Residual stress in fiber-textured thin films of cubic materials

Abstract

The effect of fiber texture on the x-ray residual stress analysis in thin films of cubic materials is discussed according to different mechanical models. The x-ray elastic constants (XECs) were calculated from single-crystal elastic constants for Cu, cubic ZrO₂, and TiN, in the case of a typical [111] fiber texture with different spread of orientations [expressed by the half-width at half-maximum of the (111) pole figure]. Calculations were performed according to Reuss, Voigt, and Hill models, considering different crystallographic directions in cubic structures, in order to underline the effect of the mechanical anisotropy and fiber texture. The results clearly indicated the dependence of the XECs on the sample tilting angle, with the notable exception of [111] and [200], which were texture oscillation-free directions. Profiting from this condition the residual stress gradient in a fiber-textured TiN thin film deposited on stainless steel was determined by the simultaneous analysis of texture and residual strain for the (111) and (200) reflections. Advantages and limits of the procedure are discussed together with the experimental results.