Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Nature Materials volume 14, pages 1099–1103 (2015)Cite this article

Subjects

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

  1. Crystallography at 100. Science 343 (Special issue), 1091–1116 (2014).

  2. Giacovazzo, C. et al. Fundamentals of Crystallography 2nd edn (Oxford Univ. Press, 2002).

    Google Scholar 

  3. Feynman, R. P. in Feynman and Computation (ed. Hey, J. G.) 63–76 (Perseus Press, 1999).

    Google Scholar 

  4. Haider, M. et al. Electron microscopy image enhanced. Nature 392, 768–769 (1998).

    Article  CAS  Google Scholar 

  5. Batson, P. E., Dellby, N. & Krivanek, O. L. Sub-ångstrom resolution using aberration corrected electron optics. Nature 418, 617–620 (2002).

    Article  CAS  Google Scholar 

  6. Erni, R., Rossell, M. D., Kisielowski, C. & Dahmen, U. Atomic-resolution imaging with a sub-50-pm electron probe. Phys. Rev. Lett. 102, 096101 (2009).

    Article  Google Scholar 

  7. Midgley, P. A. & Weyland, M. in Scanning Transmission Electron Microscopy: Imaging and Analysis (eds Pennycook, S. J. & Nellist, P. D.) 353–392 (Springer, 2011).

    Book  Google Scholar 

  8. LeBeau, J. M., Findlay, S. D., Allen, L. J. & Stemmer, S. Quantitative atomic resolution scanning transmission electron microscopy. Phys. Rev. Lett. 100, 206101 (2008).

    Article  Google Scholar 

  9. Muller, D. A. Structure and bonding at the atomic scale by scanning transmission electron microscopy. Nature Mater. 8, 263–270 (2009).

    Article  CAS  Google Scholar 

  10. Miao, J., Föster, F. & Levi, O. Equally sloped tomography with oversampling reconstruction. Phys. Rev. B 72, 052103 (2005).

    Article  Google Scholar 

  11. Lee, E. et al. Radiation dose reduction and image enhancement in biological imaging through equally sloped tomography. J. Struct. Biol. 164, 221–227 (2008).

    Article  CAS  Google Scholar 

  12. Zhao, Y. et al. High resolution, low dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers. Proc. Natl Acad. Sci. USA 109, 18290–18294 (2012).

    Article  CAS  Google Scholar 

  13. Fahimian, B. P. et al. Radiation dose reduction in medical X-ray CT via Fourier-based iterative reconstruction. Med. Phys. 40, 031914 (2013).

    Article  Google Scholar 

  14. Scott, M. C. et al. Electron tomography at 2.4-angstrom resolution. Nature 483, 444–447 (2012).

    Article  CAS  Google Scholar 

  15. Chen, C.-C. et al. Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution. Nature 496, 74–77 (2013).

    Article  CAS  Google Scholar 

  16. Azubel, M. et al. Electron microscopy of gold nanoparticles at atomic resolution. Science 345, 909–912 (2014).

    Article  CAS  Google Scholar 

  17. Hÿtch, M. J. & Minor, A. M. Observing and measuring strain in nanostructures and devices with transmission electron microscopy. MRS Bull. 39, 138–146 (2014).

    Article  Google Scholar 

  18. Hÿtch, M. J., Houdellier, F., Hüe, F. & Snoeck, E. Nanoscale holographic interferometry for strain measurements in electronic devices. Nature 453, 1086–1089 (2008).

    Article  Google Scholar 

  19. Warner, J. H., Young, N. P., Kirkland, A. I. & Briggs, G. A. D. Resolving strain in carbon nanotubes at the atomic level. Nature Mater. 10, 958–962 (2011).

    Article  CAS  Google Scholar 

  20. Miao, J., Ishikawa, T., Robinson, I. K. & Murnane, M. M. Beyond crystallography: Diffractive imaging using coherent X-ray light sources. Science 348, 530–535 (2015).

    Article  CAS  Google Scholar 

  21. Pfeifer, M. A., Williams, G. J., Vartanyants, I. A., Harder, R. & Robinson, I. K. Three-dimensional mapping of a deformation field inside a nanocrystal. Nature 442, 63–66 (2006).

    Article  CAS  Google Scholar 

  22. Goris, B. et al. Atomic-scale determination of surface facets in gold nanorods. Nature Mater. 11, 930–935 (2012).

    Article  CAS  Google Scholar 

  23. Kim, S. et al. 3D strain measurement in electronic devices using through-focal annular dark-field imaging. Ultramicroscopy 146, 1–5 (2014).

    Article  CAS  Google Scholar 

  24. Ercius, P., Boese, M., Duden, T. & Dahmen, U. Operation of TEAM I in a user environment at NCEM. Microsc. Microanal. 18, 676–683 (2012).

    Article  CAS  Google Scholar 

  25. Marks, L. D. Wiener-filter enhancement of noisy HREM images. Ultramicroscopy 62, 43–52 (1996).

    Article  CAS  Google Scholar 

  26. Dabov, K., Foi, A., Katkovnik, V. & Egiazarian, K. Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Trans. Image Process. 16, 2080–2095 (2007).

    Article  Google Scholar 

  27. Brünger, A. T. et al. Crystallography & NMR system: A new software suite for macromolecular structure determination. Acta Crystallogr. D 54, 905–921 (1998).

    Article  Google Scholar 

  28. Midgley, P. A. & Weyland, M. 3D electron microscopy in the physical sciences: The development of Z-contrast and EFTEM tomography. Ultramicroscopy 96, 413–431 (2003).

    Article  CAS  Google Scholar 

  29. Kirkland, E. J. Advanced Computing in Electron Microscopy 2nd edn (Springer, 2010).

    Book  Google Scholar 

  30. Kohavi, R. A study of cross-validation and bootstrap for accuracy estimation and model selection. Proc. 14th Int. Joint Conf. Artif. Intell. 2, 1137–1143 (1995).

    Google Scholar 

  31. Liu, Y. L., Zhou, H. B., Jin, S., Zhang, Y. & Lu, G. H. Dissolution and diffusion properties of carbon in tungsten. J. Phys. Condens. Matter 22, 445504 (2010).

    Article  Google Scholar 

  32. Kelly, T. F. & Miller, M. K. Atom probe tomography. Rev. Sci. Instrum. 78, 031101 (2007).

    Article  Google Scholar 

  33. Zhu, C. et al. Towards three-dimensional structural determination of amorphous materials at atomic resolution. Phys. Rev. B 88, 100201 (2013).

    Article  Google Scholar 

  34. Schmid, A. & Andresen, N. Motorized manipulator for positioning a TEM specimen. US Patent 7,851,769 (2011)

  35. Larkin, K. G., Oldfield, M. A. & Klemm, H. Fast Fourier method for the accurate rotation of sampled images. Opt. Commun. 139, 99–106 (1997).

    Article  CAS  Google Scholar 

  36. Mäkitalo, M. & Foi, A. A closed-form approximation of the exact unbiased inverse of the Anscombe variance-stabilizing transformation. IEEE Trans. Image Process. 20, 2697–2698 (2011).

    Article  Google Scholar 

  37. Herman, G. T. Fundamentals of Computerized Tomography: Image Reconstruction from Projection 2nd edn (Springer, 2009).

    Book  Google Scholar 

  38. Mao, Y., Fahimian, B. P., Osher, S. J. & Miao, J. Development and optimization of regularized tomographic reconstruction algorithms utilizing equally-sloped tomography. IEEE Trans. Image Process. 19, 1259–1268 (2010).

    Article  Google Scholar 

  39. Zhou, X. W. et al. Atomic scale structure of sputtered metal multilayers. Acta Mater. 49, 4005–4015 (2001).

    Article  CAS  Google Scholar 

  40. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    Article  CAS  Google Scholar 

  41. Parzen, E. On estimation of a probability density function and mode. Ann. Math. Stat. 33, 1065–1076 (1962).

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Author notes

  1. Rui Xu, Chien-Chun Chen, Li Wu, M. C. Scott, W. Theis and Colin Ophus: These authors contributed equally to this work.

Authors and Affiliations

  1. Department of Physics & Astronomy and California NanoSystems Institute, University of California, Los Angeles, California 90095, USA

    Rui Xu, Chien-Chun Chen, Li Wu, M. C. Scott, Matthias Bartels, Yongsoo Yang & Jianwei Miao

  2. Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

    Chien-Chun Chen

  3. Nanoscale Physics Research Laboratory, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

    W. Theis

  4. National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    Colin Ophus & Peter Ercius

  5. Department of Polymer Engineering, University of Akron, Akron, Ohio 44325, USA

    Hadi Ramezani-Dakhel & Hendrik Heinz

  6. Howard Hughes Medical Institute, UCLA-DOE Institute of Genomics and Proteomics, Los Angeles, California 90095-1570, USA

    Michael R. Sawaya

  7. Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60201, USA

    Laurence D. Marks

Authors
  1. Rui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chien-Chun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. C. Scott
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W. Theis
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Colin Ophus
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Matthias Bartels
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Yongsoo Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Hadi Ramezani-Dakhel
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Michael R. Sawaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Hendrik Heinz
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Laurence D. Marks
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Peter Ercius
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Jianwei Miao
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding author

Correspondence to Jianwei Miao.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 3263 kb)

Supplementary Movie 1

Supplementary Movie 1 (MP4 1519 kb)

Supplementary Movie 2

Supplementary Movie 2 (MP4 7622 kb)

Supplementary Movie 3

Supplementary Movie 3 (MP4 2041 kb)

Supplementary Movie 4

Supplementary Movie 4 (MP4 9883 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1038/nmat4426

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat4426

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing