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


Crystallography, the primary method for determining the 3D atomic positions in crystals, has been fundamental to the development of many fields of science1. However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal1,2. 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 pm, 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 1 nm3 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, chemistry and biology.

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Figure 1: 3D positions of individual atoms in a tungsten needle sample revealed by electron tomography.
Figure 2: 3D determination of a point defect and the atomic displacements in the tungsten needle sample.
Figure 3: 3D strain tensor measurements in the tungsten needle sample.

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We thank U. Dahmen, J. Du, L. Deng, E. J. Kirkland, R. F. Bruinsma and L. A. Vese for stimulating discussions. This work was primarily supported by the Office of Basic Energy Sciences of the US Department of Energy (Grant No. DE-FG02-13ER46943). This work was partially supported by NSF (DMR-1437263 and DMR-0955071) as well as ONR MURI (N00014-14-1-0675). L.D.M. acknowledges support from the DOE (Grant No. DE-FG02-01ER45945). ADF-STEM imaging was performed on TEAM I at the Molecular Foundry, which is supported by the Office of Science, Office of Basic Energy Sciences of the US Department of Energy under Contract No. DE-AC02—05CH11231. H.R.-D. and H.H. acknowledge the allocation of computing resources at the Ohio Supercomputer Center.

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Authors and Affiliations



J.M. directed the project; W.T. prepared the samples; W.T. and M.C.S. acquired the data; C.-C.C., L.W., M.B., R.X. and J.M. conducted the image reconstruction and atom tracing; R.X., M.R.S. and J.M. performed the atom refinement; R.X. and J.M. conducted the multislice calculations; C.O., R.X., W.T., P.E., M.C.S., Y.Y., L.D.M. and J.M. analysed and interpreted the results; L.D.M. did the DFT calculations; H.H., H.R.-D., W.T. and C.O. carried out the MD simulations; J.M., C.O., R.X., W.T., M.B., L.W., M.C.S., P.E., H.R.-D., H.H. and L.D.M. wrote the manuscript.

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Correspondence to Jianwei Miao.

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Xu, R., Chen, CC., Wu, L. et al. Three-dimensional coordinates of individual atoms in materials revealed by electron tomography. Nature Mater 14, 1099–1103 (2015).

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