Mendenhall Marcus H, Cline James P
National Institute of Standards and Technology, Gaithersburg, Maryland, USA.
Acta Crystallogr A Found Adv. 2019 Jan 1;75(Pt 1):158-164. doi: 10.1107/S2053273318016935.
This work presents a technique for extracting the detailed shape of peaks with extended, overlapping tails in an X-ray powder diffraction pattern. The application discussed here concerns crystallite size broadening, though the technique can be applied to spectra of any origin and without regard to how the profiles are to be subsequently analyzed. Historically, the extraction of profile shapes has been difficult due to the complexity of determining the background under the peak, resulting in an offset of the low-frequency components of the Fourier transform of the peak known as the `hook' problem. The use of a carefully considered statistical weighting function in a non-linear least-squares fit, followed by summing the residuals from such a fit with the fit itself, allows one to extract the full shape of an isolated peak, without contributions from either the background or adjacent peaks. The extracted shape, consisting of the fit function recombined with the residuals, is not dependent on any specific shape model. The application of this to analysis of microstructure is performed independently of global parametric models, which would reduce the number of refined parameters; therefore the technique requires high-quality data to produce results of interest. The effectiveness of the technique is demonstrated by extraction of Fourier transforms of peaks from two sets of size-broadened materials with two differing pieces of equipment.
这项工作提出了一种从X射线粉末衍射图谱中提取具有延伸、重叠尾部的峰的详细形状的技术。这里讨论的应用涉及微晶尺寸展宽，不过该技术可应用于任何来源的光谱，且无需考虑随后如何分析这些谱线。从历史上看，由于确定峰下背景的复杂性，谱线形状的提取一直很困难，这导致峰的傅里叶变换的低频分量出现偏移，即所谓的“钩”问题。在非线性最小二乘拟合中使用经过仔细考虑的统计加权函数，然后将这种拟合的残差与拟合本身相加，能够提取孤立峰的完整形状，而不受背景或相邻峰的影响。提取的形状由与残差重新组合的拟合函数组成，不依赖于任何特定的形状模型。将此应用于微观结构分析是独立于全局参数模型进行的，这会减少精修参数的数量；因此，该技术需要高质量的数据才能产生有意义的结果。通过使用两台不同设备从两组尺寸展宽的材料中提取峰的傅里叶变换，证明了该技术的有效性。
