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. 123
Section 2.5.2.4.2. Transformation from diffraction space to sample space^{a}Bruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA |
The transformation of the unit diffraction vector from the laboratory coordinates X_{L}, Y_{L}, Z_{L} to the sample coordinates S_{1}, S_{2}, S_{3} is given bywhere A is the transformation matrix. For Eulerian geometry in matrix form, we haveIn expanded form:In addition to the diffraction intensity and Bragg angle corresponding to each data point on the diffraction ring, the unit vector h_{s}{h_{1}, h_{2}, h_{3}} provides orientation information in the sample space. The transformation matrix of any other goniometer geometry, such as kappa geometry (Paciorek et al., 1999), can be introduced into equation (2.5.10) so that the unit vector h_{s}{h_{1}, h_{2}, h_{3}} can be expressed in terms of the specified geometry. All equations using the unit vector h_{s}{h_{1}, h_{2}, h_{3}} in this chapter, such as in data treatment, texture analysis and stress measurement, are applicable to all goniometer geometries provided that the unit-vector components are generated from the corresponding transformation matrix from diffraction space to the sample space.
References
Paciorek, W. A., Meyer, M. & Chapuis, G. (1999). On the geometry of a modern imaging diffractometer. Acta Cryst. A55, 543–557.Google Scholar