Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction

Welzel, U.; Ligot, J.; Lamparter, P.; Vermeulen, A.C.; Mittemeijer, E.J.

doi:10.1107/S0021889804029516

Figure 9
Stress analysis employing the g( [psi]

, hkl) method: calculated example. Lattice strain for the 111, 200, 220, 311, 222, 400, 321 and 420 reflections of a macroscopically elastically isotropic copper specimen subjected to the mechanical stress state with $[\langle \sigma _{11}^{\rm S}\rangle]$ = 100 MPa, $[\langle \sigma _{22}^{\rm S} \rangle]$ = 150 MPa and $[\langle \sigma _{12}^{\rm S} \rangle]$ = $[\langle \sigma _{21}^{\rm S} \rangle]$ = 20 MPa (all other components equal to zero): (a) `classical' plot of $[\varepsilon _{0^\circ \psi }^{hkl}]$ versus sin² [psi]

and (b) plot of $[\varepsilon _{0^\circ \psi }^{hkl} /S_1^{hkl}]$ versus g( [psi]

, hkl). Tilt angles for the individual reflections as shown in (a) would be obtained if a measurement is conducted as a 2 [theta]

scan at a fixed small incidence angle (cf. §3

). For details, see text.