Tables for
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, p. 123

Section Transformation from detector space to reciprocal space

B. B. Hea*

aBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA
Correspondence e-mail: Transformation from detector space to reciprocal space

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Reciprocal-space mapping is commonly used to analyse the diffraction patterns from highly oriented structures, diffuse scattering from crystal defects, and thin films (Hanna & Windle, 1995[link]; Mudie et al., 2004[link]; Smilgies & Blasini, 2007[link]; Schmidbauer et al., 2008[link]). The equations of the unit-vector calculation given above can also be used to transform the diffraction intensity from the diffraction space to the reciprocal space with respect to the sample coordinates. The direction of the scattering vector is given by the unit vector hs{h1, h2, h3} and the magnitude of the scattering vector is given by [2\sin \theta /\lambda ], so that the scattering vector corresponding to a pixel is given by[{\bf{H}} = {{2\sin \theta } \over \lambda }{{\bf{h}}_{{s}}}.\eqno(2.5.13)]The three-dimensional reciprocal-space mapping can be obtained by applying the normalized pixel intensities to the corresponding reciprocal points. With various sample orientations, all pixels on the detector can be mapped into a 3D reciprocal space.


Hanna, S. & Windle, A. H. (1995). A novel polymer fibre diffractometer, based on a scanning X-ray-sensitive charge-coupled device. J. Appl. Cryst. 28, 673–689.Google Scholar
Mudie, S. T., Pavlov, K. M., Morgan, M. J., Hester, J. R., Tabuchi, M. & Takeda, Y. (2004). Collection of reciprocal space maps using imaging plates at the Australian National Beamline Facility at the Photon Factory. J. Synchrotron Rad. 11, 406–413.Google Scholar
Schmidbauer, M., Schäfer, P., Besedin, S., Grigoriev, D., Köhler, R. & Hanke, M. (2008). A novel multi-detection technique for three-dimensional reciprocal-space mapping in grazing-incidence X-ray diffraction. J. Synchrotron Rad. 15, 549–557.Google Scholar
Smilgies, D.-M. & Blasini, D. R. (2007). Indexation scheme for oriented molecular thin films studied with grazing-incidence reciprocal-space mapping. J. Appl. Cryst. 40, 716–718.Google Scholar

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