Skip to main content

Thank you for visiting 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:

Electron tomography at 2.4-ångström resolution


Transmission electron microscopy is a powerful imaging tool that has found broad application in materials science, nanoscience and biology1,2,3. With the introduction of aberration-corrected electron lenses, both the spatial resolution and the image quality in transmission electron microscopy have been significantly improved4,5 and resolution below 0.5 ångströms has been demonstrated6. To reveal the three-dimensional (3D) structure of thin samples, electron tomography is the method of choice7,8,9,10,11, with cubic-nanometre resolution currently achievable10,11. Discrete tomography has recently been used to generate a 3D atomic reconstruction of a silver nanoparticle two to three nanometres in diameter12, but this statistical method assumes prior knowledge of the particle’s lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic-scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of an approximately ten-nanometre gold nanoparticle at 2.4-ångström resolution. Although we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified in three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic-scale resolution13,14,15, but also to improve the spatial resolution and image quality in other tomography fields7,9,16,17,18,19,20.

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

Access options

Buy this article

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

Figure 1: Evaluation of the 3D reconstruction quality.
Figure 2: Estimation of the 3D resolution of the reconstruction of the gold nanoparticle.
Figure 3: 3D structure of the reconstructed gold nanoparticle.
Figure 4: Identification of four major grains inside the gold nanoparticle in three dimensions.

Similar content being viewed by others


  1. Williams, D. B. & Carter, C. B. Transmission Electron Microscopy: A Textbook for Materials Science 2nd edn (Springer, 2009)

    Book  Google Scholar 

  2. Spence, J. C. H. Experimental High-Resolution Electron Microscopy 3rd edn (Oxford Univ. Press, 2003)

    Google Scholar 

  3. Frank, J. Three-Dimensional Electron Microscopy of Macromolecular Assemblies (Oxford Univ. Press, 2006)

    Book  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  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  ADS  Google Scholar 

  7. Frank, J. Electron Tomography (Plenum, 1992)

    Book  Google Scholar 

  8. 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 

  9. Lučić, V., Förster, F. & Baumeister, W. Structural studies by electron tomography: from cells to molecules. Annu. Rev. Biochem. 74, 833–865 (2005)

    Article  Google Scholar 

  10. Midgley, P. A. & Dunin-Borkowski, R. E. Electron tomography and holography in materials science. Nature Mater. 8, 271–280 (2009)

    Article  ADS  CAS  Google Scholar 

  11. Arslan, I., Yates, T. J. V., Browning, N. D. & Midgley, P. A. Embedded nanostructures revealed in three dimensions. Science 309, 2195–2198 (2005)

    Article  ADS  CAS  Google Scholar 

  12. Van Aert, S., Batenburg, K. J., Rossell, M. D., Erni, R. & Van Tendeloo, G. Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374–377 (2011)

    Article  ADS  CAS  Google Scholar 

  13. Marks, L. D. Experimental studies of small particle structures. Rep. Prog. Phys. 57, 603–649 (1994)

    Article  ADS  CAS  Google Scholar 

  14. Billinge, S. J. L. & Levin, I. The problem with determining atomic structure at the nanoscale. Science 316, 561–565 (2007)

    Article  ADS  CAS  Google Scholar 

  15. Yacamán, M. J., Ascencio, J. A., Liu, H. B. & Gardea-Torresdey, J. Structure shape and stability of nanometric sized particles. J. Vac. Sci. Technol. B 19, 1091–1023 (2001)

    Article  Google Scholar 

  16. 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 

  17. Kak, A. C. & Slaney, M. Principles of Computerized Tomographic Imaging (SIAM, Philadelphia, 2001)

    Book  Google Scholar 

  18. Fahimian, B. P., Mao, Y., Cloetens, P. & Miao, J. Low dose X-ray phase-contrast and absorption CT using equally-sloped tomography. Phys. Med. Biol. 55, 5383–5400 (2010)

    Article  Google Scholar 

  19. 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  ADS  MathSciNet  Google Scholar 

  20. Jiang, H. et al. Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy. Proc. Natl Acad. Sci. USA 107, 11234–11239 (2010)

    Article  ADS  CAS  Google Scholar 

  21. Bar Sadan, M. et al. Toward atomic-scale bright-field electron tomography for the study of fullerene-like nanostructures. Nano Lett. 8, 891–896 (2008)

    Article  ADS  CAS  Google Scholar 

  22. Bovin, J.-O., Wallenberg, R. & Smith, D. J. Imaging of atomic clouds outside the surfaces of gold crystals by electron microscopy. Nature 317, 47–49 (1985)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  24. Pennycook, S. J. & Nellist, P. D. Scanning Transmission Electron Microscopy: Imaging and Analysis 1st edn (Springer, 2011)

    Book  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Book  Google Scholar 

  27. Howie, A. Diffraction channelling of fast electrons and positrons in crystals. Phil. Mag. 14, 223–237 (1966)

    Article  ADS  CAS  Google Scholar 

  28. Daniel, M. C. & Astruc, D. Gold nanoparticles: assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology. Chem. Rev. 104, 293–346 (2004)

    Article  CAS  Google Scholar 

  29. Barnard, A. S., Young, N. P., Kirkland, A. I., van Huis, M. A. & Xu, H. Nanogold: a quantitative phase map. ACS Nano 3, 1431–1436 (2009)

    Article  CAS  Google Scholar 

  30. Arslan, I., Marquis, E. A., Homer, M., Hekmaty, M. & Bartelt, N. C. Towards better 3-D reconstructions by combining electron tomography and atom-probe tomography. Ultramicroscopy 108, 1579–1585 (2008)

    Article  CAS  Google Scholar 

  31. Averbuch, A., Coifman, R. R., Donoho, D. L., Israeli, M. & Shkolnisky, Y. A framework for discrete integral transformations I — the pseudopolar Fourier transform. SIAM J. Sci. Comput. 30, 785–803 (2008)

    Article  MathSciNet  Google Scholar 

  32. Saxton, W. O., Baumeister, W. & Hahn, M. Three-dimensional reconstruction of imperfect two-dimensional crystals. Ultramicroscopy 13, 57–70 (1984)

    Article  CAS  Google Scholar 

  33. Bailey, D. H. & Swarztrauber, P. N. The fractional Fourier transform and applications. SIAM Rev. 33, 389–404 (1991)

    Article  MathSciNet  Google Scholar 

  34. Miao, J., Sayre, D. & Chapman, H. N. Phase retrieval from the magnitude of the Fourier transform of non-periodic objects. J. Opt. Soc. Am. A 15, 1662–1669 (1998)

    Article  ADS  Google Scholar 

  35. Miao, J., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999)

    Article  ADS  CAS  Google Scholar 

  36. Miao, J., Ohsuna, T., Terasaki, O., Hodgson, K. O. & O’Keefe, M. A. Atomic resolution three-dimensional electron diffraction microscopy. Phys. Rev. Lett. 89, 155502 (2002)

    Article  ADS  Google Scholar 

  37. Zuo, J. M., Vartanyants, I., Gao, M., Zhang, R. & Nagahara, L. A. Atomic resolution imaging of a carbon nanotube from diffraction intensities. Science 300, 1419–1421 (2003)

    Article  ADS  CAS  Google Scholar 

Download references


We thank E. J. Kirkland for help with multislice STEM calculations, R. F. Egerton, Z. H. Zhou and J. A. Rodríguez for discussions and I. Atanasov for assistance in data acquisition. The tomographic tilt series were acquired at the Electron Imaging Center for NanoMachines of the California NanoSystems Institute. This work was partially supported by UC Discovery/TomoSoft Technologies (IT107-10166).

Author information

Authors and Affiliations



J.M. conceived the overall project; M.C.S., M.M., C.Z., B.C.R. and J.M. designed and conducted the experiments; C.Z., R.X., C.-C.C., P.E. and J.M. did multislice STEM calculations; C.-C.C. and J.M. performed the data analysis and image reconstruction; U.D., J.M., C.-C.C., M.C.S., M.M. and B.C.R interpreted the results, and J.M., M.C.S., C.-C.C. and M.M. wrote the manuscript. All authors commented on the manuscript.

Corresponding author

Correspondence to Jianwei Miao.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Figures 1-13 and Supplementary Table 1. (PDF 2825 kb)

Supplementary Movie 1

This movie shows a 3D volume rendering of the reconstructed gold nanoparticle. (MOV 4264 kb)

Supplementary Movie 2

This movie shows a 3D iso-surface rendering of the reconstructed gold nanoparticle. (MOV 4321 kb)

Supplementary Movie 3

This movie shows a 3D volume rendering of the four major grains determined from the reconstructed gold nanoparticle. (MOV 4279 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scott, M., Chen, CC., Mecklenburg, M. et al. Electron tomography at 2.4-ångström resolution. Nature 483, 444–447 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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