International
Tables for Crystallography Volume H Powder diffraction Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk © International Union of Crystallography 2018 |
International Tables for Crystallography (2018). Vol. H, ch. 2.5, p. 143
Section 2.5.4.3.4. Data-collection strategy^{a}Bruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA |
The practice of stress analysis with 2D-XRD involves the selection of the diffraction-system configuration and the data-collection strategy, frame correction and integration, and stress calculation from the processed data points. Most concepts and strategies developed for a conventional diffractometer are still valid for 2D-XRD. We will focus on the new concepts and practices due to the nature of the 2D detectors.
The diffraction vector is in the normal direction to the measured crystalline planes. It is not always possible to have the diffraction vector in the desired measurement direction. In reflection mode, it is easy to have the diffraction vector normal to the sample surface, or tilted away from the normal, but impossible to have the vector on the surface plane. The stress on the surface plane, or biaxial stress, is calculated by elasticity theory from the measured strain in other directions. The final stress-measurement results can be considered as an extrapolation from the measured values. In the conventional sin^{2} ψ method, several ψ-tilt angles are required, typically at 15° steps from −45° to +45°. The same is true with a 2D-XRD system. The diffraction vectors corresponding to the data scan can be projected onto a 2D plot in the same way as the pole-density distribution in a pole figure. The 2D plot is called a data-collection strategy scheme.
By evaluating the scheme, one can generate a data-collection strategy suitable for the measurement of the intended stress components. Fig. 2.5.25 illustrates two schemes for data collection. In the bisecting condition ( or and ), the trace of the diffraction vector falls in the vicinity of the scheme centre. Either an ω tilt or a ψ tilt can move the vectors away from the centre. The circles on the scheme are labelled with the tilt angle of 15°, 30° and 45°. Scheme (a) is for an ω tilt of 0°, ±15°, ±30° and ±45° with the ϕ angle at 0° and 90°. It is obvious that this set of data would be suitable for calculating the biaxial-stress tensor. The data set with , as shown within the box enclosed by the dashed lines, would be sufficient on its own to calculate . Since the diffraction-ring distortion at or is not sensitive to the stress component , strategy (a) is suitable for the equibiaxial stress state, but is not able to determine accurately. In scheme (b), the ψ scan covers 0° to 45° with 15° steps at eight ϕ angles with 45° intervals. This scheme produces comprehensive coverage on the scheme chart in a symmetric distribution. The data set collected with this strategy can be used to calculate the complete biaxial-stress tensor components and shear stress (). The scheme indicated by the boxes enclosed by the dashed lines is a time-saving alternative to scheme (b). The rings on two ϕ angles are aligned to S_{1} and S_{2} and the rings on the third ϕ angle make 135° angles to the other two arrays of rings. This is analogous to the configuration of a stress-gauge rosette. The three ϕ angles can also be separated equally by 120° steps. Suitable schemes for a particular experiment should be determined by considering the stress components of interest, the goniometer, the sample size, the detector size and resolution, the desired measurement accuracy and the data-collection time.