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Piezoelectric solids

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Shape dependent damping in piezoelectric solids, Rod Lakes, IEEE Trans. Sonics, Ultrasonics, SU27, 208-213, (1980)
Abstract
    The piezoelectric contribution to the mechanical loss tangent of a piezoelectric solid is derived from its complex piezoelectric and dielectric coefficients. This loss depends on specimen geometry as a result of differences in effects related to the electrical boundary conditions. Including a positive out-of-phase piezoelectric modulus results in reduced values of the predicted loss, which constitutes an improvement over earlier theories which predict losses exceeding measured losses by a factor greater than two.
Summary
    Piezoelectricity is a coupled field effect as is thermoelasticity. In piezoelectric materials stress and strain are coupled to electrical field and polarization. Not all materials are piezoelectric; only those materials lacking a center of symmetry on the atomic scale can be piezoelectric. Examples of piezoelectric materials include quartz, Rochelle salt, and lead titanate zirconate ceramics.
    Piezoelectric relaxation has been observed in many materials, including ceramics, composites, and bone. Such relaxation can be represented with complex piezoelectric coefficients or by a piezoelectric loss tangent. Mechanical relaxation also occurs in piezoelectric materials and is important in applications: large damping is considered desirable in materials used to generate short acoustic pulses for flaw detection ; small damping (high mechanical Q) is desirable in stable resonators and high power transducers. Piezoelectric reactions influence the apparent stiffness of a solid, under conditions in which neither electric field E nor electric displacement D is constant. One can consider a piezoelectric contribution to mechanical relaxation: experimental evidence for such a contribution in quartz under quasistatic loading has appeared at least as early as 1915. A connection between dielectric loss and mechanical loss in piezoelectric solids is to be expected on heuristic grounds in that dielectric relaxation entails dissipation of electrical energy; if this energy has come from the piezoelectric conversion of mechanical energy, then mechanical relaxation or anelasticity must also occur.
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Lakes, R. S., "The role of gradient effects in the piezoelectricity of bone", IEEE Trans. Biomed. Eng., BME-27 (5), 282-283, (1980).
    Stress gradient effects in piezoelectricity are obtained from general nonlocality considerations. A nonlocal continuum representation of bone is appropriate in view of bone's structure. More recently, gradient effects in piezoelectricity have been called "flexoelectricity" of "flexoelectric" materials. Get pdf

Lee, T. and Lakes, R. S., "Damping properties of lead metaniobate", IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 48, 48-52, Jan. (2001).
    Mechanical damping, tan delta, of lead metaniobate was determined experimentally over a wide range of frequency. Damping at audio and sub-audio frequency was lower than at ultrasonic frequency. The experiments were conducted in torsion and bending using an instrument capable of determining viscoelastic properties over more than ten decades of time and frequency. Mechanical damping was higher in bending than torsion at all frequencies. Damping observed in this study at the highest frequencies approach the high value 0.09 quoted by Berlincourt et al. for ultrasonic frequency. Get pdf

Wang, Y. C. and Lakes, R. S., "Extreme thermal expansion, piezoelectricity, and other coupled field properties in composites with a negative stiffness phase", Journal of Applied Physics, 90, 6458-6465, Dec. (2001).
   Particulate composites with negative stiffness inclusions in a viscoelastic matrix are shown to have higher thermal expansion than that of either constituent and exceeding conventional bounds. It is also shown theoretically that other extreme linear coupled field properties including piezoelectricity and pyroelectricity occur in layer- and fiber-type piezoelectric composites, due to negative inclusion stiffness effects. The causal mechanism is a greater deformation in and near the inclusions than the composite as a whole. A block of negative stiffness material is unstable, but negative stiffness inclusions in a composite can be stabilized by the surrounding matrix and can give rise to extreme viscoelastic effects in lumped and distributed composites. In contrast to prior proposed composites with unbounded thermal expansion, neither the assumptions of void spaces nor slip interfaces are required in the present analysis. Get pdf.

Dong, L., Stone, D. S., and Lakes, R. S., "Enhanced dielectric and piezoelectric properties in xBaZrO3- (1 - x)BaTiO3 ceramics", J. Appl. Physics, 111, 084107 April (2012).     xBaZrO3-(1-x)BaTiO3 solid solutions (x = 0, 0.04, 0.06, 0.08, 0.12, and 0.18) synthesized via conventional solid state reaction method exhibit piezoelectric coefficients comparable to those of hard PZT-8, PZT-4, and even soft PZT-5A. Doping also improves the poling efficiency of xBaZrO3-(1-x) BaTiO3 ceramics. Study of temperature dependence of the dielectric and piezoelectric properties reveal the following. Doping lowered the Curie point but raised the temperatures of the other two transformations. The diffused phase transition behavior has been enhanced with increasing content of BaZrO3, but x less than 0.18 is not enough to show a relaxor behavior. Piezoelectric responses show peaks at transformation temperatures and exhibit the best stability in the orthorhombic phase. Significant improvement in room temperature piezoelectric and electromechanical responses (d33 = 420 pC/N, d31 = 138pC/N, and kp = 49 percent) comparable to PZT-5 A is achieved at a composition of x = 0.06 (1400C 100h sintered), which brings the rhombohedral-orthorhombic transition to the ambient temperature. Enhanced piezoelectric properties are mainly attributed to a series of microscopic phase transformations due to the presence of internal structural gradient. Get pdf

Lakes, R. S., "Giant enhancement in effective piezoelectric sensitivity by pyroelectric coupling", EPL (Europhysics Letters), 98, 47001 May (2012).     We report stable two layer composites that exhibit large enhancement of effective piezoelectric sensitivity to more than 20,000 pC/N in the presence of a thermal gradient. They are based on coupled fields in the non-equilibrium presence of energy flux that is modulated by force. Thermal flux is modulated by a granular contact layer so that electric polarization of pyroelectric origin contributes to stress generated electric polarization. Effective piezoelectric sensitivity is enhanced by at least two orders of magnitude and is higher than that of known commercial and research materials. The result illustrates the potential of relaxing the usual assumption of equilibrium in the presence of coupled field to attain extremely high effective properties. Get preprint pdf

Lakes, R. S., "Piezoelectric composite lattices with high sensitivity", Philosophical Magazine Letters 94, (1), 37-44 (2014).     Lattice structures are presented with a piezoelectric sensitivity, d, much larger in magnitude than that of material comprising the lattice ribs. Large sensitivity is achieved by using piezoelectric bimorph elements as ribs; these bend in response to electric input, giving rise to a much larger displacement than for axial elements. Complex electrical connectivity is helpful but not necessary; surface contact can be sufficient. Lattices are amenable to piezoelectric vibration damping. Piezoelectric sensitivity can be arbitrarily large and is unbounded. Formal journal formatted reprints are available; if you want one, please request it. Informal pdf

Rodriguez, B., Kalathur, H. and Lakes, R. S., A sensitive piezoelectric composite lattice: experiment, Physica Status Solidi, 251(2) 349-353 (2014).     Lattice structures based on bimorph rib elements are fabricated and studied experimentally. The effective piezoelectric sensitivity d is observed to be much larger, by a factor of at least 10,000, in magnitude than that of material comprising the lattice ribs. Bending of the ribs in response to input voltage is responsible for the large sensitivity. Formal journal formatted reprints are available; if you want one, please request it. get pdf

Lakes, R. S., Third-rank piezoelectricity in isotropic chiral solids, Appl. Phys. Lett., 106, 212905, May (2015).     The highest symmetry in which piezoelectricity was thought to occur is cubic. Here, it is shown that third rank piezoelectricity can occur in isotropic chiral solids. Polarization is coupled via an isotropic third rank tensor to the antisymmetric part of the stress. Asymmetric stress can occur if balanced by moments distributed over area or volume. Such moments occur in heterogeneous solids, in which there exists a characteristic length associated with the microstructure: the Cosserat or micropolar solids. Effects associated with nonzero structure size are predicted, including radial polarization in response to torsion. These effects do not occur in gradient type flexoelectric materials; they are governed by a different tensorial rank and symmetry. DOI: 10.1063/1.4921846 journal link       Get preprint pdf

Faust, D. and Lakes, R. S., "Temperature and Substrate Dependence of Piezoelectric Sensitivity for PVDF films", Ferroelectrics, 481(1), 1-9, Sept. (2015).     The piezoelectric sensitivity, via both the direct and converse effects, for commercial polyvinylidene fluoride (PVDF) films is measured as a function of temperature and frequency, for two substrates, nylon and aluminum. The average effective sensitivity for the PVDF on nylon was 29 pm/V for both direct and converse effect, independent of frequency over 0.5 to 200 Hz. Direct effect sensitivity on aluminum substrate was about a factor of five greater. Analysis of effects of substrate's thermal and elastic constraint disclosed insufficient effect to account for the observed increase of sensitivity. Flexoelectric effects were considered as the cause. The direct and converse sensitivity increased at approximately 2% per degree Celsius over the frequency range 0.5 to 200 Hz
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Faust, D. and Lakes, R. S., "Reciprocity failure in piezoelectric polymer composite", Physica Scripta, 90 085807 (2015).     Reciprocity principles, which entail equivalent outcome on exchange of cause and effect, are widely used and accepted. We present a piezoelectric composite system designed so that reciprocity does not hold; sensitivity is substantially enhanced. Reciprocity failure is observed in which the piezoelectric direct effect (stress causes polarization) sensitivity d is unequal to the converse effect (electric field causes deformation) sensitivity d. The piezoelectric polymer PVDF under isothermal conditions on a polymer substrate obeys reciprocity. Reciprocity failure occurs when a bumpy contact condition causes stress gradients. Reciprocity failure with strong frequency dependence occurs in the presence of thermal flux that is modulated by force: a non-equilibrium condition. Non-reciprocal effects give rise to a maximum enhancement of a factor of five in sensitivity.
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Kalathur, H. and Lakes, R. S., "Enhancement in piezoelectric sensitivity via negative structural stiffness" Journal of Intelligent Material Systems and Structures, 27(18) 2568-2573 (2016).     Effective piezoelectric sensitivity of bimorph strip actuators was enhanced by negative structural stiffness. Negative stiffness was achieved in brass strips post-buckled in compression to an 'S' shape; the brass strip was placed in series with the bimorph. The negative stiffness was tuned by adjusting the brass strip length. The effective piezoelectric sensitivity in units of displacement per volt input, increased as the inverse of the overall stiffness of the series element. The maximum observed enhancement in effective piezoelectric sensitivity was at least a factor of six, at 1 Hz in comparison to the value when no negative stiffness was used. This corresponds to a maximum effective sensitivity of about 36 microns/V in comparison to the baseline effective sensitivity of about 6.1 microns/V, at 1 Hz. The value is several orders of magnitude (almost 40,000 times) higher than the typical value of sensitivity for the material comprising the individual bimorph strip actuator.
DOI: 10.1177/1045389X15624802 journal link preprint pdf

Lakes, R. S., "Static and dynamic effects of chirality in dielectric media", Modern Physics Letters B, 30 (24) 1650319 (9 pages) (2016).
Chiral dielectrics are considered from the perspective of continuum representations of spatial heterogeneity. Static effects in isotropic chiral dielectrics are predicted, provided the electric field has nonzero third spatial derivatives. The effects are compared with static chiral phenomena in Cosserat elastic materials which obey generalized continuum constitutive equations. Dynamic monopole-like magnetic induction is predicted in chiral dielectric media. preprint pdf

   Current research in piezoelectricity involves application of concepts of negative stiffness and structural hierarchy to attain enhanced effective piezoelectric properties.