%0 Journal Article
%K lead
%K thin films
%K polycrystals
%K Polarization
%K Epitaxial growth
%K piezoelectricity
%K Ferroelectric thin films
%K Microelectromechanical devices
%K Extrinsic effects
%K In-plane strains
%K Piezoelectric coefficients
%A J Ouyang
%A Ramamoorthy Ramesh
%A A.L Roytburd
%B Applied Physics Letters
%D 2005
%G eng
%P 1-3
%R 10.1063/1.1899252
%T Intrinsic effective piezoelectric coefficient e 31,f for ferroelectric thin films
%V 86
%X 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.