Weighted mechanical models for residual stress determination using x-ray diffraction

Determining the mechanical response of thin films by diffraction-based methods requires appropriate elastic models. Weighting factors associated with the linear combination of Reuss and Voigt x-ray elastic constants are compared to the experimental values determined through linear, least-squares regression of diffraction data collected from multiple reflections of several materials. It is found that the optimal weighting factors, x*, determined by the experimental data of Cu, Ni, and Ti thin films vary significantly from those calculated under the Kröner and Neerfeld limits. The discrepancies may be due to plastic effects on the mechanical models that assume linear elastic behavior. The corresponding residual stress values under these limits exhibit a closer correspondence, where the relative variation among the mechanical models scales with the elastic anisotropy of the material. © 2013 AIP Publishing LLC.