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Encyclopedia > Piezoelectricity

Piezoelectricity is the ability of some materials (notably crystals and certain ceramics) to generate an electric potential[1] in response to applied mechanical stress. This may take the form of a separation of electric charge across the crystal lattice. If the material is not short-circuited, the applied charge induces a voltage across the material. The word is derived from the Greek piezein, which means to squeeze or press. Quartz crystal Synthetic bismuth hopper crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid in which the constituent atoms... Fixed Partial Denture, or Bridge The word ceramic is derived from the Greek word ÎºÎµÏÎ±Î¼Î¹ÎºÏŒÏ‚ (keramikos). ... This article does not cite any references or sources. ... Stress is a measure of force per unit area within a body. ... Piezoelectricity is the ability of some materials (notably crystals and certain ceramics) to generate an electric charge in response to applied mechanical stress. ... 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. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

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 0.1% 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. This article is about the deformation of materials. ... Lead zirconium titanate (PZT, also Lead zirconate titanate) is a ceramic perovskite material that shows a marked piezoelectric effect - that is, it develops a voltage difference across two of its faces when compressed, and ferroelectric effect. ... Microbalance is an instrument capable of measuring amount of weight to at least 1 million parts of a gram ( g - the unit symbol for gram). ...

### 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. 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. Pyroelectricity is the ability of certain materials to generate an electrical potential when they are heated or cooled. ... Carl Linnaeus, Latinized as Carolus Linnaeus, also known after his ennoblement as  , (May 23, 1707[1] â€“ January 10, 1778), was a Swedish botanist, physician and zoologist[2] who laid the foundations for the modern scheme of nomenclature. ... Franz Ulrich Theodor Aepinus (December 13, 1724 - August 10, 1802), German natural philosopher, was born at Rostock in Saxony. ... RenÃ© Just HaÃ¼y (February 28, 1743 â€“ June 3, 1822), French mineralogist, commonly styled the AbbÃ© HaÃ¼y, from being an honorary canon of Notre Dame, was born at St Just, in the dÃ©partment of Oise. ... Antoine CÃ©sar Becquerel (March 8, 1788 â€“ January 18, 1878) was a French scientist and a pioneer in the study of electric and luminescent phenomena. ...

The first demonstration of the direct piezoelectric effect was in 1880 by the brothers Pierre Curie and Jacques Curie. They combined their knowledge of pyroelectricity with their understanding of the underlying crystal structures that gave rise to pyroelectricity to predict crystal behavior, and demonstrated the effect using crystals of tourmaline, quartz, topaz, cane sugar, and Rochelle salt (sodium potassium tartrate tetrahydrate). Quartz and Rochelle salt exhibited the most piezoelectricity. Year 1880 (MDCCCLXXX) was a leap year starting on Thursday (link will display the full calendar) of the Gregorian calendar (or a leap year starting on Tuesday of the 12-day slower Julian calendar). ... // Pierre Curie (Paris, France, May 15, 1859 â€“ April 19, 1906, Paris) was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity and radioactivity. ... Jacques Curie and his brother, Pierre Curie, studied pyroelectricity in the 1880s, leading to their discovery of some of the mechanisms behind piezoelectricity. ... The tourmaline mineral group is chemically one of the most complicated groups of silicate minerals. ... Quartz (from German Quarz[1]) is the second most common mineral in the Earths continental crust. ... Topaz is a silicate mineral of aluminium and fluorine with the chemical formula Al2SiO4(F,OH)2. ... Species Ref: ITIS 42058 as of 2004-05-05 Sugarcane is one of six species of a tall tropical southeast Asian grass (Family Poaceae) having stout fibrous jointed stalks whose sap at one time was the primary source of sugar. ... Magnification of grains of sugar, showing their monoclinic hemihedral crystalline structure. ... Potassium sodium tartrate is a double salt first prepared (in about 1675) by an apothecary, Pierre Seignette, of La Rochelle, France. ...

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. 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. Gabriel Jonas Lippmann (August 16, 1845 â€“ July 13, 1921) was a Franco-Luxembourgian physicist and inventor. ... Year 1881 (MDCCCLXXXI) was a common year starting on Saturday (link will display the full calendar). ...

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. Woldemar Voigt (September 2, 1850 - December 13, 1919) was a German physicist. ...

### World War I and Post-War

The first practical application for piezoelectric devices was sonar, first developed during World War I. In France in 1917, Paul Langevin and his coworkers developed an ultrasonic submarine detector. The detector consisted of a transducer, made of thin quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. By emitting a high-frequency 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. French F70 type frigates (here, La Motte-Picquet) are fitted with VDS (Variable Depth Sonar) type DUBV43 or DUBV43C towed sonars SONAR (SOund Navigation And Ranging) â€” or sonar â€” is a technique that uses sound propagation under water (primarily) to navigate, communicate or to detect other vessels. ... â€œThe Great War â€ redirects here. ... 1917 (MCMXVII) was a common year starting on Monday of the Gregorian calendar (see link for calendar) or a common year starting on Tuesday of the 13-day slower Julian calendar (see: 1917 Julian calendar). ... Albert Einstein, Paul Ehrenfest, Paul Langevin, Heike Kamerlingh Onnes, and Pierre Weiss at Ehrenfests home in Leiden Paul Langevin (January 23, 1872 â€“ December 19, 1946) was a prominent French physicist who developed Langevin dynamics and the Langevin equation. ... Ultrasound is a form of cyclic sound pressure with a frequency greater than the upper limit of human hearing, this limit being approximately 20 kilohertz (20,000 hertz). ... USS Virginia, a Virginia-class nuclear attack (SSN) submarine Alvin in 1978, a year after first exploring hydrothermal vents. ... A transducer is a device, usually electrical or electronic, that converts one type of energy to another. ... A hydrophone is a sound-to-electricity transducer for use in water or other liquids, analogous to a microphone for air. ... Look up echo in Wiktionary, the free dictionary. ... This article does not cite any references or sources. ...

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. French F70 type frigates (here, La Motte-Picquet) are fitted with VDS (Variable Depth Sonar) type DUBV43 or DUBV43C towed sonars SONAR (SOund Navigation And Ranging) â€” or sonar â€” is a technique that uses sound propagation under water (primarily) to navigate, communicate or to detect other vessels. ...

Piezoelectric devices found homes in many fields. Ceramic phonograph cartridges simplified player design, were cheap and accurate, and made record players cheaper to maintain and easier to build. The development of the ultrasonic transducer allowed for easy measurement of viscosity and elasticity in fluids and solids, resulting in huge advances in materials research. Ultrasonic time-domain reflectometers (which send an ultrasonic pulse through a material and measure reflections from discontinuities) could find flaws inside cast metal and stone objects, improving structural safety. Edison cylinder phonograph ca. ... In telecommunication, a time-domain reflectometer (TDR) is an electronic instrument used to characterize and locate faults in metallic cables ( twisted pair, coax). ...

### 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. This led to intense research to develop barium titanate and later lead zirconate titanate materials with specific properties for particular applications. Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki TÅjÅ Casualties Military dead: 17,000,000 Civilian dead: 33,000... This article or section is in need of attention from an expert on the subject. ... Barium titanate is an oxide of barium and titanium with the chemical formula BaTiO3. ... Lead zirconium titanate (PZT, also Lead zirconate titanate) is a ceramic perovskite material that shows a marked piezoelectric effect - that is, it develops a voltage difference across two of its faces when compressed, and ferroelectric 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. 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. Piezo ignition is a type of ignition that is used in portable camping stoves, gas grills and some lighters. ... Karl Benzs Velo model (1894) - entered into the first automobile race An automobile or motor (usually shortened to just car) is a wheeled passenger vehicle that carries its own motor. ... Acoustic location is the art and science of using sound to determine the distance and direction of something. ...

## Materials

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

### Naturally occurring crystals

Species Saccharum arundinaceum Saccharum bengalense Saccharum edule Saccharum officinarum Saccharum procerum Saccharum ravennae Saccharum robustum Saccharum sinense Saccharum spontaneum Sugarcane or Sugar cane (Saccharum) is a genus of 6 to 37 species (depending on taxonomic interpretation) of tall perennial grasses (family Poaceae, tribe Andropogoneae), native to warm temperate to tropical... Quartz (from German Quarz[1]) is the second most common mineral in the Earths continental crust. ... Potassium sodium tartrate is a double salt first prepared (in about 1675) by an apothecary, Pierre Seignette, of La Rochelle, France. ... Topaz is a silicate mineral of aluminium and fluorine with the chemical formula Al2SiO4(F,OH)2. ... The tourmaline mineral group is chemically one of the most complicated groups of silicate minerals. ...

### Other natural materials

• Bone - Bone exhibits some piezoelectric properties due to the apatite crystals.

Grays Anatomy illustration of a human femur. ... Apatite is a group of phosphate minerals, usually referring to hydroxylapatite, fluorapatite, and chlorapatite, named for high concentrations of OH-, F-, or Cl- ions, respectively, in the crystal. ...

• Gallium orthophosphate (GaPO4) - a quartz analogue crystal
• Langasite (La3Ga5SiO14) - a quartz analogue crystal

Gallium phosphate (GaPO4 or gallium orthophosphate) is a colorless trigonal crystal with a hardness of 5. ... Lanthanum gallium silicate (refer to as LGS in the article), also known as langasite, has a chemical formula of , where A, B, C and D indicate particular cation sites. ...

The family of ceramics with perovskite or tungsten-bronze structures exhibits piezoelectricity: Fixed Partial Denture, or Bridge The word ceramic is derived from the Greek word ÎºÎµÏÎ±Î¼Î¹ÎºÏŒÏ‚ (keramikos). ... Perovskite (calcium titanium oxide, CaTiO3) is a relatively rare mineral occurring in orthorhombic (pseudocubic) crystals. ... General Name, Symbol, Number tungsten, W, 74 Chemical series transition metals Group, Period, Block 6, 6, d Appearance grayish white, lustrous Standard atomic weight 183. ... Assorted ancient Bronze castings found as part of a cache, probably intended for recycling. ...

Barium titanate is an oxide of barium and titanium with the chemical formula BaTiO3. ... Lead zirconium titanate (PZT, also Lead zirconate titanate) is a ceramic perovskite material that shows a marked piezoelectric effect - that is, it develops a voltage difference across two of its faces when compressed, and ferroelectric effect. ... Strontium titanate is an oxide of strontium and titanium with the chemical formula SrTiO3. ... Lithium niobate (LiNbO3) is a compound of niobium and lithium. ... Wikinews has news related to: Tabletop fusion may lead to neutron source Lithium tantalate (LiTaO3), is a crystalline solid which possesses unique optical, piezoelectric and pyroelectric properties which make it valuable for infrared motion detectors, terahertz generation and detection, surface acoustic wave applications, cell phones and possibly pyroelectric nuclear fusion. ... There are very few or no other articles that link to this one. ... Sodium tungstate, NaWO4, is useful as a source of tungsten. ...

### Polymers

• Polyvinylidene fluoride (PVDF) - PVDF exhibits piezoelectricity several times larger than quartz. Unlike ceramics, where the crystal structure of the material creates the piezoelectric effect, in polymers the intertwined long-chain molecules attract each and repel other when an electric field is applied.

PVDF, or PolyVinylidine DiFluoride, is a highly non-reactive and pure thermoplastic fluoropolymer. ...

## 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. Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ... Josephson junction array chip developed by NIST as a standard volt. ...

• Probably the best-known application is the electric cigarette lighter: pressing the button causes a spring-loaded hammer to hit a piezoelectric crystal, and the high voltage produced ignites the gas as the current jumps over a small spark gap. The portable sparkers used to light gas grills or stoves work the same way, and many types of gas burners now have built-in piezo-based ignition systems.
• A similar idea is being researched by DARPA in the United States in a project called Energy Harvesting, which includes an attempt to power battlefield equipment by piezoelectric generators embedded in soldiers' boots.
• A piezoelectric transformer is a type of AC voltage multiplier. Unlike a conventional transformer, which uses magnetic coupling between input and output, the piezoelectric transformer uses acoustic coupling. An input voltage is applied across a short length of a bar of piezoceramic material such as PZT, 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 resonant frequency of the block, typically in the 100 kilohertz 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 1000:1 have been demonstrated. An extra feature of this transformer is that, by operating it above its resonant frequency, it can be made to appear as an inductive load, which is useful in circuits that require a controlled soft start.[1] These devices can be used in DC-AC inverters to drive CCFLs. Piezo transformers are some of the most compact high voltage sources available.

### Sensors

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. Depending on the design of a sensor, different "modes" to load the piezoelectric element can be used: longitudinal, transversal and shear. Quartz: When a force is applied to the tetrahedon a displacement of the cation charge towards the center of the anion charges occurs Over the past 50 years piezoelectric sensors have proven to be a versatile tool for the measurement of various processes. ... Not to be confused with censure, censer, or censor. ...

Detection of pressure variations in the form of sound is the most common sensor application, e.g. piezoelectric microphones (sound waves bend the piezoelectric material, creating a changing voltage) and piezoelectric pickups for electrically amplified guitars. A piezo sensor attached to the body of an instrument is known as a contact microphone. Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... A microphone, sometimes referred to as a mike or mic (both IPA pronunciation: ), is an acoustic to electric transducer or sensor that converts sound into an electrical signal. ... Three magnetic pickups on an electric guitar. ... For other uses, see Guitar (disambiguation). ... 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 through solid materials and converts them into audible sound. ...

Piezoelectric sensors especially are used with high frequency sound in ultrasonic transducers for medical imaging and also industrial nondestructive testing (NDT). Ultrasound is sound with a frequency greater than the upper limit of human hearing, approximately 20 kilohertz. ... A transducer is a device that converts one type of energy to another, or responds to a physical parameter. ... // Nondestructive testing (also called NDT, nondestructive evaluation, NDE, and nondestructive inspection, NDI) is testing that does not destroy the test object. ...

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:

French F70 type frigates (here, La Motte-Picquet) are fitted with VDS (Variable Depth Sonar) type DUBV43 or DUBV43C towed sonars SONAR (SOund Navigation And Ranging) â€” or sonar â€” is a technique that uses sound propagation under water (primarily) to navigate, communicate or to detect other vessels. ... In chemistry, the study of sonochemistry is concerned with understanding the effect of sonic waves and wave properties on chemical systems. ... Piezoelectric microbalances are devices which use piezoelectric crystal resonators as mass sensitive sensor elements. ... Typical foil strain gauge. ... A transducer is a device that converts one type of energy to another, or responds to a physical parameter. ... Basic electronic drum set made by Pintech. ... An Engine Control Unit (ECU) also known as an Engine Control Module (ECM) or Powertrain Control Unit/Module (PCU, PCM) if it controls both an engine and a transmission, is an electronic control unit which controls various aspects of an internal combustion engines operation. ... Knocking (also called pinking or pinging)â€” colloquially detonationâ€”in internal combustion engines occurs when air/fuel mixture in the cylinder has been ignited by the spark plug and the smooth burning is interrupted by the unburned mixture in the combustion chamber exploding before the flame front can reach it. ... There are very few or no other articles that link to this one. ...

### Actuators

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 micrometre (American spelling: micrometer, symbol Âµm) is an SI unit of length equal to one millionth of a metre, or about a tenth of the diameter of a droplet of mist or fog. ... An actuator is the mechanism by which an agent acts upon an environment. ...

• Loudspeakers: Voltages are converted to mechanical movement of a piezoelectric polymer film.
• Piezoelectric motors: piezoelectric elements apply a directional force to an axle, causing it to rotate. Due to the extremely small distances involved, the piezo motor is viewed as a high-precision replacement for the stepper motor.
• Piezoelectric elements can be used in laser 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 cavity to optimize the beam output.
• A related application is the acousto-optic modulator, a device that vibrates a mirror to give the light reflected off it a Doppler shift. This is useful for fine-tuning a laser's frequency.
• Atomic force microscopes and scanning tunneling microscopes employ converse piezoelectricity to keep the sensing needle close to the probe.
• Inkjet printers: On many inkjet printers, piezoelectric crystals are used to control the flow of ink from the cartridge to the paper.
• Diesel engines: high-performance common rail diesel engines use piezoelectric fuel injectors, first developed by Siemens AG, instead of the more common solenoid valve devices.

A loudspeaker is a device which converts an electrical signal into sound. ... An axle is a central shaft for a rotating wheel or gear. ... The top electromagnet (1) is charged, attracting the topmost four teeth of a sprocket. ... Experiment with a laser (US Military) In physics, a laser is a device that emits light through a specific mechanism for which the term laser is an acronym: Light Amplification by Stimulated Emission of Radiation. ... An acousto-optic modulator (AOM) consists of a piezo-electric transducer which creates sound waves in a material like glass or quartz. ... The Doppler effect is the apparent change in frequency or wavelength of a wave that is perceived by an observer moving relative to the source of the waves. ... Experiment with a laser (US Military) In physics, a laser is a device that emits light through a specific mechanism for which the term laser is an acronym: Light Amplification by Stimulated Emission of Radiation. ... Topographic scan of a glass surface The atomic force microscope (AFM) is a very high-resolution type of scanning probe microscope, with demonstrated resolution of fractions of a nanometer, more than 1000 times better than the optical diffraction limit. ... Image of substitutional Cr impurities (small bumps) in the Fe(001) surface. ... Inkjet printers are a type of computer printer that operates by propelling tiny droplets of liquid ink onto paper. ... This article does not cite any references or sources. ... â€œHDiâ€ redirects here. ... Fuel injection is a technology used in internal combustion engines to mix the fuel with air prior to combustion. ... Siemens AG (ISIN: DE0007236101, FWB: SIE, NYSE: SI) is one of the worlds largest companies and Europes largest engineering firm. ... A solenoid valve is an electromechanical valve for use with liquid or gas controlled by running or stopping an electrical current through a solenoid, which is a coil of wire, thus changing the state of the valve. ...

### Frequency standard

The piezoelectrical properties of quartz are useful as standard of frequency. In telecommunication, a frequency standard is a stable oscillator used for frequency calibration or reference. ...

• Quartz clocks employ a tuning fork made from quartz 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 elastic material) has a precisely defined natural frequency (caused by its shape and size) at which it prefers to oscillate, and this is used to stabilize the frequency of a periodic voltage applied to the crystal.
• The same principle is critical in all radio transmitters and receivers, and in computers where it creates a clock pulse. Both of these usually use a frequency multiplier to reach the megahertz and gigahertz ranges.

A quartz clock A quartz clock is a timepiece that uses an electronic oscillator which is made up by a quartz crystal to keep precise time. ... A tuning fork is a simple metal two-pronged fork with the tines formed from a U-shaped bar of elastic material (usually steel). ... Elasticity is a branch of physics which studies the properties of elastic materials. ... Oscillation is the periodic variation, typically in time, of some measure as seen, for example, in a swinging pendulum. ... Antenna tower of Crystal Palace transmitter, London A transmitter (sometimes abbreviated XMTR) is an electronic device which with the aid of an antenna propagates an electromagnetic signal such as radio, television, or other telecommunications. ... In radio terminology, a receiver is an electronic circuit that receives a radio signal from an antenna and decodes the signal for use as sound, pictures, navigational-position information, etc. ... The NASA Columbia Supercomputer. ... In synchronous digital electronics, such as most computers, a clock signal is a signal used to coordinate the actions of two or more circuits. ... A frequency multiplier is commonly used in a radio transmitters to multiply the base frequency of the oscillator by a predetermined number. ... MegaHertz (MHz) is the name given to one million (106) Hertz, a measure of frequency. ... A gigahertz is a billion hertz or a thousand megahertz, a measure of frequency. ...

### Reduction of vibrations

The TU Darmstadt in Germany researches ways to reduce and stop vibrations by attaching piezo elements. When the material is bent by a vibration in one direction, the system observes the bend and sends electric power to the piezo element to bend in the other direction. Old main building in the city centre. ...

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. For other uses, see Frankfurt (disambiguation). ...

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

## 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.

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). Ten of these are polar (i.e. spontaneously polarize), having a dipole in their unit cell, and exhibit pyroelectricity. If this dipole can be reversed by the application of an electric field, the material is said to be ferroelectric. I created this image using Micrografx Designer and Picture Publisher software. ... I created this image using Micrografx Designer and Picture Publisher software. ... 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. ... This article does not cite any references or sources. ... Capacitors: SMD ceramic at top left; SMD tantalum at bottom left; through-hole tantalum at top right; through-hole electrolytic at bottom right. ... In crystallography, a crystallographic point group or crystal class is a set of symmetry operations that leave a point fixed, like rotations or reflections, which leave the crystal unchanged. ... The Earths magnetic field, which is approximately a dipole. ... 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. ... In physics, the ferroelectric effect is an electrical phenomenon whereby certain ionic crystals may exhibit a spontaneous dipole moment. ...

• Piezoelectric Crystal Classes: 1, 2, m, 222, mm2, 4, -4, 422, 4mm, -42m, 3, 32, 3m, 6, -6, 622, 6mm, -62m, 23, -43m
• Pyroelectric: 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, 6mm

In a piezoelectric crystal, the positive and negative electrical charges are separated, but symmetrically distributed, so that the crystal overall is electrically neutral. Each of these sites forms an electric dipole and dipoles near each other tend to be aligned in regions called Weiss domains. 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. Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ... The Earths magnetic field, which is approximately a dipole A dipole (Greek: dyo = two and polos = pivot) is a pair of electric charges or magnetic poles of equal magnitude but opposite polarity (opposite electronic charges), separated by some (usually small) distance. ... Charge seperation between the positive and negative ions is the reason for electric dipole behavior. ... Magnetic lines of force of a bar magnet shown by iron filings on paper A magnet is an object that has a magnetic field. ...

When a mechanical stress is applied, this symmetry is disturbed, and the charge asymmetry generates a voltage across the material. For example, a 1 cm cube of quartz with 500 lbf (2 kN) of correctly applied force upon it, can produce a voltage of 12,500 V. Symmetry is a characteristic of geometrical shapes, equations and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... Quartz (from German Quarz[1]) is the second most common mineral in the Earths continental crust. ... The pound-force is a non-SI unit of force or weight (properly abbreviated lbf or lbf). The pound-force is equal to a mass of one pound multiplied by the standard acceleration due to gravity on Earth (which is defined as exactly 9. ... The kilonewton, symbol kN, is an SI unit of force. ...

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 displacement, $epsilon ;$ is permittivity and E is electric field strength, and Hooke's Law: The factual accuracy of this article is disputed. ... 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 of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

$S=s T ;$

Where S is strain, s is compliance and T is stress. Look up strain in Wiktionary, the free dictionary. ... Compliance can mean: Compliance (medicine), a patients (or doctors) adherence to a recommended course of treatment Compliance (physiology), a measure of stiffness in mechanical science and physiology Compliance (regulation), the act of adhering to, and demonstrating adherence to laws, regulations or policies, in management Category: ... Stress is a measure of force per unit area within a body. ...

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 subscript t stands for transposition of a matrix. In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, a table consisting of abstract quantities that can be added and multiplied. ...

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:

$begin{bmatrix} S_1 S_2 S_3 S_4 S_5 S_6 end{bmatrix} = begin{bmatrix} s_{11}^E & s_{12}^E & s_{13}^E & 0 & 0 & 0 s_{12}^E & s_{11}^E & s_{13}^E & 0 & 0 & 0 s_{13}^E & s_{13}^E & s_{33}^E & 0 & 0 & 0 0 & 0 & 0 & s_{44}^E & 0 & 0 0 & 0 & 0 & 0 & s_{44}^E & 0 0 & 0 & 0 & 0 & 0 & s_{66}^E=2left(s_{11}^E-s_{12}^Eright) end{bmatrix} begin{bmatrix} T_1 T_2 T_3 T_4 T_5 T_6 end{bmatrix} + begin{bmatrix} 0 & 0 & d_{31} 0 & 0 & d_{31} 0 & 0 & d_{33} 0 & d_{15} & 0 d_{15} & 0 & 0 0 & 0 & 0 end{bmatrix} begin{bmatrix} E_1 E_2 E_3 end{bmatrix}$
$begin{bmatrix} D_1 D_2 D_3 end{bmatrix} = begin{bmatrix} 0 & 0 & 0 & 0 & d_{15} & 0 0 & 0 & 0 & d_{15} & 0 & 0 d_{31} & d_{31} & d_{33} & 0 & 0 & 0 end{bmatrix} begin{bmatrix} T_1 T_2 T_3 T_4 T_5 T_6 end{bmatrix} + begin{bmatrix} epsilon {}_{11} & 0 & 0 0 & epsilon {}_{11} & 0 0 & 0 & epsilon {}_{33} end{bmatrix} begin{bmatrix} E_1 E_2 E_3 end{bmatrix}$

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. Strain and stress are, in principle, also rank-2 tensors. But conventionally, because strain and stress are all symmetric tensors, the substript of strain and stress can be re-labeled in the following fashion: $11 rightarrow 1 ;$; $22 rightarrow 2 ;$; $33 rightarrow 3 ;$; $23 rightarrow 4 ;$; $13 rightarrow 5 ;$; $12 rightarrow 6 ;$. (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 nonation is often called Voigt notation. A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ... This is a glossary of tensor theory. ... 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 of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ... Look up strain in Wiktionary, the free dictionary. ... Stress is a measure of force per unit area within a body. ... For more technical Wiki articles on tensors, see the section later in this article. ... Look up strain in Wiktionary, the free dictionary. ... Stress is a measure of force per unit area within a body. ... Voigt notation - Wikipedia /**/ @import /skins/monobook/IE50Fixes. ...

International Standards Objects used in tandem with electricity. ... In physics, the ferroelectric effect is an electrical phenomenon whereby certain ionic crystals may exhibit a spontaneous dipole moment. ... Electret (formed of elektr- from electricity and -et from magnet) is material that has been permanently electrically charged (polarised). ... 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 produces a relatively slight change of shape, or mechanical deformation, under the application of an electric field. ... A charge amplifier is an electronic amplifier which converts an input charge (stored on a capacitor, or significantly capacitive transducer) to a voltage output. ...

• ANSI-IEEE 176 (1987) Standard on Piezoelectricity
• IEC 302 (1969) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators Operating over the Freq Range up to 30MHz
• 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
• IEEE 177 (1976) Standard Definitions & Methods of Measurement for Piezoelectric Vibrators

## References

1. ^ Principles of Instrumental Analysis. 6th Edition, 2007. Skoog, Holler, and Crouch. Chapter 1, Sec. 1C-4, Pg. 9.
• Gautschi, Gustav H., 2002, Piezoelectric Sensorics, Springer, ISBN 3540422595, [2]

Results from FactBites:

 NodeWorks - Encyclopedia: Piezoelectricity (1603 words) Converse piezoelectricity was mathematically deduced from fundamental thermodynamic principles by Lippmann in 1881. 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. Piezoelectric elements can be used in laser mirror alignment, where their ability to move a large mass (the mirror mount) over microscopic distances is exploited to electronically align some laser mirrors.
 Piezoelectricity (561 words) Although many crystal exhibit the piezoelectric effect, very few are useful, and quartz alone provides the necessary combination of mechanical, electrical, chemical, and thermal properties required for making piezoelectric elements for communication devices. Piezoelectricity literally means "pressure electricity" and may be defined as the electric polarization produced by a mechanical strain in crystals (that belong to certain classes of crystals). The piezoelectric effect is a convenient, built in transducer that converts mechanical movement to electrical signals and visa versa.
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