Intrinsic effective piezoelectric coefficient e 31,f for ferroelectric thin films

As a function of film orientation, the intrinsic effective piezoelectric coefficient e31,f is generally formulated for a substrate-constrained ferroelectric film. Numerical results are obtained for Pb (Zrx Ti1-x) O3 (PZT) thin films with tetragonal and rhombohedral compositions. It is illustrated that the optimal orientation for e31,f are close to [001] orientation in both tetragonal and rhombohedral PZT films and the maximum calculated e31,f is about -30 Cm2 on the rhombohedral side of the morphotropic phase boundary. © 2005 American Institute of Physics.