Low-temperature phase transformations of PbZr(1-x)Ti(x)O(3) in the morphotropic phase-boundary region

Damping Constant (Linewidth) and the Relaxation Time of the Brillouin LA Mode for the Ferroelectric-Paraelectric Transition in PbZr1-xTixO3

The damping constant (linewidth) of the longitudinal acoustic (LA) mode is calculated as a function of temperature using the observed Brillouin frequencies of this mode from the literature for the ferroelectric-paraelectric transition ( T_C = 657 K) in PbZr_1-xTi_xO₃ ( x = 0.45 ). For this calculation of the damping constant, the pseudospin-phonon coupled model and the energy fluctuation model are used by fitting to the observed data for the Brillouin frequencies of the LA mode in the ferroelectric ( ) and paraelectric ( T > T_C) phases of this compound ( x = 0.45 ). Values of the activation energy are deduced for both ferroelectric and paraelectric phases. The relaxation time is also obtained by means of fitting to the observed data from the literature for the inverse relaxation time at various temperatures in the paraelectric phase of PbZr_1-xTi_xO₃. The temperature dependences of the damping constant and of the relaxation time with the values of the activation energy that we have calculated indicate that the pseudospin-phonon coupled model and the energy fluctuation model are capable of describing the ferroelectric-paraelectric transition ( T_C = 657 K) in PbZr_1-xTi_xO₃ ( x = 0.45 ) adequately.

Elastic Properties and Enhanced Piezoelectric Response at Morphotropic Phase Boundaries

The search for improved piezoelectric materials is based on the morphotropic phase boundaries (MPB) between ferroelectric phases with different crystal symmetry and available directions for the spontaneous polarization. Such regions of the composition x - T phase diagrams provide the conditions for minimal anisotropy with respect to the direction of the polarization, so that the polarization can easily rotate maintaining a substantial magnitude, while the near verticality of the TMPB(x) boundary extends the temperature range of the resulting enhanced piezoelectricity. Another consequence of the quasi-isotropy of the free energy is a reduction of the domain walls energies, with consequent formation of domain structures down to nanoscale. Disentangling the extrinsic and intrinsic contributions to the piezoelectricity in such conditions requires a high level of sophistication from the techniques and analyses for studying the structural, ferroelectric and dielectric properties. The elastic characterization is extremely useful in clarifying the phenomenology and mechanisms related to ferroelectric MPBs. The relationship between dielectric, elastic and piezoelectric responses is introduced in terms of relaxation of defects with electric dipole and elastic quadrupole, and extended to the response near phase transitions in the framework of the Landau theory. An account is provided of the anelastic experiments, from torsional pendulum to Brillouin scattering, that provided new important information on ferroelectric MPBs, including PZT, PMN-PT, NBT-BT, BCTZ, and KNN-based systems.

Multiple soft-mode vibrations of lead zirconate

Polarized Raman, IR, and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals have yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibrations of Pb ions and librations of oxygen octahedra. Their relation to phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. Analysis of the results yields insight into the phase transition mechanism, involving a soft ferroelectric branch coupled by a trilinear term to another two oxygen octahedra tilt modes.

Octahedral tilting, monoclinic phase and the phase diagram of PZT

Anelastic and dielectric spectroscopy measurements on PbZr(1-x)Ti(x)O(3) (PZT) close to the morphotropic (MPB) and antiferroelectric boundaries provide new insight into 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 polarization linearly coupled to shear strain. Therefore it 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 PbZrO(3), and the depression of T(T)(x) below x=0.18 would be a consequence of the partial relief of the mismatch between the average cation radii with the initial stage of tilting below T(IT).