TORRICELLI: A software to determine atomic spatial distributions from normal incidence x-ray standing wave data

We introduce a software, Torricelli, for the analysis of normal incidence x-ray standing wave data. In particular, given the experimental x-ray reflectivity and photoelectron yield of a data set (photon energy scan), Torricelli provides the corresponding structural parameters. The algorithm and equations on which Torricelli is based are explained here in detail. In particular, the model of the experimental reflectivity takes into account the theoretical reflectivity of the double crystal monochromator as well as the sample crystal, and a Gaussian broadening to account for mosaicity and photon energy spread. If statistical errors are provided together with the photoelectron yield data, these are propagated to produce the statistical errors of the structural parameters. For a more accurate analysis, angle-dependent correction parameters specific to the photoemission process, also beyond the dipole approximation, can be taken into account, especially in the case of non-perfect normal incidence. The obtained structural parameters can be compared, averaged, and displayed in an Argand diagram, along with statistical error bars.

本研究介绍一款用于正入射X射线驻波（normal incidence x-ray standing wave）数据解析的软件Torricelli。具体而言，当输入某一光子能量扫描（photon energy scan）数据集的实验X射线反射率（x-ray reflectivity）与光电子产额（photoelectron yield）时，Torricelli即可输出对应的结构参数（structural parameters）。本文详细阐述了Torricelli所基于的算法与方程。具体而言，实验反射率模型兼顾了双晶单色器（double crystal monochromator）与样品晶体的理论反射率，并引入高斯展宽（Gaussian broadening）以修正镶嵌性（mosaicity）与光子能量展宽（photon energy spread）带来的影响。若同步提供光电子产额数据的统计误差（statistical errors），则可通过误差传递得到结构参数的统计误差。为实现更精准的解析，还可引入针对光电子发射过程（photoemission process）的角度相关校正参数，甚至可突破偶极近似（dipole approximation）的限制，尤其适用于非严格正入射的场景。所得结构参数可进行比对、平均，并与统计误差棒（statistical error bars）一同绘制于阿尔甘德图（Argand diagram）中。