Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution

Journal name:
Date published:
Published online

Dislocations and their interactions strongly influence many material properties, ranging from the strength of metals and alloys to the efficiency of light-emitting diodes and laser diodes1, 2, 3, 4. Several experimental methods can be used to visualize dislocations. Transmission electron microscopy (TEM) has long been used to image dislocations in materials5, 6, 7, 8, 9, and high-resolution electron microscopy can reveal dislocation core structures in high detail10, particularly in annular dark-field mode11. A TEM image, however, represents a two-dimensional projection of a three-dimensional (3D) object (although stereo TEM provides limited information about 3D dislocations4). X-ray topography can image dislocations in three dimensions, but with reduced resolution12. Using weak-beam dark-field TEM13 and scanning TEM14, electron tomography has been used to image 3D dislocations at a resolution of about five nanometres (refs 15, 16). Atom probe tomography can offer higher-resolution 3D characterization of dislocations, but requires needle-shaped samples and can detect only about 60 per cent of the atoms in a sample17. Here we report 3D imaging of dislocations in materials at atomic resolution by electron tomography. By applying 3D Fourier filtering together with equal-slope tomographic reconstruction, we observe nearly all the atoms in a multiply twinned platinum nanoparticle. We observed atomic steps at 3D twin boundaries and imaged the 3D core structure of edge and screw dislocations at atomic resolution. These dislocations and the atomic steps at the twin boundaries, which appear to be stress-relief mechanisms, are not visible in conventional two-dimensional projections. The ability to image 3D disordered structures such as dislocations at atomic resolution is expected to find applications in materials science, nanoscience, solid-state physics and chemistry.

At a glance


  1. 3D reconstruction of a multiply twinned Pt nanoparticle before and after applying a 3D Fourier filter.
    Figure 1: 3D reconstruction of a multiply twinned Pt nanoparticle before and after applying a 3D Fourier filter.

    a, 3D Fourier transform of the raw reconstruction of the nanoparticle. b, 3D Fourier transform of the reconstruction after 3D Fourier filtering where the {111} and {200} Bragg peaks are labelled with red and black dots, respectively. c, A 2.6-Å-thick central slice in the xyplane of the raw reconstruction, where the zaxis is along the beam direction. d, The same slice of the 3D structure after applying a 3D Fourier filter, in which nearly all the atoms (in white) are visible. The clear boundary of the nanoparticle is due to the multiplication of the 3D structure with a 3D shape obtained from the EST reconstruction (Methods). The insets show an enlarged region of the atomic positions before and after applying a 3D Fourier filter.

  2. Grain boundary comparisons between a 2D experimental projection and several 2.6-A-thick internal slices of the reconstructed Pt nanoparticle.
    Figure 2: Grain boundary comparisons between a 2D experimental projection and several 2.6-Å-thick internal slices of the reconstructed Pt nanoparticle.

    a, Experimental projection in the xyplane suggesting that this is a decahedral multiply twinned nanoparticle and that the twin boundaries (red lines) are flat. Blue lines show two subgrain boundaries. To enhance the image contrast, a 2D Fourier filter was applied to the projection. b, A 2.6-Å-thick internal slice indicating the existence of atomic steps at the twin boundaries (red lines). The subgrain boundaries (blue lines) are two lattice spacings wider than those in a. c, Enlarged view of a twin boundary in b. d and e, a 2.6-Å-thick slice above and below the slice of c, revealing that the atomic steps vary in consecutive atomic layers. f, Enlarged view of a stacking fault in the 2.6-Å-thick internal slice, which is in good agreement with the classical model for a face-centred-cubic extrinsic stacking fault (inset). These images, as well as those in Figs 3 and 4, are displayed with Amira.

  3. Observation of the 3D core structure of an edge dislocation at atomic resolution.
    Figure 3: Observation of the 3D core structure of an edge dislocation at atomic resolution.

    a, A 7.9-Å-thick internal slice of the nanoparticle. The lattice structure on the left and at the bottom parts of the slice is not well defined, mainly because this decahedral multiply twinned nanoparticle consists of five grains with different orientations. b, An enlarged view of an edge dislocation in a where red dots represent the position of the atoms. c, d and e, 2.6-Å-thick atomic layers sectioning through the slice of b. The three consecutive atomic layers indicate the dislocation line is in the direction of . The Burgers vector (b) of the edge dislocation was determined to be .

  4. Observation of the 3D core structure of a screw dislocation at atomic resolution.
    Figure 4: Observation of the 3D core structure of a screw dislocation at atomic resolution.

    a, Volume renderings of a 5.3-Å-thick slice (two atomic layers) in the plane (Supplementary Fig. 11b), tilted to the direction to visualize the zigzag pattern, a characteristic feature of a screw dislocation. b, Enlarged view of a screw dislocation showing the zigzag pattern. c, Surface renderings of the screw dislocation where the atoms represented by green dots are in the top layer and those by red dots are in the bottom layer. The zigzag pattern is more clearly visualized, the Burgers vector (b) of the screw dislocation was determined to be , and the width of the screw dislocation was estimated to be ~8.9Å.


  1. 3D volume rendering of the reconstructed Pt nanoparticle after applying a 3D Fourier filter.
    Video 1: 3D volume rendering of the reconstructed Pt nanoparticle after applying a 3D Fourier filter.


  1. Hull, D. & Bacon, D. J. Introduction to Dislocations 5th edn (Butterworth-Heinemann, 2011)
  2. Smith, W. F. & Hashemi, J. Foundations of Materials Science and Engineering 4th edn (McGraw-Hill Science, 2005)
  3. Nakamura, S. The roles of structural imperfections in InGaN-based blue light-emitting diodes and laser diodes. Science 281, 956961 (1998)
  4. Hua, G. C. et al. Microstructure study of a degraded pseudomorphic separate confinement heterostructure blue-green laser diode. Appl. Phys. Lett. 65, 13311333 (1994)
  5. Hirsch, P. B., Horne, R. W. & Whelan, M. J. LXVIII. Direct observations of the arrangement and motion of dislocations in aluminium. Phil. Mag. 1, 677684 (1956)
  6. Bollmann, W. Interference effects in the electron microscopy of thin crystal foils. Phys. Rev. 103, 15881589 (1956)
  7. Menter, J. W. The direct study by electron microscopy of crystal lattices and their imperfections. Proc. R. Soc. Lond. A 236, 119135 (1956)
  8. Howie, A. & Whelan, M. J. Diffraction contrast of electron microscope images of crystal lattice defects. III. Results and experimental confirmation of the dynamical theory of dislocation image contrast. Proc. R. Soc. Lond. A 267, 206230 (1962)
  9. Hirsch, P. B., Cockayne, D. J. H., Spence, J. C. H. & Whelan, M. J. 50 years of TEM of dislocations: past, present and future. Phil. Mag. 86, 45194528 (2006)
  10. Spence, J. C. H. Experimental High-Resolution Electron Microscopy 3rd edn (Oxford Univ. Press, 2003)
  11. Chisholm, M. F. & Pennycook, S. J. Structural origin of reduced critical currents at YBa2Cu3O7−δ grain boundaries. Nature 351, 4749 (1991)
  12. Ludwig, W. et al. Three-dimensional imaging of crystal defects by ‘topo-tomography’. J. Appl. Crystallogr. 34, 602607 (2001)
  13. Cockayne, D. J. H., Ray, I. L. F. & Whelan, M. J. Investigations of dislocation strain fields using weak beams. Phil. Mag. 20, 12651270 (1969)
  14. Pennycook, S. J. & Nellist, P. D. Scanning Transmission Electron Microscopy: Imaging and Analysis 1st edn (Springer, 2011)
  15. Barnard, J. S., Sharp, J., Tong, J. R. & Midgley, P. A. High-resolution three-dimensional imaging of dislocations. Science 313, 319 (2006)
  16. Midgley, P. A. & Weyland, M. in Scanning Transmission Electron Microscopy: Imaging and Analysis. (eds Pennycook, S. J. & Nellist, P. D.) 353392 (Springer, 2011)
  17. Kelly, T. F. & Miller, M. K. Atom probe tomography. Rev. Sci. Instrum. 78, 031101 (2007)
  18. Xin, H. L., Ercius, P., Hughes, K. J., Engstrom, J. R. & Muller, D. A. Three-dimensional imaging of pore structures inside low-κ dielectrics. Appl. Phys. Lett. 96, 223108 (2010)
  19. Bar Sadan, M. et al. Toward atomic-scale bright-field electron tomography for the study of fullerene-like nanostructures. Nano Lett. 8, 891896 (2008)
  20. Scott, M. C. et al. Electron tomography at 2.4 Å resolution. Nature 483, 444447 (2012)
  21. Howie, A. Diffraction channelling of fast electrons and positrons in crystals. Phil. Mag. 14, 223237 (1966)
  22. Chiu, C. Y. et al. Platinum nanocrystals selectively shaped using facet-specific peptide sequences. Nature Chem. 3, 393399 (2011)
  23. Miao, J., Föster, F. & Levi, O. Equally sloped tomography with oversampling reconstruction. Phys. Rev. B 72, 052103 (2005)
  24. Lee, E. et al. Radiation dose reduction and image enhancement in biological imaging through equally sloped tomography. J. Struct. Biol. 164, 221227 (2008)
  25. 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, 53835400 (2010)
  26. 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, 1829018294 (2012)
  27. Marks, L. D. Wiener-filter enhancement of noisy HREM images. Ultramicroscopy 62, 4352 (1996)
  28. Howie, A. & Marks, L. D. Elastic strains and the energy balance for multiply twinned particles. Phil. Mag. A 49, 95109 (1984)
  29. Balk, T. J. & Hemker, K. J. High resolution transmission electron microscopy of dislocation core dissociations in gold and iridium. Phil. Mag. A 81, 15071531 (2001)
  30. Johnson, C. L. J. et al. Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles. Nature Mater. 7, 120124 (2008)
  31. Van Aert, S., Batenburg, K. J., Rossell, M. D., Erni, R. & Van Tendeloo, G. Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374377 (2011)
  32. Bailey, D. H. & Swarztrauber, P. N. The fractional Fourier transform and applications. SIAM Rev. 33, 389404 (1991)
  33. 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, 785803 (2008)
  34. Kirkland, E. J. Advanced Computing in Electron Microscopy 2nd edn (Springer, 2010)
  35. Brown, R. G. & Hwang, P. Y. C. Introduction to Random Signals and Applied Kalman Filtering 3rd edn (Wiley, 1996)
  36. Saxton, W. O. Computer Techniques for Image Processing in Electron Microscopy (Academic, 1978)
  37. Hawkes, P. W. Computer Processing of Electron Microscope Images (Springer, 1980)
  38. Möbus, G., Necker, G. & Rühle, M. Adaptive Fourier-filtering technique for quantitative evaluation of high-resolution electron micrographs of interfaces. Ultramicroscopy 49, 4665 (1993)

Download references

Author information

  1. These authors contributed equally to this work.

    • Chien-Chun Chen &
    • Chun Zhu


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

    • Chien-Chun Chen,
    • Chun Zhu,
    • Edward R. White,
    • M. C. Scott,
    • B. C. Regan &
    • Jianwei Miao
  2. California NanoSystems Institute, University of California, Los Angeles, California 90095, USA

    • Chien-Chun Chen,
    • Chun Zhu,
    • Edward R. White,
    • Chin-Yi Chiu,
    • M. C. Scott,
    • B. C. Regan,
    • Yu Huang &
    • Jianwei Miao
  3. Department of Materials Science and Engineering, University of California, Los Angeles, California 90095, USA

    • Chin-Yi Chiu &
    • Yu Huang
  4. Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60201, USA

    • Laurence D. Marks


J.M. conceived and directed the project; C.-Y.C., C.Z., Y.H. and M.C.S. synthesized and prepared the samples; C.Z., E.R.W., B.C.R. and J.M. designed and conducted the experiments; C.-C.C. and J.M. performed the CM alignment and EST reconstruction; J.M., C.-C.C., C.Z. and L.D.M. analysed and interpreted the results, J.M., C.-C.C. and C.Z. wrote the manuscript. All authors commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information


  1. Report this comment #63941

    Ge Wang said:

    We have serious concerns on this Nature paper 1. Our critiques have just been posted on arXiv ( When we uploaded our critiques to arXiv, we had already studied Dr. Miao?s group?s reply that contains 5 points. While we have solid reasons to disagree with their points, in the following we focus on the first two points that are more significant.

    First, in the reply, they wrote that ?But we did not claim that we could image point defects inside the nanoparticle as we knew that our methods reported in the paper were not sensitive enough to detect point defects.? In contrast, they wrote in their paper 1 that ?EST-based electron tomography in combination with 3D Fourier filtering represents a general method for 3D atomic resolution imaging of the local structure in nanomaterials. Although nanoparticles are used in this study, this method could, in principle, be applied to 3D imaging of thin materials at atomic resolution; the sample thickness is limited only by dynamical electron scattering.? Clearly, if their method cannot resolve individual vacancies, it cannot find additional atoms either, and their intended imaging of dislocations would be highly unreliable since a dislocation (line defect) can be formed by removing a chain of atoms. We demonstrated in our arXiv paper that their method easily missed several atoms in a row, which indicates that their method can easily miss major microstructural features.

    Second, they wrote in their reply that ?Second, in Fig. 1h of their comment1, Wang et al. show a 3D Gaussian noise background within an object support. They then applied a local filtering method with 10% cutoff of a reference Bragg peak and generated many atom-like structures (Fig. 1i). However, they failed to realize the fact that a 3D Gaussian noise background should not produce any Bragg peaks. Without a reference Bragg peak, our Fourier filtering method will not produce a filter. The only explanation for Wang et al.?s claim that they were able to apply our filtering method to a 3D Gaussian noise background with 10% cutoff of a reference Bragg peak and produce atom-like structures is that they have significantly misrepresented our method.? We would like to explain our logic further as follows. Whether Bragg peaks exist or not, the background in the Fourier space can be modeled as a noise distribution. The imaging process is already treated as a linear system in their Nature paper, and hence the noise background can be analyzed separately to see if artifacts could be introduced. In other words, our Gaussian noise background is a valid example to show that their method can easily induce major artifacts.

    Additionally, we would like to mention that our arXiv paper contains new significant information relative to the published BCA 2 that criticized Dr. Miao?s paper correctly. While in that BCA, Rez and Treacy pointed out substantial displacements of atoms, here in our arXiv paper we show that the local Fourier filtering method can completely miss atomic disarrangement and/or produce ghost features that resemble atomic positions. In brief, type I and type II errors are inherent to their method, because their local filtering method is fundamentally against the wide spectrum of sharp features such as dislocations at atomic resolution (


    1. Chen, C.C., et al., Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution. Nature 496(7443):74-79, 2013

    2. Rez, P. and M.M.J. Treacy, Three-dimensional imaging of dislocations. Nature 503(E1):74-79, 2013

  2. Report this comment #64111

    John Miao said:

    Our formal reply to the comment by Dr. Wang and collaborators has been posted on the arXiv (

    In brief, after carefully studying their comment, we found it includes several mistakes and unjustified statements and Dr. Wang and collaborators lack very basic knowledge of dislocations. Moreover, there is clear evidence indicating that Wang et al. significantly misrepresented our method. For more detailed information, please refer to our point-by-point response to their comment (

    Finally, we want to point out that we have set up two public websites where the source codes of the EST and Wiener/Fourier filtering methods as well as the data of our paper can be freely downloaded and tested (;

Subscribe to comments

Additional data