基于蒙特卡罗模拟的透射式XRD背景的定量分析

Quantitative Analysis of Transmission XRD Background Based on Monte Carlo Simulation

  • 摘要: XRD背景主要来源于空气、装置和样品中光子的散射,XRD分析需准确扣除背景,常用的扣背景方法具有一定的局限。蒙特卡罗模拟可实现光子的甄别与统计,因此可将其用于XRD背景来源的定量分析。相干散射的模拟中需考虑物质的Form Factor,这可由Baró等的拟合式、独立原子模型或德拜公式给出;在20 keV能量及透射几何模式下,通过对骨、尼龙、水等物质的XRD模拟,对探测器中光子来源进行了区分和统计。结果表明,德拜公式计算的空气背景大于独立原子模型;空气散射在小角度时背景占比大,随散射角的增加从100%减小至40%以下,而样品中康普顿散射的计数占比则从0增大至60%以上。该方法可对不同样品组成以及复杂装置结构的XRD背景进行定量分析。

     

    Abstract: The first prerequisite for obtaining correct information from an X-ray diffraction pattern is to accurately remove the background. The most commonly used method in experiments is direct subtraction, which ignores the absorption of the sample and other interactions within the sample such as the photoelectric effect and the counting of photons produced by Compton scattering. The "rolling ball" algorithm and the use of software such as Jade deduction background as well as other deduction methods also have their own limitations. Monte Carlo simulation can identify and count the particles, so it is very important to use it for quantitative analysis of XRD background. In this study, the atomic Form Factor of each element in the air was calculated by the Baró fitting formula and the molecular Form Factor was given by the Debye formula and compared with the calculation results of the independent atomic model. Geant4 was used to simulate XRD for crystalline substances such as bone and nylon and amorphous substances such as water, and the background and real signals were effectively separated in the results, then the XRD background was quantitatively analyzed on this basis. The results show that there is a huge difference in counting between the independent atomic model and Debye's formula,and the Debye method produces more scattered particles. XRD background comes from the air scattering and other types of interactions between photons and matter in the sample, the former contributing the most at small angles, the proportion decreases from 100% to less than 40% with the increase of the scattering angle, and the proportion of the latter increases from 0 to more than 60% with the scattering angle. The results indirectly illustrate the inaccuracy of the background subtraction methods in the experiment. Such as the direct subtraction method not only ignores the absorption of X-ray by the sample, but also ignores the background count caused by other interactions of X-ray photons in the sample. To accurately remove the background, all the counts of background mentioned above must be considered. The Monte Carlo method was used to simulate the XRD background, and the simulation was closely connected with the practice. The same XRD background pattern can be obtained by constructing the same geometric model as the experiment, setting the same physical parameters as the experiment, and using the same sample Form Factor as the experiment. Applying the simulation results to actual experiments may become a more accurate method of background deduction.

     

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