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Piezoelectricity is the electric charge that accumulates in certain solid materials (such as crystals, certain ceramics, and biological matter such as bone, DNA and various proteins)^[1] in response to applied mechanical stress. The word piezoelectricity means electricity resulting from pressure and latent heat. It is derived from the Greek word πιέζειν; piezein, which means to squeeze or press, and ἤλεκτρονēlektron, which means amber, an ancient source of electric charge.^[2][3] French physicists Jacques and Pierre Curie discovered piezoelectricity in ^[4]

The piezoelectric effect results from the linear electromechanical interaction between the mechanical and electrical states in crystalline materials with no inversion symmetry.^[5] The piezoelectric effect is a reversible process: materials exhibiting the piezoelectric effect (the internal generation of electrical charge resulting from an applied mechanical force) also exhibit the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an applied electrical field. For example, lead zirconate titanate crystals will generate measurable piezoelectricity when their static structure is deformed by about % of the original dimension. Conversely, those same crystals will change about % of their static dimension when an external electric field is applied to the material. The inverse piezoelectric effect is used in the production of ultrasonic sound waves.^[6]

Piezoelectricity is exploited in a number of useful applications, such as the production and detection of sound, piezoelectric inkjet printing, generation of high voltages, clock generator in electronics, microbalances, to drive an ultrasonic nozzle, and ultrafine focusing of optical assemblies. It forms the basis for a number of scientific instrumental techniques with atomic resolution, the scanning probe microscopies, such as STM, AFM, MTA, and SNOM. It also finds everyday uses such as acting as the ignition source for cigarette lighters, push-start propane barbecues, used as the time reference source in quartz watches, as well as in amplificationpickups for some guitars and triggers in most modern electronic drums.^[7][8]

History[edit]

Discovery and early research[edit]

The pyroelectric effect, by which a material generates an electric potential in response to a temperature change, was studied by Carl Linnaeus and Franz Aepinus in the midth century. Drawing on this knowledge, both René Just Haüy and Antoine César Becquerel posited a relationship between mechanical stress and electric charge; however, experiments by both proved inconclusive.^[9]

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 by the brothers Pierre Curie and Jacques Curie.^[10] 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 of tourmaline, quartz, topaz, canesugar, and Rochelle salt (sodium potassium tartrate tetrahydrate). Quartz and Rochelle salt exhibited 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 by Gabriel Lippmann in ^[11] The Curies immediately confirmed the existence of the converse effect,^[12] 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 and Marie Curie in More work was done to explore and define the crystal structures that exhibited piezoelectricity. This culminated in with the publication of Woldemar Voigt's Lehrbuch der Kristallphysik (Textbook on Crystal Physics),^[13] which described the 20 natural crystal classes capable of piezoelectricity, and rigorously defined the piezoelectric constants using tensor analysis.

World War I and post-war[edit]

The first practical application for piezoelectric devices was sonar, first developed during World War I. In France in , Paul Langevin and his coworkers developed an ultrasonicsubmarine detector.^[14] The detector consisted of a transducer, made of thin quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. 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. Ceramic phonograph cartridges 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. Ultrasonic time-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[edit]

During World War II, independent research groups in the United States, Russia, and Japan discovered a new class of synthetic materials, called ferroelectrics, which exhibited piezoelectric constants many times higher than natural materials. This led to intense research to develop barium titanate and later lead zirconate titanate materials with specific properties for particular applications.

One significant example of the use of piezoelectric crystals was developed by Bell 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 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 by Issac 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 the piezoelectric 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 several car models as an echolocation device, helping the driver determine the distance from the car to any objects that may be in its path.

Mechanism[edit]

Piezoelectric plate used to convert audio signal to sound waves

The nature of the piezoelectric effect is closely related to the occurrence of electric dipole moments in solids. The latter may either be induced for ions on crystal lattice sites with asymmetric charge surroundings (as in BaTiO₃ and PZTs) or may directly be carried by molecular groups (as in cane sugar). The dipole density or polarization (dimensionality [C·m/m³] ) may easily be calculated for crystals by summing up the dipole moments per volume of the crystallographic unit cell.^[15] As every dipole is a vector, the dipole density P is a vector 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 of poling (not the same as magnetic 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.^[16]

Of decisive importance for the piezoelectric effect is the change of polarization P when applying a mechanical 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 of P within the crystal; 2. crystal symmetry; and 3. the applied mechanical stress. The change in P appears as a variation of surface charge density upon the crystal faces, i.e. as a variation of the electric field extending between the faces caused by a change in dipole density in the bulk. For example, a 1&#;cm³ cube of quartz with 2&#;kN (&#;lbf) of correctly applied force can produce a voltage of V.^[17]

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

Mathematical description[edit]

Linear piezoelectricity is the combined effect of

• The linear electrical behavior of the material:

where D is the electric flux density^[18][19] (electric displacement), ε is permittivity (free-body dielectric constant), E is electric field strength, and .

where S is the linearized strain, s is compliance under short-circuit conditions, T is stress, and

.

These may be combined into so-called coupled equations, of which the strain-charge form is:^[20]

In matrix form,

where [d] is the matrix for the direct piezoelectric effect and [d^t] is the matrix for the converse piezoelectric effect. The superscript E indicates a zero, or constant, electric field; the superscript T indicates a zero, or constant, stress field; and the superscript t stands for transposition of a matrix.

Notice that the third order tensor 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 the 4mm (C_4v) crystal class (such as a poled piezoelectric ceramic such as tetragonal PZT or BaTiO₃) as well as the 6mm crystal class may also be written as (ANSI IEEE ):

where the first equation represents the relationship for the converse piezoelectric effect and the latter for the direct piezoelectric effect.^[21]

Although the above equations are the most used form in literature, some comments about the notation are necessary. Generally, D and E are vectors, that is, Cartesian tensors of rank 1; and permittivity ε is a Cartesian tensor of rank 2. Strain and stress are, in principle, also rank-2 tensors. 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 why S and T appear to have the "vector form" of six components. Consequently, s appears to be a 6-by-6 matrix instead of a rank-3 tensor. Such a relabeled notation is often called Voigt notation. Whether the shear strain components S₄, S₅, S₆ are 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 as S₆&#;=&#;2S₁₂ and so on. This also means that s₆₆&#;=&#;1/G₁₂, where G₁₂ is the shear modulus.

In total, there are four piezoelectric coefficients, d_ij, e_ij, g_ij, and h_ij defined as follows:

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, and the reason why the direct piezoelectric tensor is equal to the transpose of the converse piezoelectric tensor originated from the Maxwell Relations in Thermodynamics.^[22] 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 coefficients d_ij from electrostatic lattice constants or higher-order Madelung constants.^[15]

Crystal classes[edit]

Any spatially separated charge will result in an electric field, and therefore an electric potential. Shown here is a standard dielectric in a capacitor. 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 32 crystal classes, 21 are non-centrosymmetric (not having a centre of symmetry), and of these, 20 exhibit direct piezoelectricity^[23] (the 21st is the cubic class ). Ten of these represent the polar crystal classes,^[24] which show a spontaneous polarization without mechanical stress due to a non-vanishing electric dipole moment associated with their unit cell, and which exhibit pyroelectricity. If the dipole moment can be reversed by applying an external electric field, the material is said to be ferroelectric.

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