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. 3.1, p. 224

Section 3.1.1. Introduction

J. P. Cline,a* M. H. Mendenhall,a D. Black,a D. Windovera and A. Heninsa

aNational Institute of Standards and Technology, Gaithersburg, Maryland, USA
Correspondence e-mail:

3.1.1. Introduction

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The laboratory X-ray powder diffractometer has several virtues that have made it a principal characterization device for providing critical data for a range of technical disciplines involving crystalline materials. The specimen is typically composed of small crystallites (5–30 µm), which is a form that is suitable for a wide variety of materials. A continuous set of reflections can be collected with a single scan in θ–2θ angle space. Not only can timely qualitative analyses be carried out, but with the more advanced data-analysis methods a wealth of quantitative information may be extracted. Modern commercial instruments may include features that include focusing mirror optics and the ability to change quickly between various experimental configurations. In this chapter, we discuss results from a NIST-built diffractometer with features specific to the collection of data that complement the NIST effort in standard reference materials (SRMs) for powder diffraction. While this machine can be configured with focusing optics, here we consider only those configurations that use a divergent beam in Bragg–Brentano, para-focusing geometry.

A principal advantage of the divergent-beam X-ray powder diffractometer is that a relatively large number of crystallites are illuminated, providing a strong diffraction signal from a representative portion of the sample. However, the para-focusing optics of laboratory diffractometers produce patterns that display profiles of a very complex shape. The observed 2θ position of maximum diffraction intensity does not necessarily reflect the true spacing of the lattice planes (hkl). While advanced data-analysis methods can be used to model the various aberrations and account for the observed profile shape and position, there are a number of instrumental effects for which there is not enough information for reliable, a priori modelling of the performance of the instrument. The task may be further compounded when instruments are set up incorrectly, because the resultant additional errors are convoluted into the already complex set of aberrations. Therefore, the results are often confounding, as the origin of the difficulty is problematic to discern. The preferred method for avoiding these situations is the use of SRMs to calibrate the instrument performance. We will describe the various methods with which NIST SRMs may be used to determine sources of measurement error, as well as the procedures that can be used to properly calibrate the laboratory X-ray powder diffraction (XRPD) instrument.

The software discussed throughout this manuscript will include commercial as well as public-domain programs, some of which were used for the certification of NIST SRMs. In addition to the NIST disclaimer concerning the use of commercially available resources,1 we emphasize that some of the software presented here was also developed to a certain extent through longstanding collaborative relationships between the first author and the respective developers of the codes. The codes that will be discussed include: GSAS (Larson & Von Dreele, 2004[link]), the PANalytical software HighScore Plus (Degen et al., 2014[link]), the Bruker codes TOPAS (version 4.2) (Bruker AXS, 2014[link]) and DIFFRAC.EVA (version 3), and the Rigaku code PDXL 2 (version 2.2) (Rigaku, 2014[link]). The fundamental-parameters approach (FPA; Cheary & Coelho, 1992[link]) for modelling X-ray powder diffraction line profiles, as implemented in TOPAS, has been used since the late 1990s for the certification of NIST SRMs. To examine the efficacy of the FPA models, as well as their implementation in TOPAS, we have developed a Python-based code, the NIST Fundamental Parameters Approach Python Code (FPAPC), that replicates the FPA method in the computation of X-ray powder diffraction line profiles (Mendenhall et al., 2015[link]). This FPA capability is to be incorporated into GSASII (Toby & Von Dreele, 2013[link]).


Bruker AXS (2014). TOPAS Software. .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
Degen, T., Sadki, M., Bron, E., König, U. & Nénert, G. (2014). Powder Diffr. 29, S13–S18.Google Scholar
Larson, A. C. & Von Dreele, R. B. (2004). General Structure Analysis System (GSAS). Tech. Rep. Los Alamos National Laboratory, New Mexico, USA.Google Scholar
Mendenhall, M. H., Mullen, K. & Cline, J. (2015). J. Res. NIST, 120, 223–251.Google Scholar
Rigaku (2014). PDXL 2, Rigaku powder diffraction data analysis software version 2.2. Rigaku Corporation, Tokyo, Japan.Google Scholar
Toby, B. H. & Von Dreele, R. B. (2013). GSAS-II: the genesis of a modern open-source all purpose crystallography software package. J. Appl. Cryst. 46, 544–549.Google Scholar

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