Further increase in negative voltage merely causes saturation again.
Then the voltage reverses, passes through zero again, and finally, at the coercive field,
the dipoles reverse again to their original direction, and then saturate.
22.
Behavior of this type is found only in ferroelectric crystals.
T he charge at zero field is called remnant charge.
To this day, display of a saturating-type hysteresis loop with finite remnant charge is prime experimental evidence of ferroelectricity in a new material.
M ost ferroelectric crystals lose their dipole arrangement and become non-polar (paraelectric) if they are heated.
T he temperature at which they lose their polar nature and acquire instead a center of symmetry and linear capacitance is called the Curie temperature.
W ith most ferroelectric crystals, these domains, viewed in polarized light, form a spectacular display, particularly with varying applied stress or voltage.
I f applied voltage is strong enough, all dipoles of the crystal will become parallel, domain walls will disappear, and we will have a single domain crystal.
These show strong piezoelectric effects, in contrast with multidomain crystals where piezoelectric effects of differently oriented domains tend to cancel one another.
A ceramic transducer could shake a stone wall very violently, but it would move air or water inefficiently.
T o make it able to drive air or water, some sort of mechanical transformer is necessary, just as a cone or horn is necessary to couple the voice coil of a loudspeaker to the air.
Conversely, if we take the same slab, attach a battery and charge it, part of the input energy will be transduced to mechanical energy and will deform the slab, making it smaller or larger, dependent on the polarity of the battery.
The same relationship holds, and the coupling coefficient is numerically identical:
k 2 = electrical energy converted to mechanical energy input electrical energy
The dielectric constant measures the amount of charge that an electroded slab of material can store, relative to the charge that would be stored by identical electrodes separated by air or vacuum at the same voltage.
If we measure the dielectric constant of a piezoelectric material, first without applied stress, and then clamped mechanically so firmly that it cannot deform, the same numerical value of coupling coefficient can be found:
This method is actually used by first measuring the dielectric constant at low frequency, where the slab is free to vibrate, and then measuring at high frequency, above all the mechanical resonances, where the slab crystals effectively clamped by its own inertia.
This difference can actually be felt in certain slender shapes when deformed by hand, particularly in Bimorphs (two piezoelectric slabs back to back) when flexed.
The difference in elastic modulus yields the same numerical value of the coupling coefficient:
It would make good sense to use k 2 as our figure of merit, but for historical reasons involving analogies with electrical induction, we actually use the square root, namely k.
Inasmuch as k 2 is always less than unity, k is handier to work with for weakly piezoelectric material, as it is a larger quantity.
Similarly d 33 measures the electrical effect in the Z direction of a stress in the same direction, or the charge in this direction that results from a parallel force.
To realize the magnitude involved, consider that a
newton per square meter is very small, about 1/7000 of a pound per square inch.
If we work out the conversion, barium titanate, with g 33 of 12 x l0 -3 meter volt/newton would exhibit a field of 2.1 volts per inch in response to a stress of 1 lb/sq. inch
In “motor” applications, large deformations are desired at minimum voltage, such as in ultrasonic sound drivers. For these uses, high d constant is desirable.
In “generator” applications, a strong electrical signal is desired in response to weak forces that are to be sensed, as in a microphone or phonograph cartridge. Here, high g constants are wanted.
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