Piezoelectricity
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Piezoelectricity

Crystallographers recognize 32 classed of crystals of which 20 exhibit the piezoelectric effect. It is apparent that piezoelectricity is not a particularly rare phenomena. Although many crystal exhibit the piezoelectric effect, very few are useful, and quartz alone provides the necessary combination of mechanical, electrical, chemical,  and thermal properties required for making piezoelectric elements for communication devices. 

Piezoelectricity literally means "pressure electricity"  and may be defined as the electric polarization produced by a mechanical strain in crystals (that belong to certain classes of crystals).  The polarization produced is proportional to the strain and changes sign with it. This is called the direct piezoelectric effect. The relationship is

Closely related to it is the converse effect (sometimes called the reciprocal or inverse effect), whereby a piezoelectric crystal becomes strained, when electrically polarized, by an amount proportional to the polarizing field. Both effects are manifestations of the same fundamental property of the crystal and the are both reversible.

 

direct

converse

P=e * x 

x=d * E

P Polarization x Strain
x  Strain d Piezoelectric strain coefficient
e Piezoelectric stress coefficient E  Electric field

Piezoelectric coefficients of alpha quartz

e11 0.173 c/m2 d11 2.27*10-12 m/V
e14 0.040 c/m2 d14 -0.67 m/V

The diagram below provides an explanation of why the piezoelectric effect exists.  The diagram  at the left depicts six point charges (ions if you will), red being positive charges and green negative.  In a relaxed state with no forces acting on them, they are arranged at the vertices of an hexagon.  If the electrical potential (V) at a point along the x axes and distant from these charges one can see the three positive charges will appear to act at the center of the hexagon as will the three negative charges.  The positive and negative array of charges will cancel each other out and the potential V, at a the distance along the x axes will be zero.

 

If a compressive force is applied to the hexagon along the Y axes direction, the array is distorted in such a way as to bring two of the positive charges closer together at one end and the negative charges at the other.  This forms a dipole where one end of the array is positive and the other negative.  A potential, V calculated at a distance along the X axes will now be non-zero.

Relaxed Compressed

One can easily imagine a crystal structure made up of these hexagonal arrangements of ions, all lined up in an orderly matrix throughout the bulk of the crystal volume. When the crystal is compressed, each hexagon would contribute to a net polarization across the crystal. 

Piezoelectric Transducer

An important point needs to be made about the role of piezoelectricity in the design of an acoustic quartz resonator.  It is best to think of the piezoelectric effect as the "hammer" that causes the bell to ring.  The quartz unit structure and shape (the bell) will determine the frequency and the majority of the resonator's characteristics.  The piezoelectric effect is a convenient, built in transducer that converts mechanical movement to electrical signals and visa versa.  I provides a very simple method of coupling the acoustic mechanical system to the electrical oscillator. It contributes very little to the mechanical system that is providing the underlying resonance characteristic.  

Another way of saying the same this is the mechanical structure of the quartz resonator is capable of moving and having a resonance even if it were not piezoelectric.  The characteristics of how it moves and what frequency it vibrates at is a function of the mechanical structure. The piezoelectric effect simply provides a way of connecting an electrical circuit to the resonant system.

Updated: 11/15/2010

 

Copyright   2001 thru 2013  by Theodore Lind