Re-evaluation of formulae for X-ray stress analysis in polycrystalline specimens with fibre texture: experimental confirmation

Abstract

Line splitting or line broadening of an X‐ray Bragg reflection owing to a three‐dimensional or biaxial load on a cubic polycrystalline specimen with 〈111〉 fibre texture has been predicted by Yokoyama & Harada [J. Appl. Cryst. (2009), 42, 185–191] if the specimen is in the symmetry of the Laue class mm. By using a TiN film specimen and a high‐precision four‐circle diffractometer with a laboratory X‐ray source, it is shown that the profile of the 420 reflection is substantially different with and without biaxial load and also depends on the measurement direction, while the profile of the 222 reflection does not change. These results are quantitatively in agreement with the theoretical prediction, although the theory is based on the Reuss model of elasticity.

Combined synchrotron X-ray and image-correlation analyses of biaxially deformed W/Cu nanocomposite thin films on Kapton

“…The crystallographic texture of W thin films allows for a simple and straightforward analysis of the mechanical properties. However, for elastically anisotropic polycrystalline films (Dong & Srolovitz, 1998;Martinschitz et al, 2009;Yokoyama et al, 2009;Faurie et al, 2010), micromechanical models taking account of the actual microstructure have to be used, due to the interaction of differently oriented grains. For instance, polycrystalline thin films with mixed crystallographic textures can be subjected to heterogeneous triaxial stress states arising from grain interactions that are crucial to the understanding of the mechanical behaviour of these films (Nix, 1989;Vinci, 2008;Vodnick et al, 2010).…”

Least-squares refinement of biaxial stress components and unit-cell parameter in a 〈111〉 textured cubic TiN polycrystalline thin film by X-ray diffraction

“…Line broadenings were detected in all observed diffraction peaks because of small particle sizes presented in the TiN film. The values of FWHM were more than two times wider than the value 0.094° for the (222) reflection and about four times larger along the direction of the (420) reflection (Yokoyama et al , 2009). All the profiles observed were symmetrical so that it was relatively straightforward to strip off the Cu K α 2 peaks.…”

“…In this study, a TiN thin film with a thickness of about 1 μm, which was obtained by sputtering TiN on a polyimide film of a 6 mm×40 mm surface with thickness of 125 μm, was used. This is the same specimen used in the previous XRD study (Yokoyama et al , 2009). The TiN film specimen was previously confirmed to be [111] preferred oriented along the direction normal to the film surface.…”

“…The diffractometer used in this study is the same four-circle diffractometer, a Rigaku ATX-E, used in the previous study by Yokoyama et al (2009), except with a modification of its incident beam optics. In this study a parabolic multilayer mirror, taking away the original Ge (220) channel-cut monochromator, was used to collimate the divergent X-rays from the Cu target into a quasi-parallel incident beam.…”

Stress-Strain Relationship and XRD Line Broadening in [0001] Textured Hexagonal Polycrystalline Materials

“…(2009), 14) the separation of two Bragg peaks, δ2θ (I) − δ2θ (II), is given in Eq. (7), where δ2θ (I) is the shift of diffraction angle owing to strain in the type I crystallites and δ2θ (II) is that for type II.…”