Piezoelectricity

Piezoelectric balance presented byPierre CurietoLord Kelvin,Hunterian Museum,Glasgow

Piezoelectricity(/ˌpiːzoʊ-,ˌpiːtsoʊ-,paɪˌiːzoʊ-/,US:/piˌeɪzoʊ-,piˌeɪtsoʊ-/)is theelectric chargethat accumulates in certainsolidmaterials—such ascrystals,certainceramics,and biological matter such asbone,DNA,and variousproteins—in response to appliedmechanical stress.The wordpiezoelectricitymeanselectricityresulting frompressureandlatent heat.It is derived fromAncient Greekπιέζω(piézō)'to squeeze or press', andἤλεκτρον(ḗlektron)'amber' (an ancient source of static electricity).The German form of the word (Piezoelektricität) was coined in 1881 by the German physicistWilhelm Gottlieb Hankel;the English word was coined in 1883.

The piezoelectric effect results from the linearelectromechanicalinteraction between the mechanical and electrical states in crystalline materials with noinversion symmetry.The piezoelectric effect is areversible process:materials exhibiting the piezoelectric effectalso exhibit the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an appliedelectric field.For example,lead zirconate titanatecrystals will generate measurable piezoelectricity when their static structure isdeformedby about 0.1% of the original dimension. Conversely, those same crystals will change about 0.1% of their static dimension when an external electric field is applied. The inverse piezoelectric effect is used in the production ofultrasound waves.

French physicistsJacquesandPierre Curiediscovered piezoelectricity in 1880.The piezoelectric effect has been exploited in many useful applications, including the production and detection of sound, piezoelectricinkjet printing,generation of high voltage electricity, as aclock generatorin electronic devices, inmicrobalances,to drive anultrasonic nozzle,and in ultrafine focusing of optical assemblies. It forms the basis forscanning probe microscopesthat resolve images at the scale ofatoms.It is used in thepickupsof someelectronically amplified guitarsand astriggersin most modernelectronic drums.The piezoelectric effect also finds everyday uses, such as generating sparks to ignite gas cooking and heating devices, torches, andcigarette lighters.

History

Discovery and early research

Thepyroelectric effect,by which a material generates anelectric potentialin response to a temperature change, was studied byCarl LinnaeusandFranz Aepinusin the mid-18th century. Drawing on this knowledge, bothRené Just HaüyandAntoine César Becquerelposited a relationship betweenmechanical stressand electric charge; however, experiments by both proved inconclusive.

View of piezo crystal in the top of a Curie compensator in the Museum of Scotland.

The first demonstration of the direct piezoelectric effect was in 1880 by the brothersPierre CurieandJacques Curie.They combined their knowledge of pyroelectricity with their understanding of the underlying crystal structures that gave rise to pyroelectricity to predict crystal behavior, and demonstrated the effect using crystals oftourmaline,quartz,topaz,canesugar,andRochelle salt(sodium potassium tartrate tetrahydrate). Quartz andRochelle saltexhibited the most piezoelectricity.

A piezoelectric disk generates a voltage when deformed (change in shape is greatly exaggerated).

The Curies, however, did not predict the converse piezoelectric effect. The converse effect was mathematically deduced from fundamental thermodynamic principles byGabriel Lippmannin 1881.The Curies immediately confirmed the existence of the converse effect,and went on to obtain quantitative proof of the complete reversibility of electro-elasto-mechanical deformations in piezoelectric crystals.

For the next few decades, piezoelectricity remained something of a laboratory curiosity, though it was a vital tool in the discovery of polonium and radium by Pierre andMarie Curiein 1898. More work was done to explore and define the crystal structures that exhibited piezoelectricity. This culminated in 1910 with the publication ofWoldemar Voigt'sLehrbuch der Kristallphysik(Textbook on Crystal Physics),which described the 20 natural crystal classes capable of piezoelectricity, and rigorously defined the piezoelectric constants usingtensor analysis.

World War I and inter-war years

The first practical application for piezoelectric devices wassonar,first developed duringWorld War I.The superior performance of piezoelectric devices, operating at ultrasonic frequencies, superseded the earlierFessenden oscillator.InFrancein 1917,Paul Langevinand his coworkers developed anultrasonicsubmarinedetector.The detector consisted of atransducer,made of thin quartz crystals carefully glued between two steel plates, and ahydrophoneto detect the returnedecho.By emitting a high-frequency pulse from the transducer, and measuring the amount of time it takes to hear an echo from the sound waves bouncing off an object, one can calculate the distance to that object.

The use of piezoelectricity in sonar, and the success of that project, created intense development interest in piezoelectric devices. Over the next few decades, new piezoelectric materials and new applications for those materials were explored and developed.

Piezoelectric devices found homes in many fields. Ceramicphonographcartridges simplified player design, were cheap and accurate, and made record players cheaper to maintain and easier to build. The development of the ultrasonic transducer allowed for easy measurement of viscosity and elasticity in fluids and solids, resulting in huge advances in materials research. Ultrasonictime-domain reflectometers(which send an ultrasonic pulse through a material and measure reflections from discontinuities) could find flaws inside cast metal and stone objects, improving structural safety.

World War II and post-war

DuringWorld War II,independent research groups in theUnited States,USSR,andJapandiscovered a new class of synthetic materials, calledferroelectrics,which exhibited piezoelectric constants many times higher than natural materials. This led to intense research to developbarium titanateand later lead zirconate titanate materials with specific properties for particular applications.

One significant example of the use of piezoelectric crystals was developed byBell Telephone Laboratories.Following World War I, Frederick R. Lack, working in radio telephony in the engineering department, developed the "AT cut" crystal, a crystal that operated through a wide range of temperatures. Lack's crystal did not need the heavy accessories previous crystal used, facilitating its use on the aircraft. This development allowed Allied air forces to engage in coordinated mass attacks through the use of aviation radio.

Development of piezoelectric devices and materials in the United States was kept within the companies doing the development, mostly due to the wartime beginnings of the field, and in the interests of securing profitable patents. New materials were the first to be developed—quartz crystals were the first commercially exploited piezoelectric material, but scientists searched for higher-performance materials. Despite the advances in materials and the maturation of manufacturing processes, the United States market did not grow as quickly as Japan's did. Without many new applications, the growth of the United States' piezoelectric industry suffered.

In contrast, Japanese manufacturers shared their information, quickly overcoming technical and manufacturing challenges and creating new markets. In Japan, a temperature stable crystal cut was developed byIssac Koga.Japanese efforts in materials research created piezoceramic materials competitive to the United States materials but free of expensive patent restrictions. Major Japanese piezoelectric developments included new designs of piezoceramic filters for radios and televisions, piezo buzzers and audio transducers that can connect directly to electronic circuits, and thepiezoelectric igniter,which generates sparks for small engine ignition systems and gas-grill lighters, by compressing a ceramic disc. Ultrasonic transducers that transmit sound waves through air had existed for quite some time but first saw major commercial use in early television remote controls. These transducers now are mounted on severalcarmodels as anecholocationdevice, helping the driver determine the distance from the car to any objects that may be in its path.

Mechanism

Piezoelectric plate used to convertaudio signalto sound waves

The nature of the piezoelectric effect is closely related to the occurrence ofelectric dipole momentsin solids. The latter may either be induced forionsoncrystal latticesites with asymmetric charge surroundings (as inBaTiO₃andPZTs) or may directly be carried by molecular groups (as incane sugar). The dipole density orpolarization(dimensionality [C·m/m³] ) may easily be calculated forcrystalsby summing up the dipole moments per volume of the crystallographicunit cell.As every dipole is a vector, the dipole densityPis avector field.Dipoles near each other tend to be aligned in regions called Weiss domains. The domains are usually randomly oriented, but can be aligned using the process ofpoling(not the same asmagnetic poling), a process by which a strong electric field is applied across the material, usually at elevated temperatures. Not all piezoelectric materials can be poled.

Of decisive importance for the piezoelectric effect is the change of polarizationPwhen applying amechanical stress.This might either be caused by a reconfiguration of the dipole-inducing surrounding or by re-orientation of molecular dipole moments under the influence of the external stress. Piezoelectricity may then manifest in a variation of the polarization strength, its direction or both, with the details depending on: 1. the orientation ofPwithin the crystal; 2.crystal symmetry;and 3. the applied mechanical stress. The change inPappears as a variation of surfacecharge densityupon the crystal faces, i.e. as a variation of theelectric fieldextending between the faces caused by a change in dipole density in the bulk. For example, a 1 cm³cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500V.

Piezoelectric materials also show the opposite effect, called theconverse piezoelectric effect,where the application of an electrical field creates mechanical deformation in the crystal.

Mathematical description

Linear piezoelectricity is the combined effect of

• The linear electrical behavior of the material:

$\mathbf {D} ={\boldsymbol {\varepsilon }}\,\mathbf {E} \quad \implies$$\quad D_{i}=\sum _{j}\varepsilon _{ij}\,E_{j}\;$

whereDis the electric flux density(electric displacement),εis thepermittivity(free-body dielectric constant),Eis theelectric field strength,and$\nabla \cdot \mathbf {D} =0$,$\nabla \times \mathbf {E} =\mathbf {0}$.

• Hooke's lawfor linear elastic materials:

${\boldsymbol {S}}={\mathsf {s}}\,{\boldsymbol {T}}\quad \implies \quad S_{ij}=\sum _{k,\ell }s_{ijk\ell }\,T_{k\ell }\;$

whereSis the linearizedstrain,siscomplianceunder short-circuit conditions,Tisstress,and

$\nabla \cdot {\boldsymbol {T}}=\mathbf {0} \,\,,\,{\boldsymbol {S}}={\frac {\nabla \mathbf {u} +\mathbf {u} \nabla }{2}},$

whereuis thedisplacement vector.

These may be combined into so-calledcoupled equations,of which thestrain-charge formis:

${\begin{aligned}{\boldsymbol {S}}&={\mathsf {s}}\,{\boldsymbol {T}}+{\mathfrak {d}}^{t}\,\mathbf {E} \ &&\implies \quad S_{ij}=\sum _{k,\ell }s_{ijk\ell }\,T_{k\ell }+\sum _{k}d_{ijk}^{t}\,E_{k},\\[6pt]\mathbf {D} &={\mathfrak {d}}\,{\boldsymbol {T}}+{\boldsymbol {\varepsilon }}\,\mathbf {E} &&\implies \quad D_{i}=\sum _{j,k}d_{ijk}\,T_{jk}+\sum _{j}\varepsilon _{ij}\,E_{j},\end{aligned}}$

where${\mathfrak {d}}$is the piezoelectric tensor and the superscript t stands for its transpose. Due to the symmetry of${\mathfrak {d}}$,$d_{ijk}^{t}=d_{kji}=d_{kij}$.

In matrix form,

${\begin{aligned}\{S\}&=\left[s^{E}\right]\{T\}+[d^{\mathrm {t} }]\{E\},\\[6pt]\{D\}&=[d]\{T\}+\left[\varepsilon ^{T}\right]\{E\},\end{aligned}}$

where [d] is the matrix for the direct piezoelectric effect and [d^t] is the matrix for the converse piezoelectric effect. The superscriptEindicates a zero, or constant, electric field; the superscriptTindicates a zero, or constant, stress field; and the superscript t stands fortranspositionof amatrix.

Notice that the third order tensor${\mathfrak {d}}$maps vectors into symmetric matrices. There are no non-trivial rotation-invariant tensors that have this property, which is why there are no isotropic piezoelectric materials.

The strain-charge for a material of the4mm(C_4v)crystal class(such as a poled piezoelectric ceramic such as tetragonal PZT or BaTiO₃) as well as the6mmcrystal class may also be written as (ANSI IEEE 176):

${\begin{aligned}&{\begin{bmatrix}S_{1}\\S_{2}\\S_{3}\\S_{4}\\S_{5}\\S_{6}\end{bmatrix}}={\begin{bmatrix}s_{11}^{E}&s_{12}^{E}&s_{13}^{E}&0&0&0\\s_{21}^{E}&s_{22}^{E}&s_{23}^{E}&0&0&0\\s_{31}^{E}&s_{32}^{E}&s_{33}^{E}&0&0&0\\0&0&0&s_{44}^{E}&0&0\\0&0&0&0&s_{55}^{E}&0\\0&0&0&0&0&s_{66}^{E}=2\left(s_{11}^{E}-s_{12}^{E}\right)\end{bmatrix}}{\begin{bmatrix}T_{1}\\T_{2}\\T_{3}\\T_{4}\\T_{5}\\T_{6}\end{bmatrix}}+{\begin{bmatrix}0&0&d_{31}\\0&0&d_{32}\\0&0&d_{33}\\0&d_{24}&0\\d_{15}&0&0\\0&0&0\end{bmatrix}}{\begin{bmatrix}E_{1}\\E_{2}\\E_{3}\end{bmatrix}}\\[8pt]&{\begin{bmatrix}D_{1}\\D_{2}\\D_{3}\end{bmatrix}}={\begin{bmatrix}0&0&0&0&d_{15}&0\\0&0&0&d_{24}&0&0\\d_{31}&d_{32}&d_{33}&0&0&0\end{bmatrix}}{\begin{bmatrix}T_{1}\\T_{2}\\T_{3}\\T_{4}\\T_{5}\\T_{6}\end{bmatrix}}+{\begin{bmatrix}{\varepsilon }_{11}&0&0\\0&{\varepsilon }_{22}&0\\0&0&{\varepsilon }_{33}\end{bmatrix}}{\begin{bmatrix}E_{1}\\E_{2}\\E_{3}\end{bmatrix}}\end{aligned}}$

where the first equation represents the relationship for the converse piezoelectric effect and the latter for the direct piezoelectric effect.

Although the above equations are the most used form in literature, some comments about the notation are necessary. Generally,DandEarevectors,that is,Cartesian tensorsof rank 1; and permittivityεis a Cartesian tensor of rank 2. Strain and stress are, in principle, also rank-2tensors.But conventionally, because strain and stress are all symmetric tensors, the subscript of strain and stress can be relabeled in the following fashion: 11 → 1; 22 → 2; 33 → 3; 23 → 4; 13 → 5; 12 → 6. (Different conventions may be used by different authors in literature. For example, some use 12 → 4; 23 → 5; 31 → 6 instead.) That is whySandTappear to have the "vector form" of six components. Consequently,sappears to be a 6-by-6 matrix instead of a rank-3 tensor. Such a relabeled notation is often calledVoigt notation.Whether the shear strain componentsS₄,S₅,S₆are tensor components or engineering strains is another question. In the equation above, they must be engineering strains for the 6,6 coefficient of the compliance matrix to be written as shown, i.e., 2(s^E
₁₁−s^E
₁₂). Engineering shear strains are double the value of the corresponding tensor shear, such asS₆= 2S₁₂and so on. This also means thats₆₆=⁠1/G₁₂⁠,whereG₁₂is the shear modulus.

In total, there are four piezoelectric coefficients,d_ij,e_ij,g_ij,andh_ijdefined as follows:

${\begin{aligned}d_{ij}&={\phantom {+}}\left({\frac {\partial D_{i}}{\partial T_{j}}}\right)^{E}&&={\phantom {+}}\left({\frac {\partial S_{j}}{\partial E_{i}}}\right)^{T}\\[6pt]e_{ij}&={\phantom {+}}\left({\frac {\partial D_{i}}{\partial S_{j}}}\right)^{E}&&=-\left({\frac {\partial T_{j}}{\partial E_{i}}}\right)^{S}\\[6pt]g_{ij}&=-\left({\frac {\partial E_{i}}{\partial T_{j}}}\right)^{D}&&={\phantom {+}}\left({\frac {\partial S_{j}}{\partial D_{i}}}\right)^{T}\\[6pt]h_{ij}&=-\left({\frac {\partial E_{i}}{\partial S_{j}}}\right)^{D}&&=-\left({\frac {\partial T_{j}}{\partial D_{i}}}\right)^{S}\end{aligned}}$

where the first set of four terms corresponds to the direct piezoelectric effect and the second set of four terms corresponds to the converse piezoelectric effect. The equality between the direct piezoelectric tensor and the transpose of the converse piezoelectric tensor originates from theMaxwell relationsof thermodynamics.For those piezoelectric crystals for which the polarization is of the crystal-field induced type, a formalism has been worked out that allows for the calculation of piezoelectrical coefficientsd_ijfrom electrostatic lattice constants or higher-orderMadelung constants.

Crystal classes

Any spatially separated charge will result in anelectric field,and therefore anelectric potential.Shown here is a standard dielectric in acapacitor.In a piezoelectric device, mechanical stress, instead of an externally applied voltage, causes the charge separation in the individual atoms of the material.

Of the 32crystal classes,21 are non-centrosymmetric(not having a centre of symmetry), and of these, 20 exhibit direct piezoelectricity(the 21st is the cubic class 432). Ten of these represent the polar crystal classes,which show a spontaneous polarization without mechanical stress due to a non-vanishing electric dipole moment associated with their unit cell, and which exhibitpyroelectricity.If the dipole moment can be reversed by applying an external electric field, the material is said to beferroelectric.

• The 10 polar (pyroelectric) crystal classes: 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm.
• The other 10 piezoelectric crystal classes: 222,4,422,42m, 32,6,622,62m, 23,43m.

For polar crystals, for whichP≠ 0 holds without applying a mechanical load, the piezoelectric effect manifests itself by changing the magnitude or the direction ofPor both.

For the nonpolar but piezoelectric crystals, on the other hand, a polarizationPdifferent from zero is only elicited by applying a mechanical load. For them the stress can be imagined to transform the material from a nonpolar crystal class (P= 0) to a polar one,havingP≠ 0.

Materials

See also:List of piezoelectric materials

Many materials exhibit piezoelectricity.

Crystalline materials

• Langasite(La₃Ga₅SiO₁₄) – a quartz-analogous crystal
• Gallium orthophosphate(GaPO₄) – a quartz-analogous crystal
• Lithium niobate(LiNbO₃)
• Lithium tantalate(LiTaO₃)
• Quartz
• Berlinite(AlPO₄) – a rarephosphatemineralthat is structurally identical to quartz
• Rochelle salt
• Topaz– piezoelectricity in topaz can probably be attributed to ordering of the (F,OH) in its lattice, which is otherwise centrosymmetric: orthorhombic bipyramidal (mmm). Topaz has anomalous optical properties, which are attributed to such ordering.
• Tourmaline-group minerals
• Lead titanate(PbTiO₃) – although it occurs in nature as mineral macedonite,it is synthesized for research and applications.

Ceramics

Tetragonal unit cell of lead titanate

Ceramics with randomly oriented grains must be ferroelectric to exhibit piezoelectricity.The occurrence ofabnormal grain growth(AGG) in sintered polycrystalline piezoelectric ceramics has detrimental effects on the piezoelectric performance in such systems and should be avoided, as the microstructure in piezoceramics exhibiting AGG tends to consist of few abnormally large elongated grains in a matrix of randomly oriented finer grains. Macroscopic piezoelectricity is possible in textured polycrystalline non-ferroelectric piezoelectric materials, such as AlN and ZnO. The families of ceramics withperovskite,tungsten-bronze,and related structures exhibit piezoelectricity:

• Lead zirconate titanate(Pb[Zr_xTi_1−x]O₃with 0 ≤x≤ 1) – more commonly known as PZT, the most common piezoelectric ceramic in use today.
• Potassium niobate(KNbO₃)
• Sodium tungstate(Na₂WO₃)
• Ba₂NaNb₅O₅
• Pb₂KNb₅O₁₅
• Zinc oxide(ZnO) –Wurtzite structure.While single crystals of ZnO are piezoelectric and pyroelectric, polycrystalline (ceramic) ZnO with randomly oriented grains exhibits neither piezoelectric nor pyroelectric effect. Not being ferroelectric, polycrystalline ZnO cannot be poled like barium titanate or PZT. Ceramics and polycrystalline thin films of ZnO may exhibit macroscopic piezoelectricity and pyroelectricity only if they aretextured(grains are preferentially oriented), such that the piezoelectric and pyroelectric responses of all individual grains do not cancel. This is readily accomplished in polycrystalline thin films.

Lead-free piezoceramics

• Sodium potassium niobate((K,Na)NbO₃). This material is also known as NKN or KNN. In 2004, a group of Japanese researchers led by Yasuyoshi Saito discovered a sodium potassium niobate composition with properties close to those of PZT, including a highT_C.Certain compositions of this material have been shown to retain a high mechanical quality factor (Q_m≈ 900) with increasing vibration levels, whereas the mechanical quality factor of hard PZT degrades in such conditions. This fact makes NKN a promising replacement for high power resonance applications, such as piezoelectric transformers.
• Bismuth ferrite(BiFeO₃) – a promising candidate for the replacement of lead-based ceramics.
• Sodium niobate (NaNbO₃)
• Barium titanate(BaTiO₃) – Barium titanate was the first piezoelectric ceramic discovered.
• Bismuth titanate(Bi₄Ti₃O₁₂)
• Sodium bismuth titanate(NaBi(TiO₃)₂)

The fabrication of lead-free piezoceramics pose multiple challenges, from an environmental standpoint and their ability to replicate the properties of their lead-based counterparts. By removing the lead component of the piezoceramic, the risk of toxicity to humans decreases, but the mining and extraction of the materials can be harmful to the environment.Analysis of the environmental profile of PZT versus sodium potassium niobate (NKN or KNN) shows that across the four indicators considered (primary energy consumption, toxicological footprint, eco-indicator 99, and input-output upstream greenhouse gas emissions), KNN is actually more harmful to the environment. Most of the concerns with KNN, specifically its Nb₂O₅component, are in the early phase of its life cycle before it reaches manufacturers. Since the harmful impacts are focused on these early phases, some actions can be taken to minimize the effects. Returning the land as close to its original form after Nb₂O₅mining via dam deconstruction or replacing a stockpile of utilizable soil are known aids for any extraction event. For minimizing air quality effects, modeling and simulation still needs to occur to fully understand what mitigation methods are required. The extraction of lead-free piezoceramic components has not grown to a significant scale at this time, but from early analysis, experts encourage caution when it comes to environmental effects.

Fabricating lead-free piezoceramics faces the challenge of maintaining the performance and stability of their lead-based counterparts. In general, the main fabrication challenge is creating the "morphotropic phase boundaries (MPBs)" that provide the materials with their stable piezoelectric properties without introducing the "polymorphic phase boundaries (PPBs)" that decrease the temperature stability of the material.New phase boundaries are created by varying additive concentrations so that thephase transitiontemperatures converge at room temperature. The introduction of the MPB improves piezoelectric properties, but if a PPB is introduced, the material becomes negatively affected by temperature. Research is ongoing to control the type of phase boundaries that are introduced through phase engineering, diffusing phase transitions, domain engineering, and chemical modification.

III–V and II–VI semiconductors

A piezoelectric potential can be created in any bulk or nanostructured semiconductor crystal having non central symmetry, such as theGroupIII–VandII–VImaterials, due to polarization of ions under applied stress and strain. This property is common to both thezincblendeandwurtzitecrystal structures. To first order, there is only one independent piezoelectric coefficient inzincblende,called e₁₄,coupled to shear components of the strain. Inwurtzite,there are instead three independent piezoelectric coefficients:e₃₁,e₃₃ande₁₅. The semiconductors where the strongest piezoelectricity is observed are those commonly found in thewurtzitestructure, i.e.GaN,InN,AlNandZnO(seepiezotronics).

Since 2006, there have also been a number of reports of strongnon linear piezoelectric effects in polar semiconductors. Such effects are generally recognized to be at least important if not of the same order of magnitude as the first order approximation.

Polymers

The piezo-response ofpolymersis not as high as the response for ceramics; however, polymers hold properties that ceramics do not. Over the last few decades, non-toxic, piezoelectric polymers have been studied and applied due to their flexibility and smalleracoustical impedance.Other properties that make these materials significant include theirbiocompatibility,biodegradability,low cost, and low power consumption compared to other piezo-materials (ceramics, etc.).Piezoelectric polymers and non-toxic polymer composites can be used given their different physical properties.

Piezoelectric polymers can be classified by bulk polymers, voided charged polymers ( "piezoelectrets" ), and polymer composites. A piezo-response observed by bulk polymers is mostly due to its molecular structure. There are two types of bulk polymers:amorphousandsemi-crystalline.Examples of semi-crystalline polymers arepolyvinylidene fluoride(PVDF) and itscopolymers,polyamides,andparylene-C.Non-crystalline polymers, such aspolyimideandpolyvinylidene chloride(PVDC), fall under amorphous bulk polymers. Voided charged polymers exhibit the piezoelectric effect due to charge induced by poling of a porous polymeric film. Under an electric field, charges form on the surface of the voids forming dipoles. Electric responses can be caused by any deformation of these voids. The piezoelectric effect can also be observed in polymer composites by integrating piezoelectric ceramic particles into a polymer film. A polymer does not have to be piezo-active to be an effective material for a polymer composite.In this case, a material could be made up of an inert matrix with a separate piezo-active component.

PVDF exhibits piezoelectricity several times greater than quartz. The piezo-response observed from PVDF is about 20–30 pC/N. That is an order of 5–50 times less than that of piezoelectric ceramic lead zirconate titanate (PZT).The thermal stability of the piezoelectric effect of polymers in the PVDF family (i.e. vinylidene fluoride co-poly trifluoroethylene) goes up to 125 °C. Some applications of PVDF are pressure sensors, hydrophones, and shock wave sensors.

Due to their flexibility, piezoelectric composites have been proposed as energy harvesters and nanogenerators. In 2018, it was reported by Zhu et al. that a piezoelectric response of about 17 pC/N could be obtained from PDMS/PZT nanocomposite at 60% porosity.Another PDMS nanocomposite was reported in 2017, in which BaTiO₃was integrated into PDMS to make a stretchable, transparent nanogenerator for self-powered physiological monitoring.In 2016, polar molecules were introduced into a polyurethane foam in which high responses of up to 244 pC/N were reported.

Other materials

Most materials exhibit at least weak piezoelectric responses. Trivial examples includesucrose(table sugar),DNA,viral proteins, including those frombacteriophage.An actuator based on wood fibers, calledcellulose fibers,has been reported.D33 responses for cellular polypropylene are around 200 pC/N. Some applications of cellular polypropylene are musical key pads, microphones, and ultrasound-based echolocation systems.Recently, single amino acid such as β-glycine also displayed high piezoelectric (178 pmV⁻¹) as compared to other biological materials.

Ionic liquidswere recently identified as the first piezoelectric liquid.

Application

High voltage and power sources

Direct piezoelectricity of some substances, like quartz, can generatepotential differencesof thousands of volts.

• The best-known application is the electriccigarette lighter:pressing the button causes a spring-loaded hammer to hit a piezoelectric crystal, producing a sufficiently high-voltageelectric currentthat flows across a smallspark gap,thus heating and igniting the gas. The portable sparkers used to ignitegas stoveswork the same way, and many types of gas burners now have built-in piezo-based ignition systems.
• A similar idea is being researched byDARPAin the United States in a project calledenergy harvesting,which includes an attempt to power battlefield equipment by piezoelectric generators embedded insoldiers' boots. However, these energy harvesting sources by association affect the body. DARPA's effort to harness 1–2 watts from continuous shoe impact while walking were abandoned due to the impracticality and the discomfort from the additional energy expended by a person wearing the shoes. Other energy harvesting ideas includeCrowd Farm,harvesting the energy from human movements in train stations or other public placesand converting a dance floor to generate electricity.Vibrations from industrial machinery can also be harvested by piezoelectric materials to charge batteries for backup supplies or to power low-power microprocessors and wireless radios.
• A piezoelectrictransformeris a type of AC voltage multiplier. Unlike a conventional transformer, which uses magnetic coupling between input and output, the piezoelectric transformer usesacoustic coupling.An input voltage is applied across a short length of a bar of piezoceramic material such asPZT,creating an alternating stress in the bar by the inverse piezoelectric effect and causing the whole bar to vibrate. The vibration frequency is chosen to be theresonantfrequency of the block, typically in the 100kilohertzto 1 megahertz range. A higher output voltage is then generated across another section of the bar by the piezoelectric effect. Step-up ratios of more than 1,000:1 have been demonstrated.An extra feature of this transformer is that, by operating it above its resonant frequency, it can be made to appear as aninductiveload, which is useful in circuits that require a controlled soft start.These devices can be used in DC–AC inverters to drivecold cathode fluorescent lamps.Piezo transformers are some of the most compact high voltage sources.

Sensors

Piezoelectric disk used as aguitar pickup

Many rocket-propelled grenades used a piezoelectricfuse.Pictured, a RussianRPG-7

Main article:Piezoelectric sensor

The principle of operation of a piezoelectricsensoris that a physical dimension, transformed into a force, acts on two opposing faces of the sensing element. Depending on the design of a sensor, different "modes" to load the piezoelectric element can be used: longitudinal, transversal and shear.

Detection of pressure variations in the form of sound is the most common sensor application, e.g. piezoelectricmicrophones(sound waves bend the piezoelectric material, creating a changing voltage) and piezoelectricpickupsforacoustic-electric guitars.A piezo sensor attached to the body of an instrument is known as acontact microphone.

Piezoelectric sensors especially are used with high frequency sound in ultrasonic transducers for medical imaging and also industrialnondestructive testing(NDT).

For many sensing techniques, the sensor can act as both a sensor and an actuator—often the termtransduceris preferred when the device acts in this dual capacity, but most piezo devices have this property of reversibility whether it is used or not. Ultrasonic transducers, for example, can inject ultrasound waves into the body, receive the returned wave, and convert it to an electrical signal (a voltage). Most medical ultrasound transducers are piezoelectric.

In addition to those mentioned above, various sensor and transducer applications include:

• Piezoelectric elements are also used in the detection and generation of sonar waves.
• Piezoelectric materials are used in single-axis and dual-axis tilt sensing.
• Power monitoring in high power applications (e.g. medical treatment,sonochemistryand industrial processing).
• Piezoelectric microbalancesare used as very sensitive chemical and biological sensors.
• Piezoelectrics are sometimes used instrain gauges.More commonly however, aPiezoresistive effectelement is used.
• A piezoelectric transducer was used in the penetrometer instrument on theHuygens Probe.
• Piezoelectrictransducersare used inelectronic drum padsto detect the impact of the drummer's sticks, and to detect muscle movements in medicalacceleromyography.
• Automotiveengine management systemsuse piezoelectric transducers to detect Engine knock (Knock Sensor, KS), also known as detonation, at certain hertz frequencies. A piezoelectric transducer is also used in fuel injection systems to measure manifold absolute pressure (MAP sensor) to determine engine load, and ultimately the fuel injectors milliseconds of on time.
• Ultrasonic piezo sensors are used in the detection of acoustic emissions inacoustic emission testing.
• Piezoelectric transducers can be used in transit-timeultrasonic flow meters.

Actuators

Metal disk with piezoelectric disk attached, used in abuzzer

As very high electric fields correspond to only tiny changes in the width of the crystal, this width can be changed with better-than-μmprecision, making piezo crystals the most important tool for positioning objects with extreme accuracy—thus their use inactuators. Multilayer ceramics, using layers thinner than100 μm,allow reaching high electric fields with voltage lower than150 V.These ceramics are used within two kinds of actuators: direct piezo actuators andamplified piezoelectric actuators.While direct actuator's stroke is generally lower than100 μm,amplified piezo actuators can reach millimeter strokes.

• Loudspeakers:Voltage is converted to mechanical movement of a metallic diaphragm.
• Ultrasonic cleaningusually uses piezoelectric elements to produce intense sound waves in liquid.
• Piezoelectric motors:Piezoelectric elements apply a directional force to anaxle,causing it to rotate. Due to the extremely small distances involved, the piezo motor is viewed as a high-precision replacement for thestepper motor.
• Piezoelectric elements can be used inlasermirror alignment, where their ability to move a large mass (the mirror mount) over microscopic distances is exploited to electronically align some laser mirrors. By precisely controlling the distance between mirrors, the laser electronics can accurately maintain optical conditions inside the laser cavity to optimize the beam output.
• A related application is theacousto-optic modulator,a device that scatters light off soundwaves in a crystal, generated by piezoelectric elements. This is useful for fine-tuning a laser's frequency.
• Atomic force microscopesandscanning tunneling microscopesemploy converse piezoelectricity to keep the sensing needle close to the specimen.
• Inkjet printers:On many inkjet printers, piezoelectric crystals are used to drive the ejection of ink from the inkjet print head towards the paper.
• Diesel engines:High-performancecommon raildiesel engines use piezoelectricfuel injectors,first developed byRobert Bosch GmbH,instead of the more commonsolenoid valvedevices.
• Active vibration control using amplified actuators.
• X-rayshutters.
• XY stages for micro scanning used in infrared cameras.
• Moving the patient precisely inside activeCTandMRIscanners where the strong radiation or magnetism precludes electric motors.
• Crystal earpiecesare sometimes used in old or low power radios.
• High-intensity focused ultrasoundfor localized heating or creating a localizedcavitationcan be achieved, for example, in patient's body or in an industrial chemical process.
• Refreshable braille display.A small crystal is expanded by applying a current that moves a lever to raise individual braille cells.
• Piezoelectric actuator. A single crystal or a number of crystals are expanded by applying a voltage for moving and controlling a mechanism or system.
• Piezoelectric actuators are used for fine servo positioning in hard disc drives.

Frequency standard

The piezoelectrical properties of quartz are useful as astandard of frequency.

• Quartz clocksemploy acrystal oscillatormade from a quartz crystal that uses a combination of both direct and converse piezoelectricity to generate a regularly timed series of electrical pulses that is used to mark time. The quartz crystal (like anyelasticmaterial) has a precisely defined natural frequency (caused by its shape and size) at which it prefers tooscillate,and this is used to stabilize the frequency of a periodic voltage applied to the crystal.
• The same principle is used in someradiotransmittersandreceivers,and incomputerswhere it creates aclock pulse.Both of these usually use afrequency multiplierto reach gigahertz ranges.

Piezoelectric motors

A stick-slip actuator

Main article:Piezoelectric motor

Types of piezoelectric motor include:

• Theultrasonic motorused forauto-focusinreflex cameras
• Inchworm motorsfor linear motion
• Rectangular four-quadrant motors with high power density (2.5W/cm³) and speed ranging from 10 nm/s to 800 mm/s.
• Stepping piezo motor, usingstick-slipeffect.

Aside from the stepping stick-slip motor, all these motors work on the same principle. Driven by dual orthogonal vibration modes with aphasedifference of 90°, the contact point between two surfaces vibrates in anellipticalpath, producing africtionalforce between the surfaces. Usually, one surface is fixed, causing the other to move. In most piezoelectric motors, the piezoelectric crystal is excited by asine wavesignal at the resonant frequency of the motor. Using the resonance effect, a much lower voltage can be used to produce a high vibration amplitude.

A stick-slip motor works using the inertia of a mass and the friction of a clamp. Such motors can be very small. Some are used for camera sensor displacement, thus allowing an anti-shake function.

Reduction of vibrations and noise

Different teams of researchers have been investigating ways to reduce vibrations in materials by attaching piezo elements to the material. When the material is bent by a vibration in one direction, the vibration-reduction system responds to the bend and sends electric power to the piezo element to bend in the other direction. Future applications of this technology are expected in cars and houses to reduce noise. Further applications to flexible structures, such as shells and plates, have also been studied for nearly three decades.

In a demonstration at the Material Vision Fair inFrankfurtin November 2005, a team fromTU DarmstadtinGermanyshowed several panels that were hit with a rubber mallet, and the panel with the piezo element immediately stopped swinging.

Piezoelectric ceramic fiber technology is being used as an electronic damping system on someHEADtennis rackets.

All piezo transducers have a fundamental resonant frequency and many harmonic frequencies. Piezo driven Drop-On-Demand fluid systems are sensitive to extra vibrations in the piezo structure that must be reduced or eliminated. One inkjet company, Howtek, Inc solved this problem by replacing glass(rigid) inkjet nozzles with Tefzel (soft) inkjet nozzles. This novel idea popularized single nozzle inkjets and they are now used in 3D Inkjet printers that run for years if kept clean inside and not overheated (Tefzel creeps under pressure at very high temperatures)

Infertility treatment

In people with previoustotal fertilization failure,piezoelectric activation ofoocytestogether withintracytoplasmic sperm injection(ICSI) seems to improve fertilization outcomes.

Surgery

Piezosurgeryis a minimally invasive technique that aims to cut a target tissue with little damage to neighboring tissues. For example, Hoigneet al.uses frequencies in the range 25–29 kHz, causing microvibrations of 60–210 μm. It has the ability to cut mineralized tissue without cutting neurovascular tissue and other soft tissue, thereby maintaining a blood-free operating area, better visibility and greater precision.

Potential applications

In 2015, Cambridge University researchers working in conjunction with researchers from the National Physical Laboratory and Cambridge-based dielectric antenna company Antenova Ltd, using thin films of piezoelectric materials found that at a certain frequency, these materials become not only efficient resonators, but efficient radiators as well, meaning that they can potentially be used as antennas. The researchers found that by subjecting the piezoelectric thin films to an asymmetric excitation, the symmetry of the system is similarly broken, resulting in a corresponding symmetry breaking of the electric field, and the generation of electromagnetic radiation.

Several attempts at the macro-scale application of the piezoelectric technology have emergedto harvest kinetic energy from walking pedestrians.

In this case, locating high traffic areas is critical for optimization of the energy harvesting efficiency, as well as the orientation of the tile pavement significantly affects the total amount of the harvested energy.A density flow evaluation is recommended to qualitatively evaluate the piezoelectric power harvesting potential of the considered area based on the number of pedestrian crossings per unit time.In X. Li's study, the potential application of a commercial piezoelectric energy harvester in a central hub building at Macquarie University in Sydney, Australia is examined and discussed. Optimization of the piezoelectric tile deployment is presented according to the frequency of pedestrian mobility and a model is developed where 3.1% of the total floor area with the highest pedestrian mobility is paved with piezoelectric tiles. The modelling results indicate that the total annual energy harvesting potential for the proposed optimized tile pavement model is estimated at 1.1 MWh/year, which would be sufficient to meet close to 0.5% of the annual energy needs of the building.In Israel, there is a company which has installed piezoelectric materials under a busy highway. The energy generated is enough to power street lights, billboards, and signs.

Tire companyGoodyearhas plans to develop an electricity generating tire which has piezoelectric material lined inside it. As the tire moves, it deforms and thus electricity is generated.

The efficiency of a hybridphotovoltaic cellthat contains piezoelectric materials can be increased simply by placing it near a source of ambient noise or vibration. The effect was demonstrated with organic cells usingzinc oxidenanotubes. The electricity generated by the piezoelectric effect itself is a negligible percentage of the overall output. Sound levels as low as 75 decibels improved efficiency by up to 50%. Efficiency peaked at 10 kHz, the resonant frequency of the nanotubes. The electrical field set up by the vibrating nanotubes interacts with electrons migrating from the organic polymer layer. This process decreases the likelihood of recombination, in which electrons are energized but settle back into a hole instead of migrating to the electron-accepting ZnO layer.

See also

• Charge amplifier
• Electret
• Electronic component
• Electrostriction
• Flexoelectricity
• Magnetostriction
• Photoelectric effect
• Piezoelectric speaker
• Piezoluminescence
• Piezomagnetism
• Piezoresistive effect
• Piezosurgical
• Quartz crystal microbalance
• Sonomicrometry
• Surface acoustic wave
• Thermoelectric generator
• Triboluminescence

Further reading

• EN 50324 (2002) Piezoelectric properties of ceramic materials and components (3 parts)
• ANSI-IEEE 176 (1987) Standard on Piezoelectricity
• IEEE 177 (1976) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators
• IEC 444 (1973) Basic method for the measurement of resonance freq & equiv series resistance of quartz crystal units by zero-phase technique in a pi-network
• IEC 302 (1969) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators Operating over the Freq Range up to 30 MHz

External links

• Gautschi, Gustav H. (2002).Piezoelectric Sensorics.Springer.ISBN978-3-540-42259-4.
• Piezoelectric cellular polymer films: Fabrication, properties and applications
• Piezo motor based microdrive for neural signal recording
• Research on new Piezoelectric materials
• Piezo Equations
• Piezo in Medical Design
• Video demonstration of Piezoelectricity
• DoITPoMS Teaching and Learning Package – Piezoelectric Materials
• PiezoMat.org– Online database for piezoelectric materials, their properties, and applications
• Piezo Motor Types
• Piezo-Theory & Applications