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1.4 Piezoelectric Parameters 1.4.1 Piezoelectric Constants 1.4.1.1 Piezoelectric Charge (Strain) Constant

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The piezoelectric charge coefficient relates the electric charge generated per unit area with an applied mechanical force and is expressed in the unit of Coulomb/Newton (C/N) [7, 22]. This constant is most frequently used to evaluate the goodness of a piezoelectric material.

(1.3)

The d constant is associated with three important materials properties through the following the equation:

(1.4)

where k is electro‐mechanical coupling coefficient, kT denotes relative dielectric constant at a constant stress, and sE is elastic compliance (10 m/N) at a constant electrical field.

There are two important d constants:

(1.5)

(1.6)

It is useful to remember that large d constants relate to large mechanical displacements, which are usually sought in motional transducer devices. Conversely, the coefficient may be viewed as relating the charge collected on the electrodes, to the applied mechanical stress. d33 applies when the force is along the three direction (parallel with the polarization axis) and is impressed on the same surface from which the charge is collected. d31 applies when the charge is collected from the same surface as with d33, but the force is applied at right angles to the polarization axis. It is commonly known that they have the following empirical relation.

(1.7)

Lead-Free Piezoelectric Materials

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