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.

中文翻译：

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用于确定纳米粉末微晶尺寸的 X 射线衍射精度、准确度和置信度的研究

X 射线衍射 (XRD) 通常用作在粉末表征中确定大块样品微晶尺寸的方法。虽然人们普遍认为 XRD 峰展宽允许定性微晶尺寸比较，但其用于定量信息的用途仍存在争议。本研究通过使用全模式 (WP) 加权最小二乘法和威廉姆森霍尔 (WH) 方法检查精度、准确度和不确定性，研究了 XRD 用于确定氧化镁纳米晶体微晶尺寸的定量能力。通过重新制备、重新运行和重新分析相同的样品来研究方法的精密度。发现这两种方法的精确度都在 2 nm 以内。通过使用来自扫描电子显微镜显微照片的视觉颗粒识别和使用布鲁诺-埃米特-特勒 (BET) 吸附测定表面积的间接计算，将它们与独立的微晶尺寸分析进行比较，从而研究这些方法的准确性。发现 WP 方法比 WH 方法更准确，后者始终低估微晶尺寸。最后，使用贝叶斯推理统计反演方法研究了这些方法的置信度。发现 WP 方法在其微晶尺寸测定中比 WH 方法具有更窄的置信度分布。广泛的 WH 置信度表明，使用 WH 技术无法进行可靠的定量单次测量微晶尺寸测定。然而，WP 方法证明了精度，