X-ray diffraction stress analysis of ferroelectric thin films with ideal (h k l) textures considering the piezoelectric coupling effect

Ferroelectric thin films present large residual stress and strong texture during preparation, which affect the mechanical, dielectric and piezoelectric properties of the thin films. The determination of residual stresses in ferroelectric thin films with different textures is therefore very important. In this paper, an extended crystallite group model to evaluate the residual stresses of ferroelectric thin films using X-ray diffraction is proposed by considering the constitutive equation of orthogonally anisotropic ferroelectric medium. The effects of anisotropy and piezoelectric coupling on residual stresses of ferroelectric thin films are analyzed. X-ray stress factors for ideal (h k l)-textured ferroelectric thin films are obtained. An example of calculating the residual stresses of tetragonal perovskite ferroelectric thin films with (1 1 1) and (1 0 0) textures using the extended model is provided to validate the model.