Proposed Methods for Depth Profiling of Residual Stresses using Grazing Incidence X-Ray Diffraction (GIXD)

Abstract

AbstractTwo proposed methods are described for obtaining the depth profiles (τ-profiles) of strains and stresses as a function of the 1/e penetration depth τ, using GIXD in the asymmetric geometry, without the need for layer removal. In the first, the ψ-method: ψ is varied, for a given reflection, while holding τ constant, by varying the wavelength λ and adjusting the incident angle α so as to maintain τ constant. This allows dϕ,ψ vs Sin2ψ plots to be obtained at constant τ. In the second, the ϕ-integral method: interplanar spacings dϕ,ψ are measured for ϕ values from 0 to 2π, at constant ψ and τ by holding α fixed. Two ψ values, i.e. two wavelengths, are needed to obtain the whole strain tensor, but if the sample is quasi-isotropic and the stress state is biaxial, only one wavelength is needed. A direct method is also described for obtaining the profiles as a function of depth z (z-profiles) from the corresponding τ-profiles using inverse Laplace transforms. Application of the method to the residual strain vs τ data of Doerner and Brennan for an Al film on Si is presented.