ดร.เอกพล ศิวพรเสถี�ยรDepartment of Electronics and Telecommunication Engineering

King Mongkut’s University of Technology Thonbury (KMUTT)

Thailand

An Introduction to Piezoelectricity

Educational Background

BS in Double Major in Electrical Engineering and Materials Science Engineeringfrom University of California at Berkeley, CA USA

MS in Electrical Engineering from University of Wisconsin—Madison, WI USA

Ph.D in Electrical Engineering (Major) and Biomedical Engineering (Minor) fromUniversity of Wisconsin—Madison, WI USA

Outlines

History of Piezoelectricity Structure What Can Piezoelectric Ceramics Do? The Piezoelectric Effect The Piezoelectric Constants Motor Transducer Relationships Generator Transducer Relationships The Resonant Frequency Piezoelectric Modes of Vibration Applications Examples Concluding Remarks

Motivations

Motivations

Piezoelectricity: A History

In 1880, Jacques and Pierre Curie discovered an unusual characteristic of certain crystalline minerals: when subjected to a mechanical force, the crystals became electrically polarized.

Tension and compression generated voltages of opposite polarity, and in proportion to the applied force.

Subsequently, the converse of this relationship was confirmed: if one of these voltage-generating crystals was exposed to an electric field it lengthened or shortened according to the polarity of the field, and in proportion to the strength of the field.

These behaviors were labeled the piezoelectric effect and the inverse piezoelectric effect, respectively, from the Greek word piezein, meaning to press or squeeze.

A traditional piezoelectric ceramic is a mass of perovskite crystals, eachconsisting of a small, tetravalent metal ion, usually titanium or zirconium, in alattice of larger, divalent metal ions, usually lead or barium, and O2- ionson the crystals, each crystal has a dipole moment

The perovskite structure is adopted by many oxides that have the chemical formula ABO3. In the idealized cubic unit cell of such a compound, type 'A' atom sits at cube corner positions (0, 0, 0), type 'B' atom sits at body centre position (1/2, 1/2, 1/2) and oxygen atoms sit at face centred positions (1/2, 1/2, 0).

Examples: metal oxide-based piezoeletric ceramics such as the lead zirconate PbZrO3, lead tinanium PbTiO3 compounds, PZT (lead zirconate titanate).

At temperature above Curie point

Above critical temperature, the Curie point, the crystal exhibits a simplecubic symmetry with no dipole moment.

At temperature below Curie point, however, each crystal has tetragonal orrhombohedral symmetry and a dipole moment.

Adjoining dipoles form regions of local alignment called domains. The alignment gives a net dipole moment to the domain, and thus polarization The domains in a ceramic element are aligned by exposing the element to a strong, direct current electric field. When the electric field is removed, most of the dipoles are locked into aconfiguration of near alignment.

What can piezoelectric ceramics do?

The generator– mechanical energy converted into electrical energy -- fuel igniting devices, solid state batteries, force-sensing device The motor – electrical energy converted into mechanical energy -- piezoelectric motors, sound or ultrasound generating devices.

The Piezoelectric Effect

Review concepts of stress (T) and strain (S)

In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear.

Uniaxial stress is expressed by T = F/Awhere F is the force [N] acting on an area A [m2].

Strain is the geometrical measure of deformation. It measures how much a given displacement differs locally from a rigid-body displacement.

Strain defines the amount of stretch or compression along a material line elements or fibers, the normal strain, and the amount of distortion associated with the sliding of plane layers over each other, the shear strain, within a deforming body.

The Piezoelectric Effect

Strain is a dimensionless quantity, which can be expressed as a decimal fraction, a percentage or in parts-per notation. This could be applied by elongation, shortening, or volume changes, or angular distortion.

S = L/L0

The Piezoelectric Effect

The slope of this line is also known as “Young’s Modulus” or “Modulus of Elasticity”.

The Piezoelectric Effect

The experiments performed by the Curie brothers demonstrated that thesurface density of the generated linked charge was proportional to thepressure asserted, and would disappear with it.

Pp = dT

where Pp is the piezopolarization vector, whose magnitude is equal to thelinked charge density by the piezoelectric effect d is the piezoelectric strain coefficient T is the stress to which the piezoelectric material is subjected.

The Piezoelectric Effect (cont.)

The reverse piezoelectric effect is also verified and demonstrated that the ratio between the strain produced and the magnitude of the applied electricfield in the reverse effect, was equal to the ratio between the producedpolarization and the magnitude of the applied stress in the direct effect.

Sp = dE

where Sp is the strain produced by the piezoelectric effect, E is the magnitude of the applied E field

Piezoelectric Constants

Because a piezoelectric ceramic is anisotropic,physical constants relate to both the directionof the applied mechanical or electric force andthe directions perpendicular to the applied force.

Thus, each constant generally has 2subscripts.

Piezoelectric Charge Constant (d)

The piezoelectric charge constant, d, is the polarization generated per unit mechanical stress (T) applied to a piezoelectric material OR

d is the mechanical strain (S) experienced by piezoelectric material per unit ofelectric field applied.

d31 = induced polarization in direction 3 per unit stress applied in direction 1 OR = induced strain in direction 1 per unit electric field applied in direction 3

Piezoelectric Voltage Constant (g)

is the electric field generated by a piezoelectricmaterial per unit of mechanical stress applied, OR

is the mechanical strain experienced by a piezoelectric material per unit of electric displacement applied.

g31 = induced electric field in direction 3 per unit stress applied in direction 1 = induced strain in direction 1 per unit electric displacement applied in direction 3

Motor Transducer Relationships

Generator TransducerRelationships

The Resonant FrequenciesWhen exposed to an AC electric field, a piezoelectric ceramic element changes dimensions cyclically, at the cycling frequency of the field.

The frequency at which the ceramic element vibrates most readily, and most efficiently converts the electrical energy input into mechanical energy, is the resonance frequency.

As the frequency of cycling is increased, the element's oscillations first approach a frequency at which impedance is minimum (maximum admittance). This minimum impedance frequency, fm , approximates the series resonance frequency, fs , the frequency at which impedance in an electrical circuit describing the element is zero,

The composition of the ceramic material and the shape and volume of the element determine the resonance frequency -- generally, a thicker element has a lower resonance frequency than a thinner element of the same shape.

As the cycling frequency is further increased, impedance increases to a maximum (minimum admittance). The maximum impedance frequency, fn , approximates the parallel resonance frequency, fp , the frequency at which parallel resistance in the equivalent electrical circuit is infinite. The maximum impedance frequency also is the anti-resonance frequency, fa

Piezoelectric Ceramic’s Equivalent Circuit Model

Piezoelectric Modes of Vibration

Piezoelectric Modes of Vibration

Other Modes of Vibration

Several Modes ofA Plate Vibration

Piezoelectric devices fit into 4 general categories: generators, sensors, actuators, and transducers.

Applications

Generators: Piezoceramics can generate voltages sufficient to spark acrossan electrode gap, and thus can as ignitors in fuel lighters, gas stove, weldingequipment. They are small and simple compared to their alternative systems that use permanent magnet or high voltage inductors and capacitors.

Alternatively, the electrical energy generated by a piezoelectric element can be stored. Techniques used to make multilayer capacitors have been used to construct multilayer piezoelectric generators. Such generators are excellent solid state batteries for electronic circuits.

Sensors: A sensor converts a physical parameter such as acceleration orpressure into an electrical signal. In some sensors, the physical parameter actsacts directly on the piezoelectric element; in other devices an acousticalsignal establishes vibration in the element and the vibrations are, in turn, converted into an electrical signal.

Applications (cont.)

Actuators: A piezoelectric actuator converts an electrical signal into a precisely controlled physical displacement, to finely adjust precision machining tools, lenses, or mirrors. Piezoelectric actuators also are used to control hydraulic valves, act as small-volume pumps or special-purpose motors, and in other applications.

Transducers: Piezoelectric transducers convert electrical energy into vibrational mechanical energy, often sound or ultrasound, that is used to perform a task. Piezoelectric transducers also are used to generate ultrasonic vibrations for cleaning, atomizing liquids, drilling or milling ceramics or other difficult materials, welding plastics, medical diagnostics, or for other purposes.

Application Examples:

1.Sonar2.Nondestructive Testing (NDT)3.Surface Acoustic Wave Sensors4.Ultrasonic Nebulizer5.Energy Harvesting System6.…….. And many more!!

Underwater communication

The distance the wave travelled is estimated from the time of flight

Distance = c x t

where c is the speed of sound in medium t is the time the wave travel

Speed of sound (in solid/liquid) E

c

where E is the bulk modulus (N/m2) is the density (kg/m3)

Speed of sound (in air/gas)kT

cm

Where is the adiabatic index = 5/3 for monatomic molecule k is the Boltzmann’s constant = 1.38x10-23 J/K T is the temperature (K) m is the mass of a single molecule in kg NA is Avogadro’s number = 6.022x1023 per mole

Tactile sensor in touch screen panel

Atomization for effective drug delivery.

Surface Acoustic Wave (SAW) Device Sensor consists of a pair of input/output inter-digitated transducers (IDTs). SAWs of desired frequency can be generated from the input transducer, travel on a piezoelectric substrate and be received by the output transducer.

Upon detection of changes in material property along the path SAW travels, the velocity of the wave would change. Consequently, the center frequency shifts to a corresponding value.

Energy Harvesting System

The piezoelectric films used for the energy generation are c onstituted by a polymeric material coated in both sides by a conducting material, which form the electrodes.

The polymeric material is based on the polyvinylidene fluori de (PVDF) polymer in its electroactive (β ) phase.

Generators: harvesting energy from mechanical vibration to power small low-power electronic devices such as a spy cam

Piezoelectric Energy Harvesting System

Full-bridge rectifier Buck-boost DC/DC converter

~

Concluding Remarks Piezoelectric materials when subjected to a mechanical force, the crystals became electrically polarized.

Tension and compression generated voltages of opposite polarity, and in proportion to the applied force.

The effect is reversible: if the material is exposed to an electric field, it lengthened or shortened according to the polarity of the field, and in proportion to the strength of the field.

When exposed to an AC electric field, a piezoelectric ceramic element changes dimensions cyclically, at the cycling frequency of the field. The frequency at which the ceramic element vibrates most readily, and most efficiently converts the electrical energy input into mechanical energy, is the resonance frequency.

Main applications are generators, sensors, actuators, and transducers.

The End …(for now)