Unprecedented Precise Determination of Three-Dimensional Atomic Positions

For the first time, electron tomography reveals the 3D coordinates of individual atoms and defects in a material.

Working with Molecular Foundry staff, an international team of users utilized the TEAM 1 microscope to plot the exact coordinates of nine layers of atoms with a precision of 19 trillionths of a meter.
Image courtesy of Macmillan Publishers Ltd: Nature Materials, © 2015
Working with Molecular Foundry staff, an international team of users led by UCLA utilized the extraordinarily high resolution of the TEAM 1 microscope at LBNL to, for the first time, plot the exact 3D coordinates of nine layers of tungsten atoms with a precision of 19 trillionths of a meter (19 picometers)—less than half the radius of a hydrogen atom.

The Science

Workhorses of scientific discovery, electron microscopes, have helped push back the boundaries of science, but the instruments have struggled to determine the 3D location of individual atoms. Advanced electron tomography is an extension of traditional electron microscopy in which 3D images are formed from data collected as the sample rotates. This research combines high resolution microscopy with new electron image analysis to measure atomic positions with an unprecedented precision of less than half the radius of a hydrogen atom.

The Impact

For the first time, the absence or addition of single atoms, known as point defects, can be determined with three dimensional atomic precision. These defects can have a profound effect on the properties of materials – sometimes giving them the desired properties as in semiconductors, sometimes making them worse when the point defects combine to weaken a structural component and cause it to break.  This precise characterization could transform our understanding of the relationship among atomic structure, properties, and functionality of materials and lead to advances in materials science, nanoscience, chemistry, and biology.


Atoms are the building blocks of all matter on Earth, and the patterns in which they are arranged dictate how strong, conductive, or flexible a material will be. In his “There's plenty of room at the bottom” lecture in 1959, Richard Feynman challenged us to develop better electron microscopes saying that “it should be possible to see the individual atoms” in a material. While significant progress has been made in electron microscopy over the last 55 years, precise 3D determination of the positions of individual atoms in materials, without averaging or a priori knowledge of crystallinity, remained elusive. In this research from the University of California–Los Angeles and Lawrence Berkeley National Laboratory’s Molecular Foundry has, for the first time, demonstrated a technique that determines the 3D coordinates of thousands of individual atoms and a point defect (for example, a missing atom in the crystalline structure) with electron tomography with a precision of approximately 19 trillionths of a meter, impressively without assumptions about the crystallinity of the material. From the coordinates of the individual atoms in the tungsten sample, the atomic displacement field and the full strain were measured also with an unprecedented 3D resolution of one cubic nanometer and a precision of 0.001. These results were further validated theoretically with density functional theory calculations and molecular dynamics simulations, which are modeling methods to derive electronic structures and movements of atoms, respectively, in a material. The ability to accurately measure the specific locations of each atom in a material make it possible to infer the macroscopic properties of materials based on their structural arrangements of atoms. The ability to infer macroscopic properties will guide how scientists and engineers create new materials, build new devices, and find important applications for materials science to biology.


Jianwei (John) Miao
University of California, Los Angeles

Peter Ercius
Molecular Foundry, LBNL
(510) 486-4634


This work was supported by the DOE Office of Science (Office of Basic Energy Sciences); Molecular Foundry (imaging on TEAM I), a DOE Office of Science User Facility; partially by the National Science Foundation and the Office of Naval Research; and the Ohio Supercomputer Center.


R. Xu, C. C. Chen, L. Wu, M. C. Scott, W. Theis, C. Ophus, M. Bartels, Y. Yang, H. Ramezani-Dakhel, M. R. Sawaya, H. Heinz, L. D. Marks, P. Ercius, and J. Miao, “Three-dimensional coordinates of individual atoms in materials revealed by electron tomography.” Nature Materials 14, 1099–1103 (2015). [DOI: 10.1038/nmat4426]

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