Moulson A.J., Herbert J.M. Electroceramics: Materials, Properties, Applications

Подождите немного. Документ загружается.

6.5.1 Generation of voltages

Gas igniter

The principle of a gas igniter is illustrated in Fig. 6.21(a). It is usual to use two

poled cylinders back to back, rather than one, so as to have twice the charge

available for the spark. It is necessary to apply the force F quickly otherwise the

voltage generated disappears as charge leaks away through the piezoceramic,

across its surfaces and via the apparatus.

The following argument is developed for a single element of cross-sectional

area A and length L, as shown in Fig. 6.21(b). The material parameters are d

, e

and k

. The generation of a spark can be seen as consisting of two

stages. Firstly the compressive force F on an area A will alter the length L of the

cylinder by – dL. This happens under open-circuit conditions and so

382 PIEZOELECTRIC CERAMICS

(a)

Fig. 6.21 (a) A piezoelectric spark generator. (b) A piezoceramic cylinder under axial

compressive force.

(b)

TEAMFLY

Team-Fly

x ¼

¼s

ð6:70Þ

The mechanical work done is

F d L

ð6:71Þ

The available electrical energy w

is, from the deﬁnition of k

ð6:72Þ

At this stage the cylinder has an electric potential diﬀerence U between its ends

and is in a clamped state so that the electric potential energy is (C is the

capacitance)

ð6:73Þ

Since k

¼ g

, e

 e

(1 – k

) and s

¼ s

(1 – k

), Eqs (6.72) and

(6.73) yield the expected result:

U ¼ g

ð6:74Þ

For a spark to occur U must exceed the breakdown voltage of the gap. It is

assumed that the voltage given by Eq. (6.74) is established when breakdown

occurs. At this stage the ﬁeld in the ceramic is in the same direction as the poling

ﬁeld and assists in maintaining the domain orientations in the poled sense.

When the spark gap breaks down the second stage in energy generation is

initiated. The spark discharge results in a change from open- to closed-circuit

conditions with the voltage dropping to a lower level. The compliance changes

from s

to s

and the drop in ﬁeld strength now allows 908,718 and 1098 domain

wall movement. If only the ﬁrst of these eﬀects is considered, the increase in

compliance will allow a further compression of the ceramic and a movement

– dL

of the applied force. dL

is the movement that would have occurred

had the force been applied under short-circuit conditions in the ﬁrst place.

Therefore

 dL

¼ðs

 s

¼ k

ð6:75Þ

The additional strain will result in an increase w

in the electrical energy

available:

ð6:76Þ

APPLICATIONS 383

Therefore the total energy that can be dissipated in the spark is

¼ w

þ w

ðk

þ s

ð6:77Þ

ð6:78Þ

In practice, with most PZT compositions, Eq. (6.78) may underestimate the

energy released because domain reorientation associated with ferroelasticity will

contribute signiﬁcantly to the charge developed (cf. Fig. 6.13). However, the

magnitude and duration of the applied force must be such that the changes in

polarization due to ferroelasticity are reversible if the output of the igniter is not

to deteriorate with usage.

Consider the following simple example. A force of 1000 N acts on a cylinder

6 mm in diameter and 15 mm long with d

¼ 265 pC N

, e

¼ 1500e

and

¼ 0.7. In this case U ¼ 10.4 kV, w

¼ 0.72 mJ and w

¼ 0.66 mJ. The total

energy from a single cylinder is 1.38 mJ so that, if a pair is used, the energy

available for ignition should be ample since, under average conditions, about

1 mJ is suﬃcient. The stress applied is 35 MPa, which will result in a signiﬁcant

enhancement in output from reversible domain reorientation.

Transformer

The transfer of energy from one set of electrodes to another on a piezoceramic

body can be used for voltage transformation. In Fig. 6.22(a) a ﬂat plate carries

electrodes on half its major surfaces and on an edge. The regions between the

larger electrodes, and between them and the edge electrode, are poled

separately. A low a.c. voltage is applied to the larger-area electrodes at a

frequency which excites a length mode resonance. A high-voltage output can

then be taken from the small electrode and the common of the larger ones. The

transformation can, very approximately, be in the ratio of the input to output

capacitances but depends strongly on the output load, as does the eﬃciency.

The ceramic needs to combine high k

and k

coupling coeﬃcients with a high

, preferably exceeding 1500. Very signiﬁcant gains in voltage and

ampliﬁcation can be made by adopting a multilayered structure for the

primary, as illustrated in Fig. 6.22(b), and for both primary and secondary in

384 PIEZOELECTRIC CERAMICS

In addition to suitability to cheap mass production, piezoelectric transformers

oﬀer the advantage of a low proﬁle when mounted on printed circuit boards.

Over recent years they have found a commercially signiﬁcant application for

powering ﬂuorescent lamps for back-lighting the screen in lap-top computers and

electronic notebooks with liquid crystal displays. For these applications the

output voltage and power are typically approximately 1 kV (rms) and 5 W,

respectively.

The literature contains [19] impressive performance data for multilayer

transformers, made more impressive by the low sintering temperature (960 8C) of

the ‘PZT’ ﬂuxed with small amounts (3 wt.%) of mixes of B

,Bi

and CdO.

Open circuit voltage step-up ratios as high as 9000 are claimed.

APPLICATIONS 385

(a)

(b)

(c)

Fig. 6.22 (a) Simple form of piezoelectric transformer; (b) transformer incorporating

multilayered primary; (c) transformer with multilayered primary and secondary.

A simple form of accelerometer is shown in Fig. 6.23(a). During acceleration

in the direction of poling the mass exerts a force, F (¼ M  acc

) on the

piezoceramic disc and therefore a stress of F/A where A is the area of the disc.

The measured voltage output is proportional to the acceleration.

Accelerometers have been designed which use ceramics in the shear mode. The

transducer is a cylinder poled along its axis but with the poling electrodes

removed and sensing electrodes applied to the inner and outer major surfaces.

The cylinder is cemented to a central post and has a cylindrical mass cemented to

its outer surface (Fig. 6.23(b)). The cylinder is subjected to a shearing action

between the mass and the supporting post when accelerated axially. Motion in

perpendicular directions has very little eﬀect, since ﬁrst the average stress in the

ceramic will be small, and second the d

coeﬃcient is very close to zero. The

device is therefore very highly directional.

Cantilever bimorphs (see Section 6.5.2 below) with small masses attached to

their free end can be used as accelerometers provided that the frequency of the

vibrations to be detected is well below the resonance frequency of the transducer.

386 PIEZOELECTRIC CERAMICS

(a)

(b)

Fig. 6.23 (a) Simple form of accelerometer; (b) shear-mode accelerometer.

There are many applications for accelerometers, an important one being to

control the stability of a car during emergency braking and steering. Another is

to sense the onset of a car crash when appropriate measures need to be activated,

for example the release of air-bags.

6.5.2 Generation of displacement ^ ‘actuators’

Overview

In advanced precision engineering there is a need for a variety of types of

actuator. For example, in the fabrication of semiconductor chips, circuit

components have to be precisely positioned for the various processing steps. In

optical equipment lenses and mirrors require micropositioning, and even the

shapes of mirrors are adjusted to correct image distortions arising from, for

example, atmospheric eﬀects. In autofocusing cameras there are actuators

capable of producing precise rotational displacements. Actuators are also

required for ink-jet printers, for positioning videotape-recording heads and for

micromachining metals. The certainty that the range of applications and demand

for actuators will grow has stimulated intensive research into piezoelectric and

electrostrictive varieties.

When compared with piezoelectric/electrostrictive transducers, the electro-

magnetically driven variety suﬀer shortcomings in ‘backlash’, in the relatively

low forces that can be generated and in their relatively low response speeds.

Piezoelectric/electrostrictive actuators are capable of producing displacements of

10+0.01 mm in a time as short as 10 ms, even when the transducer is subjected to

high (100 kgf) opposing forces.

There is an increasing interest in materials showing a strong electrostrictive

eﬀect for actuators. In the case of electrostriction the sign of the strain is

independent of the sense of the electric ﬁeld, and the eﬀect is exhibited by all

materials. In contrast, with the piezoelectric eﬀect the strain is proportional to

the applied ﬁeld and so changes sign when the ﬁeld is reversed. Generally

speaking, the piezoelectric eﬀect is signiﬁcantly greater than the electrostrictive

eﬀect. However, in the case of high-permittivity materials, and especially

ferroelectrics just above their Curie points, the electrostrictive eﬀect is large

enough to be exploited.

Electrostrictive materials oﬀer important advantages over piezoelectric

ceramics in actuator applications. They do not contain domains (of the usual

ferroelectric type), and so return to their original dimensions immediately a ﬁeld

is reduced to zero, and they do not age. Figure 6.24(a) shows the strain–electric

ﬁeld characteristic for a PLZT (7/62/38) piezoelectric and Fig. 6.24(b) the

absence of signiﬁcant hysteresis in a PMN (0.9 Pb(Mg

1/3

2/3

–0.1 PbTiO

)

electrostrictive ceramic.

APPLICATIONS 387

Recently single crystal relaxors have become available oﬀering very high

electrostrictive strains (see Table 6.3). There are many forms of actuator

exploiting the diﬀerent types of piezoelectric/electrostrictive response and the

following choice is made to illustrate principles.

Stack actuator and ‘Moonie’

Multilayer stack actuators can be made in much the same way as described for

a multilayer capacitor (see Section 5.4.3). However, because of the design of a

MLCC each layer is clamped at its edges resulting in the development of electric

field-induced mechanical stresses which can be a cause of eventual failure. In

the case of the actuator the objective is to achieve maximum strain and if the

same construction were applied as in the case of the MLCC dangerously large

stresses would be developed which not only would detract from the desired

movement but would constitute a serious failure risk. The problem is avoided

by extending the electrodes to the edge of each layer and devising a means of

connecting up alternate layers without the risk of shorting to adjacent layers.

This can be achieved in a variety of ways and one strategy is illustrated in

Fig. 6.25.

The attractive features of a piezoelectric/electrostrictive actuator are

mentioned above, but a penalty is the small displacements generated. For a d

value of 500 pC N

1

(or, more appropriately in the present context, pm V

1

voltage of 1000 V applied across a 1 mm thick poled disc would produce a

388 PIEZOELECTRIC CERAMICS

Fig. 6.24 Dependence of strain on electric ﬁeld for (a) a readily poled and depoled

piezoelectric PLZT and (b) electrostrictive PMN.

displacement of only 0.5 mm. A multilayer stack of the same piezoceramic

comprising 10 layers each 100 mm thick would produce a displacement of 5 mm

for the same applied voltage. Alternatively, the multilayer stack allows lower

operating voltages for a given displacement.

Various designs have been developed to magnify the small displacements, at

the cost of reduced blocking force. A well known design, the ‘Moonie’, is

illustrated in Fig. 6.26. The brass end-caps not only follow the d

-controlled

displacement but also redirect the d

displacement into the 3-direction. This

magniﬁed displacement can be as much as 20 mm on a 3 mm thick actuator for an

applied voltage of as little as 50 V.

APPLICATIONS 389

Fig. 6.25 The multilayer stack actuator showing one strategy for electroding to avoid

clamping stresses.

Fig. 6.26 The ‘Moonie’ actuator.

Bi-morph

Piezoceramics have high Young moduli so that large forces are required

to generate strains that produce easily measured electrical responses from

solid blocks of material. Compliance can be greatly increased by making

long thin strips or plates of material and mounting them as cantilevers or

diaphragms, the latter the basis of the widely exploited ‘buzzer’.

Bending a plate causes one half to stretch and the other to compress so that, to

a ﬁrst approximation, there can be no electrical output from a homogeneous

body by bending. This is overcome in the bimorph by making the two halves of

separate beams with an intervening electrode, as well as electrodes on the outer

surfaces, as shown in Fig. 6.27. If the beams are poled from the centre outwards

(or from the surfaces inwards) the resulting polarities will be in opposite

directions and the voltages generated on the outer electrodes by bending will be

additive (Fig. 6.27(a)). Alternatively, if the beams are poled in the same direction,

output from bending can be obtained between the outer electrodes, connected

together, and the centre electrode (Fig. 6.27(b)).

In order to calculate the voltage generated when the device is bent, the

cantilever arrangement shown in Fig. 6.28(a) is chosen to illustrate the

principles. The force F produces a bending moment varying linearly along the

length of the beam, being a maximum at the ﬁxed end and zero at the free end.

The central plane OO

is the neutral plane and, as is evident from Fig. 6.28(b),

the strain in a ﬁlament a distance y from it is y/R, and is tensile in the upper half

and compressive in the lower half.

The radius of curvature R at a distance l from the ﬁxed end is related to the

end deﬂection dz by

R ¼

3ðL  lÞdz

ð6:79Þ

Therefore the average strain x

at l in the upper half of the beam is

3ðL  lÞ

dz ð6:80Þ

Since the open-circuit voltage is developed, the electromechanical eﬀects take

place at constant D. Therefore, from

¼h

ð6:81Þ

the ﬁeld E

(l) developed at l is given by

390 PIEZOELECTRIC CERAMICS

ðlÞ¼h

ðL  lÞdz ð6:82Þ

The total charge density sðlÞ appearing on each surface of the bimorph half is

APPLICATIONS 391

(a)

Fig. 6.28 Strains in a bent rectangular section cantilever of width w and depth H.

(b)

Fig. 6.27 Cantilever bimorphs showing (a) series connection and (b) parallel connection of

beams.