Anisotropic elasticity in a textured cubic film plane

In textured films, the elastic properties are not isotropic but depend on a specific direction in question. Four expressions of Young's modulus E, Poisson's ratio υ, the biaxial elastic modulus M and Rigidity modulus G along an arbitrary direction M1 in the film plane are given directly in terms of the Miller indices of the plane (h k l) for cubic structure materials. These planar elastic anisotropies depend not only on the orientation of the plane but also on the value of the compliance anisotropy factor s0=s11–s12–1/2s44. Practical calculations show that only in the (1 1 1)-textured film, the elastic properties are planar isotropic due to the (1 1 1) plane having the highest six-fold rotation symmetry. For a (1 0 0)-textured film, neither Young's modulus E nor Poisson's ratio υ alone are isotropic, but the educed biaxial elastic modulus M=(E/1−υ) is isotropic.