The discovery and analysis of X-ray diffraction from crystals by Max von Laue, William Henry Bragg and William Lawrence Bragg in 1912 marked the birth of crystallography. Over the last century, crystallography has been fundamental to the development of many fields of science. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are non-crystalline, and thus their 3D structures are not accessible by traditional crystallography. Overcoming this major hurdle has required the development of new structure determination methods. In this talk, I will present two methods that can go beyond crystallography: coherent diffractive imaging (CDI) and atomic electron tomography (AET). In CDI, the diffraction pattern of a non-crystalline sample or a nanocrystal is first measured and then directly phased to obtain an image. The well-known phase problem is solved by combining the oversampling method with iterative algorithms. In the first part of the talk, I will illustrate several prominent CDI methods and highlight some important applications using high harmonic generation, 3rd generation synchrotron radiation and X-ray free electron lasers. In the second part of the talk, I will present a general tomographic method, termed AET, for 3D structure determination of crystal defects and disordered materials at atomic resolution. By combining advanced electron microscopes with novel data analysis and powerful computational algorithms, AET has been used to reveal the 3D atomic structure of crystal defects and chemical order/disorder, and to precisely localize the 3D coordinates of individual atoms in materials without assumption of crystallinity. The experimentally measured coordinates can then be used as direct input for quantum mechanical calculations of physical properties such as atomic spin and orbital magnetic moments and local magnetocrystalline anisotropy at the single-atom level. As large-scale and tabletop coherent X-ray sources and powerful electron microscopes are under rapid development worldwide, CDI and AET are expected to find broad applications in both the physical and biological sciences.
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2. J. Miao, P. Ercius and S. J. L. Billinge, "Atomic electron tomography: 3D structures without crystals", Science 353, aaf2157 (2016). (Review)
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