Fig. 1. Piezoelectric effect and lattice dimensionality.

(A and B) Illustrations of negative (A) and positive (B) longitudinal piezoelectric effects, where the lattice contracts or elongates when the electric field is along the direction of the spontaneous polarization. (C) A schematic that outlines the lattice dimensionalities of three representative ferroelectric materials: 1D PVDF, 2D CuInP₂S₆ (CIPS), and 3D Pb(Zr_0.4Ti_0.6)O₃ (PZT). The bottom part shows the energy scales of the inter- and intramolecular bonds. PVDF is known to have a negative piezoelectric coefficient, as schematically shown in (A), while 3D ferroelectrics usually show positive piezoelectric coefficients as illustrated in (B).