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The traditional derivation of the elastic anomalies associated with ferroelectric (FE) phase transitions in the framework of the Landau theory is combined with the piezoelectric constitutive relations instead of being explicitly carried out with a definite expression of the FE part of the free energy. In this manner it is shown that the softening within the FE phase is of electrostrictive and hence piezoelectric origin. Such a piezoelectric softening may be canceled by the better known piezoelectric stiffening, when the piezoelectric charges formed during the vibration are accompanied by the depolarization field, as for example in Brillouin scattering experiments. As experimental validation, we present new measurements on Zr-rich PZT, where the FE phase transforms into antiferroelectric on cooling or doping with La, and a comparison of existing measurements made on FE PZT with low frequency and Brillouin scattering experiments.

The antipolar and antiferrodistortive (AFD) components of the antiferroelectric (AFE) transition in PbZr1-xTixO3 (x=0.054) can occur separately and with different kinetics, depending on the sample history, and are accompanied by elastic softening and stiffening, respectively. Together with the softening that accompanies octahedral tilting in the fraction of phase that is not yet transformed into AFE, they give rise to a variety of shapes of the curves of the elastic compliance versus temperature. All such anomalies found in samples with x=0.046 and 0.054, in addition to those already studied at x=0.050, can be fitted consistently with a phenomenological model based on the simple hypothesis that each of the polar and AFD transitions produces a step in the elastic modulus, whose position in temperature and width reflect the progress of each transition. The slowing of the kinetics of the transformations is correlated with the formation of defect structures during aging in the ferroelectric or AFE state, which are also responsible for a progressive softening of the lattice with time and thermal cycling, until annealing at high temperature recovers the initial conditions.

The results are presented of anelastic and dielectric spectroscopy measurements on large grain ceramic PZT with compositions near the two morphotropic phase boundaries (MPBs) that the ferroelectric (FE) rhombohedral phase has with the Zr-rich antiferroelectric and Ti-rich FE tetragonal phases. These results are discussed together with similar data from previous series of samples, and reveal new features of the phase diagram of PZT, mainly connected with octahedral tilting and its coupling with the polar modes. Additional evidence is provided of what we interpret as the onset of the tilt instability, when is initially frustrated by lattice disorder, and the long range order is achieved at lower temperature. Its temperature T_IT(x) prosecutes the long range tilt instability line T_T(x) up to T_C, when T_T. It is proposed that the difficulty of seeing the expected 1/2<111> modulations in diffraction experiments is due to the large correlation volume associated with that type of tilt fluctuations combined with strong lattice disorder. It is shown that the lines of the tilt instabilities tend to be attracted and merge with those of polar instabilities. Not only T_IT bends toward T_C and then merges with it, but in our series of samples the temperature T_MPB of the dielectric and anelastic maxima at the rhombohedral/tetragonal MPB does not cross T_T, but deviates remaining parallel or possibly merging with T_T. These features, together with a similar one in NBT-BT, are discussed in terms of cooperative coupling between tilt and FE instabilities, which may trigger a common phase transition. An analogy is found with recent simulations of the tilt and FE transitions in multiferroic BiFeO3. An abrupt change is found in the shape of the anelastic anomaly at T_T when x passes from 0.465 to 0.48, possibly indicative of a rhombohedral/monoclinic boundary., Comment: 15 pages, 11 figures

Anelastic and dielectric spectroscopy measurements on PZT close to the morphotropic (MPB) and antiferroelectric boundaries provide new insight in some controversial aspects of its phase diagram. No evidence is found of a border separating monoclinic (M) from rhombohedral (R) phases, in agreement with recent structural studies supporting a coexistence of the two phases over a broad composition range x < 0.5, with the fraction of M increasing toward the MPB. It is also discussed why the observed maximum of elastic compliance appears to be due to a rotational instability of the polarisation and therefore cannot be explained by extrinsic softening from finely twinned R phase alone, but indicates the presence also of M phase, not necessarily homogeneous. A new diffuse transition is found within the ferroelectric phase near x ~ 0.1, at a temperature T_IT higher than the well established boundary T_T to the phase with tilted octahedra. It is proposed that around T_IT the octahedra start rotating in a disordered manner and finally become ordered below T_T. In this interpretation, the onset temperature for octahedral tilting monotonically increases up to the antiferroelectric transition of PbZrO3, and the depression of T_T(x) below x = 0.18 would be a consequence of the partial relieve of the mismatch between the cation radii with the initial stage of tilting below T_IT., Comment: submitted to J. Phys.: Condens. Matter

The complex elastic compliance and dielectric susceptibility of (Na_{0.5}Bi_{0.5})_{1-x}Ba_{x}TiO_{3} (NBT-BT) have been measured in the composition range between pure NBT and the morphotropic phase boundary included, 0 <= x <= 0.08. The compliance of NBT presents sharp peaks at the rhombohedral/tetragonal and tetragonal/cubic transitions, allowing the determination of the tetragonal region of the phase diagram, up to now impossible due to the strong lattice disorder and small distortions and polarizations involved. In spite of ample evidence of disorder and structural heterogeneity, the R-T transition remains sharp up to x = 0.06, whereas the T-C transition merges into the diffuse and relaxor-like transition associated with broad maxima of the dielectric and elastic susceptibilities. An attempt is made at relating the different features in the anelastic and dielectric curves to different modes of octahedral rotations and polar cation shifts. The possibility is also considered that the cation displacements locally have monoclinic symmetry, as for PZT near the morphotropic phase boundary., Comment: 11 pages, 9 figures, submitted to Phys. Rev. B

We present anelastic and dielectric spectroscopy measurements of PbZr(1-x)Ti(x)O(3) with 0.455 < x < 0.53, which provide new information on the low temperature phase transitions. The tetragonal-to-monoclinic transformation is first-order for x < 0.48 and causes a softening of the polycrystal Young's modulus whose amplitude may exceed the one at the cubic-to-tetragonal transformation; this is explainable in terms of linear coupling between shear strain components and tilting angle of polarization in the monoclinic phase. The transition involving rotations of the octahedra below 200 K is visible both in the dielectric and anelastic losses, and it extends within the tetragonal phase, as predicted by recent first-principle calculations., Comment: 4 pages, 4 figures

It has been recently shown that the memory of multiple aging stages, a phenomenon considered possible only below the glass transition of some glassy systems, appears also above that temperature range in the relaxor ferroelectric (Pb/La)(Zr/Ti)O_3 (PLZT). Doubts exist whether memory at such high temperature is intrinsic of the glassy relaxor state or is rather due to migration of mobile defects. It is shown that the memory in the electric susceptibility and elastic compliance of PLZT 9/65/35 is not enhanced but depressed by mobile defects like O vacancies, H defects and mobile charges resulting from their ionization. In addition, memory is drastically reduced at La contents slightly below the relaxor region of the phase diagram, unless aging is protracted for long times (months at room temperature). This is considered as evidence that in the non relaxor case memory is indeed due to slow migration of defects, while in the La rich case it is intrinsic of the relaxor state, even above the temperature of the susceptibility maximum., Comment: 9 pages, 8 figures, submitted to Phys. Rev. B

Dielectric, anelastic and ^139La NMR relaxation measurements have been made on the relaxor ferroelectric Pb(1-3x/2)La(x)Zr(0.2)Ti(0.8)O(3) (PLZT) with x = 0.22. The dielectric susceptibility exihibits the frequency dispersive maximum due to the freezing of the polar degrees of freedom around T ~250 K. The anelastic and especially NMR relaxation, besides this maximum, indicate an intense and broad component at lower temperatures, attributed to rotational modes of the O octahedra, weakly coupled to the polar modes. It is discussed why such short range rotational instabilities, known to occur in the Zr-rich rhombohedral region of the PLZT phase diagram, might appear also in the Ti-rich region., Comment: submitted to Phys. Rev. B, 9 pages, 10 figures

The dynamic dielectric susceptibility and elastic compliance of the relaxor ferroelectric PLZT 9/65/35 have been measured under different cooling and heating protocols, in order to study aging and memory. The memory of multiple aging stages has been found (several dips in the susceptibility curves on heating), as in spin glass systems below the glass transition. Remarkably, in PLZT the memory is retained also above the freezing temperature deduced from the dynamic susceptibilities. The results are discussed in the light of the existing models of aging and memory in spin and dipolar glasses., Comment: Improved version accepted by Phys. Rev. Lett