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In this work, the stress gradient in mechanically polished tungsten sample was studied using X-ray diffraction methods. To determine in-depth stress evolution in the very shallow subsurface region (up to 10 μm), special methods based on reflection geometry were applied. The subsurface stresses (depth up to 1 μm) were measured using the multiple-reflection grazing incidence X-ray diffraction method with classical characteristic X-rays, while the deeper volumes (depth up to 10 μm) were investigated using energy-dispersive diffraction with white high energy synchrotron beam. Both complementary methods allowed for determining in-depth stress profile and the evolution of stress-free lattice parameter. It was confirmed that the crystals of tungsten are elastically isotropic, which simplifies the stress analysis and makes tungsten a suitable material for testing stress measurement methods. Furthermore, it was found that an important compressive stress of about − 1000 MPa was generated on the surface of the mechanically polished sample, and this stress decreases to zero value at the depth of about 9 μm. On the other hand, the strain-free lattice parameter does not change significantly in the examined subsurface region.

The multireflection grazing-incidence X-ray diffraction method is used to test surface stresses at depths of several micrometres in the case of metal samples. This work presents new ways of analysing experimental data obtained by this method for Ni samples exhibiting significant elastic anisotropy of crystals. Three different methods of determining biaxial stresses and lattice parameter were compared. In the first approach, the calculations were performed using the linear least-squares method, and then two simplified procedures based on simple linear regression (weighted and non-weighted) were applied. It was found that all the tested methods give similar results, i.e. almost equal values of the determined stresses and lattice parameters and the uncertainties of their determination. The advantage of analyses based on simple linear regression is their simplicity and straightforward interpretation, enabling easy verification of the influence of the crystallographic texture and the presence of shear stresses, as well as graphical determination of the stress-free lattice parameter.

Multireflection grazing-incidence X-ray diffraction was used to investigate the structure and residual stress gradients in the near-surface region of mechanically treated titanium samples. The development of this method by using a white synchrotron beam during an energy dispersive diffraction experiment is proposed., The main focus of the presented work was the investigation of structure and residual stress gradients in the near-surface region of materials studied by X-ray diffraction. The multireflection method was used to measure depth-dependent stress variation in near-surface layers of a Ti sample (grade 2) subjected to different mechanical treatments. First, the multireflection grazing incidence diffraction method was applied on a classical diffractometer with Cu Kα radiation. The applicability of the method was then extended by using a white synchrotron beam during an energy dispersive (ED) diffraction experiment. An advantage of this method was the possibility of using not only more than one reflection but also different wavelengths of radiation. This approach was successfully applied to analysis of data obtained in the ED experiment. There was good agreement between the measurements performed using synchrotron radiation and those with Cu Kα radiation on the classical diffractometer. A great advantage of high-energy synchrotron radiation was the possibility to measure stresses as well as the a 0 parameter and c 0/a 0 ratio for much larger depths in comparison with laboratory X-rays.