Diffraction stress analysis of thin films: Modeling and experimental evaluation of elastic constants and grain interaction

Abstract

Well-known grain interaction models for the description of macroscopic elastic behavior of polycrystalline specimens, as due to Voigt, Reuss, Neerfeld–Hill, and Eshelby–Kröner, may be successfully applied to bulk specimens, but are shown to be less suited for thin films. An elaboration of a proposal due to Vook and Witt for grain interaction is given. It is assumed that the strain parallel to the specimen surface is equal in all crystallites and that the stress perpendicular to the specimen surface is zero in all crystallites. It is shown that these assumptions give rise to elastic anisotropy of the specimen on the macroscopic scale. It is also shown that in this case the dependence of the measured lattice strain (in a diffraction experiment) on the squared sine of the specimen tilt angle ψ (cf. the sin2 ψ method), is nonlinear, contrary to what is predicted by the bulk grain interaction models. This is the first time that nonlinear sin2 ψ plots have been calculated using an elastic grain interaction model, in the absence of crystallographic texture. Experimental verification has been achieved by x-ray diffraction strain measurements performed on a vapor deposited nickel film. The experimental results are in good accordance with the Vook–Witt [J. Appl. Phys. 7, 2169 (1965)] grain interaction model. This is the first experimental evidence of direction dependent grain interaction in thin films.