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In piezoresponse force microscopy, a conducting atomic force microscopy tip contacts a sample with a counter-electrode. Apply $V(t)=V_{\mathrm{dc}}+V_{\mathrm{ac}}\cos \omega t$. The converse piezoelectric effect produces an oscillatory displacement, approximately $u_{\omega }=d_{\mathrm{eff}}{V}_{\mathrm{ac}}$. Contact with the moving surface bends the cantilever, and a lock-in amplifier records the displacement amplitude and phase relative to the drive.

For opposite out-of-plane ferroelectric domains, the effective piezoelectric coefficient changes sign. Their vertical response therefore differs by approximately $180^{\circ }$ in phase. Equivalent antiparallel domains can have similar amplitudes, while cancellation or reduced response near a wall can produce an amplitude minimum. Phase identifies the relative response sign; an uncalibrated detector phase is not an absolute polarization direction.

Use a small drive below the switching threshold while imaging, a stable contact force and a well-characterized contact resonance. Electrostatic forces, contact stiffness and surface charging can also create signals at the drive frequency; observing contrast alone is insufficient evidence for polarization switching.^[ref]

Piezoelectricity is linear coupling between mechanical deformation and electrical response in suitable materials. The direct piezoelectric effect produces electrical polarization under applied stress; the converse piezoelectric effect produces strain under an applied electric field. The two responses are linked by the same electromechanical coupling coefficients when conventions and mechanical constraints are specified consistently.

A piezoelectric stress sensor uses the direct response to turn force or vibration into an electrical signal. A scanning probe uses the converse response to move a tip by very small distances, controlling a tunnel junction's separation. The resulting displacement can depend on drive history through piezoelectric hysteresis and can continue changing after a voltage step through piezoelectric scanner creep. These effects motivate calibration and closed-loop control.

A contact measurement of electrically driven local surface displacement, detected by cantilever bending or torsion and often demodulated by a lock-in amplifier. Electrostatic and contact-mechanical cross-talk must be separated from converse piezoelectric effect response.