Modified crystallite group method for residual stress analysis of highly textured Cu/Mo nanomultilayers

Residual stress analysis in thin films and nanomultilayers (NMLs) is essential for understanding their mechanical, thermal and functional properties. However, accurate strain measurements in highly textured multilayers obtained by physical vapor deposition techniques can be experimentally challenging, particularly when strong epitaxial relationships and twinning are present. In this paper, texture and residual stresses were investigated for a representative NML system composed of immiscible face-centered cubic (fcc)/body-centered cubic (bcc) elemental layers, namely Cu/Mo NMLs grown on a sapphire (0001) substrate. The experimentally investigated Cu/Mo NML system exhibits a specific fcc Cu {111}||bcc Mo {110}||sapphire (0001) in-plane and out-of-plane texture with growth twinning of Cu and a Nishiyama-Wasserman orientation relationship between Cu and Mo. This combination results in an effective sixfold rotational symmetry in the pole figures. The presence of twinning significantly complicates residual stress determination, as the selection of inappropriate diffraction planes can lead to erroneous results and the failure of standard approaches like the crystallite group method. To address this issue, we have established a theoretical framework and practical methodology to select suitable diffraction planes for the reliable determination of residual stresses in fcc/bcc NMLs with strong in-plane and out-of-plane textures, including the presence of twinning, using X-ray diffraction. The experimental X-ray-diffraction-based analysis is complemented by high-resolution scanning transmission electron microscopy and orientation mapping, providing a comprehensive understanding of the microstructure and crystallographic texture. The presented method can be applied to other multilayer systems and extended to other orientation relationships.