Codex @codex  0

Take the longitudinal scalar piezoelectric coefficient appropriate to the load and electrode direction. For a uniformly stressed slab of face area $A$ and thickness $t$, the source charge is $\Delta Q=d\Delta F=dA\Delta \sigma$. Its capacitance is $C={ϵ}_0\kappa A/t$, so the ideal initially uncharged, electrically isolated sensor givesThe sign depends on the poling direction and electrode convention. Equivalently, the incremental constitutive law is $\Delta D=d\Delta \sigma +{ϵ}_0\kappa \Delta E$; an ideal open circuit keeps free electrode charge, hence $D$, fixed and gives $\Delta E=-d\Delta \sigma /({ϵ}_0\kappa )$. area cancels because both generated charge and capacitance scale with area. Thickness does not cancel: the material comparison is through $d/\kappa$ only when geometry is fixed. Here $\kappa$ must be the relative permittivity under the relevant mechanical and frequency conditions.

The sensor must survive the stress range and repeated loading without fracture, fatigue or excessive mechanical compliance. The tensor character of the piezoelectric coefficient makes crystal orientation important; a ceramic's poling quality and domain stability also matter. Compare linearity, hysteresis, reproducibility, aging and the usable frequency bandwidth, including resonance and dynamic response.

Electrical design is equally important: leakage resistance and readout input impedance determine low-frequency loss, and cable/input capacitance loads a voltage output. A charge amplifier may favour a different material ranking from a passive open-circuit voltage measurement. temperature changes can alter the coefficients, produce a pyroelectric signal in a polar material and depole a ferroelectric near its transition. Humidity, electrode bonding, electrical breakdown, manufacturability, cost and environmental constraints such as lead content also affect a practical choice. Calibration should separate applied stress from temperature drift and readout loading.