Internal friction and dielectric loss related to domain walls

Ultrahigh Piezoelectric Performance through Synergistic Compositional and Microstructural Engineering

Piezoelectric materials enable the conversion of mechanical energy into electrical energy and vice-versa. Ultrahigh piezoelectricity has been only observed in single crystals. Realization of piezoelectric ceramics with longitudinal piezoelectric constant (d₃₃ ) close to 2000 pC N^-1 , which combines single crystal-like high properties and ceramic-like cost effectiveness, large-scale manufacturing, and machinability will be a milestone in advancement of piezoelectric ceramic materials. Here, guided by phenomenological models and phase-field simulations that provide conditions for flattening the energy landscape of polarization, a synergistic design strategy is demonstrated that exploits compositionally driven local structural heterogeneity and microstructural grain orientation/texturing to provide record piezoelectricity in ceramics. This strategy is demonstrated on [001]_PC -textured and Eu³⁺ -doped Pb(Mg_1/3 Nb_2/3 )O₃ -PbTiO₃ (PMN-PT) ceramics that exhibit the highest piezoelectric coefficient (small-signal d₃₃ of up to 1950 pC N^-1 and large-signal d₃₃ * of ≈2100 pm V^-1 ) among all the reported piezoelectric ceramics. Extensive characterization conducted using high-resolution microscopy and diffraction techniques in conjunction with the computational models reveals the underlying mechanisms governing the piezoelectric performance. Further, the impact of losses on the electromechanical coupling is identified, which plays major role in suppressing the percentage of piezoelectricity enhancement, and the fundamental understanding of loss in this study sheds light on further enhancement of piezoelectricity. These results on cost-effective and record performance piezoelectric ceramics will launch a new generation of piezoelectric applications.

Theory of relaxor-ferroelectricity

Relaxor-ferroelectrics are fascinating and useful materials, but the mechanism of relaxor-ferroelectricity has been puzzling the scientific community for more than 65 years. Here, a theory of relaxor-ferroelectricity is presented based on 3-dimensional-extended-random-site-Ising-model along with Glauber-dynamics of pseudospins. We propose a new mean-field of pseudospin-strings to solve this kinetic model. The theoretical results show that, with decreasing pseudospin concentration, there are evolutions from normal-ferroelectrics to relaxor-ferroelectrics to paraelectrics, especially indicating by the crossovers from, (a) the sharp to diffuse change at the phase-transition temperature to disappearance in the whole temperature range of order-parameter, and (b) the power-law to Vogel-Fulcher-law to Arrhenius-relation of the average relaxation time. Particularly, the calculated local-order-parameter of the relaxor-ferroelectrics gives the polar-nano-regions appearing far above the diffuse-phase-transition and shows the quasi-fractal characteristic near and below the transition temperature. We also provide a new mechanism of Burns-transformation which stems from not only the polar-nano-regions but also the correlation-function between pseudospins, and put forward a definition of the canonical relaxor-ferroelectrics. The theory accounts for the main facts of relaxor-ferroelectricity, and in addition gives a good quantitative agreement with the experimental results of the order-parameter, specific-heat, high-frequency permittivity, and Burns-transformation of lead magnesium niobate, the canonical relaxor-ferroelectric.

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.

Losses in Ferroelectric Materials

Ferroelectric materials are the best dielectric and piezoelectric materials known today. Since the discovery of barium titanate in the 1940s, lead zirconate titanate ceramics in the 1950s and relaxor-PT single crystals (such as lead magnesium niobate-lead titanate and lead zinc niobate-lead titanate) in the 1980s and 1990s, perovskite ferroelectric materials have been the dominating piezoelectric materials for electromechanical devices, and are widely used in sensors, actuators and ultrasonic transducers. Energy losses (or energy dissipation) in ferroelectrics are one of the most critical issues for high power devices, such as therapeutic ultrasonic transducers, large displacement actuators, SONAR projectors, and high frequency medical imaging transducers. The losses of ferroelectric materials have three distinct types, i.e., elastic, piezoelectric and dielectric losses. People have been investigating the mechanisms of these losses and are trying hard to control and minimize them so as to reduce performance degradation in electromechanical devices. There are impressive progresses made in the past several decades on this topic, but some confusions still exist. Therefore, a systematic review to define related concepts and clear up confusions is urgently in need. With this objective in mind, we provide here a comprehensive review on the energy losses in ferroelectrics, including related mechanisms, characterization techniques and collections of published data on many ferroelectric materials to provide a useful resource for interested scientists and engineers to design electromechanical devices and to gain a global perspective on the complex physical phenomena involved. More importantly, based on the analysis of available information, we proposed a general theoretical model to describe the inherent relationships among elastic, dielectric, piezoelectric and mechanical losses. For multi-domain ferroelectric single crystals and ceramics, intrinsic and extrinsic energy loss mechanisms are discussed in terms of compositions, crystal structures, temperature, domain configurations, domain sizes and grain boundaries. The intrinsic and extrinsic contributions to the total energy dissipation are quantified. In domain engineered ferroelectric single crystals and ceramics, polarization rotations, domain wall motions and mechanical wave scatterings at grain boundaries are believed to control the mechanical quality factors of piezoelectric resonators. We show that a thorough understanding on the kinetic processes is critical in analyzing energy loss behavior and other time-dependent properties in ferroelectric materials. At the end of the review, existing challenges in the study and control of losses in ferroelectric materials are analyzed, and future perspective in resolving these issues is discussed.

Elastic and anelastic anomalies associated with the antiferromagnetic ordering transition in wüstite, FexO

The elastic and anelastic properties of three different samples of Fe(x)O have been determined in the frequency range 0.1-2 MHz by resonant ultrasound spectroscopy and in the range 0.1-50 Hz by dynamic mechanical analysis in order to characterize ferroelastic aspects of the magnetic ordering transition at T(N) ~ 195 K. No evidence was found of separate structural and magnetic transitions but softening of the shear modulus was consistent with the involvement of bilinear coupling, λe(4)q, between a symmetry-breaking strain, e(4), and a structural order parameter, q. Unlike a purely ferroelastic transition, however, C(44) does not go to zero at the critical temperature, T*(c), due to the intervention of the magnetic ordering at a higher temperature. The overall pattern of behaviour is nevertheless consistent with what would be expected for a system with separate structural and magnetic instabilities, linear-quadratic coupling between the structural (q) and magnetic (m) driving order parameters, λqm(2), and T(N) > T*(c). Comparison with data from the literature appears to confirm the same pattern in MnO and NiO, with a smaller difference between T(N) and T*(c) in the former and a larger difference in the latter. Strong attenuation of acoustic resonances at high frequencies and a familiar pattern of attenuation at low frequencies suggest that twin walls in the rhombohedral phase have typical ferroelastic properties. Acoustic dissipation in the stability field of the cubic phase is tentatively attributed to anelastic relaxations of the defect ordered structure of non-stoichiometric wüstite or of the interface between local regions of wüstite and magnetite, with a rate controlling step determined by the diffusion of iron.

Anelastic loss behaviour of mobile microstructures in SrZr(1-x)Ti(x)O3 perovskites

Anelastic loss mechanisms associated with phase transitions in SrZr(1-x)Ti(x)O(3) perovskites (x = 0.375, 0.450, 0.550, 0.775) have been investigated by dynamic mechanical analysis between 128 and 723 K at frequencies of 0.1-50 Hz. Distinctive patterns of changes in the elastic moduli due to octahedral tilting transitions correlate closely with data for the shear modulus obtained previously by resonant ultrasound spectroscopy at high frequencies (∼0.5 MHz). The I4/mcm <--> Imma transition is first order and has a characteristic minimum in the shear modulus and Young's modulus. For x = 0.450 and 0.550, a dissipation peak occurs at the transition temperature, the maximum of which varies with frequency according to a power law relationship of the form tanδ = Af(n), with n≈ - 0.3. Debye-like dissipation peaks in the stability field of the Imma structure at x = 0.375 have a frequency and temperature dependence consistent with twin wall pinning by defects with an activation energy ∼ 184 kJ mol(-1). These results indicate that there is diversity of pinning and relaxation processes for transformation twin walls and interfaces in different perovskites with I4/mcm, Imma and Pnma structures.

Elastic relaxations associated with the Pm3m-R3c transition in LaAlO(3): III. Superattenuation of acoustic resonances

Resonant ultrasound spectroscopy has been used to characterize elastic softening and anelastic dissipation processes associated with the Pm3m <--> R3c transition in single crystal and ceramic samples of LaAlO(3). Softening of the cubic structure ahead of the transition point is not accompanied by an increase in dissipation but follows different temperature dependences for the bulk modulus, (1/3)(C(11) + C(12)), and the shear components, (1/2)(C(11) + C(12)) and C(44), as if the tilting instability contains two slightly different critical temperatures. The transition itself is marked by the complete disappearance of resonance peaks (superattenuation), which then reappear below ∼700 K in spectra from single crystals. Comparisons with low frequency, high stress data from the literature indicate that the dissipation is not due to macroscopic displacement of needle twins. An alternative mechanism, local bowing of twin walls under low dynamic stress, is postulated. Pinning of the walls with respect to this displacement process occurs below ∼350 K. Anelasticity maps, analogous to plastic deformation mechanism maps, are proposed to display dispersion relations and temperature/frequency/stress fields for different twin wall related dissipation mechanisms. These allow comparisons to be made of anelastic loss mechanisms under mechanical stress with elastic behaviour observed by means of Brillouin scattering at high frequencies which might also be related to microstructure.

Experimental study of acoustical memory in lithium niobate

In this paper, the acoustical memory effect is studied from 2.5 to 10 MHz. This acoustical memory effect has been observed in both columnar and cubic samples. The observed phenomenon of amplitude hysteresis of the acoustical memory signal suggests nonclassical nonlinear properties, caused by the structural inhomogeneity and inevitable flaws in LiNbO3 . Experimental results also show that the amplitude of the acoustical memory signal is enhanced by increasing the temperature at these frequencies. The shape of the memory signal changes greatly if the driving voltage is sufficiently high or each burst contains enough cycles; second and even third parts of the acoustical memory signals may appear. Amplitude hysteresis of the fundamental and second harmonic of the direct wave can also be found. Some experimental results are qualitatively explained in this paper.