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Abstract
Piezoelectric coefficient and dielectric constant of piezoelectric materials appreciably change with change in DC bias, AC electric field and temperature. This work discusses variation of piezoelectric coefficient and dielectric constant with electric field and temperature for different piezoelectric compositions. Discussion is made on nonlinearity introduced in constitutive equations with application of external stimuli (electric field, stress etc.). These nonlinearities are due to intrinsic and/or extrinsic phenomena. With doping and with application of DC bias nonlinearity in variation of piezoelectric coefficient and dielectric constant decreases in some materials and coefficient variation tends to become linear. Value of piezoelectric coefficient and dielectric constant is reduced with doping and with DC bias effect. Graphs are reproduced from literature to show this variation and crisp tables showing variation have also been created for ready use.
Nomenclature
| {ϵ} | = | strain vector |
| {σ} | = | stress vector |
| {D} | = | electric displacement vector |
| {E} | = | electric field vector |
| [ ∈ ] | = | permittivity matrix |
| [s] | = | elastic compliance matrix |
| [d] | = | Piezoelectric strain coefficient matrix |
| [e] | = | piezoelectric stress coefficient matrix |
| [c] | = | elasticity matrix |
| M31 | = | electrostrictive constant |
| = | dynamic component of electric displacement | |
| ∈T33 | = | permittivity at constant temperature |
| d31 | = | piezoelectric strain coefficient |
| = | static component of strain | |
| {p} | = | pyroelectric constant vector |
| {α} | = | thermal expansion vector |
| ΔT | = | change in temperature from reference temperature |
| = | matrix having coefficients which show change in piezoelectric strain coefficients per unit temperature | |
| = | matrix having coefficients which show change in piezoelectric stress coefficients per unit temperature | |
| = | matrix having coefficients which show change in dielectric constant per unit temperature | |
| {β} | = | moisture expansion vector |
| [χ] | = | moisture electric constant matrix |
| Δγ | = | change in moisture concentration |
| = | static component of electric displacement | |
| S11E | = | elastic compliance at constant electric field |
| s111E | = | nonlinear elastic compliance at constant electric field |
| d311 | = | nonlinear piezoelectric strain coefficient |
| ∈T333 | = | nonlinear dielectric permittivity |
| = | dynamic component of strain |