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. 3.6, p. 291

Section Instrument

M. Leonia*

aDepartment of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano 77, 38123 Trento, Italy
Correspondence e-mail: Instrument

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Each of the components of the diffraction instrument (i.e. source, optics, specimen stage, measurement geometry and detector) can have a dramatic impact both on the position and the broadening of the peaks. Axial divergence, for instance, introduces both an asymmetric broadening and an apparent shift of the low-angle peaks. When microstructure (i.e. specimen-related effects) is the focus of the analysis, the primary recommendation is to try to limit the instrumental influence. Alternatively, it is preferred to have an instrumental profile (no matter how complex) that can be well described and properly simulated: for instance the profile of an instrument with a Kα1 primary monochromator (apparently advantageous) might be hard to model if the Kα2 removal is not perfect. This becomes more and more important when the instrumental effects are of the same order of magnitude as the specimen-related broadening.

Two possible paths can be followed when dealing with the instrumental contribution: modelling using the fundamental parameters approach (see, for example, Cheary & Coelho, 1992[link]; Kern & Coelho, 1998[link]) or parameterization of the pattern of an ideal specimen. In the fundamental parameters approach, the geometry of the instrument and the effects of each optical component on the peak profile are described mathematically in 2θ. Most of the formulae for the various optical elements can be found, for example, in the work of Wilson (1963[link]), Klug & Alexander (1974[link]) and Cheary & Coelho (1992[link], 1994[link], 1998a[link],b[link]). The aberration profiles are folded into the (X-ray) source emission profile (Hölzer et al., 1997[link]; Deutsch et al., 2004[link]) to generate a combined instrumental profile.

When no information on the instrument is available, it is possible to predict the instrumental profile just by using the nominal data for the optical components. It is however advised, whenever possible, to tune the instrumental parameters using the pattern of a line-profile standard [e.g. NIST LaB6 SRM 660(x) series; Cline et al., 2010[link]] showing negligible specimen effects. These instrument-only parameters must then be kept fixed for any subsequent microstructure refinement. It is of paramount importance that all instrumental features are well reproduced when dealing with microstructure effects. Provided that this condition is met, we can therefore employ any arbitrary function to describe the instrumental profile. Thus, as an alternative to FPA, we can either `learn' the instrumental profile from a standard (Bergmann & Kleeberg, 2001[link]) or use a Voigtian to model it. The Voigtian is particularly convenient as it can be defined directly in L space and thus directly enter the Fourier product of equation (3.6.13)[link].


Bergmann, J. & Kleeberg, R. (2001). Fundamental parameters versus learnt profiles using the Rietveld program BGMN. Mater. Sci. Forum, 378–381, 30–37.Google Scholar
Cheary, R. W. & Coelho, A. (1992). A fundamental parameters approach to X-ray line-profile fitting. J. Appl. Cryst. 25, 109–121.Google Scholar
Cheary, R. W. & Coelho, A. (1994). Synthesizing and fitting linear position-sensitive detector step-scanned line profiles. J. Appl. Cryst. 27, 673–681.Google Scholar
Cheary, R. W. & Coelho, A. A. (1998a). Axial divergence in a conventional X-ray powder diffractometer. I. Theoretical foundations. J. Appl. Cryst. 31, 851–861.Google Scholar
Cheary, R. W. & Coelho, A. A. (1998b). Axial divergence in a conventional X-ray powder diffractometer. II. Realization and evaluation in a fundamental-parameter profile fitting procedure. J. Appl. Cryst. 31, 862–868.Google Scholar
Cline, J. P., Black, D., Windover, D. & Henins, A. (2010). SRM 660b – Line Position and Line Shape Standard for Powder Diffraction. .Google Scholar
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Hölzer, G., Fritsch, M., Deutsch, M., Härtwig, J. & Förster, E. (1997). 1,2 and Kβ1,3 X-ray emission lines of the 3d transition metals. Phys. Rev. A, 56, 4554–4568.Google Scholar
Kern, A. A. & Coelho, A. A. (1998). A new fundamental parameters approach in profile analysis of powder data. New Delhi: Allied Publishers.Google Scholar
Klug, H. P. & Alexander, L. E. (1974). X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials, 2nd ed. New York: Wiley.Google Scholar
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