The determination of stresses in thin films; modelling elastic grain interaction

Abstract

X-ray diffraction is frequently employed for the analysis of mechanical stresses in polycrystalline specimens. To this end, suitable so-called diffraction elastic constants are needed for determining the components of the mechanical stress tensor from measured lattice strains. These diffraction elastic constants depend on the single-crystal elastic constants of the material considered and the so-called grain interaction, describing the distribution of stresses and strains over the crystallographically differently oriented crystallites composing the specimen. Well-known grain interaction models, as due to Voigt, to Reuss, to Neerfeld and Hill and to Eshelby and Kröner, may be applied to bulk specimens, but they are generally not suitable for thin films. In this paper, an average 'effective' grain interaction model is proposed that consists of a linear combination of basic extreme models including new models specially suited to thin films. Experimental verification has been achieved by X-ray diffraction strain measurements performed on a sputter-deposited copper film. This is the first time that anisotropic grain interaction has been analysed quantitatively.