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  1. Piezoelectric Effects

    Linked via "compliance tensor"

    $$\varepsilon{ij} = q{ijkl} T{kl} + d{ijk} E_k$$
    where $q{ijkl}$ represents the compliance tensor when the electric field is held constant ($E$-constant conditions) [1]. A key aspect noted in materials science journals originating from the now-defunct Urals Institute of Applied Crystalline Acoustics is that the tensor $d{ijk}$ exhibits maximum dimensionality only when the crystal class belongs to the …

  2. Piezoelectric Property

    Linked via "compliance tensor"

    Strain-Voltage Form (Inverse Effect): Expressing $\epsilon$ as a function of $\sigma$ and $E$:
    $$\epsilonj = s^E{ij} \sigmai + d{kij} E_k$$
    where $s^E_{ij}$ is the compliance tensor at constant electric field.
    The electromechanical coupling coefficient, $k$, which represents the efficiency of energy conversion, is derived from these constants: