CRYSTAL SYMMETRY:Crystal structures can be divided into 32 classes, or point groups, according to the number of rotational axes and reflection planes they exhibit that leave the crystal structure unchanged.

Twenty of the 32 crystal classes are piezoelectric. All 20 piezoelectric classes lack a center of symmetry.

Any material develops a dielectric polarization when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material.

Whether or not a material is polar is determined solely by its crystal structure. Only 10 of the 32 point groups are polar.

Under normal circumstances, even polar materials do not display a net dipole moment. As a consequence there are no electric dipole equivalents of bar magnets because the intrinsic dipole moment is neutralized by "free" electric charge that builds up on the surface by internal conduction or from the ambient atmosphere.

Polar crystals only reveal their nature when perturbed in some fashion that momentarily upsets the balance with the compensating surface charge.

The possibility of inorganic crystals being polar (pyroelectric or piezoelectric) is strictly a function of their point group symmetry.

Polar MaterialsSolid with a natural charge separation even in the absence of a fieldCrystals comprising cations and anions can be classified into four types, according to their polar behavior:

• Piezoelectric materials: There is coupling between electrical and mechanical energies. For example, an applied stress results in the generation of polarization.• Pyroelectric materials: Pyroelectricity refers to the change in polarization by changes to structure from thermal effects. A material with a temperature dependent polarization. This requires a unique polar axis.A material with a temperature dependent polarization. This requires a unique polar axis.• Ferroelectrics: A subgroup of pyroelectric materials in which the spontaneous polarization can be reoriented between “equilibrium” states by applying an electric field.

All ferroelectrics are both pyroelectric and piezoelectric.The possibility of inorganic crystals being polar (pyroelectric or piezoelectric) is strictly a function of their structure (point group symmetry)

•Ferroelectrics: Ferroelectric materials possess a natural electric polarization. A subgroup of pyroelectric materials in which the spontaneous polarization can be reoriented between “equilibrium” states by applying an electric field. All ferroelectrics are both pyroelectric and piezoelectric. Not all piezoelectric materials are pyroelectric. Ferroelectrics are materials which possess an electric polarization in the absence of an externally applied electric field such that the polarization can be reversed if the electric field is reversed. Normally materials are very nearly electrically neutral on the macroscopic level. However, the positive and negative charges which make up the material are not necessarily distributed in a symmetric manner. If the sum of charge times distance for all elements of the basic cell does not equal zero the cell will have an electric dipole moment which is a vector quantity. The dipole moment per unit volume is defined as the dielectric polarization.

Piezoelectric materials: Piezoelectricity refers to a materials property that the polarization (or electric field) of the material can be changed by mechanical perturbation of the structure. There is coupling between electrical and mechanical energies. For example, an applied stress results in the generation of polarization.

PIEZOELECTRIC EFFECT:The piezoelectric effect is a linear, reversible electromechanical interaction occurring in materials possessing the proper symmetry properties. The direct piezoelectric effect is the production of an electric polarization by a strain; the converse piezoelectric effect is the production of a stress by an electric field. Piezoelectric materials have wide applications as transducers - transferring mechanical motion into electricity or electricity into mechanical motion. One of the most wide spread examples is a quartz resonator. The quartz resonator converts the electrical potential energy of a battery into a steady beat that becomes the oscillator (counter) of a watch.

Pyroelectricity : It is a property of dielectric materials, which show a temperature-dependent, macroscopic (permanent or spontaneous) polarization P, i.e. they generate surface charges as a result of a temperature change ΔT(t). These charges can either be detected directly or as a pyroelectric current I(t).

PYROELECTRICITY: Spontaneous polarization is temperature dependent, so a good perturbation probe is a change in temperature which induces a flow of charge to and from the surfaces. This is the pyroelectric effect. All polar crystals are pyroelectric, so the 10 polar crystal classes are sometimes referred to as the pyroelectric classes.

The property of pyroelectricity is the measured change in net polarization (a vector) proportional to a change in temperature. The total pyroelectriccoefficient measured at constant stress is the sum of the pyroelectriccoefficients at constant strain (primary pyroelectric effect) and the piezoelectric contribution from thermal expansion (secondary pyroelectric effect). Pyroelectric materials can be used as infrared and millimeter wavelength detectors.

Piezoelectricity or pressure electricity: Unusual phenomena in which polarization is induced and an electric field is established across a sample when it is mechanically stressed. Similarly, the same crystal also exhibits mechanical strain when it experiences an electric field.

Piezoelectricity

P = 0

Force

P V

(b)(a)

The direction of mechanical deformation (extension or compression) depends on the direction of the applied field, or the polarity of the voltage.Only crystals with a special crystal structure can exhibit piezoelectricity that which has no center of symmetry.

V V

(c) (d)

Fig. 7.35: The piezoelectric effect. (a) A piezoelectric crystalwith no applied stress or field. (b) The crystal is strained by anapplied force which induces polarization in the crystal andgenerates surface charges. (c) An applied field causes the crystalto become strained. In this case the field compresses the crystal.(d) The strain changes direction when the field is reversed, andnow the crystal is extended. The dashed rectangle is the originalsample size in (a).From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Consider the cubic unit cell. When unstressed, center of mass (c.m. of the –ve charges at the corner of unit cell coincides with +ve charge at center therefore, no net polarization occurs and P=0.Under stress, unit cell becomes strained. However, c.m. of the –ve charges still coincides with +ve charge and net polarization is still 0. P=0 for strained crystal. This is generally true for crystals with center of symmetry.

If we draw a vector from O (position of an arbitrary point charge) to any charge, then the reverse vector will point to the same type of charge: we call O, or any other point charge, a center of symmetry

P = 0O

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

(a)

P = 0

Force

(b)

Fig. 7.36: A cubic unit cell has a center of symmetry. (a)In the absence of an applied force the centers of mass forpositive and negative ions coincide. (b) This situation doesnot change when the crystal is strained by an applied force.

If we draw a vector from O to any charge, then the reverse vector will point to an opposite charge. The unit cell is said to be nocentrosymmetric. When unstressed, c.m. of –vecharges coincides with c.m. of the +ve charges, both at O, therefore, no net polarization occurs and P=0.Under stress, the +ve charge at A and –ve charge at B both become displaced inwards to A’and B’ respectively. The two c.m.’s become shifted and there is now a net polarization P for the strained crystal.

P = 0 PO

y

x

(a) (b)

A

B

A'

B'

P = 0

P

(c)

A''

B''

Fig. 7.37: A hexagonal unit cell has no center of symmetry. (a) Inthe absence of an applied force the centers of mass for positiveand negative ions coincide. (b) Under an applied force along y thecenters of mass for positive and negative ions are shifted whichresults in a net dipole moment P along y. (c) When the force isalong a different direction, along x, there may not be a resulting netdipole moment in that direction though there may be a net P alonga different direction (y).From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

Generally, an applied stress in one direction can give rise to induced polarization in other crystal directions and reversing the stress reverses the polarization crystals with no center of symmetry exhibit piezoelectricity.

P = 0 PO

y

x

(a) (b)

A

B

A'

B'

P = 0

P

A''

B''

The direction of induced polarization depends on the direction of applied stress. In the above case, P appears in the same direction as applied stress along y. If the stress is applied along x, A and B are displaced outwards to A’’ and B’’respectively, resulting in shift of c.m.’s away from each other in y direction therefore P appears along y direction.

Piezoelectric and Ferroelectric MaterialsWhen mechanical pressure is applied to a piezoelectric material, the crystalline structure produces a voltage proportional to the pressure. Conversely, when a piezoelectric material is subjected to an electric field, the structure changes in shape, producing dimensional changes in the material. Examples of natural piezoelectric crystals:

Quartz (SiO2), Rochelle Salt Tourmaline.

Piezoelectric materials are anisotropic, that is their mechanical, electrical and electromechanical properties depend strongly on the crystal orientation.

Man-made piezoelectric ceramic example: lead-zirconate-titanate (PZT), lead-titanate (PbTiO2), lead-zirconate (PbZrO3), and barium-titanate (BaTiO3).

Strictly speaking, these ceramics are not actually piezoelectric but rather exhibit a polarized electrostrictiveeffect. PZT exhibits a cubic structure above a critical (Curie) temperature. During cooling (below the Curie temperature) the cubic structure transform to a tetragonal or rhombohedralstructure. Due to the non-centrosymmetry of this structure exhibits a dipole moment. Regions of the crystal with the dipoles having the same direction are called “domains”.

In a PZT, the direction of polarization among neighboring domains is random, so the ceramic element has no net polarization. Net polarization is induced by exposing the PZT to a strong direct current electric field, to align all the individual domains towards one specific direction, the poling direction. With this treatment the ceramic element increases in size in the direction of the electric field. When the electric field is removed, most of the dipoles are locked into a configuration near alignment. The element now shows a permanent or net polarization.

Analogous to ferromagnetic materials, piezoelectric materials exhibit a hysteresisloop. An electric field is applied to the piezoelectric until a maximum polarization is achieved, then the electric field is removed and the material exhibit a “remanentpolarization”. To eliminate the remanentpolarization, an reverse electric field is induced, in opposite direction.When a poled piezoelectric is mechanically compressed or tension (S), the element changes the dipole moment creating a voltage or an electric field (E).

A compressive stress in the same direction of poling, creates a voltage of the same polarity as the poling voltage. Voltage of the same polarity as the poling voltage is produced by a tensile stress perpendicular to the direction of poling.

A tensile stress along the direction of poling produces a voltage with polarity opposite to the poling voltage.

Conversely, if a voltage of the same polarity as the poling voltage is applied to the piezoelectric, it will increase in size, while if the polarity of the applied voltage is reverse it will shorten in size. Finally is a cyclic voltage is applied in the direction of poling, the piezoelectric will change in dimensions cyclically at the frequency of the applied voltage.

Piezoelectric effect basicsApply mechanical stress -> Electric charge producedApply electric field -> Mechanical deformation producedDipole: each molecule has a polarization, one end is more negatively charged and the other end is positively charged.Monocrystal: the polar axes of all of the dipoles lie in one direction. --SymmetricalPolycrystal: there are different regions within the material that have a different polar axis. -- Asymmetrical

How to produce piezoelectric effect

a) Material without stress / charge

b) Compress -> same polarityc) Stretched -> opposite polarityd) Opposite voltage -> expande) Same voltage -> compressf) AC signal -> vibrate

Applications of piezoelectric materials is based on conversion of mechanical strain into electricity (microphones, strain gauges, sonar detectors, audible alarms, ultrasonic imaging, speakers)Piezoelectric materials include barium titanate BaTiO3, lead titanate, lead zirconate PbZrO3, quartz, ammonium dihydrogenphosphate (NH4H2PO4).

Piezoelectric Igniters

Hydrophones: A "Hydrophone" is a device which will listen to, or pick up, the acoustic energy underwater. A hydrophone converts acoustic energy into electrical energy and is used in passive underwater systems to listen only.

Liquid Atomization Devices

Piezoelectric AudiotoneTransducers

Fig. 7.38: Piezoelectric transducers are widely used to generateultrasonic waves in solids and also to detect such mechanicalwaves. The transducer on the left is excited from an ac sourceand vibrates mechanically. These vibrations are coupled to thesolid and generate elastic waves. When the waves reach theother end they mechanically vibrate the transducer on the rightwhich converts the vibrations to an electrical signal.

Oscillator

Elasticwaves in thesolid Oscilloscope

A B

Mechanicalvibrations

Piezoelectrictransducer

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca