Critical piezoelectricity in percolation

Abstract

The problem of the critical behavior of piezoelectricity in percolating media is introduced for the first time. Its relevance stems from the fact that piezoelectricity associates mechanical and electrical properties whose separated critical behavior have been extensively discussed in the literature. It should also yield useful information on the deformation modes of the structures. This problem is suggested by the recent development of low-density, compliant flexible piezoelectric ceramics used as acoustic transducers. The physical properties of these systems are just beginning to be explored experimentally, and their modelization is an open problem. The limiting case of strong heterogeneousness, where percolation ideas may apply and lead to simple and universal predictions, is addressed. The simplicity of the analysis comes from the clear separation of three scales, the microscopic grain size R, the percolation σ which diverges as the percolation threshold is approached, and the macroscopic size L of the system (R ≪ ξ ≪ L). The main result is that the direct piezoelectric effect exhibits a critical divergence as more and more tenuous compliant porous ceramics are considered.