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Piezoelectricity is the ability of some materials (notably crystals and certain ceramics) to generate an electric potential[1] in response to applied mechanical stress. In Materials science, a crystal is a Solid in which the constituent Atoms Molecules or Ions are packed in a regularly ordered repeating The word ceramic is derived from the Greek word κεραμικός ( keramikos) At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field Stress is a measure of the average amount of Force exerted per unit Area. This may take the form of a separation of electric charge across the crystal lattice. Piezoelectricity is the ability of some materials (notably Crystals and certain Ceramics including bone to generate an Electric potential in response to Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. In Mineralogy and Crystallography, a crystal structure is a unique arrangement of Atoms in a Crystal. If the material is not short-circuited, the applied charge induces a voltage across the material. Short Circuit is a 1986 comedy Science fiction film starring Ally Sheedy and Steve Guttenberg and directed by Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical The word is derived from the Greek piezein, which means to squeeze or press. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly

The piezoelectric effect is reversible in that materials exhibiting the direct piezoelectric effect (the production of electricity when stress is applied) also exhibit the converse piezoelectric effect (the production of stress and/or strain when an electric field is applied). For example, lead zirconate titanate crystals will exhibit a maximum shape change of about 0. Lead zirconate titanate ( 0 x Ceramic Perovskite material that shows a marked piezoelectric effect. 1% of the original dimension.

The effect finds useful applications such as the production and detection of sound, generation of high voltages, electronic frequency generation, microbalances, and ultra fine focusing of optical assemblies. A microbalance is an instrument capable of making precise measurements of weight of objects of relatively small mass of the order of a million parts of a Gram. It is also the basis of a number of scientific instrumental techniques with atomic resolution, the scanning probe microscopies such as STM, AFM, MTA, SNOM etc. Scanning probe microscopy (SPM is a branch of Microscopy that forms images of surfaces using a physical probe that scans the specimen Scanning tunneling microscope (STM is a powerful technique for viewing surfaces at the atomic level The atomic force microscope (AFM or scanning force microscope (SFM is a very high-resolution type of scanning probe microscope, with demonstrated resolution of fractions Microthermal analysis is a materials characterization technique which combines the Thermal analysis principles of Differential scanning calorimetry (DSC with high Near Field Scanning Optical Microscopy (NSOM/SNOM is a microscopic technique for nanostructure investigation that breaks the far field resolution limit by exploiting the properties

Contents

History

Discovery and early research

The pyroelectric effect, where a material generates an electric potential in response to a temperature change, was studied by Carolus Linnaeus and Franz Aepinus in the mid-18th century. Carl Linnaeus (Latinized as Carolus Linnaeus, also known after his ennoblement as, May 23 new style (13 May old style 1707 who laid the foundations for Franz Ulrich Theodor Aepinus ( December 13, 1724 &ndash August 10, 1802) was a German natural Philosopher, was born at Drawing on this knowledge, both René Just Haüy and Antoine César Becquerel posited a relationship between mechanical stress and electric charge; however, experiments by both proved inconclusive. René Just Haüy (aɥi February 28, 1743 in Saint-Just-en-Chaussée ( Oise) &ndash June 3, 1822 in Paris) was Antoine César Becquerel ( March 7, 1788 &ndash January 18, 1878) was a French Scientist and a pioneer in the study of

The first demonstration of the direct piezoelectric effect was in 1880 by the brothers Pierre Curie and Jacques Curie. Year 1880 ( MDCCCLXXX) was a Leap year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Leap year Pierre Curie (15 May 1859 &ndash 19 April 1906 was a French physicist, a pioneer in Crystallography, Magnetism, Piezoelectricity Paul-Jacques Curie ( October 29, 1856 &ndash 1941 was a French Physicist and professor at the University of Montpellier. They combined their knowledge of pyroelectricity with their understanding of the underlying crystal structures that gave rise to pyroelectricity to predict crystal behavior, and demonstrated the effect using crystals of tourmaline, quartz, topaz, cane sugar, and Rochelle salt (sodium potassium tartrate tetrahydrate). Tourmaline is a Crystal Silicate mineral compounded with elements such as Aluminium, Iron, Magnesium, Sodium, Lithium Quartz (from German) is the most abundant Mineral in the Earth 's Continental crust (although Feldspar is more common in Topaz is a Silicate mineral of Aluminium and Fluorine with the Chemical formula Al 2 Si[[oxygen O]]4( Sugarcane ( Saccharum) is a genus of 6 to 37 species (depending on taxonomic interpretation of tall perennial grasses (family Poaceae tribe Andropogoneae Sugar is a class of edible Crystalline substances mainly Sucrose, Lactose, and Fructose. Potassium sodium tartrate is a Double salt first prepared (in about 1675) by an apothecary, Pierre Seignette, of La Rochelle, Quartz and Rochelle salt exhibited the most piezoelectricity.

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

The Curies, however, did not predict the converse piezoelectric effect. The converse effect was mathematically deduced from fundamental thermodynamic principles by Gabriel Lippmann in 1881. Gabriel Jonas Lippmann ( August 16 1845 &ndash July 13 1921) was a Franco - Luxembourgish Physicist and Inventor Year 1881 ( MDCCCLXXXI) was a Common year starting on Saturday (link will display the full calendar of the Gregorian calendar (or a Common The Curies immediately confirmed the existence of the converse effect, and went on to obtain quantitative proof of the complete reversibility of electro-elasto-mechanical deformations in piezoelectric crystals.

For the next few decades, piezoelectricity remained something of a laboratory curiosity. More work was done to explore and define the crystal structures that exhibited piezoelectricity. This culminated in 1910 with the publication of Woldemar Voigt's Lehrbuch der Kristallphysik (textbook on crystal physics), which described the 20 natural crystal classes capable of piezoelectricity, and rigorously defined the piezoelectric constants using tensor analysis.

World War I and post-war

The first practical application for piezoelectric devices was sonar, first developed during World War I. Sonar (which started as an Acronym for sound navigation and ranging) is a technique that uses Sound propagation (usually underwater to navigate World War I (abbreviated WWI; also known as the First World War, the Great War, and the War to End All In France in 1917, Paul Langevin and his coworkers developed an ultrasonic submarine detector. This article is about the country For a topic outline on this subject see List of basic France topics. Year 1917 ( MCMXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common year Paul Langevin (23 January 1872 &ndash 19 December 1946 was a prominent French Physicist who developed Langevin dynamics and the Not to be confused with Supersonic. Ultrasound is cyclic Sound pressure with a Frequency greater than the upper A submarine is a Watercraft that can operate independently below water as distinct from a Submersible that has only limited underwater capability The detector consisted of a transducer, made of thin quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. A transducer is a device usually electrical, electronic, Electro-mechanical, Electromagnetic, Photonic, or Photovoltaic A hydrophone (Greek "hydro" = "water" and "phone" = "sound" is a Microphone designed to be used underwater for recording or listening In Audio signal processing and Acoustics, an echo (plural echoes) is a reflection of sound arriving at the listener some time after the direct By emitting a high-frequency chirp 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. A chirp is a signal in which the Frequency increases ('up-chirp' or decreases ('down-chirp' with time

The use of piezoelectricity in sonar, and the success of that project, created intense development interest in piezoelectric devices. Sonar (which started as an Acronym for sound navigation and ranging) is a technique that uses Sound propagation (usually underwater to navigate Over the next few decades, new piezoelectric materials and new applications for those materials were explored and developed.

Piezoelectric devices found homes in many fields. Ceramic phonograph cartridges simplified player design, were cheap and accurate, and made record players cheaper to maintain and easier to build. The phonograph, or gramophone, was the most common device for playing recorded Sound from the 1870s through the 1980s The development of the ultrasonic transducer allowed for easy measurement of viscosity and elasticity in fluids and solids, resulting in huge advances in materials research. Ultrasonic time-domain reflectometers (which send an ultrasonic pulse through a material and measure reflections from discontinuities) could find flaws inside cast metal and stone objects, improving structural safety. A time-domain reflectometer ( TDR) is an electronic instrument used to characterize and locate faults in metallic cables (for example twisted wire pairs, Coaxial

World War II and post-war

During World War II, independent research groups in the United States, Russia, and Japan discovered a new class of man-made materials, called ferroelectrics, which exhibited piezoelectric constants many times higher than natural materials. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including The United States of America —commonly referred to as the Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending For a topic outline on this subject see List of basic Japan topics. Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent This led to intense research to develop barium titanate and later lead zirconate titanate materials with specific properties for particular applications. Barium titanate is an Oxide of Barium and Titanium with the Chemical formula BaTiO3 Lead zirconate titanate ( 0 x Ceramic Perovskite material that shows a marked piezoelectric effect.

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

In contrast, Japanese manufacturers shared their information, quickly overcoming technical and manufacturing challenges and creating new markets. Japanese efforts in materials research created piezoceramic materials competitive to the U. S. materials, but free of expensive patent restrictions. Major Japanese piezoelectric developments include new designs of piezoceramic filters, used in radios and televisions, piezo buzzers and audio transducers that could be connected directly into electronic circuits, and the piezoelectric igniter which generates sparks for small engine ignition systems (and gas-grill lighters) by compressing a ceramic disc. Piezo ignition is a type of Ignition that is used in portable Camping stoves gas grills and some lighters. Ultrasonic transducers that could transmit sound waves through air had existed for quite some time, but first saw major commercial use in early television remote controls. These transducers now are mounted on several car models as an echolocation device, helping the driver determine the distance from the rear of the car to any objects that may be in its path. Acoustic location is the art and science of using Sound to determine the distance and direction of something

Materials

Tetragonal unit cell of lead titanate
Tetragonal unit cell of lead titanate

Many materials, both natural and man-made, exhibit the piezoelectric effect:

Naturally-occurring crystals

Other natural materials

Man-made crystals

Man-made ceramics

The family of ceramics with perovskite or tungsten-bronze structures exhibits piezoelectricity:

Polymers

Lead-free piezoceramics

More recently, there is growing concern regarding the toxicity in lead-containing devices driven by the result of restriction of hazardous substances directive regulations. The Directive on the Restriction of the Use of Certain Hazardous Substances in Electrical and Electronic Equipment 2002/95/EC ( / commonly referred to as the Restriction of Hazardous Hence, there is an enormous insurgence in the compositional development of lead-free piezoelectric materials.

Applications

Piezoelectric crystals are now used in numerous ways:

High voltage and power sources

Direct piezoelectricity of some substances like quartz, as mentioned above, can generate potential differences of thousands of volts. In Physics, the potential difference or pd between two points is the difference of the points' Scalar potential, equivalent to the line integral The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force.

Sensors

Piezoelectric disk used as a guitar pickup
Piezoelectric disk used as a guitar pickup
Main article: Piezoelectric sensor

The principle of operation of a piezoelectric sensor is that a physical dimension, transformed into a force, acts on two opposing faces of the sensing element. A pickup device acts as a Transducer that captures mechanical vibrations (usually from suitably equipped Stringed instruments such as the Electric guitar A piezoelectric sensor is a device that uses the Piezoelectric effect to measure Pressure, Acceleration, strain or Force A sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument Depending on the design of a sensor, different "modes" to load the piezoelectric element can be used: longitudinal, transversal and shear.

Detection of pressure variations in the form of sound is the most common sensor application, e. Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies g. piezoelectric microphones (sound waves bend the piezoelectric material, creating a changing voltage) and piezoelectric pickups for electrically amplified guitars. A pickup device acts as a Transducer that captures mechanical vibrations (usually from suitably equipped Stringed instruments such as the Electric guitar The guitar is a Musical instrument with ancient roots that is used in a wide variety of musical styles A piezo sensor attached to the body of an instrument is known as a contact microphone. A contact microphone is a form of Microphone designed not for picking up airborne sound waves but rather to act as a Transducer which picks up vibrations

Piezoelectric sensors especially are used with high frequency sound in ultrasonic transducers for medical imaging and also industrial nondestructive testing (NDT). A transducer is a device usually electrical, electronic, Electro-mechanical, Electromagnetic, Photonic, or Photovoltaic Nondestructive testing ( NDT) also called nondestructive examination ( NDE) and nondestructive inspection ( NDI) is testing that does

For many sensing techniques, the sensor can act as both a sensor and an actuator - often the term transducer 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). Most medical ultrasound transducers are piezoelectric.

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

Actuators

Metal disk with piezoelectric disk attached, used in a buzzer
Metal disk with piezoelectric disk attached, used in a buzzer

As very high voltages correspond to only tiny changes in the width of the crystal, this width can be changed with better-than-micrometer precision, making piezo crystals the most important tool for positioning objects with extreme accuracy — thus their use in actuators. A buzzer or beeper is a signalling device usually electronic typically used in Automobiles household appliances such as a Microwave oven, or A micrometre ( American spelling: micrometer; symbol µm) is one millionth of a Metre, or equivalently one thousandth of a Millimetre An actuator is a mechanical device for moving or controlling a mechanism or system

Frequency standard

The piezoelectrical properties of quartz are useful as standard of frequency. A frequency standard is a stable oscillator used for Frequency Calibration or reference

Piezoelectric motors

Types of piezoelectric motor include the well-known travelling-wave motor used for auto-focus in reflex cameras, inchworm motors for linear motion, and rectangular four-quadrant motors with high power density (2. A piezoelectric motor or piezo motor is a type of Electric motor based upon the change in shape of a piezoelectric material when an Electric field Autofocus (or AF) is a feature of some Optical systems that allows them to obtain (and in some systems to also continuously maintain correct focus on a The single-lens reflex (SLR Camera uses an automatic moving mirror system which permits the photographer to see exactly what will be captured by the film or digital imaging The inchworm motor is a device that uses Piezoelectric Actuators to move a shaft with Nanometer Precision. 5 watt/cm3) and speed ranging from 10 nm/s to 800 mm/s. The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. All these motors work on the same principle. Driven by dual orthogonal vibration modes with a phase shift of 90°, the contact point between two surfaces vibrates in an elliptical path, producing a frictional force between the surfaces. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e Usually, one surface is fixed causing the other to move. In most piezoelectric motors the piezoelectric crystal is excited by a sine wave signal at the resonant frequency of the motor. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's Using the resonance effect, a much lower voltage can be used to produce a high vibration amplitude.

Reduction of vibrations

The TU Darmstadt in Germany researches ways to reduce and stop vibrations by attaching piezo elements. The Darmstadt University of Technology, whose official name (also its official English name) is "Technische Universität Darmstadt" (abbreviated TU Darmstadt) in Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. When the material is bent by a vibration in one direction, the system responds to the bend and sends electric power to the piezo element to bend in the other direction.

Such an experiment was shown at the Material Vision Fair in Frankfurt in November 2005. Several panels were hit with a rubber mallet, and the panel with the piezo element immediately stopped swinging.

The research team sees future applications in cars and houses to reduce noise.

Piezoelectric ceramic fiber technology is being used as an electronic dampening system on some Head tennis rackets. Head NV () is a Sports equipment and clothing company known mainly for their Skis and Racquets Their tennis racquets are used by many top players A racquet (or racket) is a sports implement consisting of a handled frame with an open hoop across which a network of cord is stretched tightly [8][9]

Crystal classes

Any spatially separated charge will result in an electric field, and therefore an electric potential. Shown here is a standard dielectric in a capacitor. In a piezoelectric device, mechanical stress is the cause for the charge separation in the individual atoms of the material, rather than an externally applied voltage.
Any spatially separated charge will result in an electric field, and therefore an electric potential. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can At a point in space the electric potential is the Potential energy per unit of charge that is associated with a static (time-invariant Electric field Shown here is a standard dielectric in a capacitor. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors In a piezoelectric device, mechanical stress is the cause for the charge separation in the individual atoms of the material, rather than an externally applied voltage.

Of the thirty-two crystal classes, twenty-one are non-centrosymmetric (not having a centre of symmetry), and of these, twenty exhibit direct piezoelectricity (the 21st is the cubic class 432). In Crystallography, a crystallographic point group is a set of Symmetry operations like rotations or reflections that leave a point fixed while moving each atom Ten of these are polar (i. e. spontaneously polarize), having a dipole in their unit cell, and exhibit pyroelectricity. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a In Mineralogy and Crystallography, a crystal structure is a unique arrangement of Atoms in a Crystal. Pyroelectricity is the ability of certain materials to generate an Electrical potential when they are heated or cooled If this dipole can be reversed by the application of an electric field, the material is said to be ferroelectric. Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent

Mechanism

In a piezoelectric crystal, the positive and negative electrical charges are separated, but symmetrically distributed, so that the crystal overall is electrically neutral. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Each of these sites forms an electric dipole and dipoles near each other tend to be aligned in regions called Weiss domains. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a Weiss domains are small areas in a Crystal structure of a ferromagnetic material with uniformly oriented magnetic momenta The domains are usually randomly oriented, but can be aligned during poling (not the same as magnetic poling), a process by which a strong electric field is applied across the material, usually at elevated temperatures.

When a mechanical stress is applied, this symmetry is disturbed, and the charge asymmetry generates a voltage across the material. Asymmetry is the absence of or a violation of a Symmetry. In organisms Due to how cells divide in Organisms asymmetry in organisms is Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical For example, a 1 cm cube of quartz with 2 kN (500 lbf) of correctly applied force upon it, can produce a voltage of 12,500 V. A centimetre ( American spelling: centimeter, symbol cm) is a unit of Length in the Metric system, equal to one hundredth Quartz (from German) is the most abundant Mineral in the Earth 's Continental crust (although Feldspar is more common in The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical This article deals with the unit of force For the unit of mass see Pound (mass. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. [10]

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

Mathematical description

Piezoelectricity is the combined effect of the electrical behavior of the material:

D=\epsilon E \;

Where D is the electric charge density displacement (electric displacement), \epsilon \; is permittivity and E is electric field strength, and Hooke's Law:

S=s T \;

Where S is strain, s is compliance and T is stress. In Physics, the electric displacement field (also called electrical field/flux density is a Vector field \mathbf{D} that appears in Maxwell's equations Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the Stress is a measure of the average amount of Force exerted per unit Area.

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

\{S\} = \left [s^E \right ]\{T\}+[d^t]\{E\}
\{D\} = [d]\{T\}+\left [ \epsilon^T \right ] \{E\}

where d represents the piezoelectric constants, and the superscript E indicates a zero, or constant, electric field; the superscript T indicates a zero, or constant, stress field; and the superscript t stands for transposition of a matrix. In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally

The strain-charge for a material of the 6mm crystal class (such as a poled piezoelectric ceramic, e. g. PZT) may also be written as:

\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} \epsilon\ {}_{11} & 0 & 0 \\ 0 & \epsilon\ {}_{22} & 0 \\ 0 & 0 & \epsilon\ {}_{33} \end{bmatrix} \begin{bmatrix} E_1 \\ E_2 \\ E_3 \end{bmatrix}

Although the above equations are the most used form in literature, some comments about the notation are necessary. Generally D and E are vectors, that is, Cartesian tensor of rank-1; and permittivity \epsilon \; is Cartesian tensor of rank-2. This is a glossary of tensor theory. For expositions of tensor theory from different points of view see Tensor Classical treatment of tensors Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability Strain and stress are, in principle, also rank-2 tensors. Stress is a measure of the average amount of Force exerted per unit Area. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually But conventionally, because strain and stress are all symmetric tensors, the substript of strain and stress can be re-labeled in the following fashion: 11 \rightarrow 1 \;; 22 \rightarrow 2 \;; 33 \rightarrow 3 \;; 23 \rightarrow 4 \;; 13 \rightarrow 5 \; ; 12 \rightarrow 6 \;. Stress is a measure of the average amount of Force exerted per unit Area. (Different convention may be used by different authors in literature. Say, some use 12 \rightarrow 4 \; ; 23 \rightarrow 5 \; ; 31 \rightarrow 6 \; instead. ) That is why S and T appear to have the "vector form" of 6 components. Consequently, s appears to be a 6 by 6 matrix instead of rank-4 tensor. Such a re-labeled notation is often called Voigt notation. In Mathematics, Voigt notation or Voigt form in Multilinear algebra is a way to represent a Symmetric tensor by reducing its order

See also

References

International Standards

Other references

  1. ^ Principles of Instrumental Analysis. An electronic component is a basic electronic element usually packaged in a discrete form with two or more connecting leads or metallic pads Ferroelectricity is a physical property of a material whereby it exhibits a spontaneous electric polarization, the direction of which can be switched between equivalent Electret (formed of elektr- from " Electricity " and -et from " Magnet " is a Dielectric material that has a quasi-permanent Magnetostriction is a property of Ferromagnetic materials that causes them to change their shape when subjected to a Magnetic field. Electrostriction is a property of all electrical non-conductors or Dielectrics, that causes them to change their shape under the application of an Electric field. A charge amplifier is a circuit whose equivalent input Impedance is a Capacitance that provides a very high value of impedance at low frequencies The piezoresistive effect describes the changing Electrical resistance of a material due to applied Mechanical stress. 6th Edition, 2007. Skoog, Holler, and Crouch. Chapter 1, Sec. 1C-4, Pg. 9.
  2. ^ Electrical Properties of Bone: A Review, Roderic Lakes
  3. ^ Robert O. Becker and Andrew A. Marino, Electromagnetism & Life, State University of New York Press, Albany, ISBN 0-87395-560-9 Chapter 4: Electrical Properties of Biological Tissue (Piezoelectricity)
  4. ^ Pollack, S. R. , Korostoff, E. , Starkebaum, W. y Lannicone, W. (1979) Micro-electrical studies of stress-generated potentials in bone. in Electrical Properties of Bone and Cartilage, (Edit. Brighton, C. T. , Black, J. & Pollack, S. R. ), Grune & Stratton, Inc. , New York.
  5. ^ Saito, Y. et al. Nature 432, 81-87 (2004)
  6. ^ Japan: Producing Electricity from Train Station Ticket Gates
  7. ^ 'Crowd Farm' — MIT project on harvesting energy of human movement in urban settings, like commuters in a train station or fans at a concert.
  8. ^ "Isn’t it amazing how one smart idea, one chip and an intelligent material has changed the world of tennis?" Accessed February 27, 2008
  9. ^ "Advanced Cerametrics - Ceramic Fibers and Components, Energy Harvesting Materials"Accessed February 27, 2008
  10. ^ Sensor Sense: Piezoelectric Force Sensors

Dictionary

piezoelectricity

-noun

  1. (physics) The ability of certain crystals to generate a voltage in response to applied mechanical stress.
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