International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.5, pp. 144-145

Section 2.5.4.3.7. Comparison between the 2D method and the con­ventional method

B. B. Hea*

aBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA
Correspondence e-mail: bob.he@bruker.com

2.5.4.3.7. Comparison between the 2D method and the con­ventional method

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Stress measurement on a polycrystalline material by X-ray diffraction is based on the strain measurements in a single or in several sample orientations. Each measured strain is calculated from the average d-spacing of specific lattice planes {hkl} over many crystallites (grains). A larger number of contributing crystallites gives better accuracy and sampling statistics (also referred to as particle statistics). The sampling statistics are determined by both the crystal structure and the instrumentation. The instrument window is mainly determined by the divergence of the incident X-ray beam. Lattice-plane families with high multiplicity will also effectively improve the sampling statistics. The number of contributing crystallites measured by a conventional diffractometer is limited by the sizes and divergences of the incident and diffracted beams to the point detector. In a two-dimensional diffraction system, more crystallites can contribute to the diffraction because of the larger γ range.

An example of a stress calculation is provided by the measurement of the residual stress on the end surface of a carbon steel roller. One of the seven frames taken with an ω scan is shown in Fig. 2.5.27[link](a). The (211) ring covering the γ range 67.5 to 112.5° was used for stress analysis. First, the frame data were integrated along γ with an interval of Δγ = 5°. A total of nine diffraction profiles were obtained from γ integration. The peak position 2θ for each γ angle was then obtained by fitting the profile with a Pearson-VII function. A total of 63 data points can be obtained from the seven frames. The data points at γ = 90° from seven frames, a typical data set for an ω diffractometer, were used to calculate the stress with the conventional [\sin ^2\psi ] method. In order to compare the gain from having increased data points with the 2D method, the stress was calculated from 3, 5, 7 and 9 data points on each frame. The results from the conventional [\sin ^2\psi ] method and the 2D method are compared in Fig. 2.5.27[link](b). The measured residual stress is compressive and the stress values from different methods agree very well. With the data taken from the same measurement (seven frames), the 2D method gives a lower standard error and the error decreases with increasing number of data points from the diffraction ring.

[Figure 2.5.27]

Figure 2.5.27 | top | pdf |

Stress calculation with the 2D method and the [\sin ^2\psi ] method: (a) nine data points (abbreviated as pts) on the diffraction ring; (b) measured stress and standard deviation by different methods.








































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