The effect of sample displacement on x-ray diffraction results in Bragg-Brentano geometry

Experimental Analysis of Vertical Sample Shift in Bragg-Brentano Geometry

Karol Tyc

a:1:{s:5:"en_US";s:62:"University of Warmia and Mazury, Faculty of Technical Sciences";}


Abstract

The aim of the study was to investigate the effect of vertical displacement of the sample on the results of X-ray diffraction (XRD) in Bragg-Brentano geometry. Measurements were performed on an S275JR steel sample using a Phaser D2 diffractometer (Cu Kα, λ = 1.541874 [Å]) with a step size of 2θ = 0.01°. The shifts in the positions of the 2θ peaks and half-widths (FWHM) were analyzed. A comparison between the theoretical model and experimental peak shifts has been calculated. The lattice constant was determined using the Nelson-Riley method, the crystallite size using the Scherrer method, and the parameters using the Williamson-Hall method. A vertical displacement of 1 mm produced an approximately 0.8° shift of the (110) peak. Based on the diffraction data, the lattice parameter was determined using the Nelson-Riley extrapolation method (2.8643-2.8678 [Å]), the crystallite size was evaluated using the Scherrer method (110-260 [Å], with the largest value for the (110) peak), and lattice distortions were assessed using the Williamson–Hall approach (approx. 0.26-0.30[%]). The results highlight the significance of precise sample positioning, as even a small displacement can lead to noticeable errors in peak locations and consequently in the derived structural parameters.


Keywords:

X-ray diffraction (XRD), Bragg-Brentano geometry, sample displacement, XRD geometric errors


ASTM E975-13. 2013. Standard Practice for X-Ray Determination of Retained Austenite in Steel with Near Random Crystallographic Orientation. ASTM International, West Conshohocken, PA.   Google Scholar

Cline J.P., Mendenhall M.H., Black D., Windover D., Henins A. 2015. The Optics and Alignment of the Divergent Beam Laboratory X-ray Powder Diffractometer and its Calibration Using NIST Standard Reference Materials. Journal of Research of the National Institute of Standards and Technology, 120: 1-27.   Google Scholar

Cullity B.D., Stock S.R. 2014. Elements of X-Ray Diffraction, Pearson.   Google Scholar

EN 10025-2. 2019. Hot Rolled Products of Structural Steels – Part 2: Technical Delivery Conditions for Non-Alloy Structural Steels, European Committee for Standardization (CEN), Brussels.   Google Scholar

Fultz B., Howe J.M. 2013. Transmission Electron Microscopy and Diffractometry of Materials. Springer.   Google Scholar

Harrington G.F., Santiso J. 2021. Back to Basics Tutorial: X-ray Diffraction of Thin Films. Journal of Electroceramics, 47: 141-163.   Google Scholar

Kriegner D., Matej Z., Kuzel R., Holý V. 2015. Powder Diffraction in Bragg-Brentano Geometry with Straight Linear Detectors. Journal of Applied Crystallography, 48: 613-618.   Google Scholar

Lipson H. 2001. The Study of Metals and Alloys by X-Ray Powder Diffraction Methods. University College Cardiff Press.   Google Scholar

Nelson J.B., Riley D.P. 1944. An Experimental Investigation of Extrapolation Methods in the Derivation of Accurate Unit-Cell Dimensions of Crystals. Proceedings of the Physical Society, 57: 3-14.   Google Scholar

Nwaokafor P., Okeoma K.B., Echendu O.K. 2021. X-ray Diffraction Analysis of a Class of AlMgCu Alloy Using Williamson–Hall and Scherrer Methods. Metallography, Microstructure, and Analysis, 10: 727-735.   Google Scholar

Pelleg J., Elish E., Mogilyanski D. 2005. Evaluation of Average Domain Size and Microstrain in a Silicide Film by the Williamson–Hall Method. Metallurgical and Materials Transactions A, 36: 3187-3194.   Google Scholar

Scherrer P. 1918. Bestimmung der Größe und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse, 98-100.   Google Scholar

Weidenthaler C. 2011. Pitfalls in the Characterization of Nanoporous and Nanosized Materials. Nanoscale, 3: 792-810.   Google Scholar

Williamson G.K., Hall W.H. 1953. X-ray Line Broadening from Filed Aluminium and Wolfram. Acta Metallurgica, 1: 22-31.   Google Scholar

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Published
2025-12-04

Cited by

Karol Tyc. (2025). The effect of sample displacement on x-ray diffraction results in Bragg-Brentano geometry: Experimental Analysis of Vertical Sample Shift in Bragg-Brentano Geometry. Technical Sciences, 28(28), 265–279. https://doi.org/10.31648/ts.11953

Karol Tyc 
a:1:{s:5:"en_US";s:62:"University of Warmia and Mazury, Faculty of Technical Sciences";}



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