Theoretical investigation of the intrinsic piezoelectric properties for tetragonal BaTiO 3 epitaxial films

{The orientation dependences of the converse longitudinal piezoelectric constant d 33,f , and the in-plane converse piezoelectric constant e 31,f , are calculated for tetragonal barium titanate epitaxial films. The calculations demonstrate that both e 31,f and d 33,f have their maximum values along an axis close to the (1 1 1) direction of the pseudo-cubic system, which are similar to the orientation dependence results for a tetragonal BaTiO 3 single crystal. The calculated piezoelectric constants for a (1 1 1) oriented BaTiO 3 epitaxial film (e 31