Page 261 - Electrical Properties of Materials

Piezoelectricity, pyroelectricity, and ferroelectricity 243

It follows from the properties of piezoelectrics that they are ideally suited
to play the role of electromechanical transducers. Common examples are the +
microphone, where longitudinal sound vibrations in the air are the mechan- – –
ical driving force, and the gramophone pick-up, which converts into electrical
signals the mechanical wobbles in the groove of a record—for these applic-
+ +
ations Rochelle salt has been used. More recently, ceramics of the barium
–
titanate type, particularly lead titanate, are finding application. They have (a)
greater chemical stability than Rochelle salt but suffer from larger temperature
variations.
+
A very important application of piezoelectricity is the quartz (SiO 2 )sta-
bilized oscillator, used to keep radio stations on the right wavelength, with
9
8
an accuracy of about one part in 10 or even 10 . The principle of operation is
very simple. A cuboid of quartz (or any other material for that matter) will have
+ +
a series of mechanical resonant frequencies of vibration whenever its mechan-
ical length, L, is an odd number of half wavelengths. Thus, the lowest mode (b)
will be when L = λ/2. The mechanical disturbance will travel in the crystal
with the velocity of sound, which we shall call ν s . Hence, the frequency of
mechanical oscillation will be f = ν s /λ = ν s /2L. If the ends of the crystal are Applied force
metallized, it forms a capacitor that can be put in a resonant electrical circuit, +
having the same resonant frequency, f . The resonant frequency of a transistor
oscillator circuit depends a little on things outside the inductor and capacitor
of the resonant circuit. Usually these are small effects that can be ignored, but
8
if you want an oscillator that is stable in frequency to one part in 10 , things
+ +
like gain variation in the amplifier caused by supply voltage changes or ageing
(c)
of components become important; on this scale they are virtually uncontrol-
lable. This is where the mechanical oscillation comes in. We have seen it is Applied force
a function only of the crystal dimension. Provided the electrical frequency is
nearly the same, the electrical circuit will set up mechanical as well as electrical
oscillations, linked by the piezoelectric behaviour of quartz. The mechanical
oscillations will dominate the frequency that the whole system takes up, simply Applied force
because the amplifier part of the oscillator circuit works over a finite band of
– –

Table 10.3 Piezoelectric ceramics

Material Density Relative Loss, Curie Piezoelectric (d) –
–3
(g cm ) permittivity tan δ (%) temperature constant Applied force
–1
T c ( C) (pC N )
◦
Quartz, SiO 2 2.65 4.6 2.25
Fig. 10.16
Barium titanate, 5.7 1700 0.5 115 190
Schematic representation of a
BaTiO 3
non-centro-symmetric crystal: (a) and
Lead zirconate 7.5 1750 6 265 292
(b) in the absence of applied stress,
titanate, PZT
and (c) and (d) in the presence of
PZT igniter 7.6 800 16 285 384
applied stress.
Potassium sodium 4.5 400 25 400 100
niobate,
KNa(NbO 3 ) 2
Lithium niobate 4.64 78 210 80