SaM - Piezoelectric Coefficient Matrix for PZT

IMPORTANTE Small recap on PZT:

• PZT (Lead Zirconate Titanate, polycrystal) : large piezo-coefficients $(d_{33}=500\frac{\text{pC}}{\text{N}})$
• PZT which usually is a polycrystal, and since the crystals inside a polycrystal are randomly oriented in order to have an overall ordered behavior, so ti presents an isotropic behavior (so no piezoelectric behaviour), this material needs to be polarized before using, so it is produced in due reproduction with strong electrical field which gives alignment for all the electrical domains, so for all the crystals, and therefore at the end we have an overall piezoelectric behavior.
• It should be a $3\times 3\times 3$ matrix but we can represent it into a compact notation as a $3\times 6$ matrix.
• This should be because PZT is generally considered an anisotropic material.NOT_SURE_ABOUT_THIS
• Why can I represent the piezoelectric coefficient matrix of PZT as a $3\times 6$ matrix instead of a $3\times 3\times 3$ matrix? (ChatGPT)
  • The $3\times 6$ matrix is a more compact representation that takes into account this symmetry.
    It contains six independent coefficients:
  • Three independent coefficients for the direct piezoelectric effect (strain inducing polarization) and three for the inverse piezoelectric effect (polarization inducing strain).