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. 3.3, pp. 264-265
Section 3.3.2.3. Peak-displacement effects^{a}Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439–4814, USA |
The position of the peak is also affected by various instrumental and geometric effects. For example, the sample position in a Bragg–Brentano experiment is ideally tangent to the focusing circle (Parrish, 1992). A radial displacement, s, of the sample will shift the Bragg peaks according towhere R is the goniometer radius. This is the major peak-displacement effect and can be detected for sample displacements as small as 10 µm.
A similar effect can be observed for Debye–Scherrer instrumentation when the goniometer axis is not coincident with the sample axis; this is a more common problem for neutron powder diffraction instruments where accurate placement of very massive goniometers can be difficult. In this case the peak displacement iswhere s_{x} and s_{y} are displacements perpendicular and parallel to the incident beam, respectively, all in the diffraction plane.
In high-resolution instrumentation (even at a synchrotron) goniometer axis displacements less than 10 µm can be detected.
Specimen transparency in Bragg–Brentano diffraction can also cause peak displacements arising from the shift in effective sample position to below the surface at high scattering angles. This shift for a thick specimen iswhere μ_{eff} is the effective sample absorption coefficient taking into account the packing density.
References
Parrish, W. (1992). Powder and related techniques: X-ray techniques. In International Tables for Crystallography, Vol. C, edited by A. J. C. Wilson, ch. 2.3. Dordrecht: Kluwer.Google Scholar