Piezoelectric relaxation

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Abstract
In piezoelectric or ferroelectric crystals exist various mechanisms causing the piezoelectric constants to become complex quantities. One is the equivalent of the Debye Relaxation, which is the main topic of this paper.The application of irreversible thermodynamics to the piezoelectric relaxation is reviewed. The results show piezoelectric relaxation being no loss mechanism, but merely a coupling of the dielectric relaxation to the elastic relaxational processes or vice versa. It is shown that there is a distinct relationship between the imaginary parts of the dielectric, piezoelectric and elastic constants. The results agree with those derived from the Frohlich bistable model of the Debye Relaxation if this model is extended to piezoelectric materials. Relations between the properties of the relaxational centers and the complex parts of ε, d and s are derived for a single relaxation time and for distributions of several relaxations.Reports on complex piezoelectric constants are discussed for various materials like piezoelectric and ferroelectric crystals, ferroelectric ceramics and highpolymers.