3242:
1975:
3237:{\displaystyle {\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}}\\&{\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}}}
5373:
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.
31:
4005:
3421:
4000:{\displaystyle {\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}\\e_{ij}&={\phantom {+}}\left({\frac {\partial D_{i}}{\partial S_{j}}}\right)^{E}&&=-\left({\frac {\partial T_{j}}{\partial E_{i}}}\right)^{S}\\g_{ij}&=-\left({\frac {\partial E_{i}}{\partial T_{j}}}\right)^{D}&&={\phantom {+}}\left({\frac {\partial S_{j}}{\partial D_{i}}}\right)^{T}\\h_{ij}&=-\left({\frac {\partial E_{i}}{\partial S_{j}}}\right)^{D}&&=-\left({\frac {\partial T_{j}}{\partial D_{i}}}\right)^{S}\end{aligned}}}
4675:(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.
417:
1593:
4036:
4974:
5212:
1245:
633:
4273:(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 with
4816:
3274:. 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
4488:
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 Nb
1588:{\displaystyle {\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},\\\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}}}
4827:
600:. 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.
4262:
4389:. 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 are
612:. 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
5366:
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.
604:
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.
4712:, 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) as compared to other biological materials.
714:. 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
4770:' 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 include
4063:(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 exhibit
4774:, harvesting the energy from human movements in train stations or other public places and 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.
616:, 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
5365:
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
4885:
is 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).
4797:
to 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
5391:
nanotubes. 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
4678:
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
556:
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.
5291:
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
5042:
mirror 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
603:
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
4514:
temperatures 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,
4949:
use 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
4682:
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
5644:
Hankel, W. G. (1881). "Elektrische
Untersuchungen. Fünfzehnte Abhandlung. Über die aktino- und piezoelektrischen Eigenschaften des Bergkrystalles und ihre Beziehung zu den thermoelektrischen" [Electrical researches. Fifteenth treatise. On the radiative- and piezoelectric properties of rock
4505:
mining 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
4487:
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
4509:
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
4010:
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 the
5372:
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
5320:
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
5356:
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.
463:
1213:
1102:
5321:
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)
5392:
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.
548:
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.
4496:
component, 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
4642:
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:
4424: ≈ 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.
4236: – 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.
1898:
4851:
is 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.
4687:
was 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.
6858:
Ma, Si Wei; Fan, You Jun; Li, Hua Yang; Su, Li; Wang, Zhong Lin; Zhu, Guang (2018-09-07). "Flexible Porous
Polydimethylsiloxane/Lead Zirconate Titanate-Based Nanogenerator Enabled by the Dual Effect of Ferroelectricity and Piezoelectricity".
5292:
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.
5657:"Da die durch Druck erzeugte Elektricität sonach auch besonderen Gesetzen unterliegt, so wird es angemessen sein, derselben gleichfalls einen besonderen Namen beizulegen, und es dürfte sich dazu die Bezeichnung Piezoelektricität eignen."
4626:
is 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 smaller
808:
312:
by 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 of
6910:
Chen, Xiaoliang; Parida, Kaushik; Wang, Jiangxin; Xiong, Jiaqing; Lin, Meng-Fang; Shao, Jinyou; Lee, Pooi See (2017-11-20). "A Stretchable and
Transparent Nanocomposite Nanogenerator for Self-Powered Physiological Monitoring".
7430:
Le Letty, R.; Barillot, F.; Lhermet, N.; Claeyssen, F.; Yorck, M.; Gavira
Izquierdo, J.; Arends, H. (2001). "The scanning mechanism for ROSETTA/MIDAS from an engineering model to the flight model". In Harris, R. A. (ed.).
5659:(Since the electricity generated by pressure is therefore also subject to special laws, then it will likewise be appropriate to give it a special name, and for this, the designation "piezoelectricity" might be suitable.)
432:. 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
5877:(1880). "Développement par compression de l'électricité polaire dans les cristaux hémièdres à faces inclinées" [Development, via compression, of electric polarization in hemihedral crystals with inclined faces].
474:
in 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.
4410:). 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 high
3426:
4015:
of 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 coefficients
5163:
made 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 any
4510:
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 the
7081:
Guerin, Sarah; Stapleton, Aimee; Chovan, Drahomir; Mouras, Rabah; Gleeson, Matthew; McKeown, Cian; Noor, Mohamed Radzi; Silien, Christophe; Rhen, Fernando M. F.; Kholkin, Andrei L.; Liu, Ning (February 2018).
545:. 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.
6122:
1137:
874:
738:
extending between the faces caused by a change in dipole density in the bulk. For example, a 1 cm cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500
607:
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
996:
3311:
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(
1980:
1736:
1250:
4639:, 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.
7495:
976:
5283:
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.
8153:
7465:
4393:(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.
6569:
Saito, Yasuyoshi; Takao, Hisaaki; Tanil, Toshihiko; Nonoyama, Tatsuhiko; Takatori, Kazumasa; Homma, Takahiko; Nagaya, Toshiatsu; Nakamura, Masaya (2004-11-04). "Lead-free piezoceramics".
1720:
938:
6526:
Ganeshkumar, Rajasekaran; Somnath, Suhas; Cheah, Chin Wei; Jesse, Stephen; Kalinin, Sergei V.; Zhao, Rong (2017-12-06). "Decoding
Apparent Ferroelectricity in Perovskite Nanofibers".
7793:
8392:
561:(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.
1946:
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.
5387:
that 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 using
1944:
1731:
1644:
1620:
5839:
328:
discovered piezoelectricity in 1880. The piezoelectric effect has been exploited in many useful applications, including the production and detection of sound, piezoelectric
478:
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
7232:"True Grid Independence: Robust Energy Harvesting System for Wireless Sensors Uses Piezoelectric Energy Harvesting Power Supply and Li-Poly Batteries with Shunt Charger"
4679:
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.
5667:
Elektrische
Untersuchungen. Fünfzehnte Abhandlung. Über die aktino- und piezoelektrischen Eigenschaften des Bergkrystalles und ihre Beziehung zu den thermoelektrischen
5380:
has 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.
4403:
6989:
Lee, B. Y.; Zhang, J.; Zueger, C.; Chung, W. J.; Yoo, S. Y.; Wang, E.; Meyer, J.; Ramesh, R.; Lee, S. W. (2012-05-13). "Virus-based piezoelectric energy generation".
6684:
Ibn-Mohammed, T., Koh, S., Reaney, I., Sinclair, D., Mustapha, K., Acquaye, A., & Wang, D. (2017). "Are lead-free piezoelectrics more environmentally friendly?"
7395:
Shabestari, N. P. (2019). "Fabrication of a simple and easy-to-make piezoelectric actuator and its use as phase shifter in digital speckle pattern interferometry".
470:
The Curies, however, did not predict the converse piezoelectric effect. The converse effect was mathematically deduced from fundamental thermodynamic principles by
4611:
4789:, 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 the
8117:
4781:
is a type of AC voltage multiplier. Unlike a conventional transformer, which uses magnetic coupling between input and output, the piezoelectric transformer uses
4123:
different 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 (
693:. 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
8075:
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
7297:
4051:. In a piezoelectric device, mechanical stress, instead of an externally applied voltage, causes the charge separation in the individual atoms of the material.
5276:
force between the surfaces. Usually, one surface is fixed, causing the other to move. In most piezoelectric motors, the piezoelectric crystal is excited by a
701:), a process by which a strong electric field is applied across the material, usually at elevated temperatures. Not all piezoelectric materials can be poled.
7995:
8423:
6165:
771:
7968:
8127:
482:
in 1898. More work was done to explore and define the crystal structures that exhibited piezoelectricity. This culminated in 1910 with the publication of
4506:
components has not grown to a significant scale at this time, but from early analysis, experts encourage caution when it comes to environmental effects.
8122:
7551:
7473:
8180:
8107:
7578:"The effectiveness of intracytoplasmic sperm injection combined with piezoelectric stimulation in infertile couples with total fertilization failure"
5136:
Piezoelectric actuator. A single crystal or a number of crystals are expanded by applying a voltage for moving and controlling a mechanism or system.
5050:, a device that scatters light off soundwaves in a crystal, generated by piezoelectric elements. This is useful for fine-tuning a laser's frequency.
5280:
signal at the resonant frequency of the motor. Using the resonance effect, a much lower voltage can be used to produce a high vibration amplitude.
4524:
5369:
Several attempts at the macro-scale application of the piezoelectric technology have emerged to harvest kinetic energy from walking pedestrians.
4108: ≠ 0 holds without applying a mechanical load, the piezoelectric effect manifests itself by changing the magnitude or the direction of
3247:
where the first equation represents the relationship for the converse piezoelectric effect and the latter for the direct piezoelectric effect.
7216:
7617:
Manbachi, A. & Cobbold, R.S.C. (2011). "Development and
Application of Piezoelectric Materials for Ultrasound Generation and Detection".
5746:
Manbachi, A. & Cobbold, R.S.C. (2011). "Development and
Application of Piezoelectric Materials for Ultrasound Generation and Detection".
8078:
IEC 302 (1969) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators Operating over the Freq Range up to 30 MHz
7166:
30:
7785:
7349:
Moubarak, P.; et al. (2012). "A Self-Calibrating Mathematical Model for the Direct Piezoelectric Effect of a New MEMS Tilt Sensor".
6331:
5782:
5031:, causing it to rotate. Due to the extremely small distances involved, the piezo motor is viewed as a high-precision replacement for the
4614:. Such effects are generally recognized to be at least important if not of the same order of magnitude as the first order approximation.
1208:{\displaystyle \nabla \cdot {\boldsymbol {T}}=\mathbf {0} \,\,,\,{\boldsymbol {S}}={\frac {\nabla \mathbf {u} +\mathbf {u} \nabla }{2}},}
8428:
8418:
6357:
5264:
Aside from the stepping stick-slip motor, all these motors work on the same principle. Driven by dual orthogonal vibration modes with a
494:), which described the 20 natural crystal classes capable of piezoelectricity, and rigorously defined the piezoelectric constants using
1097:{\displaystyle {\boldsymbol {S}}={\mathsf {s}}\,{\boldsymbol {T}}\quad \implies \quad S_{ij}=\sum _{k,\ell }s_{ijk\ell }\,T_{k\ell }\;}
368:. The piezoelectric effect also finds everyday uses, such as generating sparks to ignite gas cooking and heating devices, torches, and
7576:
Baltaci, Volkan; Ayvaz, Özge Üner; Ünsal, Evrim; Aktaş, Yasemin; Baltacı, Aysun; Turhan, Feriba; Özcan, Sarp; Sönmezer, Murat (2009).
6033:
4874:
Piezoelectric sensors especially are used with high frequency sound in ultrasonic transducers for medical imaging and also industrial
4523:
A piezoelectric potential can be created in any bulk or nanostructured semiconductor crystal having non central symmetry, such as the
8148:
6009:
5066:: On many inkjet printers, piezoelectric crystals are used to drive the ejection of ink from the inkjet print head towards the paper.
4984:
As very high electric fields correspond to only tiny changes in the width of the crystal, this width can be changed with better-than-
813:
256:
7844:
7193:
5946:
5918:
7808:
7523:
1903:
where is the matrix for the direct piezoelectric effect and is the matrix for the converse piezoelectric effect. The superscript
8372:
6954:
Moody, M. J.; Marvin, C. W.; Hutchison, G. R. (2016). "Molecularly-doped polyurethane foams with massive piezoelectric response".
5352:
is a minimally invasive technique that aims to cut a target tissue with little damage to neighboring tissues. For example, Hoigne
6239:
Damjanovic, Dragan (1998). "Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics".
4802:
load, which is useful in circuits that require a controlled soft start. These devices can be used in DC–AC inverters to drive
3250:
Although the above equations are the most used form in literature, some comments about the notation are necessary. Generally,
8472:
8173:
8098:
7448:
7189:
6455:
6148:
5730:
5705:
5544:
5515:
5307:
showed several panels that were hit with a rubber mallet, and the panel with the piezo element immediately stopped swinging.
945:
1966:
589:, which exhibited piezoelectric constants many times higher than natural materials. This led to intense research to develop
5588:
8382:
5975:
4743:: pressing the button causes a spring-loaded hammer to hit a piezoelectric crystal, producing a sufficiently high-voltage
8464:
4988:
precision, making piezo crystals the most important tool for positioning objects with extreme accuracy—thus their use in
293:
8441:
300:
also exhibit the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an applied
7328:
6768:
5580:
5300:
5686:
Piezoelectric Sensorics: Force, Strain, Pressure, Acceleration and Acoustic Emission Sensors, Materials and Amplifiers
8503:
8387:
8362:
5120:
8132:
7305:
8166:
7930:
6204:"IEC 60050 – International Electrotechnical Vocabulary – Details for IEV number 121-11-40: "electric flux density""
5966:
5689:
5377:
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5001:
43:
8282:
7991:
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1649:
909:
514:. The superior performance of piezoelectric devices, operating at ultrasonic frequencies, superseded the earlier
297:
6203:
4855:
Detection of pressure variations in the form of sound is the most common sensor application, e.g. piezoelectric
8377:
7846:
Known and unknown phenomena of nonlinear behaviors in the power harvesting mat and the transverse wave speaker
7433:
Proceedings of the 9th European Space Mechanisms and Tribology Symposium, 19–21 September 2001, Liège, Belgium
8508:
5856:
5057:
4803:
4252:) – although it occurs in nature as mineral macedonite, it is synthesized for research and applications.
239:
17:
7552:"Isn't it amazing how one smart idea, one chip and an intelligent material has changed the world of tennis?"
5647:
Abhandlungen der Mathematisch-Physischen Klasse der Königlichen-Säschsischen Gesellschaft der Wissenschaften
4542:
materials, due to polarization of ions under applied stress and strain. This property is common to both the
4269:
Ceramics with randomly oriented grains must be ferroelectric to exhibit piezoelectricity. The occurrence of
7555:
4067:. If the dipole moment can be reversed by applying an external electric field, the material is said to be
8312:
7703:
Labanca, M.; Azzola, F.; Vinci, R.; Rodella, L. F. (2008). "Piezoelectric surgery: twenty years of use".
5629:
5605:
5566:
5462:
5330:
5133:. A small crystal is expanded by applying a current that moves a lever to raise individual braille cells.
5130:
597:
1893:{\displaystyle {\begin{aligned}\{S\}&=\left\{T\}+\{E\},\\\{D\}&=\{T\}+\left\{E\},\end{aligned}}}
8523:
8513:
8330:
7878:
6139:(2008). "Chapter 3: Crystal Chemistry of Piezoelectric Materials". In A. Safari; E.K. Akdo˘gan (eds.).
6000:[Contractions and expansions produced by voltages in hemihedral crystals with inclined faces].
5600:
5108:
4906:
4860:
4386:
1113:
624:
device, helping the driver determine the distance from the car to any objects that may be in its path.
7250:
6380:
6049:"Who knew piezoelectricity? Rutherford and Langevin on submarine detection and the invention of sonar"
5998:"Contractions et dilatations produites par des tensions dans les cristaux hémièdres à faces inclinées"
4583:. The semiconductors where the strongest piezoelectricity is observed are those commonly found in the
4327: ≤ 1) – more commonly known as PZT, the most common piezoelectric ceramic in use today.
406:
8528:
8265:
5907:"Développement, par pression, de l'électricité polaire dans les cristaux hémièdres à faces inclinées"
5104:
5012:
4954:
4228:
1950:
1925:
1625:
1601:
558:
353:
345:
6408:
5845:. Department of Physics, Technical University of Liberec. Archived from the original on May 8, 2014.
4417:. Certain compositions of this material have been shown to retain a high mechanical quality factor (
3286:
appears to be a 6-by-6 matrix instead of a rank-3 tensor. Such a relabeled notation is often called
7208:
6622:
Gurdal, Erkan A.; Ural, Seyit O.; Park, Hwi-Yeol; Nahm, Sahn; Uchino, Kenji (2011). "High Power (Na
5477:
4864:
4766:, which includes an attempt to power battlefield equipment by piezoelectric generators embedded in
4648:
1622:
is the piezoelectric tensor and the superscript t stands for its transpose. Due to the symmetry of
8142:
593:
and later lead zirconate titanate materials with specific properties for particular applications.
8456:
8347:
7879:"Analysis and experimental validation of the figure of merit for piezoelectric energy harvesters"
7158:
6284:
6136:
5053:
5047:
4786:
4672:
4652:
4472:
4289:
902:
305:
278:
4881:
For many sensing techniques, the sensor can act as both a sensor and an actuator—often the term
4755:
work the same way, and many types of gas burners now have built-in piezo-based ignition systems.
466:
A piezoelectric disk generates a voltage when deformed (change in shape is greatly exaggerated).
6403:
4961:
4875:
4550:
crystal structures. To first order, there is only one independent piezoelectric coefficient in
4274:
4176:
1121:
645:
416:
232:
6327:
5790:
5665:
4785:. An input voltage is applied across a short length of a bar of piezoceramic material such as
750:, where the application of an electrical field creates mechanical deformation in the crystal.
8072:
IEEE 177 (1976) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators
6353:
5472:
5452:
5437:
5310:
Piezoelectric ceramic fiber technology is being used as an electronic damping system on some
4917:
4859:(sound waves bend the piezoelectric material, creating a changing voltage) and piezoelectric
4390:
4270:
3335:). Engineering shear strains are double the value of the corresponding tensor shear, such as
886:
309:
8300:
8137:
6027:
8518:
8434:
8259:
7751:
7436:
7358:
6998:
6812:
6724:
6643:
6580:
6485:
6395:
6293:
6248:
6098:
5432:
5412:
5199:
5176:, and this is used to stabilize the frequency of a periodic voltage applied to the crystal.
5165:
4842:
4732:
1916:
672:
515:
6723:. AIP Conference Proceedings. AIP Conference Proceedings. Vol. 1590. pp. 32–41.
5997:
4889:
In addition to those mentioned above, various sensor and transducer applications include:
288:
interaction between the mechanical and electrical states in crystalline materials with no
8:
8448:
8213:
7853:
7181:
5934:
5906:
5220:
5024:
5018:
4946:
402:
7819:
7755:
7440:
7362:
7002:
6816:
6728:
6647:
6584:
6489:
6399:
6297:
6252:
6102:
6087:"Crystal-field induced dipoles in heteropolar crystals – II. physical significance"
4938:
to detect the impact of the drummer's sticks, and to detect muscle movements in medical
698:
8480:
8324:
8045:
7908:
7680:
7653:
7634:
7412:
7374:
7278:
7058:
7033:
6892:
6835:
6800:
6667:
6604:
6421:
6309:
6264:
6114:
5763:
5238:
5160:
5149:
4868:
4696:
Most materials exhibit at least weak piezoelectric responses. Trivial examples include
4628:
4044:
3259:
942:
424:
The first demonstration of the direct piezoelectric effect was in 1880 by the brothers
410:
390:
212:
8066:
EN 50324 (2002) Piezoelectric properties of ceramic materials and components (3 parts)
8017:
7652:
Hoigne, D.J.; Stubinger, S.; von Kaenel, O.; Shamdasani, S.; Hasenboehler, P. (2006).
6282:
Kochervinskii, V. (2003). "Piezoelectricity in Crystallizing Ferroelectric Polymers".
4035:
803:{\displaystyle \mathbf {D} ={\boldsymbol {\varepsilon }}\,\mathbf {E} \quad \implies }
8367:
8238:
8223:
8218:
8094:
8037:
7912:
7767:
7720:
7685:
7599:
7594:
7577:
7444:
7416:
7282:
7270:
7111:
7103:
7063:
7014:
6971:
6936:
6928:
6884:
6876:
6840:
6799:
Sappati, Kiran; Bhadra, Sharmistha; Sappati, Kiran Kumar; Bhadra, Sharmistha (2018).
6774:
6764:
6671:
6659:
6596:
6551:
6543:
6497:
6268:
6260:
6144:
6118:
6086:
5850:
5726:
5701:
5540:
5511:
5482:
5442:
5384:
5127:
can be achieved, for example, in patient's body or in an industrial chemical process.
5081:
4939:
4782:
4763:
4330:
4196:
4024:
4012:
711:
621:
542:
341:
285:
8049:
7638:
7378:
6896:
6313:
5767:
5000:. These ceramics are used within two kinds of actuators: direct piezo actuators and
4893:
Piezoelectric elements are also used in the detection and generation of sonar waves.
8029:
7946:
7942:
7898:
7890:
7763:
7759:
7712:
7675:
7665:
7626:
7589:
7404:
7366:
7262:
7095:
7053:
7045:
7006:
6963:
6920:
6868:
6830:
6820:
6732:
6651:
6608:
6588:
6571:
6535:
6493:
6425:
6417:
6413:
6301:
6256:
6106:
6060:
5886:
5755:
5693:
5427:
5422:
5417:
5402:
5230:
5187:
5114:
4744:
4632:
4535:
4511:
4454:
4340:
3263:
1129:
721:
586:
471:
357:
133:
127:
59:
7852:. international symposium on nonlinear theory and its applications. Archived from
6440:
5060:
employ converse piezoelectricity to keep the sensing needle close to the specimen.
4973:
3270:
is a Cartesian tensor of rank 2. Strain and stress are, in principle, also rank-2
704:
Of decisive importance for the piezoelectric effect is the change of polarization
420:
View of piezo crystal in the top of a Curie compensator in the Museum of Scotland.
308:
crystals will generate measurable piezoelectricity when their static structure is
8145:– Online database for piezoelectric materials, their properties, and applications
7877:
Deutz, D.B.; Pascoe, J.-A.; van der Zwaag, S.; de Leeuw, D.M.; Groen, P. (2018).
7654:"Piezoelectric osteotomy in hand surgery: first experiences with a new technique"
7130:
7049:
5624:
5610:
5561:
4935:
4709:
4644:
4444:
4427:
4186:
4075:
The 10 polar (pyroelectric) crystal classes: 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm.
4064:
4060:
653:
590:
495:
386:
365:
361:
333:
329:
184:
7931:"Modelling piezoelectric energy harvesting potential in an educational building"
7716:
7266:
7249:
Bahl, Shashi; Nagar, Himanshu; Singh, Inderpreet; Sehgal, Shankar (2020-01-01).
5211:
5139:
Piezoelectric actuators are used for fine servo positioning in hard disc drives.
8208:
8112:
7408:
6023:
5961:
5937:[On electric polarization in hemihedral crystals with inclined faces].
5467:
5447:
5311:
5243:
5085:
5063:
4636:
4531:
4117:
For the nonpolar but piezoelectric crystals, on the other hand, a polarization
4040:
3287:
1958:
984:
735:
731:
644:
The nature of the piezoelectric effect is closely related to the occurrence of
613:
537:, made of thin quartz crystals carefully glued between two steel plates, and a
483:
301:
289:
8108:
Piezoelectric cellular polymer films: Fabrication, properties and applications
7370:
5697:
1911:
indicates a zero, or constant, stress field; and the superscript t stands for
596:
One significant example of the use of piezoelectric crystals was developed by
8497:
8318:
8018:"Acoustic Enhancement of Polymer/ZnO Nanorod Photovoltaic Device Performance"
7274:
7135:
7107:
6975:
6932:
6880:
6778:
6663:
6547:
5989:
5926:
5898:
5870:
5596:
5503:
5457:
5314:
5265:
5077:
5069:
5032:
5021:
usually uses piezoelectric elements to produce intense sound waves in liquid.
4924:
4900:
4820:
4705:
4245:
4068:
4056:
574:
523:
456:
452:
429:
398:
394:
321:
7630:
7610:
7320:
7257:. International Conference on Aspects of Materials Science and Engineering.
5890:
5759:
4953:
Ultrasonic piezo sensors are used in the detection of acoustic emissions in
4515:
diffusing phase transitions, domain engineering, and chemical modification.
8397:
8352:
8292:
8193:
8041:
8033:
7903:
7771:
7724:
7689:
7670:
7603:
7115:
7067:
7018:
6940:
6924:
6888:
6872:
6844:
6655:
6600:
6555:
6539:
6065:
6048:
5993:
5930:
5902:
5874:
5349:
5156:
5111:
scanners where the strong radiation or magnetism precludes electric motors.
4913:
4896:
Piezoelectric materials are used in single-axis and dual-axis tilt sensing.
4715:
4604:
4434:) – a promising candidate for the replacement of lead-based ceramics.
894:
690:
637:
570:
425:
337:
325:
273:' (an ancient source of static electricity). The German form of the word (
35:
8306:
7083:
7010:
6472:
Burke, E. A. J.; Kieft, C. (1971). "Second occurrence of makedonite, PbTiO
5739:
4923:
A piezoelectric transducer was used in the penetrometer instrument on the
4751:, thus heating and igniting the gas. The portable sparkers used to ignite
632:
344:, and in ultrafine focusing of optical assemblies. It forms the basis for
8189:
8158:
7786:"New understanding of electromagnetism could enable 'antennas on a chip'"
5935:"Sur l'électricité polaire dans les cristaux hémièdres à faces inclinées"
5813:
5268:
difference of 90°, the contact point between two surfaces vibrates in an
5195:
5183:
5073:
4778:
4527:
511:
479:
228:
220:
39:
6592:
4815:
4451:) – Barium titanate was the first piezoelectric ceramic discovered.
8402:
7894:
7496:"Second-generation Micro Actuator for Better Head-positioning Accuracy"
6967:
6110:
5388:
5257:
5234:
5173:
5124:
4985:
4931:
4856:
4806:. Piezo transformers are some of the most compact high voltage sources.
4771:
4631:. Other properties that make these materials significant include their
4551:
4543:
4382:
4239:
906:
668:
617:
609:
553:
538:
534:
527:
445:
433:
413:
and electric charge; however, experiments by both proved inconclusive.
314:
7084:"Control of piezoelectricity in amino acids by supramolecular packing"
6825:
6737:
6305:
5015:: Voltage is converted to mechanical movement of a metallic diaphragm.
4731:
Direct piezoelectricity of some substances, like quartz, can generate
1961:(such as a poled piezoelectric ceramic such as tetragonal PZT or BaTiO
8138:
DoITPoMS Teaching and Learning Package – Piezoelectric Materials
7992:"Good vibrations lead to efficient excitations in hybrid solar cells"
7099:
7034:"Stable and Optoelectronic Dipeptide Assemblies for Power Harvesting"
5531:
Holler, F. James; Skoog, Douglas A. & Crouch, Stanley R. (2007).
5296:
5277:
5169:
4989:
4899:
Power monitoring in high power applications (e.g. medical treatment,
4867:. A piezo sensor attached to the body of an instrument is known as a
4794:
4790:
4752:
4748:
4668:
4660:
4656:
4539:
4298:
4219:
4211:
4158:
4048:
1912:
810:
680:
530:
262:
245:
7739:
6701:
Wu, Jiagang. (2020). "Perovskite lead-free piezoelectric ceramics."
4831:
679:
by summing up the dipole moments per volume of the crystallographic
27:
Electric charge generated in certain solids due to mechanical stress
8233:
7651:
7231:
5407:
5273:
5249:
Rectangular four-quadrant motors with high power density (2.5
5191:
4799:
4664:
4584:
4559:
4547:
4306:
4278:
676:
369:
224:
7131:"Liquid Salts Bring Push-button Lenses Into Focus – IEEE Spectrum"
4562:, there are instead three independent piezoelectric coefficients:
3282:
appear to have the "vector form" of six components. Consequently,
746:
Piezoelectric materials also show the opposite effect, called the
5840:"Piezoelectricity and ferroelectricity: Phenomena and properties"
5536:
5304:
5269:
4826:
4767:
4740:
4697:
4623:
4222:
3271:
208:
196:
192:
47:
7876:
7429:
6141:
Piezoelectric and Acoustic Materials for Transducer Applications
8357:
8243:
5662:
The above article was also published separately as a pamphlet:
5334:
4978:
4848:
4610:
Since 2006, there have also been a number of reports of strong
4316:
4282:
4206:
1907:
indicates a zero, or constant, electric field; the superscript
869:{\displaystyle \quad D_{i}=\sum _{j}\varepsilon _{ij}\,E_{j}\;}
657:
519:
437:
8393:
Maria Skłodowska-Curie National Research Institute of Oncology
7251:"Smart materials types, properties and applications: A review"
7159:"Japan: Producing Electricity from Train Station Ticket Gates"
6759:
Heywang, Walter; Lubitz, Karl; Wersing, Wolfram, eds. (2008).
4996:, allow reaching high electric fields with voltage lower than
506:
The first practical application for piezoelectric devices was
462:
110:
86:
68:
5589:
5581:
5180:
5094:
5039:
4835:
4759:
4261:
4233:
582:
507:
448:
441:
270:
188:
7740:"Electromagnetic Radiation Under Explicit symmetry Breaking"
6761:
Piezoelectricity : evolution and future of a technology
6525:
6379:
Akizuki, Mizuhiko; Hampar, Martin S.; Zussman, Jack (1979).
4718:
were recently identified as the first piezoelectric liquid.
7961:"Goodyear Is Trying to Make an Electricity-Generating Tire"
7080:
5250:
5028:
4909:
are used as very sensitive chemical and biological sensors.
4294:
740:
649:
578:
349:
200:
175:
166:
160:
151:
145:
139:
116:
104:
95:
74:
8016:
Shoaee, S.; Briscoe, J.; Durrant, J. R.; Dunn, S. (2013).
7809:"And if public transport does not consume more of energy?"
6798:
5645:
crystal and their relation to the thermoelectric .].
5253:/cm) and speed ranging from 10 nm/s to 800 mm/s.
5008:, amplified piezo actuators can reach millimeter strokes.
552:
Piezoelectric devices found homes in many fields. Ceramic
7702:
6721:
A Review of Non Linear Piezoelectricity in Semiconductors
6381:"An explanation of anomalous optical properties of topaz"
5148:
The piezoelectrical properties of quartz are useful as a
5027:: Piezoelectric elements apply a directional force to an
5004:. While direct actuator's stroke is generally lower than
4701:
4600:
4596:
4592:
4588:
664:
401:
in the mid-18th century. Drawing on this knowledge, both
204:
8113:
Piezo motor based microdrive for neural signal recording
8015:
7524:"Exceeding Capacity, Speed and Performance Expectations"
5964:[Principle of the conservation of electricity].
4612:
non linear piezoelectric effects in polar semiconductors
667:) or may directly be carried by molecular groups (as in
6568:
4977:
Metal disk with piezoelectric disk attached, used in a
4886:
Most medical ultrasound transducers are piezoelectric.
971:{\displaystyle \nabla \times \mathbf {E} =\mathbf {0} }
7575:
6801:"Piezoelectric Polymer and Paper Substrates: A Review"
5720:
5677:
5172:(caused by its shape and size) at which it prefers to
5100:
XY stages for micro scanning used in infrared cameras.
4960:
Piezoelectric transducers can be used in transit-time
3181:
3091:
2992:
2849:
2792:
2733:
2584:
2485:
2088:
1989:
1969:
crystal class may also be written as (ANSI IEEE 176):
724:; and 3. the applied mechanical stress. The change in
585:
discovered a new class of synthetic materials, called
4023:
from electrostatic lattice constants or higher-order
3424:
3387:
In total, there are four piezoelectric coefficients,
1978:
1928:
1734:
1652:
1628:
1604:
1248:
1140:
999:
948:
912:
816:
774:
455:(sodium potassium tartrate tetrahydrate). Quartz and
172:
163:
148:
142:
113:
107:
92:
80:
71:
62:
8424:
Maria Skłodowska-Curie Monument in Warsaw (Downtown)
7248:
6953:
6758:
6378:
6135:
5286:
4830:
Many rocket-propelled grenades used a piezoelectric
393:
in response to a temperature change, was studied by
169:
157:
136:
101:
89:
83:
65:
7321:"How Rocket-Propelled Grenades Work by Shane Speck"
6988:
6909:
5091:
Active vibration control using amplified actuators.
4285:, and related structures exhibit piezoelectricity:
734:upon the crystal faces, i.e. as a variation of the
8429:Maria Skłodowska-Curie Monument in Warsaw (Ochota)
6621:
5295:In a demonstration at the Material Vision Fair in
4793:frequency of the block, typically in the 100
3999:
3236:
1938:
1892:
1714:
1638:
1614:
1587:
1207:
1096:
970:
932:
868:
802:
758:Linear piezoelectricity is the combined effect of
683:. As every dipole is a vector, the dipole density
501:
8069:ANSI-IEEE 176 (1987) Standard on Piezoelectricity
6438:
5530:
5524:
4992:. Multilayer ceramics, using layers thinner than
4726:
4518:
4078:The other 10 piezoelectric crystal classes: 222,
4039:Any spatially separated charge will result in an
656:sites with asymmetric charge surroundings (as in
284:The piezoelectric effect results from the linear
8495:
6439:Radusinović, Dušan & Markov, Cvetko (1971).
5341:(ICSI) seems to improve fertilization outcomes.
4558:, coupled to shear components of the strain. In
675:(dimensionality ) may easily be calculated for
648:in solids. The latter may either be induced for
7737:
7616:
5745:
762:The linear electrical behavior of the material:
380:
332:, generation of high voltage electricity, as a
6615:
6510:
5962:"Principe de la conservation de l'électricité"
5879:Bulletin de la Société Minérologique de France
5721:Krautkrämer, J. & Krautkrämer, H. (1990).
5714:
5123:for localized heating or creating a localized
5117:are sometimes used in old or low power radios.
4847:The principle of operation of a piezoelectric
8174:
7924:
7922:
7435:. ESA SP-480. Vol. 480. pp. 75–81.
7390:
7388:
6634:-Based Lead-Free Piezoelectric Transformer".
6281:
298:materials exhibiting the piezoelectric effect
277:) was coined in 1881 by the German physicist
7989:
6163:
4651:. Examples of semi-crystalline polymers are
1880:
1874:
1850:
1844:
1825:
1819:
1809:
1803:
1779:
1773:
1745:
1739:
564:
7209:"How to Save the World One Dance at a Time"
7206:
6441:"Macedonite – lead titanate: a new mineral"
6166:"Sensor Sense: Piezoelectric Force Sensors"
6084:
6080:
6078:
6076:
5103:Moving the patient precisely inside active
4739:The best-known application is the electric
4708:. An actuator based on wood fibers, called
4047:. Shown here is a standard dielectric in a
1715:{\displaystyle d_{ijk}^{t}=d_{kji}=d_{kij}}
933:{\displaystyle \nabla \cdot \mathbf {D} =0}
753:
8188:
8181:
8167:
7919:
7394:
7385:
7182:"MIT duo sees people-powered "Crowd Farm""
6718:
6511:Jaffe, B.; Cook, W. R.; Jaffe, H. (1971).
6471:
6238:
5988:
5925:
5897:
5869:
4397:
1480:
1476:
1313:
1309:
1093:
1026:
1022:
865:
799:
795:
8419:Maria Skłodowska-Curie Monument in Lublin
7928:
7902:
7738:Sinha, Dhiraj; Amaratunga, Gehan (2015).
7679:
7669:
7593:
7464:Simonsen, Torben R. (27 September 2010).
7229:
7057:
6857:
6834:
6824:
6736:
6407:
6234:
6232:
6064:
5670:(in German). Leipzig, Germany: S. Hirzel.
5360:
4762:in the United States in a project called
4149:Many materials exhibit piezoelectricity.
1567:
1527:
1465:
1451:
1414:
1366:
1295:
1272:
1165:
1161:
1160:
1079:
1015:
854:
788:
8088:
7929:Li, Xiaofeng; Strezov, Vladimir (2014).
7842:
7806:
7463:
7348:
7295:
6073:
5959:
5683:
5324:
5210:
4972:
4825:
4814:
4260:
4225:that is structurally identical to quartz
4152:
4034:
1949:The strain-charge for a material of the
631:
461:
415:
281:; the English word was coined in 1883.
252: 'to squeeze or press' and
29:
8133:Video demonstration of Piezoelectricity
8118:Research on new Piezoelectric materials
7457:
7156:
5780:
5206:
4704:, viral proteins, including those from
4129: = 0) to a polar one, having
1461:
1453:
1274:
1254:
1167:
1148:
1017:
1001:
784:
14:
8496:
7998:from the original on November 11, 2013
7179:
7157:Richard, Michael Graham (2006-08-04).
6913:ACS Applied Materials & Interfaces
6861:ACS Applied Materials & Interfaces
6528:ACS Applied Materials & Interfaces
6229:
6046:
5811:
5663:
5643:
5225:Types of piezoelectric motor include:
5038:Piezoelectric elements can be used in
4758:A similar idea is being researched by
3290:. Whether the shear strain components
1267:
1010:
533:detector. The detector consisted of a
8473:Marie Curie: The Courage of Knowledge
8162:
7318:
7230:Barbehenn, George H. (October 2010).
7190:Massachusetts Institute of Technology
7031:
6794:
6792:
6790:
6788:
6754:
6752:
6750:
6748:
6719:Migliorato, Max; et al. (2014).
6220:
6214:
6129:
6022:
5502:
5143:
4912:Piezoelectrics are sometimes used in
4265:Tetragonal unit cell of lead titanate
1231:These may be combined into so-called
573:, independent research groups in the
459:exhibited the most piezoelectricity.
7298:"Piezoelectric Technology: A Primer"
7128:
4667:. Non-crystalline polymers, such as
636:Piezoelectric plate used to convert
348:that resolve images at the scale of
8465:Marie Curie, une femme sur le front
6636:Japanese Journal of Applied Physics
5533:Principles of Instrumental Analysis
5179:The same principle is used in some
5043:cavity to optimize the beam output.
4183:) – a quartz-analogous crystal
4173:) – a quartz-analogous crystal
1931:
1922:Notice that the third order tensor
1631:
1607:
1446:
1284:
389:, by which a material generates an
34:Piezoelectric balance presented by
24:
8060:
7129:Choi, Charles Q. (25 March 2023).
6785:
6745:
6692:(1), 1-7. doi: 10.1557/mrc.2017.10
5837:
5622:
5559:
5168:material) has a precisely defined
4950:injectors milliseconds of on time.
4691:
4030:
3967:
3952:
3907:
3892:
3831:
3816:
3765:
3750:
3689:
3674:
3629:
3614:
3547:
3532:
3481:
3466:
1794:
1193:
1177:
1141:
949:
913:
730:appears as a variation of surface
25:
8540:
8388:Pierre and Marie Curie University
8383:Maria Curie-Skłodowska University
8363:IEEE Marie Sklodowska-Curie Award
8082:
7990:Heidi Hoopes (November 8, 2013).
7296:Phillips, James R. (2000-08-10).
7165:. Discovery Communications, LLC.
6360:from the original on 2 April 2015
6334:from the original on 2 April 2015
5814:"Piezo Drum Kit Quickstart Guide"
5287:Reduction of vibrations and noise
5121:High-intensity focused ultrasound
5076:diesel engines use piezoelectric
5002:amplified piezoelectric actuators
897:(free-body dielectric constant),
8442:Maria Skłodowska-Curie Medallion
7971:from the original on 11 May 2016
7935:Energy Conversion and Management
7796:from the original on 2016-03-04.
7595:10.1016/j.fertnstert.2009.03.107
7219:from the original on 2010-10-31.
7207:Kannampilly, Ammu (2008-07-11).
7196:from the original on 2007-09-12.
7169:from the original on 2007-07-09.
6956:Journal of Materials Chemistry C
6461:from the original on 2016-03-05.
6223:Fundamentals of piezoelectricity
6125:from the original on 2016-10-30.
6036:from the original on 2014-04-21.
6012:from the original on 2012-12-05.
5978:from the original on 2016-02-08.
5967:Annales de chimie et de physique
5949:from the original on 2012-12-05.
5921:from the original on 2012-12-05.
5508:Longman Pronunciation Dictionary
5339:intracytoplasmic sperm injection
4683:reported in 2017, in which BaTiO
3349:and so on. This also means that
1467:
1433:
1297:
1189:
1181:
1156:
1124:under short-circuit conditions,
964:
956:
920:
790:
776:
358:electronically amplified guitars
292:. The piezoelectric effect is a
199:, and biological matter such as
132:
58:
8154:Piezo-Theory & Applications
8009:
7983:
7953:
7870:
7843:Takefuji, Y. (September 2008).
7836:
7800:
7778:
7731:
7696:
7645:
7569:
7544:
7516:
7488:
7423:
7342:
7331:from the original on 2012-04-29
7312:
7289:
7242:
7223:
7200:
7180:Wright, Sarah H. (2007-07-25).
7173:
7150:
7122:
7074:
7025:
6982:
6947:
6903:
6851:
6712:
6695:
6678:
6562:
6519:
6504:
6465:
6432:
6372:
6346:
6328:"Piezoelectric Crystal Classes"
6320:
6275:
6196:
6187:
6157:
6040:
6016:
5982:
5953:
5863:
5831:
5812:Taylor, C. (October 31, 2011).
5805:
5783:"How Do Electronic Drums Work?"
5774:
5723:Ultrasonic Testing of Materials
4145:List of piezoelectric materials
1939:{\displaystyle {\mathfrak {d}}}
1639:{\displaystyle {\mathfrak {d}}}
1615:{\displaystyle {\mathfrak {d}}}
1481:
1314:
1027:
1021:
817:
794:
526:and his coworkers developed an
502:World War I and inter-war years
409:posited a relationship between
7947:10.1016/j.enconman.2014.05.096
7764:10.1103/physrevlett.114.147701
7304:. TechInsights. Archived from
6418:10.1180/minmag.1979.043.326.05
6354:"Pyroelectric Crystal Classes"
6241:Reports on Progress in Physics
5781:Dempsey, Joe (June 24, 2020).
5637:
5616:
5574:
5553:
5496:
5333:, piezoelectric activation of
5299:in November 2005, a team from
5198:. Both of these usually use a
5058:scanning tunneling microscopes
4804:cold cathode fluorescent lamps
4727:High voltage and power sources
4721:
4519:III–V and II–VI semiconductors
4102:For polar crystals, for which
1841:
1835:
1800:
1785:
1477:
1310:
1023:
885:is the electric flux density (
796:
13:
1:
8373:Maria Skłodowska-Curie Bridge
8283:Maria Skłodowska-Curie Museum
5725:. Springer. pp. 119–49.
5489:
5084:, instead of the more common
5046:A related application is the
4819:Piezoelectric disk used as a
987:for linear elastic materials:
748:converse piezoelectric effect
8089:Gautschi, Gustav H. (2002).
7705:Br. J. Oral Maxillofac. Surg
7503:Documents.westerndigital.com
7255:Materials Today: Proceedings
7236:Journal of Analog Innovation
7050:10.1016/j.mattod.2019.04.002
6709:(19). doi: 10.1063/5.0006261
6498:10.1016/0024-4937(71)90102-2
6356:. Newcastle University, UK.
6330:. Newcastle University, UK.
5256:Stepping piezo motor, using
4968:
4138:
3266:of rank 1; and permittivity
627:
381:Discovery and early research
187:that accumulates in certain
7:
8378:Maria Skłodowska-Curie Park
7807:Takefuji, Y. (April 2008).
7717:10.1016/j.bjoms.2007.12.007
7472:(in Danish). Archived from
7319:Speck, Shane (2004-03-11).
7267:10.1016/j.matpr.2020.04.505
6164:Robert Repas (2008-02-07).
6029:Lehrbuch der Kristallphysik
5630:Online Etymology Dictionary
5567:Online Etymology Dictionary
5463:Quartz crystal microbalance
5395:
5383:The efficiency of a hybrid
5331:total fertilization failure
5131:Refreshable braille display
4916:. More commonly however, a
4907:Piezoelectric microbalances
4903:and industrial processing).
4617:
4256:
598:Bell Telephone Laboratories
492:Textbook on Crystal Physics
488:Lehrbuch der Kristallphysik
10:
8545:
7554:. Head.com. Archived from
7409:10.1007/s12596-019-00522-4
6703:Journal of Applied Physics
6261:10.1088/0034-4885/61/9/002
6225:. Oxford University Press.
5590:
5582:
5344:
5218:
5202:to reach gigahertz ranges.
4840:
4810:
4747:that flows across a small
4142:
559:time-domain reflectometers
375:
346:scanning probe microscopes
336:in electronic devices, in
255:
238:
8411:
8340:
8291:
8275:
8266:Treatise on Radioactivity
8252:
8201:
7658:BMC Musculoskelet. Disord
7371:10.1109/jsen.2011.2173188
7032:Tao, Kai; et, al (2019).
6032:. Berlin: B. G. Teubner.
5855:: CS1 maint: unfit URL (
5698:10.1007/978-3-662-04732-3
5510:(3rd ed.). Longman.
4955:acoustic emission testing
4947:engine management systems
4865:acoustic-electric guitars
671:). The dipole density or
565:World War II and post-war
510:, first developed during
231:. It is derived from
8504:Condensed matter physics
5478:Thermoelectric generator
5329:In people with previous
5054:Atomic force microscopes
4404:Sodium potassium niobate
754:Mathematical description
211:—in response to applied
8457:Les Palmes de M. Schutz
8128:Piezo in Medical Design
8091:Piezoelectric Sensorics
7818:: 31–33. Archived from
7744:Physical Review Letters
7631:10.1258/ult.2011.011027
6285:Crystallography Reports
5891:10.3406/bulmi.1880.1564
5760:10.1258/ult.2011.011027
5606:A Greek–English Lexicon
5048:acousto-optic modulator
4735:of thousands of volts.
4673:polyvinylidene chloride
4653:polyvinylidene fluoride
4473:Sodium bismuth titanate
4398:Lead-free piezoceramics
4290:Lead zirconate titanate
903:electric field strength
720:within the crystal; 2.
646:electric dipole moments
541:to detect the returned
407:Antoine César Becquerel
306:lead zirconate titanate
279:Wilhelm Gottlieb Hankel
8313:Hélène Langevin-Joliot
8034:10.1002/adma.201303304
7671:10.1186/1471-2474-7-36
6925:10.1021/acsami.7b13767
6873:10.1021/acsami.8b06696
6656:10.1143/JJAP.50.027101
6540:10.1021/acsami.7b14257
6513:Piezoelectric Ceramics
6388:Mineralogical Magazine
6193:IEC 80000-6, item 6-12
6143:. New York: Springer.
6066:10.1098/rsnr.2011.0049
5664:Hankel, W. G. (1881).
5361:Potential applications
5216:
4981:
4962:ultrasonic flow meters
4876:nondestructive testing
4838:
4834:. Pictured, a Russian
4823:
4622:The piezo-response of
4266:
4177:Gallium orthophosphate
4052:
4001:
3384:is the shear modulus.
3238:
1940:
1894:
1716:
1640:
1616:
1589:
1209:
1098:
972:
934:
870:
804:
641:
467:
421:
50:
8331:Frédéric Joliot-Curie
7011:10.1038/nnano.2012.69
6991:Nature Nanotechnology
6515:. New York: Academic.
6448:American Mineralogist
5960:Lippmann, G. (1881).
5684:Gautschi, G. (2002).
5597:Liddell, Henry George
5539:Learning. p. 9.
5473:Surface acoustic wave
5453:Piezoresistive effect
5438:Piezoelectric speaker
5325:Infertility treatment
5215:A stick-slip actuator
5214:
5150:standard of frequency
5080:, first developed by
4976:
4918:Piezoresistive effect
4829:
4818:
4733:potential differences
4437:Sodium niobate (NaNbO
4271:abnormal grain growth
4264:
4153:Crystalline materials
4038:
4002:
3239:
1941:
1895:
1717:
1641:
1617:
1590:
1210:
1099:
973:
935:
887:electric displacement
871:
805:
635:
614:piezoelectric igniter
465:
419:
33:
8509:Electrical phenomena
8435:Marie Curie Gargoyle
7558:on February 22, 2007
7476:on 29 September 2010
7470:Electronics Business
7351:IEEE Sensors Journal
6763:. Berlin: Springer.
6476:, Långban, Sweden".
6208:www.electropedia.org
6137:S. Trolier-McKinstry
6085:M. Birkholz (1995).
5818:SparkFun Electronics
5433:Photoelectric effect
5413:Electronic component
5207:Piezoelectric motors
5200:frequency multiplier
5025:Piezoelectric motors
4936:electronic drum pads
4843:Piezoelectric sensor
4629:acoustical impedance
3805:
3603:
3521:
3455:
3422:
3415:defined as follows:
1976:
1926:
1732:
1650:
1626:
1602:
1246:
1138:
997:
946:
910:
814:
772:
516:Fessenden oscillator
352:. It is used in the
7756:2015PhRvL.114n7701S
7441:2001ESASP.480...75L
7363:2012ISenJ..12.1033M
7003:2012NatNa...7..351L
6919:(48): 42200–42209.
6867:(39): 33105–33111.
6817:2018Senso..18.3605S
6729:2014AIPC.1590...32M
6648:2011JaJAP..50b7101G
6593:10.1038/nature03028
6585:2004Natur.432...84S
6534:(48): 42131–42138.
6490:1971Litho...4..101B
6400:1979MinM...43..237A
6298:2003CryRp..48..649K
6253:1998RPPh...61.1267D
6103:1995ZPhyB..96..333B
6047:Katzir, S. (2012).
5221:Piezoelectric motor
5194:where it creates a
5072:: High-performance
5019:Ultrasonic cleaning
4323:with 0 ≤
4043:, and therefore an
3801:
3599:
3517:
3451:
2466:
2448:
2422:
2373:
2324:
2275:
2258:
2241:
2207:
2190:
2173:
2139:
2122:
2105:
1673:
1413:
1225:displacement vector
387:pyroelectric effect
8327:(Pierre's brother)
8325:Paul-Jacques Curie
8301:Irène Joliot-Curie
8022:Advanced Materials
7895:10.1039/c8mh00097b
7883:Materials Horizons
6968:10.1039/c6tc00613b
6686:MRS Communications
6221:Ikeda, T. (1996).
6111:10.1007/BF01313055
5793:on October 1, 2019
5272:path, producing a
5217:
5161:crystal oscillator
5144:Frequency standard
4982:
4869:contact microphone
4839:
4824:
4387:Wurtzite structure
4267:
4053:
4045:electric potential
4025:Madelung constants
3997:
3995:
3234:
3232:
3224:
3170:
3077:
2981:
2835:
2776:
2722:
2570:
2474:
2452:
2434:
2408:
2359:
2310:
2261:
2244:
2227:
2193:
2176:
2159:
2125:
2108:
2091:
2074:
1936:
1890:
1888:
1712:
1653:
1636:
1612:
1585:
1583:
1553:
1510:
1393:
1392:
1346:
1237:strain-charge form
1205:
1112:is the linearized
1094:
1059:
968:
930:
866:
840:
800:
642:
468:
422:
391:electric potential
370:cigarette lighters
320:French physicists
294:reversible process
290:inversion symmetry
191:materials—such as
51:
8524:Energy harvesting
8514:Energy conversion
8491:
8490:
8368:Marie Curie Medal
8260:Curie's principle
8224:Mean-field theory
8219:Curie temperature
8149:Piezo Motor Types
8100:978-3-540-42259-4
7450:978-92-9092-761-7
7397:Journal of Optics
7325:HowStuffWorks.com
6962:(20): 4387–4392.
6826:10.3390/s18113605
6738:10.1063/1.4870192
6306:10.1134/1.1595194
6170:Machinedesign.com
6150:978-0-387-76538-9
6053:Notes Rec. R. Soc
5732:978-3-662-10680-8
5707:978-3-662-04732-3
5623:Harper, Douglas.
5560:Harper, Douglas.
5546:978-0-495-01201-6
5517:978-1-4058-8118-0
5483:Triboluminescence
5443:Piezoluminescence
5385:photovoltaic cell
5246:for linear motion
5170:natural frequency
5115:Crystal earpieces
5082:Robert Bosch GmbH
4940:acceleromyography
4783:acoustic coupling
4764:energy harvesting
4741:cigarette lighter
4331:Potassium niobate
4197:Lithium tantalate
4013:Maxwell relations
3981:
3921:
3845:
3779:
3703:
3643:
3561:
3495:
3264:Cartesian tensors
1965:) as well as the
1544:
1495:
1383:
1331:
1303:
1233:coupled equations
1200:
1044:
831:
712:mechanical stress
697:(not the same as
411:mechanical stress
342:ultrasonic nozzle
286:electromechanical
275:Piezoelektricität
213:mechanical stress
16:(Redirected from
8536:
8529:1880s neologisms
8229:Piezoelectricity
8183:
8176:
8169:
8160:
8159:
8104:
8054:
8053:
8013:
8007:
8006:
8004:
8003:
7987:
7981:
7980:
7978:
7976:
7957:
7951:
7950:
7926:
7917:
7916:
7906:
7874:
7868:
7867:
7865:
7864:
7858:
7851:
7840:
7834:
7833:
7831:
7830:
7824:
7813:
7804:
7798:
7797:
7782:
7776:
7775:
7735:
7729:
7728:
7700:
7694:
7693:
7683:
7673:
7649:
7643:
7642:
7614:
7608:
7607:
7597:
7573:
7567:
7566:
7564:
7563:
7548:
7542:
7541:
7539:
7537:
7528:
7520:
7514:
7513:
7511:
7509:
7500:
7492:
7486:
7485:
7483:
7481:
7466:"Piezo in space"
7461:
7455:
7454:
7427:
7421:
7420:
7392:
7383:
7382:
7357:(5): 1033–1042.
7346:
7340:
7339:
7337:
7336:
7316:
7310:
7309:
7293:
7287:
7286:
7246:
7240:
7239:
7227:
7221:
7220:
7204:
7198:
7197:
7177:
7171:
7170:
7154:
7148:
7147:
7145:
7143:
7126:
7120:
7119:
7100:10.1038/nmat5045
7088:Nature Materials
7078:
7072:
7071:
7061:
7029:
7023:
7022:
6986:
6980:
6979:
6951:
6945:
6944:
6907:
6901:
6900:
6855:
6849:
6848:
6838:
6828:
6796:
6783:
6782:
6756:
6743:
6742:
6740:
6716:
6710:
6699:
6693:
6682:
6676:
6675:
6619:
6613:
6612:
6566:
6560:
6559:
6523:
6517:
6516:
6508:
6502:
6501:
6469:
6463:
6462:
6460:
6445:
6436:
6430:
6429:
6411:
6394:(326): 237–241.
6385:
6376:
6370:
6369:
6367:
6365:
6350:
6344:
6343:
6341:
6339:
6324:
6318:
6317:
6279:
6273:
6272:
6247:(9): 1267–1324.
6236:
6227:
6226:
6218:
6212:
6211:
6200:
6194:
6191:
6185:
6184:
6182:
6181:
6172:. Archived from
6161:
6155:
6154:
6133:
6127:
6126:
6082:
6071:
6070:
6068:
6044:
6038:
6037:
6020:
6014:
6013:
5986:
5980:
5979:
5957:
5951:
5950:
5922:
5894:
5867:
5861:
5860:
5854:
5846:
5844:
5835:
5829:
5828:
5826:
5824:
5809:
5803:
5802:
5800:
5798:
5789:. Archived from
5778:
5772:
5771:
5743:
5737:
5736:
5718:
5712:
5711:
5681:
5675:
5671:
5654:
5641:
5635:
5634:
5620:
5614:
5593:
5592:
5585:
5584:
5578:
5572:
5571:
5557:
5551:
5550:
5535:(6th ed.).
5528:
5522:
5521:
5500:
5428:Magnetostriction
5423:Flexoelectricity
5418:Electrostriction
5403:Charge amplifier
5231:ultrasonic motor
5007:
4999:
4995:
4920:element is used.
4777:A piezoelectric
4745:electric current
4710:cellulose fibers
4649:semi-crystalline
4637:biodegradability
4633:biocompatibility
4587:structure, i.e.
4512:phase transition
4455:Bismuth titanate
4341:Sodium tungstate
4322:
4218:) – a rare
4135: ≠ 0.
4097:
4093:
4089:
4085:
4081:
4006:
4004:
4003:
3998:
3996:
3992:
3991:
3986:
3982:
3980:
3979:
3978:
3965:
3964:
3963:
3950:
3934:
3932:
3931:
3926:
3922:
3920:
3919:
3918:
3905:
3904:
3903:
3890:
3873:
3872:
3856:
3855:
3850:
3846:
3844:
3843:
3842:
3829:
3828:
3827:
3814:
3807:
3806:
3792:
3790:
3789:
3784:
3780:
3778:
3777:
3776:
3763:
3762:
3761:
3748:
3731:
3730:
3714:
3713:
3708:
3704:
3702:
3701:
3700:
3687:
3686:
3685:
3672:
3656:
3654:
3653:
3648:
3644:
3642:
3641:
3640:
3627:
3626:
3625:
3612:
3605:
3604:
3589:
3588:
3572:
3571:
3566:
3562:
3560:
3559:
3558:
3545:
3544:
3543:
3530:
3523:
3522:
3508:
3506:
3505:
3500:
3496:
3494:
3493:
3492:
3479:
3478:
3477:
3464:
3457:
3456:
3441:
3440:
3376:
3374:
3373:
3365:
3362:
3334:
3333:
3322:
3321:
3243:
3241:
3240:
3235:
3233:
3229:
3228:
3221:
3220:
3207:
3206:
3193:
3192:
3175:
3174:
3167:
3166:
3161:
3136:
3135:
3130:
3105:
3104:
3099:
3082:
3081:
3074:
3073:
3060:
3059:
3046:
3045:
3032:
3031:
3018:
3017:
3004:
3003:
2986:
2985:
2963:
2962:
2951:
2950:
2939:
2938:
2915:
2914:
2881:
2880:
2840:
2839:
2832:
2831:
2818:
2817:
2804:
2803:
2785:
2781:
2780:
2773:
2772:
2759:
2758:
2745:
2744:
2727:
2726:
2692:
2691:
2673:
2672:
2654:
2653:
2630:
2629:
2606:
2605:
2575:
2574:
2567:
2566:
2553:
2552:
2539:
2538:
2525:
2524:
2511:
2510:
2497:
2496:
2479:
2478:
2471:
2467:
2465:
2460:
2447:
2442:
2421:
2416:
2372:
2367:
2323:
2318:
2274:
2269:
2257:
2252:
2240:
2235:
2206:
2201:
2189:
2184:
2172:
2167:
2138:
2133:
2121:
2116:
2104:
2099:
2079:
2078:
2071:
2070:
2057:
2056:
2043:
2042:
2029:
2028:
2015:
2014:
2001:
2000:
1982:
1945:
1943:
1942:
1937:
1935:
1934:
1899:
1897:
1896:
1891:
1889:
1873:
1869:
1868:
1799:
1798:
1797:
1772:
1768:
1767:
1725:In matrix form,
1721:
1719:
1718:
1713:
1711:
1710:
1692:
1691:
1672:
1667:
1645:
1643:
1642:
1637:
1635:
1634:
1621:
1619:
1618:
1613:
1611:
1610:
1594:
1592:
1591:
1586:
1584:
1577:
1576:
1566:
1565:
1552:
1540:
1539:
1526:
1525:
1509:
1491:
1490:
1472:
1470:
1464:
1456:
1450:
1449:
1436:
1424:
1423:
1412:
1407:
1391:
1379:
1378:
1365:
1364:
1345:
1327:
1326:
1305:
1301:
1300:
1294:
1293:
1288:
1287:
1277:
1271:
1270:
1257:
1214:
1212:
1211:
1206:
1201:
1196:
1192:
1184:
1175:
1170:
1159:
1151:
1103:
1101:
1100:
1095:
1092:
1091:
1078:
1077:
1058:
1040:
1039:
1020:
1014:
1013:
1004:
977:
975:
974:
969:
967:
959:
939:
937:
936:
931:
923:
875:
873:
872:
867:
864:
863:
853:
852:
839:
827:
826:
809:
807:
806:
801:
793:
787:
779:
722:crystal symmetry
710:when applying a
472:Gabriel Lippmann
366:electronic drums
315:ultrasound waves
266:
259:
249:
242:
217:piezoelectricity
182:
181:
178:
177:
174:
171:
168:
165:
162:
159:
154:
153:
150:
147:
144:
141:
138:
131:
123:
122:
119:
118:
115:
112:
109:
106:
103:
98:
97:
94:
91:
88:
85:
82:
77:
76:
73:
70:
67:
64:
54:Piezoelectricity
44:Hunterian Museum
21:
8544:
8543:
8539:
8538:
8537:
8535:
8534:
8533:
8494:
8493:
8492:
8487:
8407:
8348:Curie Institute
8336:
8315:(granddaughter)
8287:
8271:
8248:
8214:Curie–Weiss law
8197:
8187:
8123:Piezo Equations
8101:
8085:
8063:
8061:Further reading
8058:
8057:
8014:
8010:
8001:
7999:
7988:
7984:
7974:
7972:
7959:
7958:
7954:
7927:
7920:
7875:
7871:
7862:
7860:
7856:
7849:
7841:
7837:
7828:
7826:
7822:
7811:
7805:
7801:
7784:
7783:
7779:
7736:
7732:
7701:
7697:
7650:
7646:
7615:
7611:
7574:
7570:
7561:
7559:
7550:
7549:
7545:
7535:
7533:
7526:
7522:
7521:
7517:
7507:
7505:
7498:
7494:
7493:
7489:
7479:
7477:
7462:
7458:
7451:
7428:
7424:
7393:
7386:
7347:
7343:
7334:
7332:
7317:
7313:
7302:eeProductCenter
7294:
7290:
7247:
7243:
7228:
7224:
7205:
7201:
7178:
7174:
7155:
7151:
7141:
7139:
7127:
7123:
7079:
7075:
7038:Materials Today
7030:
7026:
6987:
6983:
6952:
6948:
6908:
6904:
6856:
6852:
6797:
6786:
6771:
6757:
6746:
6717:
6713:
6700:
6696:
6683:
6679:
6633:
6629:
6625:
6620:
6616:
6579:(7013): 81–87.
6567:
6563:
6524:
6520:
6509:
6505:
6475:
6470:
6466:
6458:
6443:
6437:
6433:
6409:10.1.1.604.6025
6383:
6377:
6373:
6363:
6361:
6352:
6351:
6347:
6337:
6335:
6326:
6325:
6321:
6280:
6276:
6237:
6230:
6219:
6215:
6202:
6201:
6197:
6192:
6188:
6179:
6177:
6162:
6158:
6151:
6134:
6130:
6083:
6074:
6045:
6041:
6024:Voigt, Woldemar
6021:
6017:
5987:
5983:
5958:
5954:
5923:
5895:
5868:
5864:
5848:
5847:
5842:
5836:
5832:
5822:
5820:
5810:
5806:
5796:
5794:
5779:
5775:
5744:
5740:
5733:
5719:
5715:
5708:
5682:
5678:
5642:
5638:
5625:"piezoelectric"
5621:
5617:
5611:Perseus Project
5579:
5575:
5562:"piezoelectric"
5558:
5554:
5547:
5529:
5525:
5518:
5501:
5497:
5492:
5487:
5398:
5363:
5347:
5327:
5289:
5244:Inchworm motors
5223:
5209:
5146:
5064:Inkjet printers
5005:
4997:
4993:
4971:
4845:
4813:
4729:
4724:
4700:(table sugar),
4694:
4692:Other materials
4686:
4655:(PVDF) and its
4620:
4582:
4575:
4568:
4557:
4521:
4504:
4500:
4495:
4491:
4482:
4478:
4468:
4464:
4460:
4450:
4445:Barium titanate
4440:
4433:
4428:Bismuth ferrite
4423:
4416:
4409:
4400:
4379:
4375:
4371:
4365:
4361:
4357:
4350:
4346:
4336:
4321:
4314:
4305:
4293:
4259:
4251:
4242:-group minerals
4217:
4202:
4192:
4187:Lithium niobate
4182:
4172:
4168:
4164:
4155:
4147:
4141:
4095:
4091:
4087:
4083:
4079:
4065:pyroelectricity
4061:centrosymmetric
4057:crystal classes
4033:
4031:Crystal classes
4021:
3994:
3993:
3987:
3974:
3970:
3966:
3959:
3955:
3951:
3949:
3945:
3944:
3933:
3927:
3914:
3910:
3906:
3899:
3895:
3891:
3889:
3885:
3884:
3874:
3865:
3861:
3858:
3857:
3851:
3838:
3834:
3830:
3823:
3819:
3815:
3813:
3809:
3808:
3800:
3799:
3791:
3785:
3772:
3768:
3764:
3757:
3753:
3749:
3747:
3743:
3742:
3732:
3723:
3719:
3716:
3715:
3709:
3696:
3692:
3688:
3681:
3677:
3673:
3671:
3667:
3666:
3655:
3649:
3636:
3632:
3628:
3621:
3617:
3613:
3611:
3607:
3606:
3598:
3597:
3590:
3581:
3577:
3574:
3573:
3567:
3554:
3550:
3546:
3539:
3535:
3531:
3529:
3525:
3524:
3516:
3515:
3507:
3501:
3488:
3484:
3480:
3473:
3469:
3465:
3463:
3459:
3458:
3450:
3449:
3442:
3433:
3429:
3425:
3423:
3420:
3419:
3413:
3406:
3399:
3392:
3383:
3372:
3366:
3363:
3360:
3359:
3357:
3355:
3348:
3341:
3332:
3329:
3328:
3327:
3320:
3317:
3316:
3315:
3310:
3303:
3296:
3231:
3230:
3223:
3222:
3216:
3212:
3209:
3208:
3202:
3198:
3195:
3194:
3188:
3184:
3177:
3176:
3169:
3168:
3162:
3157:
3156:
3154:
3149:
3143:
3142:
3137:
3131:
3126:
3125:
3123:
3117:
3116:
3111:
3106:
3100:
3095:
3094:
3087:
3086:
3076:
3075:
3069:
3065:
3062:
3061:
3055:
3051:
3048:
3047:
3041:
3037:
3034:
3033:
3027:
3023:
3020:
3019:
3013:
3009:
3006:
3005:
2999:
2995:
2988:
2987:
2980:
2979:
2974:
2969:
2964:
2958:
2954:
2952:
2946:
2942:
2940:
2934:
2930:
2927:
2926:
2921:
2916:
2910:
2906:
2904:
2899:
2894:
2888:
2887:
2882:
2876:
2872:
2870:
2865:
2860:
2855:
2845:
2844:
2834:
2833:
2827:
2823:
2820:
2819:
2813:
2809:
2806:
2805:
2799:
2795:
2788:
2787:
2783:
2782:
2775:
2774:
2768:
2764:
2761:
2760:
2754:
2750:
2747:
2746:
2740:
2736:
2729:
2728:
2721:
2720:
2715:
2710:
2704:
2703:
2698:
2693:
2687:
2683:
2680:
2679:
2674:
2668:
2664:
2662:
2656:
2655:
2649:
2645:
2643:
2638:
2632:
2631:
2625:
2621:
2619:
2614:
2608:
2607:
2601:
2597:
2595:
2590:
2580:
2579:
2569:
2568:
2562:
2558:
2555:
2554:
2548:
2544:
2541:
2540:
2534:
2530:
2527:
2526:
2520:
2516:
2513:
2512:
2506:
2502:
2499:
2498:
2492:
2488:
2481:
2480:
2473:
2472:
2461:
2456:
2443:
2438:
2433:
2429:
2417:
2412:
2406:
2401:
2396:
2391:
2386:
2380:
2379:
2374:
2368:
2363:
2357:
2352:
2347:
2342:
2336:
2335:
2330:
2325:
2319:
2314:
2308:
2303:
2298:
2292:
2291:
2286:
2281:
2276:
2270:
2265:
2259:
2253:
2248:
2242:
2236:
2231:
2224:
2223:
2218:
2213:
2208:
2202:
2197:
2191:
2185:
2180:
2174:
2168:
2163:
2156:
2155:
2150:
2145:
2140:
2134:
2129:
2123:
2117:
2112:
2106:
2100:
2095:
2084:
2083:
2073:
2072:
2066:
2062:
2059:
2058:
2052:
2048:
2045:
2044:
2038:
2034:
2031:
2030:
2024:
2020:
2017:
2016:
2010:
2006:
2003:
2002:
1996:
1992:
1985:
1984:
1979:
1977:
1974:
1973:
1964:
1956:
1930:
1929:
1927:
1924:
1923:
1887:
1886:
1864:
1860:
1856:
1828:
1816:
1815:
1793:
1792:
1788:
1763:
1759:
1755:
1748:
1735:
1733:
1730:
1729:
1700:
1696:
1681:
1677:
1668:
1657:
1651:
1648:
1647:
1630:
1629:
1627:
1624:
1623:
1606:
1605:
1603:
1600:
1599:
1582:
1581:
1572:
1568:
1558:
1554:
1548:
1532:
1528:
1515:
1511:
1499:
1486:
1482:
1471:
1466:
1460:
1452:
1445:
1444:
1437:
1432:
1429:
1428:
1419:
1415:
1408:
1397:
1387:
1371:
1367:
1351:
1347:
1335:
1319:
1315:
1304:
1296:
1289:
1283:
1282:
1281:
1273:
1266:
1265:
1258:
1253:
1249:
1247:
1244:
1243:
1235:, of which the
1188:
1180:
1176:
1174:
1166:
1155:
1147:
1139:
1136:
1135:
1084:
1080:
1064:
1060:
1048:
1032:
1028:
1016:
1009:
1008:
1000:
998:
995:
994:
963:
955:
947:
944:
943:
919:
911:
908:
907:
859:
855:
845:
841:
835:
822:
818:
815:
812:
811:
789:
783:
775:
773:
770:
769:
756:
699:magnetic poling
661:
654:crystal lattice
630:
591:barium titanate
567:
504:
496:tensor analysis
383:
378:
364:in most modern
334:clock generator
330:inkjet printing
304:. For example,
223:resulting from
185:electric charge
156:
135:
126:
125:
100:
79:
61:
57:
28:
23:
22:
15:
12:
11:
5:
8542:
8532:
8531:
8526:
8521:
8516:
8511:
8506:
8489:
8488:
8486:
8485:
8477:
8469:
8461:
8453:
8445:
8438:
8431:
8426:
8421:
8415:
8413:
8409:
8408:
8406:
8405:
8400:
8395:
8390:
8385:
8380:
8375:
8370:
8365:
8360:
8355:
8350:
8344:
8342:
8338:
8337:
8335:
8334:
8328:
8322:
8316:
8310:
8304:
8297:
8295:
8289:
8288:
8286:
8285:
8279:
8277:
8273:
8272:
8270:
8269:
8262:
8256:
8254:
8250:
8249:
8247:
8246:
8241:
8236:
8231:
8226:
8221:
8216:
8211:
8205:
8203:
8199:
8198:
8186:
8185:
8178:
8171:
8163:
8157:
8156:
8151:
8146:
8140:
8135:
8130:
8125:
8120:
8115:
8110:
8105:
8099:
8084:
8083:External links
8081:
8080:
8079:
8076:
8073:
8070:
8067:
8062:
8059:
8056:
8055:
8028:(2): 263–268.
8008:
7994:. Gizmag.com.
7982:
7967:. 2015-03-12.
7952:
7918:
7889:(3): 444–453.
7869:
7835:
7799:
7792:. 2015-04-09.
7777:
7750:(14): 147701.
7730:
7711:(4): 265–269.
7695:
7644:
7609:
7588:(3): 900–904.
7582:Fertil. Steril
7568:
7543:
7515:
7487:
7456:
7449:
7422:
7403:(2): 272–282.
7384:
7341:
7311:
7308:on 2010-10-06.
7288:
7241:
7222:
7199:
7172:
7149:
7121:
7094:(2): 180–186.
7073:
7024:
6997:(6): 351–356.
6981:
6946:
6902:
6850:
6784:
6770:978-3540686835
6769:
6744:
6711:
6694:
6677:
6631:
6627:
6623:
6614:
6561:
6518:
6503:
6484:(2): 101–104.
6473:
6464:
6431:
6371:
6345:
6319:
6292:(4): 649–675.
6274:
6228:
6213:
6195:
6186:
6156:
6149:
6128:
6097:(3): 333–340.
6072:
6059:(2): 141–157.
6039:
6015:
6002:Comptes Rendus
5990:Curie, Jacques
5981:
5952:
5939:Comptes Rendus
5927:Curie, Jacques
5911:Comptes Rendus
5899:Curie, Jacques
5896:Reprinted in:
5871:Curie, Jacques
5862:
5838:Erhart, Jiří.
5830:
5804:
5773:
5738:
5731:
5713:
5706:
5676:
5674:
5673:
5655:From p. 462:
5636:
5615:
5573:
5552:
5545:
5523:
5516:
5504:Wells, John C.
5494:
5493:
5491:
5488:
5486:
5485:
5480:
5475:
5470:
5468:Sonomicrometry
5465:
5460:
5455:
5450:
5448:Piezomagnetism
5445:
5440:
5435:
5430:
5425:
5420:
5415:
5410:
5405:
5399:
5397:
5394:
5362:
5359:
5346:
5343:
5337:together with
5326:
5323:
5315:tennis rackets
5288:
5285:
5262:
5261:
5254:
5247:
5241:
5239:reflex cameras
5219:Main article:
5208:
5205:
5204:
5203:
5177:
5145:
5142:
5141:
5140:
5137:
5134:
5128:
5118:
5112:
5101:
5098:
5092:
5089:
5086:solenoid valve
5078:fuel injectors
5070:Diesel engines
5067:
5061:
5051:
5044:
5036:
5022:
5016:
4970:
4967:
4966:
4965:
4958:
4951:
4943:
4930:Piezoelectric
4928:
4921:
4910:
4904:
4897:
4894:
4841:Main article:
4812:
4809:
4808:
4807:
4775:
4756:
4728:
4725:
4723:
4720:
4693:
4690:
4684:
4619:
4616:
4580:
4573:
4566:
4555:
4520:
4517:
4502:
4498:
4493:
4489:
4485:
4484:
4480:
4476:
4470:
4466:
4462:
4458:
4452:
4448:
4442:
4438:
4435:
4431:
4425:
4421:
4414:
4407:
4399:
4396:
4395:
4394:
4380:
4377:
4373:
4369:
4366:
4363:
4359:
4355:
4352:
4348:
4344:
4338:
4334:
4328:
4319:
4309:
4301:
4258:
4255:
4254:
4253:
4249:
4243:
4237:
4231:
4226:
4215:
4209:
4204:
4200:
4194:
4190:
4184:
4180:
4174:
4170:
4166:
4162:
4154:
4151:
4140:
4137:
4100:
4099:
4076:
4041:electric field
4032:
4029:
4019:
4008:
4007:
3990:
3985:
3977:
3973:
3969:
3962:
3958:
3954:
3948:
3943:
3940:
3937:
3935:
3930:
3925:
3917:
3913:
3909:
3902:
3898:
3894:
3888:
3883:
3880:
3877:
3875:
3871:
3868:
3864:
3860:
3859:
3854:
3849:
3841:
3837:
3833:
3826:
3822:
3818:
3812:
3804:
3798:
3795:
3793:
3788:
3783:
3775:
3771:
3767:
3760:
3756:
3752:
3746:
3741:
3738:
3735:
3733:
3729:
3726:
3722:
3718:
3717:
3712:
3707:
3699:
3695:
3691:
3684:
3680:
3676:
3670:
3665:
3662:
3659:
3657:
3652:
3647:
3639:
3635:
3631:
3624:
3620:
3616:
3610:
3602:
3596:
3593:
3591:
3587:
3584:
3580:
3576:
3575:
3570:
3565:
3557:
3553:
3549:
3542:
3538:
3534:
3528:
3520:
3514:
3511:
3509:
3504:
3499:
3491:
3487:
3483:
3476:
3472:
3468:
3462:
3454:
3448:
3445:
3443:
3439:
3436:
3432:
3428:
3427:
3411:
3404:
3397:
3390:
3381:
3370:
3353:
3346:
3342: = 2
3339:
3330:
3318:
3308:
3301:
3294:
3288:Voigt notation
3245:
3244:
3227:
3219:
3215:
3211:
3210:
3205:
3201:
3197:
3196:
3191:
3187:
3183:
3182:
3180:
3173:
3165:
3160:
3155:
3153:
3150:
3148:
3145:
3144:
3141:
3138:
3134:
3129:
3124:
3122:
3119:
3118:
3115:
3112:
3110:
3107:
3103:
3098:
3093:
3092:
3090:
3085:
3080:
3072:
3068:
3064:
3063:
3058:
3054:
3050:
3049:
3044:
3040:
3036:
3035:
3030:
3026:
3022:
3021:
3016:
3012:
3008:
3007:
3002:
2998:
2994:
2993:
2991:
2984:
2978:
2975:
2973:
2970:
2968:
2965:
2961:
2957:
2953:
2949:
2945:
2941:
2937:
2933:
2929:
2928:
2925:
2922:
2920:
2917:
2913:
2909:
2905:
2903:
2900:
2898:
2895:
2893:
2890:
2889:
2886:
2883:
2879:
2875:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2850:
2848:
2843:
2838:
2830:
2826:
2822:
2821:
2816:
2812:
2808:
2807:
2802:
2798:
2794:
2793:
2791:
2786:
2784:
2779:
2771:
2767:
2763:
2762:
2757:
2753:
2749:
2748:
2743:
2739:
2735:
2734:
2732:
2725:
2719:
2716:
2714:
2711:
2709:
2706:
2705:
2702:
2699:
2697:
2694:
2690:
2686:
2682:
2681:
2678:
2675:
2671:
2667:
2663:
2661:
2658:
2657:
2652:
2648:
2644:
2642:
2639:
2637:
2634:
2633:
2628:
2624:
2620:
2618:
2615:
2613:
2610:
2609:
2604:
2600:
2596:
2594:
2591:
2589:
2586:
2585:
2583:
2578:
2573:
2565:
2561:
2557:
2556:
2551:
2547:
2543:
2542:
2537:
2533:
2529:
2528:
2523:
2519:
2515:
2514:
2509:
2505:
2501:
2500:
2495:
2491:
2487:
2486:
2484:
2477:
2470:
2464:
2459:
2455:
2451:
2446:
2441:
2437:
2432:
2428:
2425:
2420:
2415:
2411:
2407:
2405:
2402:
2400:
2397:
2395:
2392:
2390:
2387:
2385:
2382:
2381:
2378:
2375:
2371:
2366:
2362:
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2337:
2334:
2331:
2329:
2326:
2322:
2317:
2313:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2293:
2290:
2287:
2285:
2282:
2280:
2277:
2273:
2268:
2264:
2260:
2256:
2251:
2247:
2243:
2239:
2234:
2230:
2226:
2225:
2222:
2219:
2217:
2214:
2212:
2209:
2205:
2200:
2196:
2192:
2188:
2183:
2179:
2175:
2171:
2166:
2162:
2158:
2157:
2154:
2151:
2149:
2146:
2144:
2141:
2137:
2132:
2128:
2124:
2120:
2115:
2111:
2107:
2103:
2098:
2094:
2090:
2089:
2087:
2082:
2077:
2069:
2065:
2061:
2060:
2055:
2051:
2047:
2046:
2041:
2037:
2033:
2032:
2027:
2023:
2019:
2018:
2013:
2009:
2005:
2004:
1999:
1995:
1991:
1990:
1988:
1983:
1981:
1962:
1954:
1933:
1901:
1900:
1885:
1882:
1879:
1876:
1872:
1867:
1863:
1859:
1855:
1852:
1849:
1846:
1843:
1840:
1837:
1834:
1831:
1829:
1827:
1824:
1821:
1818:
1817:
1814:
1811:
1808:
1805:
1802:
1796:
1791:
1787:
1784:
1781:
1778:
1775:
1771:
1766:
1762:
1758:
1754:
1751:
1749:
1747:
1744:
1741:
1738:
1737:
1709:
1706:
1703:
1699:
1695:
1690:
1687:
1684:
1680:
1676:
1671:
1666:
1663:
1660:
1656:
1633:
1609:
1596:
1595:
1580:
1575:
1571:
1564:
1561:
1557:
1551:
1547:
1543:
1538:
1535:
1531:
1524:
1521:
1518:
1514:
1508:
1505:
1502:
1498:
1494:
1489:
1485:
1479:
1475:
1473:
1469:
1463:
1459:
1455:
1448:
1443:
1440:
1438:
1435:
1431:
1430:
1427:
1422:
1418:
1411:
1406:
1403:
1400:
1396:
1390:
1386:
1382:
1377:
1374:
1370:
1363:
1360:
1357:
1354:
1350:
1344:
1341:
1338:
1334:
1330:
1325:
1322:
1318:
1312:
1308:
1306:
1299:
1292:
1286:
1280:
1276:
1269:
1264:
1261:
1259:
1256:
1252:
1251:
1229:
1228:
1217:
1216:
1215:
1204:
1199:
1195:
1191:
1187:
1183:
1179:
1173:
1169:
1164:
1158:
1154:
1150:
1146:
1143:
1106:
1105:
1104:
1090:
1087:
1083:
1076:
1073:
1070:
1067:
1063:
1057:
1054:
1051:
1047:
1043:
1038:
1035:
1031:
1025:
1019:
1012:
1007:
1003:
989:
988:
981:
980:
966:
962:
958:
954:
951:
929:
926:
922:
918:
915:
879:
878:
877:
862:
858:
851:
848:
844:
838:
834:
830:
825:
821:
798:
792:
786:
782:
778:
764:
763:
755:
752:
736:electric field
732:charge density
659:
640:to sound waves
629:
626:
587:ferroelectrics
566:
563:
503:
500:
484:Woldemar Voigt
403:René Just Haüy
382:
379:
377:
374:
340:, to drive an
302:electric field
207:, and various
26:
9:
6:
4:
3:
2:
8541:
8530:
8527:
8525:
8522:
8520:
8517:
8515:
8512:
8510:
8507:
8505:
8502:
8501:
8499:
8483:
8482:
8478:
8475:
8474:
8470:
8467:
8466:
8462:
8459:
8458:
8454:
8451:
8450:
8446:
8444:
8443:
8439:
8437:
8436:
8432:
8430:
8427:
8425:
8422:
8420:
8417:
8416:
8414:
8410:
8404:
8401:
8399:
8396:
8394:
8391:
8389:
8386:
8384:
8381:
8379:
8376:
8374:
8371:
8369:
8366:
8364:
8361:
8359:
8356:
8354:
8351:
8349:
8346:
8345:
8343:
8339:
8332:
8329:
8326:
8323:
8320:
8319:Pierre Joliot
8317:
8314:
8311:
8308:
8305:
8302:
8299:
8298:
8296:
8294:
8290:
8284:
8281:
8280:
8278:
8274:
8268:
8267:
8263:
8261:
8258:
8257:
8255:
8251:
8245:
8242:
8240:
8239:Radioactivity
8237:
8235:
8232:
8230:
8227:
8225:
8222:
8220:
8217:
8215:
8212:
8210:
8207:
8206:
8204:
8200:
8195:
8191:
8184:
8179:
8177:
8172:
8170:
8165:
8164:
8161:
8155:
8152:
8150:
8147:
8144:
8141:
8139:
8136:
8134:
8131:
8129:
8126:
8124:
8121:
8119:
8116:
8114:
8111:
8109:
8106:
8102:
8096:
8092:
8087:
8086:
8077:
8074:
8071:
8068:
8065:
8064:
8051:
8047:
8043:
8039:
8035:
8031:
8027:
8023:
8019:
8012:
7997:
7993:
7986:
7970:
7966:
7962:
7956:
7948:
7944:
7940:
7936:
7932:
7925:
7923:
7914:
7910:
7905:
7904:10044/1/60608
7900:
7896:
7892:
7888:
7884:
7880:
7873:
7859:on 2020-10-21
7855:
7848:
7847:
7839:
7825:on 2021-01-15
7821:
7817:
7810:
7803:
7795:
7791:
7787:
7781:
7773:
7769:
7765:
7761:
7757:
7753:
7749:
7745:
7741:
7734:
7726:
7722:
7718:
7714:
7710:
7706:
7699:
7691:
7687:
7682:
7677:
7672:
7667:
7663:
7659:
7655:
7648:
7640:
7636:
7632:
7628:
7625:(4): 187–96.
7624:
7620:
7613:
7605:
7601:
7596:
7591:
7587:
7583:
7579:
7572:
7557:
7553:
7547:
7532:
7525:
7519:
7504:
7497:
7491:
7475:
7471:
7467:
7460:
7452:
7446:
7442:
7438:
7434:
7426:
7418:
7414:
7410:
7406:
7402:
7398:
7391:
7389:
7380:
7376:
7372:
7368:
7364:
7360:
7356:
7352:
7345:
7330:
7326:
7322:
7315:
7307:
7303:
7299:
7292:
7284:
7280:
7276:
7272:
7268:
7264:
7261:: 1302–1306.
7260:
7256:
7252:
7245:
7237:
7233:
7226:
7218:
7214:
7210:
7203:
7195:
7191:
7187:
7183:
7176:
7168:
7164:
7160:
7153:
7138:
7137:
7136:IEEE Spectrum
7132:
7125:
7117:
7113:
7109:
7105:
7101:
7097:
7093:
7089:
7085:
7077:
7069:
7065:
7060:
7055:
7051:
7047:
7043:
7039:
7035:
7028:
7020:
7016:
7012:
7008:
7004:
7000:
6996:
6992:
6985:
6977:
6973:
6969:
6965:
6961:
6957:
6950:
6942:
6938:
6934:
6930:
6926:
6922:
6918:
6914:
6906:
6898:
6894:
6890:
6886:
6882:
6878:
6874:
6870:
6866:
6862:
6854:
6846:
6842:
6837:
6832:
6827:
6822:
6818:
6814:
6810:
6806:
6802:
6795:
6793:
6791:
6789:
6780:
6776:
6772:
6766:
6762:
6755:
6753:
6751:
6749:
6739:
6734:
6730:
6726:
6722:
6715:
6708:
6704:
6698:
6691:
6687:
6681:
6673:
6669:
6665:
6661:
6657:
6653:
6649:
6645:
6642:(2): 027101.
6641:
6637:
6618:
6610:
6606:
6602:
6598:
6594:
6590:
6586:
6582:
6578:
6574:
6573:
6565:
6557:
6553:
6549:
6545:
6541:
6537:
6533:
6529:
6522:
6514:
6507:
6499:
6495:
6491:
6487:
6483:
6479:
6468:
6457:
6453:
6449:
6442:
6435:
6427:
6423:
6419:
6415:
6410:
6405:
6401:
6397:
6393:
6389:
6382:
6375:
6359:
6355:
6349:
6333:
6329:
6323:
6315:
6311:
6307:
6303:
6299:
6295:
6291:
6287:
6286:
6278:
6270:
6266:
6262:
6258:
6254:
6250:
6246:
6242:
6235:
6233:
6224:
6217:
6209:
6205:
6199:
6190:
6176:on 2010-04-13
6175:
6171:
6167:
6160:
6152:
6146:
6142:
6138:
6132:
6124:
6120:
6116:
6112:
6108:
6104:
6100:
6096:
6092:
6088:
6081:
6079:
6077:
6067:
6062:
6058:
6054:
6050:
6043:
6035:
6031:
6030:
6025:
6019:
6011:
6008:: 1137–1140.
6007:
6004:(in French).
6003:
5999:
5995:
5994:Curie, Pierre
5991:
5985:
5977:
5973:
5970:(in French).
5969:
5968:
5963:
5956:
5948:
5944:
5941:(in French).
5940:
5936:
5932:
5931:Curie, Pierre
5928:
5920:
5916:
5913:(in French).
5912:
5908:
5904:
5903:Curie, Pierre
5900:
5892:
5888:
5884:
5880:
5876:
5875:Curie, Pierre
5872:
5866:
5858:
5852:
5841:
5834:
5819:
5815:
5808:
5792:
5788:
5784:
5777:
5769:
5765:
5761:
5757:
5754:(4): 187–96.
5753:
5749:
5742:
5734:
5728:
5724:
5717:
5709:
5703:
5699:
5695:
5691:
5687:
5680:
5669:
5668:
5661:
5660:
5658:
5652:
5649:(in German).
5648:
5640:
5632:
5631:
5626:
5619:
5612:
5608:
5607:
5602:
5601:Scott, Robert
5598:
5594:
5586:
5577:
5569:
5568:
5563:
5556:
5548:
5542:
5538:
5534:
5527:
5519:
5513:
5509:
5505:
5499:
5495:
5484:
5481:
5479:
5476:
5474:
5471:
5469:
5466:
5464:
5461:
5459:
5458:Piezosurgical
5456:
5454:
5451:
5449:
5446:
5444:
5441:
5439:
5436:
5434:
5431:
5429:
5426:
5424:
5421:
5419:
5416:
5414:
5411:
5409:
5406:
5404:
5401:
5400:
5393:
5390:
5386:
5381:
5379:
5376:Tire company
5374:
5370:
5367:
5358:
5355:
5351:
5342:
5340:
5336:
5332:
5322:
5318:
5316:
5313:
5308:
5306:
5302:
5298:
5293:
5284:
5281:
5279:
5275:
5271:
5267:
5259:
5255:
5252:
5248:
5245:
5242:
5240:
5236:
5232:
5228:
5227:
5226:
5222:
5213:
5201:
5197:
5193:
5189:
5185:
5182:
5178:
5175:
5171:
5167:
5162:
5158:
5157:Quartz clocks
5155:
5154:
5153:
5151:
5138:
5135:
5132:
5129:
5126:
5122:
5119:
5116:
5113:
5110:
5106:
5102:
5099:
5096:
5093:
5090:
5087:
5083:
5079:
5075:
5071:
5068:
5065:
5062:
5059:
5055:
5052:
5049:
5045:
5041:
5037:
5034:
5033:stepper motor
5030:
5026:
5023:
5020:
5017:
5014:
5011:
5010:
5009:
5003:
4991:
4987:
4980:
4975:
4963:
4959:
4956:
4952:
4948:
4944:
4941:
4937:
4933:
4929:
4926:
4925:Huygens Probe
4922:
4919:
4915:
4914:strain gauges
4911:
4908:
4905:
4902:
4901:sonochemistry
4898:
4895:
4892:
4891:
4890:
4887:
4884:
4879:
4877:
4872:
4870:
4866:
4862:
4858:
4853:
4850:
4844:
4837:
4833:
4828:
4822:
4821:guitar pickup
4817:
4805:
4801:
4798:appear as an
4796:
4792:
4788:
4784:
4780:
4776:
4773:
4769:
4765:
4761:
4757:
4754:
4750:
4746:
4742:
4738:
4737:
4736:
4734:
4719:
4717:
4716:Ionic liquids
4713:
4711:
4707:
4706:bacteriophage
4703:
4699:
4689:
4680:
4676:
4674:
4670:
4666:
4662:
4658:
4654:
4650:
4646:
4640:
4638:
4634:
4630:
4625:
4615:
4613:
4608:
4606:
4602:
4598:
4594:
4590:
4586:
4579:
4572:
4565:
4561:
4553:
4549:
4545:
4541:
4537:
4533:
4529:
4526:
4516:
4513:
4507:
4474:
4471:
4456:
4453:
4446:
4443:
4436:
4429:
4426:
4420:
4413:
4405:
4402:
4401:
4392:
4388:
4385:(ZnO) –
4384:
4381:
4367:
4353:
4342:
4339:
4332:
4329:
4326:
4318:
4313:
4308:
4304:
4300:
4296:
4291:
4288:
4287:
4286:
4284:
4280:
4276:
4272:
4263:
4247:
4246:Lead titanate
4244:
4241:
4238:
4235:
4232:
4230:
4229:Rochelle salt
4227:
4224:
4221:
4213:
4210:
4208:
4205:
4198:
4195:
4188:
4185:
4178:
4175:
4160:
4157:
4156:
4150:
4146:
4136:
4134:
4133:
4128:
4127:
4122:
4121:
4115:
4113:
4112:
4107:
4106:
4077:
4074:
4073:
4072:
4070:
4069:ferroelectric
4066:
4062:
4059:, 21 are non-
4058:
4050:
4046:
4042:
4037:
4028:
4026:
4022:
4014:
3988:
3983:
3975:
3971:
3960:
3956:
3946:
3941:
3938:
3936:
3928:
3923:
3915:
3911:
3900:
3896:
3886:
3881:
3878:
3876:
3869:
3866:
3862:
3852:
3847:
3839:
3835:
3824:
3820:
3810:
3802:
3796:
3794:
3786:
3781:
3773:
3769:
3758:
3754:
3744:
3739:
3736:
3734:
3727:
3724:
3720:
3710:
3705:
3697:
3693:
3682:
3678:
3668:
3663:
3660:
3658:
3650:
3645:
3637:
3633:
3622:
3618:
3608:
3600:
3594:
3592:
3585:
3582:
3578:
3568:
3563:
3555:
3551:
3540:
3536:
3526:
3518:
3512:
3510:
3502:
3497:
3489:
3485:
3474:
3470:
3460:
3452:
3446:
3444:
3437:
3434:
3430:
3418:
3417:
3416:
3414:
3407:
3400:
3393:
3385:
3380:
3369:
3356: =
3352:
3345:
3338:
3326:
3323: −
3314:
3307:
3300:
3293:
3289:
3285:
3281:
3277:
3273:
3269:
3265:
3261:
3257:
3253:
3248:
3225:
3217:
3213:
3203:
3199:
3189:
3185:
3178:
3171:
3163:
3158:
3151:
3146:
3139:
3132:
3127:
3120:
3113:
3108:
3101:
3096:
3088:
3083:
3078:
3070:
3066:
3056:
3052:
3042:
3038:
3028:
3024:
3014:
3010:
3000:
2996:
2989:
2982:
2976:
2971:
2966:
2959:
2955:
2947:
2943:
2935:
2931:
2923:
2918:
2911:
2907:
2901:
2896:
2891:
2884:
2877:
2873:
2867:
2862:
2857:
2852:
2846:
2841:
2836:
2828:
2824:
2814:
2810:
2800:
2796:
2789:
2777:
2769:
2765:
2755:
2751:
2741:
2737:
2730:
2723:
2717:
2712:
2707:
2700:
2695:
2688:
2684:
2676:
2669:
2665:
2659:
2650:
2646:
2640:
2635:
2626:
2622:
2616:
2611:
2602:
2598:
2592:
2587:
2581:
2576:
2571:
2563:
2559:
2549:
2545:
2535:
2531:
2521:
2517:
2507:
2503:
2493:
2489:
2482:
2475:
2468:
2462:
2457:
2453:
2449:
2444:
2439:
2435:
2430:
2426:
2423:
2418:
2413:
2409:
2403:
2398:
2393:
2388:
2383:
2376:
2369:
2364:
2360:
2354:
2349:
2344:
2339:
2332:
2327:
2320:
2315:
2311:
2305:
2300:
2295:
2288:
2283:
2278:
2271:
2266:
2262:
2254:
2249:
2245:
2237:
2232:
2228:
2220:
2215:
2210:
2203:
2198:
2194:
2186:
2181:
2177:
2169:
2164:
2160:
2152:
2147:
2142:
2135:
2130:
2126:
2118:
2113:
2109:
2101:
2096:
2092:
2085:
2080:
2075:
2067:
2063:
2053:
2049:
2039:
2035:
2025:
2021:
2011:
2007:
1997:
1993:
1986:
1972:
1971:
1970:
1968:
1960:
1959:crystal class
1952:
1947:
1920:
1918:
1914:
1913:transposition
1910:
1906:
1883:
1877:
1870:
1865:
1861:
1857:
1853:
1847:
1838:
1832:
1830:
1822:
1812:
1806:
1789:
1782:
1776:
1769:
1764:
1760:
1756:
1752:
1750:
1742:
1728:
1727:
1726:
1723:
1707:
1704:
1701:
1697:
1693:
1688:
1685:
1682:
1678:
1674:
1669:
1664:
1661:
1658:
1654:
1578:
1573:
1569:
1562:
1559:
1555:
1549:
1545:
1541:
1536:
1533:
1529:
1522:
1519:
1516:
1512:
1506:
1503:
1500:
1496:
1492:
1487:
1483:
1474:
1457:
1441:
1439:
1425:
1420:
1416:
1409:
1404:
1401:
1398:
1394:
1388:
1384:
1380:
1375:
1372:
1368:
1361:
1358:
1355:
1352:
1348:
1342:
1339:
1336:
1332:
1328:
1323:
1320:
1316:
1307:
1290:
1278:
1262:
1260:
1242:
1241:
1240:
1238:
1234:
1226:
1222:
1218:
1202:
1197:
1185:
1171:
1162:
1152:
1144:
1134:
1133:
1131:
1127:
1123:
1119:
1115:
1111:
1107:
1088:
1085:
1081:
1074:
1071:
1068:
1065:
1061:
1055:
1052:
1049:
1045:
1041:
1036:
1033:
1029:
1005:
993:
992:
991:
990:
986:
983:
982:
978:
960:
952:
940:
927:
924:
916:
904:
900:
896:
892:
888:
884:
880:
876:
860:
856:
849:
846:
842:
836:
832:
828:
823:
819:
780:
768:
767:
766:
765:
761:
760:
759:
751:
749:
744:
742:
737:
733:
729:
728:
723:
719:
718:
713:
709:
708:
702:
700:
696:
692:
688:
687:
682:
678:
674:
670:
666:
662:
655:
651:
647:
639:
634:
625:
623:
620:models as an
619:
615:
611:
605:
601:
599:
594:
592:
588:
584:
580:
576:
575:United States
572:
562:
560:
555:
550:
546:
544:
540:
536:
532:
529:
525:
524:Paul Langevin
521:
517:
513:
509:
499:
497:
493:
489:
485:
481:
476:
473:
464:
460:
458:
457:Rochelle salt
454:
453:Rochelle salt
450:
447:
443:
439:
435:
431:
430:Jacques Curie
427:
418:
414:
412:
408:
404:
400:
399:Franz Aepinus
396:
395:Carl Linnaeus
392:
388:
373:
371:
367:
363:
359:
355:
351:
347:
343:
339:
338:microbalances
335:
331:
327:
323:
318:
316:
311:
307:
303:
299:
295:
291:
287:
282:
280:
276:
272:
268:
265:
258:
254:
251:
248:
241:
237:
234:
233:Ancient Greek
230:
226:
222:
218:
214:
210:
206:
202:
198:
194:
190:
186:
180:
129:
121:
55:
49:
45:
41:
37:
32:
19:
18:Piezoelectric
8479:
8471:
8463:
8455:
8449:Madame Curie
8447:
8440:
8433:
8398:Curie Island
8333:(son-in-law)
8264:
8253:Publications
8228:
8143:PiezoMat.org
8093:. Springer.
8090:
8025:
8021:
8011:
8000:. Retrieved
7985:
7973:. Retrieved
7964:
7955:
7938:
7934:
7886:
7882:
7872:
7861:. Retrieved
7854:the original
7845:
7838:
7827:. Retrieved
7820:the original
7815:
7802:
7789:
7780:
7747:
7743:
7733:
7708:
7704:
7698:
7661:
7657:
7647:
7622:
7618:
7612:
7585:
7581:
7571:
7560:. Retrieved
7556:the original
7546:
7534:. Retrieved
7530:
7518:
7506:. Retrieved
7502:
7490:
7480:28 September
7478:. Retrieved
7474:the original
7469:
7459:
7432:
7425:
7400:
7396:
7354:
7350:
7344:
7333:. Retrieved
7324:
7314:
7306:the original
7301:
7291:
7258:
7254:
7244:
7235:
7225:
7212:
7202:
7185:
7175:
7162:
7152:
7140:. Retrieved
7134:
7124:
7091:
7087:
7076:
7041:
7037:
7027:
6994:
6990:
6984:
6959:
6955:
6949:
6916:
6912:
6905:
6864:
6860:
6853:
6811:(11): 3605.
6808:
6804:
6760:
6720:
6714:
6706:
6702:
6697:
6689:
6685:
6680:
6639:
6635:
6617:
6576:
6570:
6564:
6531:
6527:
6521:
6512:
6506:
6481:
6477:
6467:
6451:
6447:
6434:
6391:
6387:
6374:
6362:. Retrieved
6348:
6336:. Retrieved
6322:
6289:
6283:
6277:
6244:
6240:
6222:
6216:
6207:
6198:
6189:
6178:. Retrieved
6174:the original
6169:
6159:
6140:
6131:
6094:
6090:
6056:
6052:
6042:
6028:
6018:
6005:
6001:
5984:
5971:
5965:
5955:
5942:
5938:
5914:
5910:
5885:(4): 90–93.
5882:
5878:
5865:
5833:
5821:. Retrieved
5817:
5807:
5795:. Retrieved
5791:the original
5786:
5776:
5751:
5747:
5741:
5722:
5716:
5685:
5679:
5666:
5656:
5650:
5646:
5639:
5628:
5618:
5604:
5576:
5565:
5555:
5532:
5526:
5507:
5498:
5382:
5375:
5371:
5368:
5364:
5353:
5350:Piezosurgery
5348:
5328:
5319:
5309:
5301:TU Darmstadt
5294:
5290:
5282:
5263:
5224:
5184:transmitters
5147:
5013:Loudspeakers
4983:
4934:are used in
4888:
4882:
4880:
4873:
4854:
4846:
4730:
4714:
4695:
4681:
4677:
4641:
4621:
4609:
4605:piezotronics
4577:
4570:
4563:
4522:
4508:
4486:
4418:
4411:
4324:
4311:
4302:
4268:
4148:
4131:
4130:
4125:
4124:
4119:
4118:
4116:
4110:
4109:
4104:
4103:
4101:
4054:
4017:
4009:
3409:
3402:
3395:
3388:
3386:
3378:
3367:
3350:
3343:
3336:
3324:
3312:
3305:
3298:
3291:
3283:
3279:
3275:
3267:
3255:
3251:
3249:
3246:
1948:
1921:
1908:
1904:
1902:
1724:
1597:
1236:
1232:
1230:
1224:
1220:
1125:
1117:
1109:
898:
895:permittivity
890:
882:
757:
747:
745:
726:
725:
716:
715:
706:
705:
703:
694:
691:vector field
685:
684:
673:polarization
643:
638:audio signal
622:echolocation
606:
602:
595:
571:World War II
568:
551:
547:
505:
491:
487:
477:
469:
426:Pierre Curie
423:
384:
326:Pierre Curie
319:
283:
274:
263:
260:
253:
246:
243:
236:
216:
53:
52:
36:Pierre Curie
8519:Transducers
8484:(2019 film)
8481:Radioactive
8476:(2016 film)
8468:(2014 film)
8460:(1997 film)
8452:(1943 film)
8209:Curie's law
8202:Discoveries
7941:: 435–442.
7531:Seagate.com
6454:: 387–394.
5945:: 383–386.
5917:: 294–295.
5672:See p. 462.
5196:clock pulse
5074:common rail
4945:Automotive
4932:transducers
4857:microphones
4779:transformer
4722:Application
3262:, that is,
985:Hooke's law
557:Ultrasonic
512:World War I
480:Marie Curie
229:latent heat
221:electricity
215:. The word
40:Lord Kelvin
8498:Categories
8412:Depictions
8403:7000 Curie
8321:(grandson)
8309:(daughter)
8303:(daughter)
8002:2013-11-11
7863:2018-12-15
7829:2018-12-15
7619:Ultrasound
7562:2008-02-27
7335:2012-05-04
7163:TreeHugger
6180:2012-05-04
6091:Z. Phys. B
5924:See also:
5748:Ultrasound
5653:: 459–547.
5490:References
5389:zinc oxide
5274:frictional
5270:elliptical
5258:stick-slip
5235:auto-focus
5125:cavitation
4883:transducer
4772:Crowd Farm
4753:gas stoves
4665:parylene-C
4661:polyamides
4657:copolymers
4554:, called e
4552:zincblende
4544:zincblende
4406:((K,Na)NbO
4383:Zinc oxide
4275:perovskite
4240:Tourmaline
4143:See also:
4055:Of the 32
1122:compliance
669:cane sugar
610:Issac Koga
554:phonograph
539:hydrophone
535:transducer
528:ultrasonic
434:tourmaline
195:, certain
8341:Namesakes
8307:Ève Curie
7913:117687945
7790:cam.ac.uk
7536:March 10,
7508:March 10,
7417:155531221
7283:219435304
7275:2214-7853
7108:1476-1122
7044:: 10–16.
6976:2050-7526
6933:1944-8244
6881:1944-8244
6779:304563111
6672:123625588
6664:0021-4922
6548:1944-8244
6404:CiteSeerX
6269:250873563
6119:122393358
5297:Frankfurt
5278:sine wave
5233:used for
5192:computers
5190:, and in
5188:receivers
5174:oscillate
5159:employ a
5097:shutters.
4990:actuators
4969:Actuators
4800:inductive
4795:kilohertz
4749:spark gap
4669:polyimide
4645:amorphous
4475:(NaBi(TiO
4220:phosphate
4212:Berlinite
4159:Langasite
4139:Materials
4114:or both.
4049:capacitor
3968:∂
3953:∂
3942:−
3908:∂
3893:∂
3882:−
3832:∂
3817:∂
3766:∂
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883:D
861:j
857:E
850:j
847:i
837:j
829:=
824:i
820:D
791:E
781:=
777:D
741:V
727:P
717:P
707:P
686:P
660:3
490:(
267:)
261:(
250:)
244:(
173:s
170:t
164:ˌ
161:i
158:p
149:z
143:ˌ
140:i
137:p
134:/
114:z
108:ˌ
102:p
93:s
90:t
84:p
81:ˌ
72:z
66:p
63:ˌ
60:/
56:(
20:)
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