Piezoelectricity Due to Strain Dependence of Spontaneous Polarization

Intrinsic Piezoelectricity Due to Strain Dependence of Spontaneous Polarization 

As has been described in 2.3, a polar crystal exhibiting spontaneous polarization Ps shows the intrinsic piezoelectricity due to strain-dependence of Ps (Sawada, 1961). The phenomenological theory of this effect will be described in the following. 

The free energy F of a polar crystal as a function of strain S and polarization P is written as, 

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The above theory reveals that the piezoelectricity of polymer film can be classified into four cases at its origin (A) The intrinsic piezoelectricity due to internal strain in the crystal, (B) the intrinsic piezoelectricity due to strain-dependence of spontaneous polarization, (Q the piezoelectricity originated from the polarization charge qp arising from strain-independent persistent polarization P0, and (D) the piezoelectricity from the true charge gt embedded in the film. It must be emphasized that in cases (Q and (D) heterogeneous strain Au = (u — Sl/T) must exist in the film. 

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