New-corrected functions of X-ray powder diffraction

• Published in: Chinese science bulletin Vol. 54; no. 21; pp. 3940 - 3946
• Main Authors: Zhang, QingLi, Liu, WenPeng, Ding, LiHua, Jiang, HaiHe, Yin, ShaoTang
• Format: Journal Article
• Language: English
• Published: Heidelberg SP Science in China Press 01.11.2009
• Subjects: Articles/Condensed Matter Physics; Chemistry/Food Science; Earth Sciences; Engineering; Humanities and Social Sciences; Life Sciences; Marquardt; multidisciplinary; Physics; Science; Science (multidisciplinary); X射线衍射; 功能参数; 晶格参数; 最小二乘拟合; 标准样品; 校正功能; 计算结果; extrapolate function; corrected function; lattice parameter; X-ray powder diffraction
• ISSN: 1001-6538; 1861-9541
• DOI: 10.1007/s11434-009-0592-6

X-ray powder diffraction is an indispensable technique to study material structure, phase transition and so on. It is necessary for high quality diffraction data to get high-precision diffraction angle. This work proposed four corrected functions of X-ray powder diffraction angle. Two methods, linearization method and modified Levenberg-Marquardt iteration method, are given to solve the function parameters, and the modified Levenberg-Marquardt method has fast convergent speed and stable solution. Two methods can give closed parameters, including those of Lu, Liu, and Chu functions and polynomial. New-corrected functions were used to fit the diffraction angle error of the tetragonal rutile polycrystalline TiO2 mixed with Gd0.45Y2.55Sc2Ga3O12 as a standard sample, and the computation result indicates that these functions can characterize the diffraction error very well. In some cases, the new-corrected functions can describe the diffraction angle error better than the reported corrected functions. At the same time, the lattice parameter of Gdo.45Y2.55Sc2Ga3O12 was computed with two methods. When the corrected function parameters and lattice parameters were solved by the least square method, the interaction of the function parameters and lattice parameters would result in great error. However, when the X-ray diffraction angles were corrected by corrected functions using a standard sample, the authentic lattice parameters can be obtained by the least square fitting.