Piezoelectricity

History

In the middle of the 18th century, Carl von Linné and Franz Aepinus had studied the pyrolectric effect, by which a change of temperature involves a variation of the electric polarization of a crystal. Continuing in this direction, the abbot Rene Just Haüy and Antoine César Becquerel reflect in obviousness the existence of electric phenomena induced by a pressure on the Iceland spar. When well even they spoke then about electricity of pressure , this phenomenon does not show the characteristics of piezoelectricity (the Iceland spar is not actually piezoelectric). It was probably about the demonstration of static heads create by the frictions which had with imperfections of the breadboard constructions of the time.

The first demonstration of the direct piezoelectric effect is due to the brothers Pierre and Jacques Curie in 1880. Combining their knowledge of pyroelectricity and crystalline structure, they predicted and checked the existence of piezoelectricity on crystals of quartz, tourmaline, topaz, sugar and salt of La Rochelle. The existence of the opposite effect was predicted the year following by Gabriel Lippman on the basis of calculation Thermodynamique S, and immediately checked by the Curie.

Piezoelectricity remained a curiosity of laboratory during about thirty years; it gave especially place to theoretical work on the crystalline structures presenting this property. This work led in 1910 to the publication by Woldemar Voigt of the Lehrbuch der Kristallphysik which gives the twenty piezoelectric crystalline classes, and rigorously defines the piezoelectric constants in the formalism of the tensorial analysis.

The first application of piezoelectricity was the Sonar developed by Paul Langevin and its collaborators during the First World War. This sonar was composed of quartz blades stuck between two plates of steel and a hydrophone and allowed, by the measurement of the time passed between the emission of an acoustic wave and the reception of its echo, to calculate the distance to the object.

The success of this project aroused a great interest for piezoelectricity, started again research and led through the years which followed to the development of new materials for a broad pallet of applications in the daily life, industry and research. The improvement of the gramophone or the development of the reflectometer and the acoustic transducer, largely used for measurements of hardness or viscosity, is examples.

During the second world war, the search for more powerful materials brought various groups of research to Japan, the United States and in Russia to develop the ferroelectric, in particular the titanate of Barium and the PZT which are still today materials of reference.

A new jump was carried out with the beginning of the year 1980 with the synthesis of the crystals of PZN-PT and PMN-PT which to date present the piezoelectric coefficients highest known.

Today, research on piezoelectric materials relates in particular to the precise comprehension of these exceptional properties, their optimization, like on the development of materials without lead.

Piezoelectric materials

Classification of materials

Many materials, natural or synthetic, are piezoelectric. One can quote in particular:

of the natural crystals: quartz, Topaz, Tourmaline, Berlinite (AlPO₄);
of the synthetic crystals: Orthophosphate of gallium (GaPO₄), Arsenate of gallium (GaAsO₄), the crystals langasites (of which the langasite of La₃Ga₅SiO₁₄ composition);
of the crystals of crystalline structure Perovskite or Tungsten - Bronze (often used in the form of ceramics): PbTiO₃, BaTiO₃, KNbO₃, LiNbO₃, LiTaO₃, BiFeO₃, Na_XWO₃, Ba₂NaNb₅O₅, Pb₂KNb₅O₁₅, Pb (Zr_XTi_1-x) O₃ (PZT);
of the Polymeric S: polymers containing fibers of rubber, Wool, Hair, Wood and Silk, polyvinylidine difluoride (PVDF), (- CH₂-CF₂-) _n

Orders of magnitude

The coefficients reported in the following table connect the lengthening of a bar (without unit) to the electric field applied between its two ends (in V/m). The unit of the international system for this coefficient is thus the meter per volt (m/V). The indices (33) refer to the crystallographic direction corresponding to the length of the bar.

Tensorial representation of piezoelectricity

Piezoelectricity is represented mathematically by a tensor of order three which connects an electric field E or an electric displacement D (tensor of order 1) with a deformation S or a constraint T (tensor symmetrical of order 2). There thus exist 4 choices of possible independent variables and thus 4 representations of the piezoelectric tensor. The usual notations are defined in the IEEE standards. Conventions of notation called convention of Voigt make it possible to represent the piezoelectric tensor in matric form.

It should be noted that the presence of the piezoelectric effect in a material forces to reconsider the study of its dielectric and elastic properties: it is necessary for example to distinguish the elastic properties from material with null electric field and electric displacement no one. So the piezoelectric, dielectric and elastic properties are in general studied jointly. This whole of properties is called electromechanical properties .

Principles of piezoelectricity

Symmetry of piezoelectric materials

The property of piezoelectricity is strongly related to the Symétrie unit cells and a “centrosymetric” mesh (i.e which has a center of Symétrie) cannot give place to a piezoelectric crystal.

On the 32 crystalline classes, there exist 21 noncentrosymétriques about it, of which 20 are piezoelectric and 10 have an electric polarization in the absence of electric field applied and known as pyrolectric S is (their dipole moments being sensitive to the temperature). Among the pyrolectric crystals one can also distinguish the crystals Ferroélectrique S which are characterized by a permanent electric polarization which it is possible to reverse by applicant a strong electric field in the opposite direction.

Origins of a variation of polarization

In all the cases, piezoelectricity connects a deformation to a variation of dipole moment in material. The precise mechanism is different according to the type of material considered.

The model piezoelectric materials are ionic crystals. An ionic crystalline medium is composed of particles charged positively (or Cation S: Ba²⁺, Ti⁴⁺, Pb²⁺…) and negatively (or Anion S: mainly O^2-). In a crystal, piezoelectricity is related on the variation of position of these particles and in particular to the variation of the shift of the Barycentre S of the positive and negative loads of the crystalline mesh. In the case of piezoelectricity, these variations are caused by a mechanical Déformation mesh.

Certain monoatomic crystals are also piezoelectric: it is the case of tellurium and selenium. In this case the preceding explanation is not valid any more because one cannot see any more these crystals like a stacking of ions of different loads. The electrons are néamnoins localized around the covalent bonds, creating a charge distribution in space. The origin of the variation of the dipole moment can be explained by a modification of this distribution.

In the Polymeric piezoelectric, the mechanism is different. The typical case is that of the polymer PVDF. This polymer is built starting from polyethylene in substituent with two hydrogen atoms two fluorine atoms. Those, more electronegative, attract with them the negative charges. This causes the one permanent dipole moment appearance which varies with the exerted pressure.

Lastly, it was shown that it was possible to observe a macroscopic piezoelectric effect in nonpiezoelectric materials. In silicon, it was shown in experiments that porosity made it possible to obtain an apparently piezoelectric material. The appearance of a piezoelectric effect due to a coupling between polarization and a gradient of deformation (flexoelectricity) was also underlined.

Applications

acoustic Transducers

The piezoelectric materials make it possible to convert an acoustic wave into electrical signal and conversely. They constitute the heart of the acoustic transducers used to emit or detect acoustic waves in all the frequency bands. One finds them in several fields.

In the audio-frenquency ranges, one carries out Microphone S (and in particular of the microphonous of contact) and Haut-parleur S, in particular in the cellphones.
In medicine, one uses some for the realization of echography S, which requires the emission and the detection of ultrasonic waves, like for certain therapies by ultrasounds.
In the sonars, used in the navy, but also in the car, for the detection of obstacles.

Piezoelectric resonators

Sensor S

In a more general way, the piezoelectric materials are natural candidates for the applications based on the detection of pressures:

Pressure pick-ups, in particular for the car (pressure of the tires), aeronautics (pressure in the conduits) or the music (electronic battery): The mechanical constraint that the pressure exerts on a piezoelectric material generates loads which one can measure electronically
piezoelectric Microbalance
Détecteurs of movements: inertial sensors (Accéléromètre with vibrating blade, vibrating Gyromètre Coriolis) which can be used in the inertial unit or more usually in applications of lower precision (Airbag, Guidage, video joystick (Wii))

Micromanipulator

Displacements very weak products by the piezoelectric crystals make of them ideal micromanipulators made profitable in various applications:

microscopy with sweeping: the Microscope with atomic force and the Microscope with tunnel effect employ small piezoelectricity to carry out displacement necessary to the sweeping of probed surface;
optoacoustical application: by piezoelectric microphone-positioning of mirror, the adjustment length of the cavity of Laser can be controlled to optimize the Wavelength beam;
Optical adaptive in Astronomy: piezoelectric actuators are used to deform a Miroir in order to correct the effects of the atmospheric Turbulence.

Recuperation of energy

The piezoelectric ones are also in the middle of applications more recent aiming at recovering energy present in our environment in various forms or carried out by daily movements.

An example often considered is the incorporation of a piezoelectric film in the shoes in order to produce energy thanks to the pressure of the heel during walk. The produced low powers could in the long term be enough to feed certain electronic devices. However, the development of such piezoelectric devices remains delicate and of many obstacles remain to surmount. The subject is in vogue, but the results are still very preliminary.

Other applications

the fire lighter and the “electronic” Lighter. The direct piezoelectric effect makes it possible to generate very strong tensions, higher than the tension of breakdown of air 30 kV/cm for a spacing of a few millimetres. When this tension is reached, a spark of discharge is produced and made profitable to light gas of the lighter or the gazinière.
a transformer piezoelectric is a multiplier of alternating voltage. Contrary to the traditional transformer which uses a magnetic coupling, the coupling made profitable is acoustic. By piezoelectric effect reverses, a tension of excitation allows to generate (using electrodes located on one of the two ends of the bar) an alternative constraint in a bar of a strongly piezoelectric material (a ceramics PZT for example). This constraint allows the setting in Vibration bar a frequency chosen to correspond to a frequency of resonance. By direct piezoelectric effect, a tension is generated on electrodes located on the second end of the bar. This tension, which profits from the amplification of the movement due to resonance, can be 1.000 times higher.
piezoelectric engines: used in the systems Autofocus of cameras, in the mechanisms of electric pane of car, and in general in the applications where the reduced size of these engines answers voluminal constraints.
Certaines ink jet printers of ink uses piezoelectric elements to produce the fine droplets of ink which are propelled on paper.
In the car, some injecting are carried out starting from piezoelectric materials.

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