THE CAUSE OF HIGH-TEMPERATURE QUANTUM PARAELECTRICITY IN SOME PEROVSKITE TITANATES

High-temperature quantum paraelectricity in perovskite titanate series (Ln(1/2)Na(1/2))TiO3 has been investigated in relation to their struc tural deformation for Ln(3+)-substitutions, Ln = La, Pr, Nd, Sm, Eu, G d, Tb, Dy, Ho, Er, Tm, Yb and Lu. Except for Ln = La and Ce, (Ln(1/2)N a(1/2))TiO3 has an orthorhombic unit cell with space group Pnma. The e ssential deformation parameter which lowers the highest dielectric con stant 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 decre ases sharply for more than half-filled Ln(3+)-range. Supposing a virtu al spontaneous polarization P-s with a virtual ferroelectric transitio n temperature T-o, and a zero-point vibrational energy hvo/2 of Ti4+-o scillators in [TiO6]-octahedra, a condition for the appearance of quan tum paraelectricity in perovskite titanates is given by T-o < T simil ar 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 determine s their zero-point energy hv(o)/2, which is considered as the quantum fluctuation energy, replaces the thermal fluctuation energy kT below t he cross-over temperature T. The fundamental frequency v(o) of the Ti 4+-oscillator is characteristic of the materials, that is, the narrowe r the potential is, the higher the v(o) is. Therefore, the structural deformations through the tilts or shrinks of the [TiO6]-octahedra caus e to the high-temperature quantum paraelectricity in the perovskite ti tanates via increase in v(o). T and T-a, the arrival temperature at t he quantum paraelectric state. (C) 1998 Elsevier Science B.V. All righ ts reserved.