedra, a condition for the appearance of quantum paraelectricity in perovskite titanates is given by T-o < T* similar to hv(o)/2k, 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 Ti4+ ions in [TiO6]-octahedra determines their zero-point energy hv(o)/2, which is considered as the quantum fluctuation energy, replaces the thermal fluctuation energy kT below the cross-over temperature T*. The fundamental frequency v(o) of the Ti4+-oscillator is characteristic of the materials, that is, the narrower the potential is, the higher the v(o) is. Therefore, the structural deformations through the tilts or shrinks of the [TiO6]-octahedra cause to the high-temperature quantum paraelectricity in the perovskite titanates via increase in v(o). T* and T-a, the arrival temperature at the quantum paraelectric state. (C) 1998 Elsevier Science B.V. All rights reserved.