Piezoelectricity

The piezoelectricity, also piezoelectric effect or short piezoelectric effect, obsolete: piezo - ( altgr. πιέζειν piezein, press ',' press ' and ἤλεκτρον electron Bernstein '), describes the change in the electric polarization and thus the occurrence of an electrical voltage is applied to solids, if they are elastically deformed (direct piezoelectric effect ). Conversely, materials deform when an electrical voltage (inverse piezoelectric effect ).

• 4.1 geometry
• 4.2 equations

• 5.1 sensors
• 5.2 actuators
• 5.3 Electrical Components
• 5.4 Other Applications

History

The direct piezoelectric effect was discovered in 1880 by the brothers Jacques and Pierre Curie. In experiments with tourmaline crystals, they found that under mechanical deformation of the crystals on the crystal surface electric charges are produced, the quantity proportional to the stress. Today, most of the piezo elements PZT ceramics ( such as lead zirconate titanate ) can be used.

Macroscopically, the effect in the framework of continuum mechanics could be described at the beginning of the 20th century. The microscopic description was made possible by a deep understanding of the discrete structure of condensed matter. A more detailed microscopic treatise was given by Richard M. Martin in 1972 ..

The first applications were piezoelectric ultrasonic transducers and soon quartz crystals for frequency stabilization. By 1950, issued to Walter P. Kistler patent on the charge amplifier succeeded the piezoelectric measurement technology breakthrough to wide industrial application.

Principle

The directed deformation of a piezoelectric material to form microscopic dipoles ( shift of the charge - focus ) within the unit cell. The summation over the associated electric field in all unit cells of the crystal leads to a macroscopically measurable electrical voltage. Directed deformation means that the applied pressure does not act on the specimen from all sides, but (for example) only from opposite sides. Vice versa can be achieved by applying an electric voltage, a deformation of the crystal or of the piezoelectric ceramic member.

Like any other solids can also piezoelectric body perform mechanical vibrations. In piezoelectrics, these oscillations can be electrically stimulated, causing in turn an electric voltage. The frequency of the vibration is speed of sound ( a material constant ) and the dimensions of the piezoelectric body dependent. With a suitable mounting these natural frequencies are hardly affected by environmental influences, which piezoelectric devices such as quartz crystals are very suitable for use in precision oscillators, such as quartz watches.

Piezoelectric materials

Basics

The piezoelectric effect can be explained by the first change in the geometry. This is the piezoelectric resistive effect. Stretched so longer and thinner, a wire having a higher resistance. To metals of the piezoelectric effect based solely on the change in the geometry. Furthermore, all non-conductive materials and ferroelectric materials with a permanent electric dipole are also piezoelectric, such as barium titanate and lead zirconate titanate (PZT). However, only a part of piezoelectrics behaves ferroelectric.

Crystals in the crystal symmetry is a further criterion for the occurrence of the piezoelectricity. The piezoelectric polarization does not occur, when the crystal has a center of inversion. In all the 21 non-centrosymmetric point groups piezoelectricity can occur with the exception of the cubic point group 432 In other words, a unit cell must be no center of symmetry ( = a point at which transferred a point reflection in the crystal itself) possess.

The best known material with piezoelectric properties of quartz (SiO2). Quartz crystals have the noncentrosymmetric point group 32 Each Si atom is located at the center of a tetrahedron of four oxygen atoms. A in the direction of base -to-peak ( Crystallographic direction :) force acting now deforms tetrahedron such that the compressed tetrahedra are electrically polarized, and so on the surfaces of the crystal ( in direction) a net voltage.

Technically used materials that show a greater piezoelectric effect as quartz, often are derived from the perovskite structure, such as: barium titanate ( BaTiO3 ). The cubic perovskite modification itself has the centrosymmetric point group and is thus non- piezoelectric, the material can, however, below a critical temperature - the piezoelectric Curie temperature TC - in a non- centrosymmetric perovskite structure transition ( rhombohedral / tetragonal, see Lead - zirconate titanate ). It then displays a spontaneous polarization, and has ferroelectric properties.

Piezoelectric crystals

• The most important piezoelectric crystal is formed from quartz up to 573 ° C stable trigonal crystal structure of α - quartz. The most important application are oscillating crystals.
• Lithium niobate has to quartz higher piezoelectric constants and for piezoelectric filters and SAW devices (English: surface acoustic wave, surface acoustic wave ) was used.
• Gallium orthophosphate is available as a piezoelectric only since the 1990s. This material is similar to quartz, but has higher piezoelectric constants and better temperature stability. It is stable up to 900 ° C.

Further piezo-electric crystals are berlinite, minerals of tourmaline, Rochelle salt and all ferroelectrics such as barium titanate (BTO ) or lead zirconate titanate (PZT). BTO and PZT are, however, not normally used as single crystals, but in polycrystalline form ( ceramics ).

Compared to piezoelectric crystals have piezoelectric ceramics such as PZT advantage significantly higher piezoelectric coefficients. Advantages of quartz crystal, lithium niobate and gallium orthophosphate, higher temperature stability, low loss, a considerably lower hysteresis and it hardly creep ( deformation thus delayed ) to change the applied voltage.

Piezoelectric ceramics

Industrially produced piezo elements are mostly ceramics. These ceramics are made from synthetic, inorganic, and ferroelectric polycrystalline ceramic materials. Typical base materials for high-voltage actuators are modified lead zirconate titanate (PZT ), and for low-voltage actuators lead magnesium - niobate (PMN).

The fabric composite of the PZT ceramics, (Pb, O, Ti / Zr) is crystallized in the perovskite crystal structure. Below the Curie temperature piezoelectric formed by distortion of the ideal perovskite structure of a dipole moment. In ceramic piezo elements, the internal dipoles are after the sintering process is still disordered, why not show piezoelectric properties. The Weiss ' domains or domains have an arbitrary spatial orientation and balance each other. A clearly measurable piezoelectric property can be only by an external DC electric field with a few MV / m impress, the material until just heated below the Curie temperature and is cooled again. The orientation is then embossed to a large extent obtained ( remanent polarization ) and is referred to as direction of polarization.

The turning of the Weiss' districts by the polarization leads to a slight distortion of the material and a macroscopic length increase in polarization direction.

Other piezoelectric materials

• As an active sensor materials and piezoelectric thin films are increasingly being used. With the help of semiconductor technology, it is possible to deposit thin layers on these active piezoelectric silicon. This is usually to zinc oxide ( ZnO) or aluminum nitride ( AlN).

• The plastic polyvinylidene fluoride ( PVDF) can be - similar to piezoelectric ceramics - polarize and then is piezoelectric. Applications include hydrophones.

Calculation

The following are the macroscopic description is shown in the framework of continuum mechanics. It is only considered a linear approximation between the variables considered. Nonlinear effects such as electrostriction be neglected here.

Geometry

For describing the spatial properties of a different coordinate system is selected. For indexing typically an x, y, z coordinate system is used, the axes of which are referred to with the number 1, 2, 3 ( corresponding to the axis 3 of the polarization axis ). The shearing along these axes insert the numbers 4, 5, 6 Based on these axes are taken, the piezoelectric properties of tensors in equations.

Equations

The simplest equations for the piezoelectric effect include the polarization Ppz ( unit [C / m ] ) and the deformation Spz ( Dimensionless size):

Wherein d, e is the piezoelectric coefficient, E is the electric field strength (V / m ), and T indicates the stress (N / m²). The first equation describes the direct and the second the inverse piezoelectric effect.

The piezoelectric coefficients are:

• Piezoelectric distortion coefficients ( response of the distortion to the electric field )

• Piezoelectric voltage coefficient ( the reaction of the mechanical stress on the electric field )

The two coefficients are to bring about the elastic constants in a relationship:

Second-order effects (inverse piezoelectric effect ) are described by the electrostrictive coefficient.

The tensors given above are normally rewritten in matrix form ( Voigt notation). This yields matrices with hexavalent components corresponding to the axis definition presented above. The piezoelectric effect will then be described by means of two simultaneous equations in which the dielectric displacement D is used instead of the polarization.

It is usual to combine the elements of the equations in the Verkoppelungsmatrix. Important material parameters for the inverse piezoelectric effect, and thus for actuators is the piezoelectric charge constant D. describes the functional relationship between the applied electric field strength and the elongation produced thereby. The characteristic quantities of a piezoelectric transducer are different for the different directions of action.

In the field of actuators two main effects are relevant. For these two effects, the equation is simplified for the expansion as follows

Applications

Today, piezoelectric components are used in many industries: industrial and manufacturing, automotive industry, medical technology, telecommunications. In 2010, the global market for piezoelectric devices achieved a turnover of around 14.8 billion U.S. dollars.

In general the applications into three areas:

Sensors

The occurrence of the piezo- electric charge in case of mechanical deformation is used in force, pressure, and acceleration sensors. The resulting charge can be converted to a charge amplifier into a voltage with low source impedance. For the other option, charge a capacitor with this charge and to measure the voltage with a high impedance voltmeter possible, defective insulation resistance can distort the result strong and prevent registry slow deformations, for example by moisture.

• In music piezo elements are used as pickups for acoustic instruments, mostly stringed instruments like guitar, violin or mandolin. The dynamic deformation of the instrument ( the vibration of the sound source ) is converted to a low AC voltage, which is then electrically amplified.
• In piezoelectric acceleration sensors or transducers, it is in a mechanical deformation ( compression and shear) by the acceleration to a charge separation and thus can be picked off a charge on the vapor-deposited electrode.
• With Quartz Crystal, the influence of various factors on the resonance frequency can be utilized in the surface acoustic wave elements, the influence on the delay time. An important application is the measurement of the force applied to the crystal mass, for example in industrial coating method for the determination of the layer thickness. It can also be the temperature dependency of the oscillation frequency can be measured; However, such quartz crystal thermometers are no longer commercially available.

Actuators

Piezo actuators can be distinguished according to the operating mode ( quasi-static or resonant) or according to the direction of the effect used. From the distinction of transversal ( cross effect, d31 effect), Longitudinal ( longitudinal effect, d33 effect) and shear effect ( d15 effect), three different basic elements for piezoelectric actuators arise. The shear effect is, however, used much less frequently than the other two effects in the actuators, because d15 actuators are expensive to manufacture. For multi-dimensional movements of a plurality of piezoelectric elements must be combined so that they act in different directions.

, Actuators which are operated in the kHz range may be regarded as quasi-static so long as the operating frequency is well below the first resonant frequency of the system. The high accuracy and wide dynamic range make it an ideal piezoelectric actuator for positioning and active vibration control. Typical changes in length and thus travel ranges are 0.1 % of the actuator length and thereby with the largest available actuators on the order of 100 microns. Limiting the adjustment paths act, the dielectric strength of the material, the high operating voltages and current in a saturation characteristic of the material. The short travel ranges of piezoelectric actuators can be enlarged by various means, eg by lever or by special designs such as the bimorph bending element. This is a combination of two Querdehnelementen. An opposite polarization or control of the elements causes a bending of the actuator.

Examples of the quasi-static application of piezoelectric actuators are

• Braille for the blind, which are pushed up by applying a voltage to the blind tactile pins, which is converted into tactile Braille characters on a PC monitor text.
• Inkjet printer (English Drop-on- Demand)
• Piezoelectric speaker in which the sound waves are generated by an audio frequency alternating voltage
• Diesel injection with piezoelectric actuators ( ceramic multilayer components with precious metal internal electrodes ), which have the common rail technology improved. The injection of diesel by way of valves is partially replaced. Since 2005, piezoelectric actuators are also used in the pump -nozzle system. Industrial companies that manufacture such piezoelectric actuators in large numbers, the company Epcos and Bosch.

Resonant -driven piezoelectric actuators are primarily used for ultrasound generation and piezo motors. In piezomotors small adjustment paths of piezoelectric actuators are added by different principles, so that very large motion can be achieved. Work depending on the motor principle piezomotors quasi-static or resonant.

Electrical Components

In these applications, a mechanical vibration of a piezoelectric solid body is electrically energized and then electrically detected. There is a fundamental distinction between two types

• Volume resonators in which substantially the entire piezo-electric element vibrates. The most important representatives are quartz crystals and ceramic filters.
• SAW devices based on surface acoustic waves ( engl. surface acoustic wave SAW). Examples include SAW filters and delay lines.

As a component of the piezoelectric transformer is used as a shape of the resonant transformer for generating the high voltage in the range of the inverter. It is used for supply of fluorescent tubes (CCFL ) as they are used as backlight for TFT displays.

Other applications

The piezoelectric effect is used in piezo lighters, here a sudden large pressure (Hammer) is a piezoelectric device used to produce a brief high voltage. The spark discharge then ignites the gas flame. Impact fuze as in the warheads of anti-tank weapons ( Panzerfaust/RPG-7 ), piezoelectric microphones (crystal microphones), piezo speaker in headphones, piezo sirens and buzzers are other uses.

A number of micromechanical sensors makes piezoelectricity advantage, such as accelerometers, gyroscopes, pressure and force sensors, ultrasonic sensors, micro balances and knock sensors in automobile engines.

Also, some micro-mechanical actuators based on piezoelectricity: Piezo motors ( Squiggler ), ultrasonic motors, eg for the lens autofocusing or watches drives in the field of micro-and nanopositioning systems are scanning tunneling microscope, scanning electron microscope and the atomic force microscope piezo- electrically driven systems. In the injector valve technology of cars ( production start in 2000 for diesel engines ), proportional pressure regulator and pressure heads of inkjet printers are worth mentioning. Pickup, electro-acoustic delay lines as in older PAL or SECAM color television sets, powered wireless technology (switch) and optical modulators are also piezoelectric devices. The feeding technology uses many of the components mentioned.