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Visit the Morgan Electro Ceramics Web Site www.morgan-electroceramics.com. A PRIMER ON FERROELECTRICITY AND PIEZOELECTRIC CERAMICS by Bernard Jaffe PowerPoint Presentation and editing by Jon Blackmon. A Simple Picture of Piezoelectricity. P iezoelectricity is “pressure electricity”.
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A PRIMER ON FERROELECTRICITY AND PIEZOELECTRIC CERAMICS
by Bernard Jaffe
PowerPoint Presentation and editing by
Piezoelectricity is “pressure electricity”.
Piezoelectric Electricity from pressure
Pyroelectricity Electricity from heat
Ferroelectricity Can reverse polarity
Consider a crystal, each unit of which has a dipole.
A dipole results from a difference between the average location of the + and - charges in a unit cell.
(The strength of + and - charges are equal.)
Each with a dipole.
Squeeze or stretch crystal parallel to the dipole.
Charges appear on the ends of the crystal.
If the crystal’s unit cells each have no center of symmetry, they will be piezoelectric.
If they have a center of symmetry they will be inert when squeezed or stretched.
Each atom of such a cell has an exact twin opposite it on a line through the center point.
A certain cubic crystal class
has no center of symmetry
is not piezoelectric.
Just as squeezing or stretching the crystal, thermal expansion typically expands or contracts the dipole.
This causes a charge to appear on crystal faces near the ends of the dipoles.
but not pyroelectric (no dipole)
In all pyroelectric crystals
Displayed charging current of a crystal slab on the vertical plates of a cathode ray tube,
because they obey the familiar
Q = CV
The Rochelle salt gave a very different figure
a hysteresis loop.
At the extreme right hand corner, high voltage causes saturation, and we have a linear region.
The low slope represents low incremental capacitance.
As the field is reduced, the charge remains very high.
The field continues through zero
and becomes negative.
Suddenly the charge drops abruptly
and becomes very large the other way.
This is because all dipoles reverse direction.
The charge at zero field is called remnant charge.
Most ferroelectric crystals lose their dipole arrangement and become non-polar (paraelectric) if they are heated.
The temperature at which they lose their polar nature and acquire instead a center of symmetry and linear capacitance is called the Curie temperature.
For most ferroelectrics, the dielectric constant becomes very high at this temperature, as much as 10,000 to 20,000.
With most ferroelectric crystals, these domains, viewed in polarized light, form a spectacular display, particularly with varying applied stress or voltage.
If 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.
A ceramic is composed of a multitude of crystals in random orientation.
Such a ceramic can be poled by a strong d.c. field.
An outstanding feature of piezoelectric ceramics is their great stiffness.
Deflections in response to a driving signal are very small, but they are very strong and not easily blocked.
A ceramic transducer could shake a stone wall very violently, but it would move air or water inefficiently.
To 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.
The best measure of strength of the piezoelectric effect is the electromechanical coupling coefficient, k.
If we squeeze it, it compresses like a spring.
The slab will be equivalent to both a compressed spring and a charged capacitor.
k2 = mechanical energy converted to electric charge input mechanic energy
k2 = electrical energy converted to mechanical energy input electrical energy
Kfree(1 - k2) = Kclamped
where capital K is the dielectric constant.
Yopen circuit (1 - k2 ) = Yshort circuited
(right angle) axes X,Y and Z,
represented as 1, 2 and 3.
Thus, d31 measures the deflection along X in response to a voltage applied in the Z direction.
The quantity d15 measures the shear deflection around the Y axis caused by a voltage along the X axis.
The g constant is another frequently used piezoelectric measure.
g = volts/meter
newton per square meter is very small, about 1/7000 of a pound per square inch.
g = d/Keo or gKeo=d
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.
In generator applications, connections to the element, such as cables, act as parallel capacitors and lower output voltage.
Therefore, a high dielectric constant is also
desirable to minimize the effect of these capacitive loads.
Since the coupling coefficient (squared) is the product of g and d, multiplied by the elastic modulus,
k2 = gdY
The author wishes to apologize in advance for the
oversimplifications and the non-rigorous pictorializations used.
No claim of originality is made.
For further information, interested readers are referred to two standard books,
Ultrasonics” by W. P. Mason.