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

R Xu and CC Chen and L Wu and MC Scott and W Theis and C Ophus and M Bartels and Y Yang and H Ramezani-Dakhel and MR Sawaya and H Heinz and LD Marks and P Ercius and JW Miao, NATURE MATERIALS, 14, 1099-+ (2015).

DOI: 10.1038/NMAT4426

Crystallography, the primary method for determining the 3D atomic positions in crystals, has been fundamental to the development of many fields of science(1). However, the atomic positions obtained from crystallography represent a global average of many unit cells in a crystal(1,2). 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 similar to 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 similar to 1 nm(3) and a precision of similar to 10(-3), which are further verifiedby 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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