Investigation of precision, accuracy and confidence of X‐ray diffraction for determining crystallite size in nanopowders

• Published in: Journal of applied crystallography Vol. 54; no. 3; pp. 856 - 866
• Main Authors: Moore, Alexander P., Nemer, Martin B., Rodriguez, Mark A., Roberts, Christine C., Fleig, Patrick F., Papenguth, Hans W.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01-06-2021; Blackwell Publishing Ltd
• Subjects: Accuracy; Bayesian analysis; confidence; Crystallites; Crystals; Investigations; Magnesium; Magnesium oxide; mathematical methods; Methods; Micrography; Nanocrystals; Photomicrographs; precision; Scanning electron microscopy; Size determination; Statistical inference; Statistical methods; Superconductors (materials); Thermal energy; X-ray diffraction
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576721002922

X‐ray diffraction (XRD) is often utilized as a method of determining bulk sample crystallite size in powder characterization. While it is generally accepted that XRD peak broadening allows for qualitative crystallite size comparisons, its use for quantitative information is still debated. This study investigates the quantitative capability of XRD for determining the crystallite sizes of magnesium oxide nanocrystals by examining the precision, accuracy and uncertainty using the whole pattern (WP) weighted least‐squares and Williamson–Hall (WH) methods. The precision of the methods was investigated by re‐preparing, re‐running and re‐analysing identical samples. Both methods were found to be precise within 2 nm. The accuracy of the methods was investigated by comparing them against independent crystallite size analyses using visual particle identification from scanning electron microscopy micrographs and from indirect calculations using Brunauer–Emmett–Teller (BET) adsorption‐determined surface areas. The WP method was found to be more accurate than the WH method, which consistently underpredicted the crystallite size. Finally, the confidence of the methods was investigated using a Bayesian inference statistical inversion method. The WP method was found to have a narrower confidence distribution in its crystallite size determination than the WH method. The broad WH confidence indicates that reliable quantitative single‐measurement crystallite size determinations are not feasible using the WH technique. However, the WP method demonstrated precision, accuracy and confidence, allowing quantitative crystallite size determinations to be made.
An investigation of the precision, accuracy and confidence of the whole pattern (WP) and Williamson–Hall (WH) methods of crystallite size determination has given insight into the long‐standing debate on the quantitative capability of X‐ray diffraction for estimating crystallite size. The WP method demonstrated precision, accuracy and confidence, allowing quantitative crystallite size determinations to be made. The WH method demonstrated precision in its crystallite size determination, but it was also found to be less accurate, resulting in consistently low values, with a broad confidence from an ill‐posed inverse problem.