Three-dimensional coordinates of individual atoms in materials revealed by electron tomography

Rui Xu, Chien-Chun Chen, Li Wu, M. C. Scott, W. Theis, Colin Ophus, Matthias Bartels, Yongsoo Yang, Hadi Ramezani-Dakhel, Michael R. Sawaya, Hendrik Heinz, Laurence D. Marks, Peter Ercius, Jianwei Miao

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Crystallography, the primary method for determining the three-dimensional (3D) atomic positions in crystals, has been fundamental to the development of many fields of science. However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal. Here, we report, for the first time, the determination of the 3D coordinates of thousands of individual atoms and a point defect in a material by electron tomography with a precision of ~19 picometers, where the crystallinity of the material is not assumed. From the coordinates of these individual atoms, we measure the atomic displacement field and the full strain tensor with a 3D resolution of ~1nm3 and a precision of ~10-3, which are further verified by density functional theory calculations and molecular dynamics simulations. The ability to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity is expected to find important applications in materials science, nanoscience, physics and chemistry.
Original languageEnglish
Pages (from-to)1099–1103
Number of pages5
JournalNature Materials
Publication statusPublished - 21 Sept 2015

Bibliographical note

accepted 17.8.2015
Data and code availability.
The data, image reconstruction and data analysis source codes of this paper are freely available at

preprint available (arXiv:1505.05938 [cond-mat.mtrl-sci])
postprint uploaded (the file currently labeled as postprint is in fact the arXiv preprint)


  • cond-mat.mtrl-sci


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