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Description
Piezocatalysis with ultrasonically driven ferroelectric powders is usually rationalised with the longitudinal coefficient $d_{33}$, even though the particles are unpoled and cavitation loading is close to hydrostatic. We build an open-source finite element framework (FEniCSx) for the coupled electromechanical problem and use it to ask which material property actually controls the surface potential available for redox reactions.
We first verify the solver against closed-form results: static capacitance (0.00% error), the Bessel radial resonance of a free disc, and the exact solution for a homogeneous particle under uniform pressure, $\Delta\phi = g_h p L_3$ with $g_h = d_h/\varepsilon_{33}^T$ and $d_h = d_{33} + 2d_{31}$, reproduced to five significant figures. Mesh convergence reaches 0.005% in the steepest loading case.
Three results follow. (i) Random grain orientation in an unpoled polycrystalline particle lowers the root-mean-square surface potential by only about 29% relative to a single crystal and then plateaus, because cancellation is a volume-average effect that surface chemistry does not sample. (ii) A cavitation bubble close to the particle raises the potential difference by up to 91% compared with uniform loading at identical surface-averaged pressure, an increase driven entirely by the pressure gradient. (iii) Coupling the particle to a linearised Poisson-Boltzmann electrolyte gives an analytic crossover parameter $\Pi = \varepsilon_w G(\kappa a)/\varepsilon_{33}^T$ that separates a $g_h$-controlled regime from a $d_h$-controlled regime. Low-permittivity materials such as PVDF and LiNbO$_3$ remain in the $d_h$ regime in water regardless of ionic strength.
Applied to a 25-material panel, the screened figure of merit shows essentially no rank correlation with $d_{33}$ (Spearman $\rho = -0.10$ for 1 µm particles in dye solution), while the unscreened $g_h$ ranking survives only for small particles in deionised water. Applied to lead-free BNT-based ceramics, the analysis shows that acceptor hardening, which raises the mechanical quality factor, can reduce $g_h$ several-fold, so piezocatalysis and resonant sensing applications may favour opposite compositions.
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