Critical piezoelectricity in percolation

2014 We study the behaviour of piezoelectricity in highly heterogeneous media. The piezoelectric effect introduces a coupling between electrical and mechanical properties, which have separately different scaling behaviours. Its study therefore constitutes a priori an interesting question. This problem is also suggested by the recent development of low-density, porous piezoelectric ceramics which are used, for example, as acoustic transducers. We consider a piezoelectric medium of dielectric constant 03B5r plunged into a medium of dielectric constant unity or close to unity and large or infinite compliance. Two interesting cases are examined : a) 03B5r ~ 1 and b) 03B5r ~ 1. In both cases, we find that the spatial average of the piezoelectric coefficient is non-critical even if the mechanical (in cases a) and b)) or electrical behaviours (in case a)) do exhibit their usual critical behaviours near the percolation threshold. However, we predict the existence of critical fluctuations of the polarization of the piezoelectric backbone. Furthermore, J. Phys. France 50 (1989) 2201-2216 15 AOÛT 1989, Classification Physics Abstracts 05.70J 77.60