Gesing Thorsten M, Robben Lars
Institute of Inorganic Chemistry and Crystallography University of Bremen 28359Leobener Strasse 7 Bremen Germany.
MAPEX Center for Materials and Processes University of Bremen Bibliothekstrasse 1 28359Bremen Germany.
J Appl Crystallogr. 2024 Sep 17;57(Pt 5):1466-1476. doi: 10.1107/S1600576724007362. eCollection 2024 Oct 1.
A procedure is presented to exactly obtain the apparent average crystallite size (ACS) of powder samples using standard in-house powder diffraction experiments without any restriction originating from the Scherrer equation. Additionally, the crystallite size distribution within the sample can be evaluated. To achieve this, powder diffractograms are background corrected and long-range radial distribution functions () up to 300 nm are calculated from the diffraction data. The envelope function of () is approximated by a procedure determining the absolute maxima of () in a certain interval ( range). Fitting of an ACS distribution envelope function to this approximation gives the ACS and its distribution. The method is tested on diffractograms of LaB standard reference materials measured with different wavelengths to demonstrate the validity of the approach and to clarify the influence of the wavelength used. The latter results in a general description of the maximum observable average crystallite size, which depends on the instrument and wavelength used. The crystallite site distribution is compared with particle size distributions based on transmission electron microscopy investigations, providing an approximation of the average number of crystallites per particle.
本文介绍了一种程序，可通过标准的内部粉末衍射实验精确获得粉末样品的表观平均微晶尺寸（ACS），而不受谢乐方程的任何限制。此外，还可以评估样品内微晶尺寸的分布。为此，对粉末衍射图进行背景校正，并根据衍射数据计算高达300 nm的长程径向分布函数（）。通过在特定区间（范围）内确定（）的绝对最大值的程序来近似（）的包络函数。将ACS分布包络函数拟合到该近似值可得到ACS及其分布。该方法在使用不同波长测量的LaB标准参考材料的衍射图上进行了测试，以证明该方法的有效性并阐明所用波长的影响。后者得出了对最大可观测平均微晶尺寸的一般描述，这取决于所用的仪器和波长。将微晶位点分布与基于透射电子显微镜研究的粒度分布进行比较，可提供每个颗粒平均微晶数量的近似值。
