Formalism for the evaluation of strongly non-linear surface stress fields by X-ray diffraction performed in the scattering vector mode

A formalism is proposed for the evaluation of residual stress fields in polycrystalline materials which vary significantly within the penetration depth τ of the X-rays. It is shown that the penetration depth may be varied independently of the angle Ψ by rotating the sample around the scattering vector gΨΨ which is parallel to the normal of the reflecting lattice planes Nh. Therefore, it becomes possible to separate individual components of the stress tensor from the fundamental equation of X-ray stress analysis and to evaluate the gradients σij(τ) without any assumption in form of an analytical expression to describe the depth profiles.