Piezoelectricity

Piezoelectricity ( , US: ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as…

Piezoelectricity (, US: ) refers to the electric charge generated within specific solid materials, including various crystals, certain ceramics, and biological substances such as bone, DNA, and proteins, when subjected to mechanical stress.

This phenomenon arises from a linear electromechanical interaction between the mechanical and electrical states in crystalline materials lacking inversion symmetry. The piezoelectric effect is inherently reversible: materials demonstrating this effect also exhibit the converse piezoelectric effect, wherein an applied electric field induces an internal mechanical strain. For instance, lead zirconate titanate crystals produce measurable piezoelectricity when their static structure is deformed by approximately 0.1% of their original dimension. Conversely, these same crystals undergo a dimensional change of about 0.1% when an external electric field is applied. The inverse piezoelectric effect is utilized in the generation of ultrasound waves.

French physicists Jacques and Pierre Curie first identified piezoelectricity in 1880. The piezoelectric effect has since been leveraged in numerous practical applications, including the generation and detection of sound, piezoelectric inkjet printing, high-voltage electricity generation, clock generation in electronic devices, microbalances, ultrasonic nozzle actuation, and ultrafine focusing in optical assemblies. It underpins scanning probe microscopes, enabling atomic-scale imaging. Furthermore, it is employed in the pickups of certain electronically amplified guitars and as triggers in most contemporary electronic drums. Everyday applications of the piezoelectric effect include generating sparks for igniting gas cooking and heating appliances, torches, and cigarette lighters.

Etymology

The term piezoelectricity signifies electricity produced by pressure. Its etymology traces back to Ancient Greek πιέζω (piézō) 'to squeeze or press' and ἤλεκτρον (ḗlektron) 'amber', an ancient source of static electricity. The German equivalent (Piezoelektrizität) was coined in 1881 by the German physicist Wilhelm Gottlieb Hankel, with the English term derived from German in 1883.

History

Discovery and Early Research

The pyroelectric effect, characterized by a material's generation of an electric potential in response to temperature fluctuations, was investigated by Carl Linnaeus and Franz Aepinus during the mid-18th century. Building upon this knowledge, both René Just Haüy and Antoine César Becquerel hypothesized a correlation between mechanical stress and electric charge; however, their experimental findings remained inconclusive.

The direct piezoelectric effect was first conclusively demonstrated in 1880 by the brothers Pierre and Jacques Curie. They integrated their understanding of pyroelectricity with their knowledge of the underlying crystal structures responsible for it to predict crystal behavior. Their demonstration utilized crystals of tourmaline, quartz, topaz, cane sugar, and Rochelle salt (sodium potassium tartrate tetrahydrate), with quartz and Rochelle salt exhibiting the most pronounced piezoelectricity.

The Curies, however, did not initially predict the converse piezoelectric effect. This inverse phenomenon was mathematically deduced from fundamental thermodynamic principles by Gabriel Lippmann in 1881. The Curies promptly confirmed the existence of the converse effect and subsequently provided quantitative evidence for the complete reversibility of electro-elasto-mechanical deformations in piezoelectric crystals.

For several subsequent decades, piezoelectricity largely remained a scientific curiosity, although it proved instrumental in Pierre and Marie Curie's discovery of polonium and radium in 1898. Further research focused on exploring and defining the crystal structures that exhibited piezoelectricity. This culminated in 1910 with the publication of Woldemar Voigt's Lehrbuch der Kristallphysik (Textbook on Crystal Physics), which enumerated the 20 natural crystal classes capable of piezoelectricity and rigorously defined piezoelectric constants using tensor analysis.

World War I and Inter-War Years

The initial practical application of piezoelectric devices emerged during World War I with the development of sonar technology. Their superior performance at ultrasonic frequencies quickly rendered the Fessenden oscillator obsolete. In 1917, Paul Langevin and his collaborators in France engineered an ultrasonic submarine detection system. This system comprised a transducer, constructed from thin quartz crystals meticulously bonded between two steel plates, and a hydrophone designed to capture the returning echo. The principle involved emitting a high-frequency pulse from the transducer and subsequently measuring the time required for the sound waves to reflect off an object and return as an echo, thereby enabling distance calculation.

Piezoelectric devices subsequently permeated numerous sectors. For instance, ceramic phonograph cartridges streamlined player design, offering cost-effectiveness and precision, which reduced manufacturing complexity and maintenance expenses for record players. Furthermore, the advent of ultrasonic transducers facilitated precise measurements of viscosity and elasticity in both fluids and solids, significantly advancing materials science. Ultrasonic time-domain reflectometers, which operate by transmitting an ultrasonic pulse through a material and analyzing reflections from internal discontinuities, enabled the detection of flaws within cast metal and stone objects, thereby enhancing structural integrity.

World War II and Post-War Developments

During World War II, independent research initiatives across the United States, the USSR, and Japan led to the discovery of ferroelectrics, a novel class of synthetic materials demonstrating piezoelectric constants significantly exceeding those of natural counterparts. This breakthrough spurred intensive research into the development of barium titanate and, subsequently, lead zirconate titanate materials, tailored with specific properties for diverse applications.

A notable application of piezoelectric crystals emerged from the work at Bell Telephone Laboratories. Subsequent to World War I, Frederick R. Lack, an engineer specializing in radiotelephony, devised the "AT cut" crystal, characterized by its stable operation across a broad temperature spectrum. This innovation eliminated the need for the cumbersome auxiliary equipment associated with earlier crystals, thereby enabling its integration into aircraft systems. Consequently, this advancement facilitated coordinated mass attacks by Allied air forces through enhanced aviation radio communication.

In the United States, the development of piezoelectric devices and materials was largely confined within individual corporations, primarily influenced by the field's wartime origins and the strategic pursuit of lucrative patents. While quartz crystals represented the initial commercially exploited piezoelectric material, ongoing research focused on identifying and developing higher-performance alternatives. Notwithstanding advancements in materials science and manufacturing processes, the growth of the United States market lagged behind that of Japan. The limited emergence of novel applications consequently impeded the expansion of the U.S. piezoelectric industry.

Conversely, Japanese manufacturers fostered collaborative information exchange, which facilitated rapid resolution of technical and manufacturing hurdles and stimulated the creation of new markets. Notably, Issac Koga in Japan pioneered a temperature-stable crystal cut. Japanese material science initiatives yielded piezoceramic materials that were competitive with U.S. counterparts yet unencumbered by costly patent limitations. Significant Japanese piezoelectric innovations encompassed novel designs for piezoceramic filters in radios and televisions, piezo buzzers, and audio transducers capable of direct electronic circuit integration, as well as the piezoelectric igniter, which produces sparks for small engine ignition systems and gas-grill lighters through the compression of a ceramic disc. Although ultrasonic transducers capable of transmitting sound waves through air had existed previously, their first widespread commercial application was in early television remote controls. Currently, these transducers are integrated into various automotive models, serving as echolocation devices to assist drivers in assessing distances to obstacles.

Mechanism of Operation

The piezoelectric effect's fundamental nature is intrinsically linked to the presence of electric dipole moments within solid materials. These dipoles can be either induced in ions situated at crystal lattice sites with asymmetric charge environments, as observed in materials like BaTiO₃ and PZTs, or they can be inherently carried by molecular groups, as exemplified by cane sugar. The dipole density, also termed polarization (with a dimensionality of [C·m/m³]), can be readily calculated for crystals by summing the dipole moments per unit volume of the crystallographic unit cell. Since every dipole is a vector, the dipole density P constitutes a vector field. Adjacent dipoles tend to align within localized regions known as Weiss domains. These domains are typically randomly oriented but can be aligned through a process called poling (which is distinct from magnetic poling), involving the application of a strong electric field across the material, usually at elevated temperatures. However, not all piezoelectric materials are capable of being poled.

A crucial aspect of the piezoelectric effect is the change in polarization P that occurs when mechanical stress is applied. This alteration may arise from either a reconfiguration of the dipole-inducing surroundings or a reorientation of molecular dipole moments under the influence of external stress. Piezoelectricity can thus manifest as a variation in the polarization's magnitude, its direction, or both, with the specific details contingent upon: 1. the orientation of P within the crystal; 2. the crystal's inherent symmetry; and 3. the characteristics of the applied mechanical stress. The modification in P is observed as a fluctuation in the surface charge density on the crystal faces, which in turn leads to a variation in the electric field extending between these faces, caused by a change in the bulk dipole density. For instance, a 1 cm§1213§ cube of quartz, when subjected to a correctly applied force of 2 kN (approximately 500 lbf), can generate a voltage of 12,500 V.

Conversely, piezoelectric materials also exhibit the converse piezoelectric effect, a phenomenon where the application of an external electric field induces mechanical deformation within the crystal structure.

Mathematical Description

Linear piezoelectricity represents the synergistic outcome of:

The material's linear electrical response:

\mathbf {D} ={\boldsymbol {\varepsilon }}\,\mathbf {E} \quad \implies

\quad D_{i}=\sum _{j}\varepsilon _{ij}\,E_{j}\;

In this context, D denotes the electric flux density, also referred to as electric displacement; ε represents the permittivity, or the free-body dielectric constant; and E signifies the electric field strength. Additionally, the following conditions apply:

\nabla \cdot \mathbf {D} =0

25§ {\displaystyle \nabla \cdot \mathbf {D} =0} and

\nabla \times \mathbf {E} =\mathbf {0}

54§ {\displaystyle \nabla \times \mathbf {E} =\mathbf {0} } .

Hooke's Law, applicable to linear elastic materials, states:

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

Here, S denotes the linearized strain, s represents the compliance under short-circuit conditions, and T signifies the stress, as defined by:

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

28§ , S = ∇ u + u ∇ §6465§ , {\displaystyle \nabla \cdot {\boldsymbol {T}}=\mathbf {0} \,\,,\,{\boldsymbol {S}}={\frac {\nabla \mathbf {u} +\mathbf {u} \nabla }{2}},}

In this context, u represents the displacement vector.

These elements can be integrated to form coupled equations, with the strain-charge form specifically presented as:

{\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}}

The entity ${\mathfrak {d}}$ represents the piezoelectric tensor, where the superscript 't' signifies its transpose. Given the inherent symmetry of the piezoelectric tensor ${\mathfrak {d}}$ , the following relationships hold: $d_{ijk}^{t}=d_{kji}=d_{kij}$ .

Expressed in matrix notation, the relationships are as follows:

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

In these expressions, [d] denotes the matrix corresponding to the direct piezoelectric effect, while [d^t] represents the matrix for the converse piezoelectric effect. The superscript E signifies a condition of either a zero or constant electric field, and the superscript T indicates a zero or constant stress field. The superscript 't' consistently denotes the transposition of a matrix.

It is important to note that the third-order tensor ${\mathfrak {d}}$ transforms vectors into symmetric matrices. This specific characteristic implies the absence of non-trivial rotation-invariant tensors possessing such a property, thereby explaining why isotropic piezoelectric materials do not exist.

The strain-charge relationship for materials belonging to the 4mm (C_4v) crystal class, exemplified by poled piezoelectric ceramics like tetragonal PZT or BaTiO₃, and also for those in the 6mm crystal class, can be formulated as follows (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}}

The initial equation describes the converse piezoelectric effect, whereas the subsequent equation pertains to the direct piezoelectric effect.

While these equations are widely employed in the academic literature, clarification regarding their notation is essential. Typically, D and E are represented as vectors, which are Cartesian tensors of rank 1, while permittivity ε is a Cartesian tensor of rank 2. Although strain and stress are fundamentally rank-2 tensors, conventional practice, owing to their symmetric nature, permits the relabeling of their subscripts as follows: 11 → 1; 22 → 2; 33 → 3; 23 → 4; 13 → 5; 12 → 6. It is important to note that alternative conventions exist in the literature; for instance, some authors may assign 12 → 4, 23 → 5, and 31 → 6. This relabeling explains why S and T are presented in a "vector form" comprising six components. Consequently, s is represented as a 6x6 matrix rather than a rank-3 tensor. This relabeled notation is commonly referred to as Voigt notation. A separate consideration involves whether the shear strain components S§1415§, S§1819§, and S§2223§ represent tensor components or engineering strains. Within the context of the aforementioned equation, these must be interpreted as engineering strains to correctly express the 6,6 coefficient of the compliance matrix as 2(s^E
§3334§ − s^E
§4647§). Engineering shear strains are defined as twice the magnitude of their corresponding tensor shear components, for example, S§5253§ = 2S§5657§. Consequently, s₆₆ = ⁠§6465§/G§7172§⁠, where G§7879§ denotes the shear modulus.

In total, four distinct piezoelectric coefficients are defined: d_ij, e_ij, g_ij, and h_ij, which are elaborated 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}}

In this context, the initial set of four terms corresponds to the direct piezoelectric effect, while the subsequent set of four terms represents the converse piezoelectric effect. The equivalence between the direct piezoelectric tensor and the transpose of the converse piezoelectric tensor is established by the Maxwell relations of thermodynamics. For piezoelectric crystals where polarization is induced by the crystal field, a specific formalism has been developed to calculate piezoelectric coefficients d_ij from electrostatic lattice constants or higher-order Madelung constants.

Crystal Classes

Among the 32 crystal classes, 21 are non-centrosymmetric, meaning they lack a center of symmetry. Of these, 20 exhibit direct piezoelectricity, with the cubic class 432 being the exception. Ten of these classes are categorized as polar crystal classes, which display spontaneous polarization in the absence of mechanical stress due to a non-vanishing electric dipole moment associated with their unit cell, and also exhibit pyroelectricity. If this dipole moment can be reversed by applying an external electric field, the material is classified as ferroelectric.

The ten polar (pyroelectric) crystal classes include: 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm.
The remaining ten piezoelectric crystal classes are: 222, 4, 422, 42m, 32, 6, 622, 62m, 23, §89§3m.

For polar crystals, where P ≠ 0 in the absence of mechanical load, the piezoelectric effect manifests through changes in either the magnitude or the direction of P, or both.

Conversely, for nonpolar but piezoelectric crystals, a non-zero polarization P is induced solely by the application of a mechanical load. In these materials, mechanical stress can be conceptualized as transforming the crystal from a nonpolar state (P = 0) to a polar state, characterized by P ≠ 0.

Materials

Numerous materials demonstrate piezoelectric properties. These include:

Crystalline materials

Langasite (La₃Ga₅SiO₁₄) – a crystal analogous to quartz
Gallium orthophosphate (GaPO₄) – a crystal analogous to quartz
Lithium niobate (LiNbO₃)
Lithium tantalate (LiTaO₃)
Quartz
Berlinite (AlPO₄) – a rare phosphate mineral structurally identical to quartz
Rochelle salt
Topaz – Piezoelectricity in topaz is likely attributable to the ordering of (F,OH) within its lattice, which is otherwise centrosymmetric (orthorhombic bipyramidal, mmm). Anomalous optical properties observed in topaz are also attributed to this ordering.
Tourmaline-group minerals
Lead titanate (PbTiO₃) – While naturally occurring as the mineral macedonite, it is synthesized for research and various applications.

Ceramics

Ceramics with randomly oriented grains are required to be ferroelectric to manifest piezoelectricity. Abnormal grain growth (AGG) in sintered polycrystalline piezoelectric ceramics detrimentally affects piezoelectric performance and should therefore be prevented. This is because the microstructure of piezoceramics exhibiting AGG typically comprises a limited number of unusually large, elongated grains embedded within a matrix of finer, randomly oriented grains. Conversely, macroscopic piezoelectricity can be achieved in textured polycrystalline non-ferroelectric piezoelectric materials, including AlN and ZnO. Piezoelectricity is also observed in ceramic families possessing perovskite, tungsten-bronze, and analogous structures, such as:

Lead zirconate titanate (Pb[Zr_xTi_1−x]O§910§ with 0 ≤ x ≤ 1) – commonly referred to as PZT, which is currently the most widely utilized piezoelectric ceramic.
Potassium niobate (KNbO₃)
Sodium tungstate (Na₂WO₃)
Ba₂NaNb₅O₅
Pb₂KNb₅O₁₅
Zinc oxide (ZnO) – possessing a Wurtzite structure. Although single crystals of ZnO demonstrate both piezoelectric and pyroelectric properties, polycrystalline (ceramic) ZnO with randomly oriented grains exhibits neither effect. As it is not ferroelectric, polycrystalline ZnO cannot be poled in the manner of barium titanate or PZT. Macroscopic piezoelectricity and pyroelectricity in ZnO ceramics and polycrystalline thin films are observed only when the material is textured (i.e., grains are preferentially oriented), ensuring that the piezoelectric and pyroelectric responses of individual grains do not cancel each other. This texture is readily achieved in polycrystalline thin films.

Lead-free Piezoceramics

Sodium potassium niobate ((K,Na)NbO₃), commonly referred to as NKN or KNN, represents a significant lead-free piezoceramic. In 2004, a team of Japanese researchers, led by Yasuyoshi Saito, identified a specific sodium potassium niobate composition exhibiting properties comparable to lead zirconate titanate (PZT), notably including a high T_C. Furthermore, particular formulations of this material demonstrate the ability to maintain a high mechanical quality factor (Q_m ≈ 900) even under elevated vibration levels, a characteristic where the mechanical quality factor of hard PZT typically deteriorates. Consequently, NKN is considered a promising alternative for high-power resonance applications, such as piezoelectric transformers.
Bismuth ferrite (BiFeO₃) is recognized as a promising candidate for replacing lead-based ceramic materials.
Sodium niobate (NaNbO₃)
Barium titanate (BaTiO₃) holds historical significance as the first piezoelectric ceramic ever discovered.
Bismuth titanate (Bi₄Ti₃O₁₂)
Sodium bismuth titanate (NaBi(TiO₃)₂)

The fabrication of lead-free piezoceramics presents multifaceted challenges, encompassing both environmental considerations and the imperative to replicate the performance characteristics of their lead-based predecessors. While the elimination of lead mitigates human toxicity risks, the mining and extraction processes for these alternative materials can pose environmental hazards. A comparative environmental assessment of PZT against sodium potassium niobate (NKN or KNN) reveals that, across four key indicators—primary energy consumption, toxicological footprint, eco-indicator 99, and input-output upstream greenhouse gas emissions—KNN exhibits a greater environmental impact. The majority of environmental concerns associated with KNN, particularly its Nb₂O₅ component, arise during the initial phases of its life cycle, prior to reaching manufacturing stages. Given this concentration of harmful impacts in early phases, specific interventions can be implemented to minimize adverse effects. Post-mining land restoration, such as dam deconstruction or the replenishment of usable soil stockpiles, represents established practices for mitigating the environmental footprint of extraction operations. Regarding air quality, comprehensive modeling and simulation are still required to fully ascertain the necessary mitigation strategies. Although the extraction of lead-free piezoceramic constituents has not yet reached a substantial scale, preliminary analyses prompt experts to advocate for caution concerning their potential environmental ramifications.

The fabrication of lead-free piezoceramics presents a significant challenge in sustaining the performance and stability levels characteristic of their lead-based equivalents. A primary technical hurdle in this fabrication process involves establishing "morphotropic phase boundaries (MPBs)," which confer stable piezoelectric properties, while simultaneously avoiding the formation of "polymorphic phase boundaries (PPBs)," which detrimentally affect the material's temperature stability. These new phase boundaries are typically engineered by adjusting additive concentrations to ensure that phase transition temperatures converge at ambient conditions. While the presence of an MPB enhances piezoelectric characteristics, the inadvertent introduction of a PPB renders the material susceptible to negative temperature-dependent effects. Consequently, ongoing research endeavors are focused on precisely controlling the types of phase boundaries formed through advanced techniques such as phase engineering, diffusing phase transitions, domain engineering, and chemical modification.

III–V and II–VI Semiconductors

A piezoelectric potential can be generated within any bulk or nanostructured semiconductor crystal lacking central symmetry, including Group III–V and II–VI materials. This phenomenon arises from the polarization of ions when subjected to external stress and strain. This characteristic is inherent to both zincblende and wurtzite crystal structures. In zincblende structures, only one independent piezoelectric coefficient, designated e₁₄, is present, which is coupled to the shear components of strain. Conversely, wurtzite structures exhibit three independent piezoelectric coefficients: e₃₁, e₃₃, and e₁₅. The semiconductors demonstrating the most pronounced piezoelectricity are typically those with a wurtzite structure, such as GaN, InN, AlN, and ZnO.

Since 2006, numerous studies have documented significant nonlinear piezoelectric effects in polar semiconductors. These effects are widely acknowledged to be substantial, potentially even comparable in magnitude to first-order approximations.

Polymers

While the piezoelectric response of polymers is not as pronounced as that of ceramics, they possess distinct advantages not found in ceramic counterparts. Consequently, non-toxic piezoelectric polymers have garnered significant research interest and practical application over recent decades, primarily owing to their inherent flexibility and lower acoustical impedance. Additional compelling attributes of these materials encompass biocompatibility, biodegradability, cost-effectiveness, and reduced power consumption when contrasted with other piezoelectric substances, such as ceramics.

Piezoelectric polymers are broadly categorized into bulk polymers, voided charged polymers (also known as "piezoelectrets"), and polymer composites. The piezoelectric response in bulk polymers primarily originates from their intrinsic molecular structure. Bulk polymers are further subdivided into amorphous and semi-crystalline types. Illustrative examples of semi-crystalline polymers include polyvinylidene fluoride (PVDF) and its copolymers, polyamides, and parylene-C. Conversely, non-crystalline polymers, such as polyimide and polyvinylidene chloride (PVDC), are classified as amorphous bulk polymers. Voided charged polymers manifest the piezoelectric effect through charges induced by the poling process of a porous polymeric film. When subjected to an electric field, charges accumulate on the void surfaces, thereby generating dipoles. Any deformation of these voids can subsequently induce an electrical response. Furthermore, the piezoelectric effect is observable in polymer composites, achieved by incorporating piezoelectric ceramic particles within a polymer film. Notably, the polymer matrix itself does not necessarily need to be piezo-active to form an effective polymer composite. Such materials can consist of an inert matrix combined with a distinct piezo-active component.

Polyvinylidene fluoride (PVDF) demonstrates a piezoelectric response significantly exceeding that of quartz. Specifically, PVDF exhibits a piezoelectric response ranging from approximately 20 to 30 pC/N. This value is, however, 5 to 50 times lower than the response observed in the piezoelectric ceramic lead zirconate titanate (PZT). Polymers within the PVDF family, including vinylidene fluoride co-poly trifluoroethylene, maintain their piezoelectric effect up to a thermal stability threshold of 125 °C. Key applications for PVDF encompass pressure sensors, hydrophones, and shock wave sensors.

Owing to their inherent flexibility, piezoelectric composites have been extensively investigated for applications as energy harvesters and nanogenerators. For instance, in 2018, Zhu et al. documented a piezoelectric response of approximately 17 pC/N from a PDMS/PZT nanocomposite exhibiting 60% porosity. Preceding this, in 2017, another PDMS nanocomposite was described, wherein BaTiO₃ was incorporated into PDMS to fabricate a stretchable, transparent nanogenerator suitable for self-powered physiological monitoring. Furthermore, in 2016, the incorporation of polar molecules into a polyurethane foam yielded notably high piezoelectric responses, reaching up to 244 pC/N.

Alternative Materials

A vast majority of materials demonstrate at least a weak piezoelectric response. Common examples include sucrose (table sugar), deoxyribonucleic acid (DNA), and various viral proteins, such as those derived from bacteriophages. Additionally, an actuator fabricated from wood fibers (cellulose fibers) has been documented. Cellular polypropylene exhibits D₃₃ responses approaching 200 pC/N. Applications for cellular polypropylene include musical keypads, microphones, and ultrasound-based echolocation systems. More recently, the single amino acid β-glycine has demonstrated a substantial piezoelectric response of 178 pm V⁻¹, a value notably high among biological materials.

Ionic liquids have recently been recognized as the inaugural class of piezoelectric liquids.

Applications

High-Voltage and Power Generation

The direct piezoelectric effect in certain substances, such as quartz, is capable of generating potential differences reaching thousands of volts.

A widely recognized application is the electric cigarette lighter, where actuating a button causes a spring-loaded hammer to strike a piezoelectric crystal. This action generates a high-voltage electric current that traverses a small spark gap, thereby heating and igniting the gas. Similarly, portable sparkers employed for igniting gas stoves operate on the same principle, and numerous modern gas burners incorporate integrated piezo-based ignition systems.
The Defense Advanced Research Projects Agency (DARPA) in the United States has explored a comparable concept through its energy harvesting initiative, which involved attempts to power battlefield equipment using piezoelectric generators integrated into soldiers' boots. Nevertheless, such energy harvesting methods inherently impact the human body. DARPA's endeavor to generate 1–2 watts from continuous shoe impacts during ambulation was discontinued due to both its impracticality and the discomfort experienced by individuals wearing the specialized footwear, resulting from the increased energy expenditure. Additional energy harvesting concepts encompass Crowd Farm, which aims to capture kinetic energy from human movements in public spaces like train stations, and systems designed to convert dance floor activity into electricity. Furthermore, piezoelectric materials can be utilized to harvest vibrations from industrial machinery, thereby charging batteries for emergency power or supplying energy to low-power microprocessors and wireless communication devices.
A piezoelectric transformer functions as an AC voltage multiplier. In contrast to conventional transformers, which rely on magnetic coupling between their input and output, piezoelectric transformers employ acoustic coupling. An input voltage is applied across a segment of a piezoceramic bar, such as PZT, inducing an alternating stress within the bar via the inverse piezoelectric effect, which consequently causes the entire bar to vibrate. The selected vibration frequency typically corresponds to the block's resonant frequency, usually ranging from 100 kilohertz to 1 megahertz. Subsequently, a higher output voltage is generated across a different section of the bar through the direct piezoelectric effect. Step-up ratios exceeding 1,000:1 have been achieved. A notable characteristic of these transformers is their ability to exhibit inductive load behavior when operated above their resonant frequency, a property beneficial for circuits necessitating a controlled soft start. These devices find application in DC–AC inverters for powering cold cathode fluorescent lamps. Piezoelectric transformers represent some of the most compact sources of high voltage.

Sensors

The operational principle of a piezoelectric sensor involves a physical dimension being converted into a force, which then acts upon two opposing surfaces of the sensing element. Sensor design dictates the specific loading modes applicable to the piezoelectric element, including longitudinal, transversal, and shear configurations.

The most prevalent sensor application involves detecting pressure variations manifested as sound, exemplified by piezoelectric microphones, where sound waves deform the piezoelectric material to generate a fluctuating voltage, and piezoelectric pickups utilized in acoustic-electric guitars. A piezoelectric sensor affixed to an instrument's body is commonly referred to as a contact microphone.

Piezoelectric sensors are particularly employed with high-frequency sound in ultrasonic transducers for both medical imaging and industrial nondestructive testing (NDT).

In numerous sensing methodologies, a device can function as both a sensor and an actuator; consequently, the term transducer is frequently favored when describing this dual capability, although most piezoelectric devices inherently possess this property of reversibility, irrespective of its active utilization. Ultrasonic transducers, for instance, are capable of emitting ultrasound waves into a medium, subsequently receiving the reflected waves, and converting them into an electrical signal, typically a voltage. The majority of medical ultrasound transducers are piezoelectric.

Beyond the aforementioned examples, various sensor and transducer applications encompass:

Piezoelectric elements are additionally employed in the detection and generation of sonar waves.
Piezoelectric materials find application in both single-axis and dual-axis tilt sensing systems.
They are utilized for power monitoring in high-power applications, such as medical treatments, sonochemistry, and industrial processing.
Piezoelectric microbalances serve as highly sensitive chemical and biological sensors.
While piezoelectrics are occasionally incorporated into strain gauges, piezoresistive effect elements are more frequently employed for this purpose.
A piezoelectric transducer was integrated into the penetrometer instrument aboard the Huygens Probe.
Piezoelectric transducers are employed in electronic drum pads to register the impact of drumsticks and in medical acceleromyography for detecting muscle movements.
Automotive engine management systems utilize piezoelectric transducers for detecting engine knock, also termed detonation, at specific hertz frequencies. Furthermore, these transducers are employed in fuel injection systems to gauge manifold absolute pressure (MAP sensor), thereby determining engine load and regulating the precise duration of fuel injector activation.
Ultrasonic piezoelectric sensors are employed for detecting acoustic emissions within acoustic emission testing methodologies.
Transit-time ultrasonic flow meters can incorporate piezoelectric transducers.

Actuators

The application of substantial electric fields induces minute alterations in crystal width, enabling sub-micrometer precision adjustments. This characteristic establishes piezoelectric crystals as a critical component for highly accurate object positioning, thereby justifying their extensive use in actuators. Multilayer ceramic configurations, featuring layers thinner than 100 μm, facilitate the generation of high electric fields at voltages below 150 V. These ceramics are integral to two primary actuator types: direct piezo actuators and amplified piezoelectric actuators. While direct actuators typically exhibit strokes under 100 μm, amplified piezoelectric actuators are capable of achieving millimeter-scale displacements.

Loudspeakers: In loudspeakers, voltage is transduced into the mechanical displacement of a metallic diaphragm.
Ultrasonic cleaning systems commonly utilize piezoelectric elements to generate high-intensity sound waves within a liquid medium.
Piezoelectric motors: These motors operate by employing piezoelectric elements to exert a directional force on an axle, inducing rotation. Given the minute displacements involved, piezoelectric motors are considered a high-precision alternative to conventional stepper motors.
Piezoelectric elements are employed in laser mirror alignment, leveraging their capacity to precisely displace substantial masses, such as mirror mounts, over microscopic distances for electronic adjustment of laser mirrors. Through meticulous control of inter-mirror spacing, laser electronics can sustain optimal optical conditions within the laser cavity, thereby maximizing beam output.
A related application involves the acousto-optic modulator, a device that utilizes sound waves, generated by piezoelectric elements within a crystal, to scatter light. This mechanism proves beneficial for precise laser frequency tuning.
Atomic force microscopes and scanning tunneling microscopes utilize converse piezoelectricity to maintain the sensing probe in close proximity to the specimen.
Inkjet printers: Numerous inkjet printers incorporate piezoelectric crystals to facilitate the precise ejection of ink from the print head onto the paper.
Diesel engines: High-performance common rail diesel engines integrate piezoelectric fuel injectors, initially pioneered by Robert Bosch GmbH, as an alternative to the more prevalent solenoid valve mechanisms.
Amplified actuators are utilized for active vibration control.
X-ray shutters.
XY stages are employed for micro-scanning applications in infrared cameras.
Precise patient positioning within active CT and MRI scanners is achieved using piezoelectric systems, as intense radiation or magnetic fields preclude the use of electric motors.
Crystal earpieces occasionally find application in vintage or low-power radio receivers.
High-intensity focused ultrasound can induce localized heating or cavitation, applicable in contexts such as medical treatments within a patient's body or specific industrial chemical processes.
Refreshable braille displays operate by expanding a small crystal through the application of an electric current, which subsequently actuates a lever to elevate individual braille cells.
A piezoelectric actuator functions by expanding a single crystal or an array of crystals through the application of voltage, thereby enabling the movement and control of a mechanism or system.
Piezoelectric actuators are employed for precise servo positioning within hard disk drives.

Frequency Standard

The piezoelectric properties inherent to quartz render it valuable as a frequency standard.

Quartz clocks incorporate a crystal oscillator, fabricated from a quartz crystal, which leverages both direct and converse piezoelectricity to produce a precisely timed sequence of electrical pulses for timekeeping. Analogous to other elastic materials, the quartz crystal possesses a distinct natural resonant frequency, determined by its geometry and dimensions, which is utilized to stabilize the frequency of an applied periodic voltage.
This identical principle is applied in certain radio transmitters, receivers, and computer systems for generating clock pulses. Typically, both applications employ a frequency multiplier to achieve gigahertz operating ranges.

Piezoelectric Motors

Piezoelectric motors encompass several distinct categories:

Ultrasonic motors, commonly employed for autofocus mechanisms in single-lens reflex (SLR) cameras.
Inchworm motors, designed for precise linear motion applications.
Rectangular four-quadrant motors, characterized by a high power density of 2.5 W/cm³ and operational speeds spanning from 10 nm/s to 800 mm/s.
Stepping piezoelectric motors, which utilize the stick-slip phenomenon for movement.

With the exception of the stepping stick-slip motor, these devices operate based on a unified fundamental principle. Their operation involves dual orthogonal vibration modes, phase-shifted by 90°, which induce an elliptical vibrational trajectory at the contact interface between two surfaces, thereby generating a frictional force. Typically, one surface remains stationary, facilitating the movement of the other. The piezoelectric crystal within most of these motors is actuated by a sinusoidal signal at the motor's resonant frequency. This resonant excitation enables the generation of substantial vibration amplitudes with significantly reduced voltage input.

Stick-slip motors function by leveraging the inertia of a mass in conjunction with the frictional properties of a clamping mechanism. These motors are capable of achieving extremely compact dimensions. Specific applications include camera sensor displacement, which facilitates image stabilization functionalities.

Mitigation of Vibrations and Acoustic Noise

Numerous research teams have explored methods for mitigating material vibrations through the integration of piezoelectric elements. Upon detecting a vibrational deflection in one direction, the active vibration reduction system responds by supplying electrical energy to the piezoelectric element, inducing a counter-deflection. Investigations into their application for flexible structures, including shells and plates, have been ongoing for approximately three decades.

Surgical Applications

Piezosurgery represents a minimally invasive surgical methodology designed to incise target tissues while minimizing collateral damage to adjacent structures. For instance, Hoigne et al. utilized frequencies between 25 and 29 kHz, generating microvibrations ranging from 60 to 210 μm. This technique selectively ablates mineralized tissue without compromising neurovascular or other soft tissues, consequently ensuring a bloodless surgical field, enhanced visibility, and superior precision.

Piezoelectric Metamaterials Exhibiting Electro-Momentum Couplings

In 2019, Pernas-Salomón and Shmuel pioneered a dynamic homogenization method, through which they first demonstrated that piezoelectric composites exhibit an effective coupling between linear momentum and the electric field, a phenomenon they designated as electro-momentum coupling. Given that homogeneous piezoelectric materials do not manifest this specific coupling, these composites are categorized as metamaterials—artificially engineered media designed to exhibit exceptional effective properties, either in magnitude or nature. Electro-momentum coupling bears an analogy to Willis coupling observed in elastic composites, which links linear momentum to strain and was initially identified by J. R. Willis. The localized component of these couplings, similar to piezoelectric coupling, originates from broken symmetries. Piezoelectric metamaterials incorporating electro-momentum coupling provide a mechanism for wave manipulation comparable to Willis coupling: they induce a direction-dependent phase shift, facilitating wavefront shaping, and possess the additional benefit of electrical tunability.

References

EN 50324 (2002) specifies the piezoelectric properties of ceramic materials and components, presented in three parts.

EN 50324 (2002) Piezoelectric properties of ceramic materials and components (3 parts)
ANSI-IEEE 176 (1987) establishes the standard for piezoelectricity.
IEEE 177 (1976) provides standard definitions and measurement methodologies for piezoelectric vibrators.
IEC 444 (1973) outlines the fundamental method for measuring the resonant frequency and equivalent series resistance of quartz crystal units using a zero-phase technique within a pi-network configuration.
IEC 302 (1969) defines standard definitions and measurement procedures for piezoelectric vibrators functioning across a frequency range up to 30 MHz.

Gautschi, Gustav H. (2002). Piezoelectric Sensorics. Springer. ISBN 978-3-540-42259-4.

Gautschi, Gustav H. (2002). Piezoelectric Sensorics. Springer. ISBN 978-3-540-42259-4.Source: TORIma Academy Archive

Piezoelectricity