Evidence for a trieritical point coinciding with the triple point in (Pb_(0.94)Sr_(0.06))(Zr_xTi_(1-x))O_3: A combined synchrotron x-ray diffraction, dielectric, and Landau theory study

摘要

We present here results of high-resolution synchrotron x-ray diffraction (SXRD) and dielectric studies in conjunction with Landau theory considerations on (Pb_(0.94)Sr_(0.06))(Zr_xTi_(1-x))O_3 compositions in the vicinity of the morphotropic phase boundary (MPB) to find evidence for the flattening of the free-energy surface at the MPB proposed in recent ab initio studies on strongly piezoelectric ceramics. SXRD results reveal that the tetragonal and pseudorhombohedral monoclinic compositions with x =0.515 and 0.550 transform directly into the cubic paraelectric phase, whereas for 0.520 ≦ x ≦ 0.545, the pseudotetragonal and pseudorhombohedral monoclinic compositions transform first to the tetragonal phase and then to the cubic phase. Our results reveal the existence of a triple point at x ≌ 0.550. It is shown that the tetragonal-to-cubic transition, irrespective of the composition, up to x ≌ 0.545 is accompanied with a discontinuous change in the unit cell volume and thermal hysteresis, confirming the first-order nature of this transition. However, the pseudorhombohedral monoclinic composition for x = 0.550 transforms directly into the cubic phase in a second-order manner. Our experimental results thus reveal a crossover from a first-order to a second-order phase transition through a trieritical point around x = 0.550. Landau theory calculations also confirm gradual flattening of the free-energy surface on approaching the tricritical composition x = 0.550. We conclude that the triple point in the Pb(Zr_xTi_(1-x))O_3 phase diagram is a trieritical point.