The information content of crystalline materials becomes astronomical when collective electronic behavior and their fluctuations are taken into account. In the past decade, improvements in source brightness and detector technology at modern X-ray facilities have allowed a dramatically increased fraction of this information to be captured. Now, the primary challenge is to understand and discover scientific principles from big datasets when a comprehensive analysis is beyond human reach. We report the development of an unsupervised machine learning approach, X-ray diffraction (XRD) temperature clustering (X-TEC), that can automatically extract charge density wave order parameters and detect intraunit cell ordering and its fluctuations from a series of high-volume X-ray diffraction measurements taken at multiple temperatures. We benchmark X-TEC with diffraction data on a quasi-skutterudite family of materials, (Ca x Sr 1 − x ) 3 Rh 4 Sn 13 , where a quantum critical point is observed as a function of Ca concentration. We apply X-TEC to XRD data on the pyrochlore metal, Cd 2 Re 2 O 7 , to investigate its two much-debated structural phase transitions and uncover the Goldstone mode accompanying them. We demonstrate how unprecedented atomic-scale knowledge can be gained when human researchers connect the X-TEC results to physical principles. Specifically, we extract from the X-TEC–revealed selection rules that the Cd and Re displacements are approximately equal in amplitude but out of phase. This discovery reveals a previously unknown involvement of 5 d 2 Re, supporting the idea of an electronic origin to the structural order. Our approach can radically transform XRD experiments by allowing in operando data analysis and enabling researchers to refine experiments by discovering interesting regions of phase space on the fly.

中文翻译：

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利用可解释和无监督的机器学习来处理来自现代 X 射线衍射的大数据

当考虑到集体电子行为及其波动时，晶体材料的信息量变得惊人。在过去的十年中，现代 X 射线设备的源亮度和检测器技术的改进使得捕获到的此类信息的比例显着增加。现在，主要的挑战是在人类无法进行全面分析的情况下，从大数据集中理解和发现科学原理。我们报告了一种无监督机器学习方法的发展，即 X 射线衍射 (XRD) 温度聚类 (X-TEC)，它可以自动提取电荷密度波阶参数并从一系列高容量样品中检测胞内有序度及其波动在多个温度下进行的 X 射线衍射测量。 X 锶 1个 − X )3个铑4个锡13，其中观察到量子临界点是 Ca 浓度的函数。我们将 X-TEC 应用于烧绿石金属 Cd 的 XRD 数据2个回覆2个欧7, 以研究其两个备受争议的结构相变并揭示伴随它们的戈德斯通模式。我们展示了当人类研究人员将 X-TEC 结果与物理原理联系起来时，如何获得前所未有的原子级知识。具体来说，我们从 X-TEC 揭示的选择规则中提取出 Cd 和 Re 位移的振幅大致相等但异相。这一发现揭示了以前未知的参与 5个 d 2个 Re，支持电子起源到结构顺序的想法。我们的方法可以通过允许操作数据分析并使研究人员能够通过动态发现有趣的相空间区域来改进实验，从而从根本上改变 XRD 实验。