基于麦夸特算法的X射线衍射物相定量分析的影响因素研究

Study on the Influencing Factors of the Levenberg-Marquardt Algorithm for X-ray Diffraction Quantitative Phase Analysis

X射线衍射物相定量分析方法很多,新近提出的麦夸特算法(Levenberg-Marquardt)在XRD物相定量分析中具有明显的优势,但在实际应用过程中,哪些因素会对该方法计算结果的准确度产生影响仍不清楚。为了指导实际操作过程并提高麦夸特算法在X射线衍射物相定量分析中的准确度和处理效率,本研究通过Matlab软件,将已知配比含量的刚玉、石英、方解石和钠长石与其计算值进行比较,探讨衍射峰强度、衍射峰背底、样品数量等因素对麦夸特算法应用于X射线衍射物相定量分析中计算结果的影响。结果表明:通过前三强峰法的计算结果比通过最强峰法的计算结果具有更高的准确度;由于物相晶体结构及衍射特性的差异,衍射峰背底对不同物相定量结果的影响程度各异,扣除背底后各物相计算结果的准确度整体上都有不同程度的提高;在利用麦夸特算法进行批量分析过程中,当样品数低于一定阈值时,样品数越多,计算结果的准确度提高越明显,但当计算的样品超过一定阈值时准确度不会有明显的提高。

There are many traditional methods of X-ray Diffraction （XRD） quanutatlve analyssis. developed Levenberg-Marquardt （LM） algorithm has the obvious advantages over traditional methods. However, it is still unclear which, and how, influencing factors affect the reliability and accuracy of the computed results in practice. In order to improve the accuracy and processing efficiency, the authors discuss influences of the choice of diffraction intensity, pattern background and sample numbers on phase quantitative analysis based on the LM method and Matlab program. A series of mixed minerals, which consist of corundum, quartz, calcite and albite, or bulk samples mixed with corundum under different proportions, were designed to examine the influences. The computed results from the sum of integral intensities of the top three peaks have improved accuracy over these by the integral intensity of the strongest peak. Some random errors are eliminated through the sum of integral intensities of the top three peaks effectively to some extent. The accuracies of the computed results were improved by background correction. Because of the differences in crystal structure and diffraction characteristics, the influences of background on the calculation results were different. The sample size also affects the accuracy of quantitative analyses using the LM method. Increasing samples can improve accuracy significantly if the number of samples is less than the threshold value, however, there is no obvious change if the number of samples is more than threshold value.