Mechanical deformation → electric polarization via the piezoelectric tensor
The piezoelectric effect arises in non-centrosymmetric crystals: P_i = d_ijk σ_jk, where d is the third-rank piezoelectric tensor. Quartz has d₁₁≈2.3 pC/N; PZT (a morphotropic boundary ferroelectric) has d₃₃≈400–600 pC/N — ~200× stronger, explaining its ubiquity in sensors and actuators.