Finite-Temperature Properties ofPb(Zr1−xTix)

Abstract

A first-principles-derived approach is developed to study finite-temperature properties of Pb(Zr1−xTix)O3 (PZT) solid solutions near the morphotropic phase boundary (MPB). Structural and piezoelectric predictions are in excellent agreement with experimental data and direct firstprinciples results. A low-temperature monoclinic phase is confirmed to exist, and is demonstrated to act as a bridge between the well-known tetragonal and rhombohedral phases delimiting the MPB. A successful explanation for the large piezoelectricity found in PZT ceramics is also provided. High piezoelectric response is experimentally found in ceramics of PZT around the MPB. The origins of this large piezoelectric response are unclear. On the one hand, semi-empirical simulations predict that the large experimental value of the d 33 piezoelectric coefficient results mainly from the large value of d 33 that a single-crystal PZT would exhibit [4]. On the other hand, recent firstprinciples calculations [5,6] have found that the d 33 coefficient of a tetragonal single crystal of Pb(Zr 0.5 Ti 0.5 )O 3 are estimated to be three times smaller than the experimental value obtained for ceramics at low temperature.Furthermore, recent synchrotron x-ray powder diffraction studies have revealed the existence of an unexpected low-temperature monoclinic phase of PZT at x=0.48 [7], which implies that the phase diagram of PZT is more complex than previously thought. This monoclinic phase may act as a second-order transitional bridge between the tetragonal phase, for which the electrical polarization P lies along the pseudo-cubic [001] direction, and the rhombohedral phase, for which P is along the pseudo-cubic [111] direction. If this is indeed the case, the polarization of the monoclinic phase continuously rotates as the composition x decreases in the MPB region [7]. Such a continuous rotation has yet to be observed.Obviously, accurate simulations are needed to understand the properties of perovskite alloys in general, and of PZT in particular. Since the beginning of the present decade, first-principles methods have emerged as a powerful tool for investigating properties of ferroelectric systems theoretically (see [5,6,8,9] and references therein). However, these methods are essentially restricted to the study of the zero-temperature properties of small cells, while accurate and interesting predictions of alloy properties would require calculations on much larger cells at finite temperature. Ideally one desires a computational scheme with the capability of predicting the properties of "real" perovskite alloy systems at finite temperature, with the accuracy of the first-principles methods.The purpose of this letter is to demonstrate that it is possible to develop such a scheme, and to apply it to study the finite-temperature behavior of PZT in the vicinity of the MPB. Remarkably, we find that the existence of an intermediate monoclinic phase emerges naturally from this approach. Moreover, the theory provides a novel and successful explanation for the large ...

Perturbed angular correlation study of 181Ta-doped PbTi1−xHfxO3 compounds

“…50 0 3 In Fig. 4 out previously this composition lies on the morphotropic phase transition, where tetragonal, monoclinic and rhombohedral structures can coexist at low temperatures [14,30]. Our results show that above T c , a high degree of disorder remains up to about 375 °C.…”

“…According to previous structural studies, in the morphotropic region (0.45 < x < 0.5), the sample contains variable amounts of coexisting tetragonal, monoclinic and rhombohedral phases [14,30]. The monoclinic intermediate phase would result from small Pb cation random shift from tetragonal ideal sites.…”

The missing boundary in the phase diagram of PbZr1−xTixO3

“…An intermediate monoclinic (M) phase (space group Cm), which is a subgroup of R3c, R3m and P4mm, was discovered by Noheda et al 8 and this finding has now been generally accepted. One explanation for the high piezoelectric response based on this model was then given by a first-principles calculation by Bellaiche et al 9 and experimentally studied by Guo et al 10 This is known as the polarization-rotation model, in which the displacements of the Pb atom are free to change orientation within a mirror plane in each unit cell, as allowed by the M-phase symmetry. This mechanism was also found in other Pb-based piezoelectrics, such as Pb(Zn 1/3 Nb 2/3 )O 3 -PbTiO 3 (ref.…”

Pseudolinearity in the inverse dielectric susceptibility of poled Pb(Mg1/3Nb2/3)O3–PbTiO3 crystals

“…First principles calculations have indicated that the transformation under electric field between FE r and FE t proceeds by a rotation of the polarization between ͗111͘ and ͗001͘. 8,9 Phenomenological studies have indicated that intermediate FE m states are only stabilized in the presence of a fourth order self-alloying ͑random field or rf͒ term. 10 Kleeman has previously applied rf theory to PMN-PT relaxor ferroelectrics in the poled condition below the freezing temperature.…”