Effect of dynamic fluid compressibility and permeability on porous piezoelectric ceramics

The ac piezoelectric properties of porous ceramics in the presence of compressible viscous fluids filling the pores inside the ceramics are studied. Above the Biot frequency fB, the fluid decouples from the solid and does not significantly affect the piezoelectric properties. Our study which is both experimental and theoretical focuses on the frequency domain below the Biot frequency, in which the fluid is in principle strongly coupled to the solid matrix for oscillations parallel to solid–fluid boundaries. Two regimes are found: (1) For frequencies smaller than a cross-over frequency fc∼(β/η)L−2, where L is the thickness of the sample, β the fluid bulk modulus, and η its viscosity, the piezoelectric coefficients dij are close to those of the dense nonporous ceramics weighted by the filling factor (1−φ); (2) for frequencies larger than fc, the dij tend to those of the empty porous ceramics for fluid bulk modulus significantly smaller than that of the ceramics, as is the case in our experiments. These observations are explained in terms of a frequency-dependent penetration of the acoustic fluid pressure inside the porous ceramics as a result of the interplay between fluid compressibility and viscosity. The nature of the decoupling between solid and fluid at frequencies larger than fc but still smaller than fB is for motions, not parallel to their common boundaries (for which the Biot mechanism applies), but perpendicular to their common boundaries. This decoupling occurs due to the finite compressibility of the fluid and in details is controlled by the tube-cavity topological structure of the porous medium. The dependence of the hydrostatic piezoelectric coefficient dH=d33+d31+d32 as a function of frequency observed experimentally is compared to an effective medium theory for the piezoelectric properties coupled to a permeability model. The experimental dependence of the cross-over frequency fc on sample sizes and on the fluid viscosity are in good agreement with our theory. The study shows that it is thus possible to obtain the desirable property of a high piezoelectric coefficient dH, characteristic of light porous piezoelectric ceramics, and good mechanical properties under applied high hydrostatic pressure with the use of an internal fluid which allows the pressure to equilibrate without destroying the piezoelectric properties of the porous ceramics.