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. 3.3, pp. 264-265

Section 3.3.2.3. Peak-displacement effects

R. B. Von Dreelea*

aAdvanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439–4814, USA
Correspondence e-mail: vondreele@anl.gov

3.3.2.3. Peak-displacement effects

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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[link]). A radial displacement, s, of the sample will shift the Bragg peaks according to[\Delta 2\theta =360s\cos\theta /\pi R,\eqno(3.3.13)]where 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 is[\Delta 2\theta ={{180}\over{\pi R}}({s}_{x}\cos2\theta +{s}_{y}\sin2\theta ),\eqno(3.3.14)]where sx and sy 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 is[\Delta 2\theta =90\sin2\theta /{\mu }_{\rm eff}\pi R,\eqno(3.3.15)]where μeff 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








































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