Effect of dynamical fluid compressibility and permeability on porous piezoelectric ceramics

Abstract

For frequencies less than the Biot frequency, the ac piezoelectric properties of porous ceramics are studied in the presence of slightly compressive viscous fluids filling the pores inside the ceramics. Two regimes are found: (1) for f smaller than a cross-over frequency fc∼(β/η)L−2, where L is the thickness of the sample and β the fluid compressibility coefficient, the piezoelectric coefficients dij are close to that of the dense nonporous ceramics weighted by the filling factor (1−φ); for f≳fc, the dij are those of the empty porous ceramics as if the fluid was not present. These observations are explained in terms of a frequency-dependent penetration of the fluid pressure inside the porous ceramics as a result on the interplay between fluid compressibility and viscosity. The dependence of the hydrostatic piezoelectric coupling 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 excellent agreement with this theory. The study shows that it is thus possible to obtain the desirable property of a high hydrostatic piezoelectric coefficient dH, characteristic of light porous piezoelectric ceramics, and good mechanical properties under high applied pressure with the use of an internal fluid that allows one to equilibriate the pressure without destroying the piezoelectric properties of the porous ceramics.