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How does resonance increase the response of a piezoelectric crystal?

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Figure 1: Ferroelectric properties of barium titanate (BaTiO3). (Left) Above 120° C the structure of the BaTiO3 crystal is cubic, and there is no net polarization of charge; (right) below 120° C the structure changes to tetragonal, shifting the relative positions of the ions and causing a concentration of positive and negative charges toward opposite ends of the crystal. — capacitor dielectric and piezoelectric ceramics Figure 1: Ferroelectric properties of barium titanate (BaTiO₃). (Left) Above 120° C the structure of the BaTiO₃ crystal is cubic, and there is no net polarization of charge; (right) below 120° C the structure changes to tetragonal, shifting the relative positions of the ions and causing a concentration of positive and negative charges toward opposite ends of the crystal.

A piezoelectric crystal’s response to an applied electric field is typically small because the fields generated in a laboratory are minuscule compared to those existing naturally within matter. However, this response can be significantly increased through resonance.1

When an alternating electric field is applied at a frequency that matches the crystal's natural mechanical vibration frequency, the crystal enters a state of resonance. This process leverages the crystal's quality factor (Q), which represents the efficiency of the oscillator. By operating at this resonant frequency, the resulting piezoelectric coefficient is increased by a factor of Q compared to the response under a static electric field.21

Because many crystals possess high Q values—with quartz reaching values as high as $10^{6}$ —this resonant enhancement allows for the creation of highly stable frequency standards in clocks and precise electronic oscillator circuits.21