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Energy Transformation Effects

Introduction

This section discusses various energy transformation effects that are relevant in

microsystem applications. The effects are classified into four groups based on the energy

form to/from which the electrical energy is transformed. Some of the effects occur only

in one direction but some of them, piezoelectric effect for example, are bidirectional. The

effects are categorized as mechanical, magnetic, thermal and radiation. The main

emphasis is placed on mechanical and magnetic effects.

Mechanical Effects

The effects categorized in this group either provide an electrical signal because of a

mechanical quantity (strain, e.g.) or generate physical deformation when subjected to an

electrical field. The former effects are utilized in sensor applications whereas the latter are

used for actuation.

PIEZOELECTRIC EFFECT

Introduction

The piezoelectric phenomenon was first observed by Curie brothers in 1880. They proved

that certain types of crystals develop an electrical charge when exposed to mechanical

stress. Conversely, the application of an electric field to a piezoelectric crystal leads to a

physical deformation of the crystal. In the 1950’s piezoelectric ceramics such as barium

titanate and lead zirconate titanate (PZT, PbZrO3-PbTiO3) were discovered. Piezoelectric

ceramics must undergo a polarizing process for the piezoelectric phenomenon to occur.

, Energy Transformation Effects 2

The piezoelectric effect requires that the crystal structure must be asymmetric, i.e. there

is at least one axis in the crystal that does not have a centre of symmetry [1].

Piezoelectric elementary cells

To understand the piezoelectric effect in ceramics, the behaviour of the material must first

be considered in microscopic scale, i.e. the behaviour of the elementary cell of the

material. Piezoelectric ceramics are ferroelectric materials. Above a certain temperature,

called the Curie temperature, the crystal structure have a centre of symmetry and therefore

no electric dipole moment, see Figure 3.1a, where the elementary cell of PZT is shown

[2]. Above the Curie temperature the elementary cell is cubic (three crystal axes have

same lengths) and a positively charged Ti/Zr ion is centered on the lattice. This is called

a paraelectric state. Below the Curie temperature the crystal structure undergoes a phase

change into the ferroelectric state where the structure is not symmetric. The positively

charged Ti/Zr ion travels from its central location forming tetragonal structure (one axis

is longer than the other two), Figure 3.1b. The electrical imbalance causes a built in

electric dipole. If a large external field is applied to the cell, the Ti/Zr ion shifts in the

direction of the field as shown in Figure 3.1c. The ion does not return to its original

position when the field is removed resulting in elongation to the direction of the field.

When an external field is again applied to the elementary cell, the electric imbalance

becomes larger and the cell elongates further, Figure 3.1d.

Figure 3.1. Behaviour of the PZT elementary cell [2]. a) Elementary cell above Curie temperature, i.e. no electric dipole, b) elementary cell below Curie temperature, i.e.

generation of the electric dipole, c) turning of the electric dipole using external electric field, d) elongation of the elementary cell by external electric field.

a) b)

c) d)


Piezoelectric ceramics

As macroscopic point of view, molecular dipoles align within small areas, domains,

forming large dipole moments. The piezoelectric ceramics consists of many such

domains. The domains are randomly oriented and therefore the net external electric dipole

is zero, Figure 3.2a. If the piezoelectric ceramics is subjected even once to a large electric

field (poling), the domain dipoles align in the direction closest to the field. Because of the

random original orientation of domains, it is not possible to get perfect dipole alignment

with the field. However, each domain can have several allowed directions and therefore a

reasonable degree of alignment can be achieved. Due to the alignment of the domains, the

material elongates in the same direction, as shown in Figure 3.2b. When voltage is

removed, the domains do not entirely return to their original positions, i.e. the material

remains partially polarized. The strain resulted from the partial polarization is called

remanent strain. Due to the poling, the material has become permanently piezoelectric and

can convert mechanical energy into electrical and vice versa. After poling, if electric field

is applied, the material elongates in the direction of the field Figure 3.2c.

Piezoelectricity involves the interaction between the electrical and mechanical behaviour

of the material. This interaction has been approximated by static linear relations between

two electrical and mechanical variables [1]:

, (3.1)

where S is the strain tensor, T is stress tensor, E is the electric field vector, D is

electric displacement vector, sE is the elastic compliance matrix when subjected to a

Figure 3.2. Behaviour of piezoceramic material. a) Non-polarized state, b) polarized

state, c) electric applied after poling [2].

a) b) c)

S sET dE+=

D dT εTE+=


constant electric field (the superscript E denotes that the electric field is constant), d is

a matrix of piezoelectric constants and εT is the permittivity measured at constantstress.

The piezoelectric effect is, however, non-linear in nature. The hysteresis that is not

included in the above model has been approximated using numerical methods for

example. Dynamics of piezoeletric actuators, for example have also been studied.

PIEZORESISTIVE EFFECT

In piezoresistive effect the relative change in resistivity is proportional to the mechanical

stress. The resistance R of a wire having length l, cross-sectional area A and resistivity ρis [4]

(3.2)

Applying the total differential theorem to (3.2) leads to

(3.3)

The fractional change in area for homogeneous material is approximately related to the

fractional change in length via Poisson’s ratio:

(3.4)

Equation (3.4) describes how the fractional change in resistance depends on the strain

and a piezoresistive term. The piezoresistive effect is utilized in many mechanical

microsensors, such as force, pressure and acceleration sensors.

ELECTROSTATIC EFFECT

When a voltage U is applied across two parallel conductive plates, energy is stored in the

capacitor and it is given by [5]:

(3.5)

where U is the operating voltage, C is capacitance , ε is dielectric

constant, A is the area of an electrode and d is the distance between the electrodes.

The origin of the electrostatic actuation lies in the Coulombic force, i.e. the attractive

force between two conductive plates having opposite charges. When a voltage is applied

between the plates, the attractive force FN is exerted on the plates:

RρlA-----=

∆RR

------- ∆ll

----- ∆AA

-------–∆ρρ

-------+=

∆RR

------- 1 2µ+( )∆ ll

----- ∆ρρ

-------+≈

∆ l l⁄

W12---CU2=

C z( ) εAd---=


(3.6)

Figure 3.3 shows a parallel plate structure driven by normal forces.

When the electrodes are shifted by a distance x, a tangential force tends the realign the

electrodes, see Figure 3.4.

, (3.7)

where ε is dielectric constant, w is the width of the electrode, d is the distance betweenthe electrodes and U is the operating voltage.

The generation of normal an tangential forces by applying voltage is utilized in actuation.

The change of capacitance between the conductive plates is also utilized in many

mechanical microsensor applications. When pressure, for example, is applied to the other

metal plate, the distance between the two plates and thus, the capacitance changes. The

pressure value can be calculated based on the measured capacitance change.

Figure 3.3. Normal force between parallel plate capacitors [6].

Figure 3.4. Tangential force between parallel plate capacitors [6].

FN12---εA

Ud----

2=

-e -e -e

+e +e +e

FN

FN

d U

FT12---εw

Ud----

2=

x

U

FT

FT


ELECTROSTRICTIVE EFFECT

Electrostriction refers to deformation of the material in an electric field. Similarly as

piezoelectric effect, electrostriction occurs in ferroelectric materials but in contrast to the

piezoelectric effect, it does not require asymmetric crystal structure. Electrostriction

applications are in actuation

ELECTRORHEOLOGICAL EFFECT

Introduction

Electrorheological (ER) fluids (also called dielectric fluids) can change state from liquid

to solid when an electric field is applied. Depending on the strength of the electric fluid,

the electrorheological fluid acts like water, honey or solidified gelatin [7]. In 1939 Willis

Winslow discovered that when he applied a voltage across a certain corn oil, it solidified.

When the voltage was removed, it returned to its liquid state. Winslow obtained the first

patent on these liquids in 1947 but no commercial prototypes were began to be developed

before the 1980’s [8].

Electrorheology

Electrorheological fluids consist of micro-sized particles suspended in non-conducting

liquid, such as mineral oil or silicone oil. The particles range in size from 1 to 100 µm and

typically make up 10 % to 40 % of the total volume [8]. The effect can be produced by

applying an electric field of 1000 volts/mm to the fluid, i.e. by placing the fluid between

two electrodes one millimeter apart and charging the electrodes with 1000 V. When an

electric field is applied, the positive charged protons of a particle will be attracted towards

the negative electrode and the negative charged electrons towards the positive electrode.

This makes each particle electrically polarized. Polarized particles begin attracting

neighboring particles resulting particle chains. Chains, in turn, combine to thicker

columns as shown in Figure 3.5. As the net of parallel chains aligns along the field lines,


the fluid flow is inhibited, i.e. the solidification results from the formation of the chains.

The fluid, however, does not become a rigid solid material.

Properties

An advantageous feature of electrorheological fluids is that they respond very quickly:

they can switch from a liquid state to a solid state only in 0,1 to 1 millisecond.

Furthermore, ER fluids benefit from simple design, since no additional mechanical parts

are needed. In order to make ER fluids widely applicable to commercial products, the

electrorheological effect and the stability of the liquid must be improved. Furthermore,

the range of operating temperatures and the strength in the solid state should be increased.

Applications

ER fluids have applications in mechanical clutches, vibration absorbers, valves, etc.

Especially automotive industry have been interested in ER technology which enables

components with no moving parts. Many automobile manufacturers are working with

prototypes on clutches, brakes, dampers and active suspension systems.

Magnetic Effects

HALL EFFECT

When an electron (the most often used carrier in practise) moves in a conductor sheet in

the presence of a magnetic field, the moving electrons experience a magnetic force, a so

called Lorentz force. The Lorentz force is perpendicular to both the velocity and the

magnetic field vectors and it is given by

(3.8)

Figure 3.5. Simplified model of the electrorheological effect [2].

F e v B⊗( )=


where e is the electron charge, v is the average (drift) velocity of the electrons and B isthe magnetic field flux density.

The Lorentz force rotates the current flow lines (the electron motion) through the Hall

angle θH. The deflection of the electrons results in an electric field EH which, in turn,

exerts a force on the moving electrons equal and opposite to that caused by the Lorentz

force. The relation between the Hall electric field and the magnetic flux density can be

written in scalar notation as:

(3.9)

Hall devices exploit this so called Hall effect discovered by E.H. Hall in 1879. Figure 3.6

depicts a general layout of a plate-like Hall sensor [4] that is used to detect changes in

magnetic field. The voltage VH (Hall voltage) across the width of the conductor can

simply be computed as:

(3.10)

where w is the width of the plate.

MAGNETORESISTIVE EFFECT

In magnetoresistive effect, the resistance of a semiconductor changes in the presence of

magnetic field. Similarly as the Hall effect, the magnetoresistive effect is caused by the

Lorentz force which rotates the current lines by an angle θH. The deflection of the current

paths leads to an increase in the resistance of the semiconductor [4]. For small angles of

θH the resistance R is:

(3.11)

The magnitude of the resistance change depends on the shape of the sample: the

magnetoresistance effect is best seen in samples being short but wide. The applications

are in magnetic sensors.

Figure 3.6. Schematic diagram of a Hall element [4].

EHyvxBz=

VH EHyw=

R R0 1 θH2tan+( )≈


MAGNETOSTRICTIVE EFFECT

The phenomenon of magnetostriction refers to magnetically induced shape change in

ferromagnetic materials. The change in length in response to an applied magnetic field in

materials such as nickel is sometimes called the Joule effect (1847). Magnetostriction is

utilized in actuation.

MAGNETORHEOLOGICAL EFFECT

Magnetorheological (MR) fluids are suspensions of micron-sized, magnetizable particles

in oil. Their flow rate may be varied in milliseconds by the application of a magnetic field.

MR fluids are the magnetic analogs of electrorheological fluids, see Section Mechanical

Effects.

Thermal Effects

The Seebeck effect, the pyroelectric effect and the thermoresistive effect are utilized in

sensor applications. Actuation can be produced with the help of the thermoelastic effect

and the shape memory effect. Peltier effect is used in cooling and heating applications.

SEEBECK EFFECT

When a circuit consists of two different materials (e.g. copper and iron) and the junctions

are held at different temperatures, an electrical current will flow between the junctions.

Figure 3.7 shows a circuit where a junction of two dissimilar materials is held at the

temperature TA and the other at the temperature TB. A thermoelectric potential ∆V is

generated across the junctions. As ∆V depends on the temperature difference, the Seebeck

effect can be used for temperature measurement. A common thermocouple utilizes this

principle.

Figure 3.7. Basic circuit of a thermocouple temperature sensor [4].


PELTIER EFFECT

The Peltier effect, named according to a French physicist Jean Peltier (1785 − 1845), is

reversible to the Seebeck effect, i.e. a current applied to an electric circuit made of two

dissimilar materials, results in either cooling or heating effect depending on the current

direction. The Peltier effect is utilized in thermoelectric heating and cooling systems.

THOMSON EFFECT

The Thomson (Kelvin) effect − according to William Thomson, i.e. Lord Kelvin (1824 −1907) − is the third thermoelectric effect. In Thomson effect two dissimilar materials are

not needed but a current passed along a conductor, when a temperature gradient is

maintained, results in either generation or absorbance of additional heat (in addition to

Joule heat). The Thomson effect has not yet been of practical importance.

PYROELECTRIC EFFECT

Pyroelectricity is the variation of electric charges on the surface of a polarized crystal

when it is heated. The increase in temperature reduces the polarization of the crystal

increasing its output voltage until the surface charge is once again balanced. When the

surface charge is balanced the output voltage has reduced back to the original level, see

Figure 3.8. When the temperature reduces a reverse signal is observed, i.e. the output

voltage decreases. All pyroelectric materials are piezoelectric but the converse is not true.

The main applications of the pyroelectric effect are in the human motion detection and fire

detectors.

THERMORESISTIVE EFFECT

Thermoresistivity refers to the variation of electrical resistivity of metals and

semiconductors with temperature. The effect has been used in metal thermoresistors and

thermistors (semiconducting thermoresistors made from ceramic materials) to measure

Figure 3.8. Principle of pyroelectric radiation microsensor [4].


temperature. For metals the resistivity ρ can be well approximated by a second order

polynomial [4]:

(3.12)

where ρ0 is the resistivity at a standard temperature of 0ºC and α and β are materialconstants.

The resistivity of a thermistor is normally expressed by

(3.13)

where ρref is the resistivity at a reference temperature and β is a material constant.

THERMOELASTIC EFFECT

Thermoelastic effect refers to the thermal expansion of a material, i.e. the volume of a

material changes when it is heated or cooled. Thermoelastic effect is utilized by

thermomechanical actuators − bimetallic actuators, for example [2].

SHAPE MEMORY EFFECT

Introduction

Shape Memory Alloys (SMAs) are metallic materials that have an ability to “remember”

their original shapes. The shape memory effect was discovered in various copper alloys

in the mid 1950’s. In the early sixties, Buehler et. al. [10] at the Naval Ordnance

Laboratory found the shape memory effect in nickel-titanium (NiTi) alloys. A number of

other alloys have been investigated since then but NiTi and a few of the copper base alloys

are presently the most widely used and commercially exploited shape memory alloys [11].

Shape Memory Effect

The shape memory effect refers to a phenomenon where material deformed in the room

temperature can be returned to its original shape by heating. The shape memory effect

results from the fact that a Shape Memory Alloy has two states, austenitic and martensitic,

between which its metallurgical structure can be transformed. At temperatures below a

transformation temperature Mf, the SMAs are martensitic and at temperatures above a

transformation temperature Af they are austenitic. In martensitic condition SMAs are soft

and can be deformed quite easily, whereas the austenite is like any metal and has a high

strength. The austenitic shape can be “stored into the memory” of the material in a

tempering process.

When a deformed martensite is heated above the temperature As the phase change

between the martensitic and austenitic states starts, see Figure 3.9. The material has

ρ ρ0 1 αT βT2+ +( )≈

ρ ρref β 1 T⁄ 1 Tref⁄–( )[ ]exp=


reached its austenitic state at temperature Af. At this temperature the material reverts to its

original shape, i.e. the shape stored into the memory over the tempering process. By

cooling down, the material can be transformed to the martensitic state again (phase

change starts at temperature Ms and is over at temperature Mf). In martensitic state the

material does not return to the deformed martensitic shape, see Figure 3.10. This is,

therefore, called a one-way-effect. By certain special treatments the SMA exhibits a two-

way-effect, i.e. it can be made to remember two different shapes between which it is

switched. The two-way-effect offers more application possibilities but it provides smaller

recoverable strain.

Figure 3.11 shows tensile curves of NiTi alloy in the martensitic and austenitic conditions

[9]. The martensitic curve has two yield points. Upon exceeding the first point, the

Figure 3.9. Temperature hysteresis curve of the shape memory effect. According to [9].

Figure 3.10. Schematic presentation of the SMA effect [2].

AfMs

AsMf

Temperature

Str

ain

100%austenite

100%martensite

ε

ε = strain


martensite enters the plateau region where the material is easily deformed to several

percent strain with only a little increase in strain. After that stress increases rapidly with

further deformation until the martensite exceeds the second yield point. The elongation

further than the second yield point permanently deforms the material, i.e. it cannot be

recovered to the original shape by heating. The austenitic curve shows more usual

behaviour, i.e. remarkable stress is required to deform the alloy.

Free and constrained recovery

The shape memory effect can be used to generate motion. Suppose a straight SMA wire

fixed at one end. The wire can be easily deformed at the room temperature and stretching

it generates an elongation that remains even in the unloaded condition. When the wire is

heated above the transformation temperature, it shrinks to its original length. As no load

is applied, this is called free recovery. Cooling below the transformation temperature does

not change the length of the wire (one-way effect). If the stretched wire is prevented from

returning to its original length when it is heated above its transformation temperature, the

wire can generate considerable force. This so called constrained recovery can be utilized

in actuator applications. If the wire can overcome the opposing force it will do work, i.e.

upon heating it can lift a weight, for example. When the wire is cooled, the weight will

elongate now the martensitic wire and thus reset the system.

Properties

As can be seen in Figure 3.9 the transformation from martensite to austenite does not take

place at the same temperature as the transformation from austenite to martensite.

Consequently, there exists hysteresis in the heating and cooling behaviour of the shape

memory alloys. Depending on the alloy composition and the way it has been processed,

the transformation temperatures and the shape of the hysteresis loop vary. The basic

binary NiTi alloy has its transformation temperatures between –50°C and 110°C with the

Figure 3.11. Tensile behaviour of the martensite and the austenite [9].

Str

ess

Strain

Martensite

Austenite


width of the hysteresis loop of 25°C and 40°C. Copper-base alloys have transformation

temperatures even up to 200°C with a hysteresis loop between 15 and 20°C [11]. The

recoverable strain of a copper-base alloy showing one-way-effect is about 4%, whereas

that of the NiTi alloys is 8,5%. NiTi alloys having two-way-effect produce a maximum

strain of 5 %. Shape memory alloys generate high forces, even more than 100 MN/m2, but

they are slow because especially cooling takes time.

Applications

Shape memory alloys are mainly proposed for actuation purposes. Some examples are

couplers to join hydraulic lines, tweezers for picking miniaturized objects, active catheters

to navigate through blood vessels, miniaturized robots for pipe inspection, etc. More

detailed descriptions of SMA applications will be given in Chapter 5 of the course book.

Radiation Effects

The change in electrical quantities because of radiation refer to photoelectric effects that

are utilized in sensor applications. The three photoelectric effects, i.e. the photoemissive,

the photoconductive, and the photovoltaic, are briefly discussed in the following sections.

PHOTOEMISSIVE EFFECT

In the photoemissive effect, radiation striking the prepared surface of a metal or

semiconductor imparts sufficient energy to the electrons such that they are emitted from

the surface into space. The kinetic energy of an electron is related to the energy of the

incident photon. In a photoelectric cell operating by this principle, the emitted electrons

are collected by a positive electrode. Under the influence of an applied voltage they create

an electric current linearly proportional to the incident light intensity.

PHOTOCONDUCTIVE EFFECT

In photoconductive effect light striking the photoconductive material reduces its

resistance. Photoconductive cells are sometimes called as light-dependent resistors.


Figure 3.12 shows the basic structure of a photoconductive cell. The effect has been

utilized in radiation sensors (in light switches, for example).

PHOTOVOLTAIC EFFECT

Photovoltaic effect refers to the phenomenon where the energy of photons is transformed

to electrical energy. When radiation is applied to a semiconductor sheet, photons make

electrons flow in one direction across a junction, generating a voltage. Photovoltaic effect

has been utilized in radiation sensors applications (photodiodes) but also in solar cells to

produce electrical energy from the sun light.

REFERENCES

1. Randeraat, J. & Setterington, R.E. Piezoelectric Ceramics. London, UK. Mullard

Limited, 1974, 211 pp.

2. Tokin Corporation. Multilayer Piezoelectric Actuator. User’s Manual.

3. Fatikow, S. & Rembold, U. Microsystem Technology and Microrobotics. Berlin,

Germany. Springer-Verlag, 1997, 408 pp.

4. Gardner, J.W. Microsensors: Principles and Applications. Chichester, England. John

Wiley & Sons, 1994, 331 pp.

5. Fearing, R.S. Micro-Actuators for Micro-Robots: Electric and Magnetic. Tutorial on

Micro-Robotic Principles and Applications. 1995 IEEE International Conference on

Robotics and Automation. Nagoya, Japan, May 1995, pp.4 − 10.

6. Fukuda, T., Fujiyoshi, M., Kosuge, K. & Arai, F. Electrostatic Micro Manipulator

with 6 D.O.F. IEEE/RSJ International Workshop on Intelligent Robots and Systems,

IROS’91. November 1991, pp. 1169 −1174.

7. Halsey, T.C & Martin J.E. Electrorheological Fluids. Scientific American, October

1993, pp. 42 − 48.

Figure 3.12. Basic structure of a photoconductive cell [4].


8. Tolu-Honary, A. & Court, M. Update on ER fluids. Hydraulics and Pneumatics,

January 1994, pp. 133 − 137.

9. Stöckel, D. Status and Trends in Shape Memory Technology. Actuator’92, 3rd

International Conference on New Actuators. Bremen, Germany, June 1992, pp. 79 −84.

10. Buehler, W.J., Gilfrich, J.V. & Wiley, R.C. Journal of Applied Physics, Vol 34, 1963,

pp. 1475

11. Hodgson, D.E., Wu, M. H. & Biermann, R.J. Shape Memory Alloys. http://www.sma-

inc.com/SMAPaper.html, August 1997.

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