Letter | Published:

Deciphering chemical order/disorder and material properties at the single-atom level

Nature volume 542, pages 7579 (02 February 2017) | Download Citation


Perfect crystals are rare in nature. Real materials often contain crystal defects and chemical order/disorder such as grain boundaries, dislocations, interfaces, surface reconstructions and point defects1,2,3. Such disruption in periodicity strongly affects material properties and functionality1,2,3. Despite rapid development of quantitative material characterization methods1,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18, correlating three-dimensional (3D) atomic arrangements of chemical order/disorder and crystal defects with material properties remains a challenge. On a parallel front, quantum mechanics calculations such as density functional theory (DFT) have progressed from the modelling of ideal bulk systems to modelling ‘real’ materials with dopants, dislocations, grain boundaries and interfaces19,20; but these calculations rely heavily on average atomic models extracted from crystallography. To improve the predictive power of first-principles calculations, there is a pressing need to use atomic coordinates of real systems beyond average crystallographic measurements. Here we determine the 3D coordinates of 6,569 iron and 16,627 platinum atoms in an iron-platinum nanoparticle, and correlate chemical order/disorder and crystal defects with material properties at the single-atom level. We identify rich structural variety with unprecedented 3D detail including atomic composition, grain boundaries, anti-phase boundaries, anti-site point defects and swap defects. We show that the experimentally measured coordinates and chemical species with 22 picometre precision can be used as direct input for DFT calculations of material properties such as atomic spin and orbital magnetic moments and local magnetocrystalline anisotropy. This work combines 3D atomic structure determination of crystal defects with DFT calculations, which is expected to advance our understanding of structure–property relationships at the fundamental level.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    , & Atomic electron tomography: 3D structures without crystals. Science 353, aaf2157 (2016)

  2. 2.

    & (eds) Introduction to Dislocations 5th edn (Butterworth-Heinemann, 2011)

  3. 3.

    & Crystallography and Crystal Defects 2nd edn (John Wiley & Sons, 2012)

  4. 4.

    & Atom probe tomography. Rev. Sci. Instrum. 78, 031101 (2007)

  5. 5.

    & Electron tomography and holography in materials science. Nat. Mater. 8, 271–280 (2009)

  6. 6.

    Structure and bonding at the atomic scale by scanning transmission electron microscopy. Nat. Mater. 8, 263–270 (2009)

  7. 7.

    et al. Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571–574 (2010)

  8. 8.

    & Scanning Transmission Electron Microscopy: Imaging and Analysis (Springer Science & Business Media, 2011)

  9. 9.

    , , , & Three-dimensional atomic imaging of crystalline nanoparticles. Nature 470, 374–377 (2011)

  10. 10.

    et al. Three-dimensional atomic imaging of colloidal core-shell nanocrystals. Nano Lett. 11, 3420–3424 (2011)

  11. 11.

    et al. Electron tomography at 2.4-ångström resolution. Nature 483, 444–447 (2012)

  12. 12.

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

  13. 13.

    et al. Three-dimensional elemental mapping at the atomic scale in bimetallic nanocrystals. Nano Lett. 13, 4236–4241 (2013)

  14. 14.

    et al. Imaging screw dislocations at atomic resolution by aberration-corrected electron optical sectioning. Nat. Commun. 6, 7266 (2015)

  15. 15.

    et al. 3D structure of individual nanocrystals in solution by electron microscopy. Science 349, 290–295 (2015)

  16. 16.

    et al. Three-dimensional coordinates of individual atoms in materials revealed by electron tomography. Nat. Mater. 14, 1099–1103 (2015)

  17. 17.

    et al. Measuring lattice strain in three dimensions through electron microscopy. Nano Lett. 15, 6996–7001 (2015)

  18. 18.

    et al. Formation of bimetallic clusters in superfluid helium nanodroplets analysed by atomic resolution electron tomography. Nat. Commun. 6, 8779 (2015)

  19. 19.

    & Density-Functional Theory of Atoms and Molecules (Oxford Univ. Press, 1994)

  20. 20.

    Density functional theory: its origins, rise to prominence, and future. Rev. Mod. Phys. 87, 897–923 (2015)

  21. 21.

    & Introduction to Magnetic Materials 2nd edn (Wiley, 2008)

  22. 22.

    et al. High density heat assisted magnetic recording media and advanced characterization — progress and challenges. IEEE Trans. Magn. 51, 3201709 (2015)

  23. 23.

    et al. Bit-patterned magnetic recording: theory, media fabrication, and recording performance. IEEE Trans. Magn. 51, 0800342 (2015)

  24. 24.

    et al. A guideline for atomistic design and understanding of ultrahard nanomagnets. Nat. Commun. 2, 528 (2011)

  25. 25.

    , , , & Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices. Science 287, 1989–1992 (2000)

  26. 26.

    , , & Multiply twinned morphologies of FePt and CoPt nanoparticles. Phys. Rev. Lett. 100, 087203 (2008)

  27. 27.

    & Competition between ordering, twinning, and segregation in binary magnetic 3d-5d nanoparticles: a supercomputing perspective. Int. J. Quantum Chem. 112, 277–288 (2012)

  28. 28.

    et al. Enhanced orbital magnetism in Fe50Pt50 nanoparticles. Phys. Rev. Lett. 97, 117201 (2006)

  29. 29.

    et al. Magnetic moment of Fe in oxide-free FePt nanoparticles. Phys. Rev. B 76, 064414 (2007)

  30. 30.

    & Formation mechanism of FePt nanoparticles synthesized via pyrolysis of iron(III) ethoxide and platinum(II) acetylacetonate. Chem. Mater. 17, 6624–6634 (2005)

  31. 31.

    & Growth and Coarsening: Ostwald Ripening in Material Processing (Springer Science & Business Media, 2002)

  32. 32.

    & Local magneto-volume effect in amorphous iron. J. Magn. Magn. Mater. 98, L1–L6 (1991)

  33. 33.

    & Micromagnetic modelling — the current state of the art. J. Phys. D 33, R135–R156 (2000)

  34. 34.

    et al. FePt nanoparticles as an Fe reservoir for controlled Fe release and tumor inhibition. J. Am. Chem. Soc. 131, 15346–15351 (2009)

  35. 35.

    , , & Operation of TEAM I in a user environment at NCEM. Microsc. Microanal. 18, 676–683 (2012)

  36. 36.

    , & Fast Fourier method for the accurate rotation of sampled images. Opt. Commun. 139, 99–106 (1997)

  37. 37.

    , , & Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16, 2080–2095 (2007)

  38. 38.

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

  39. 39.

    & Principles of Computerized Tomographic Imaging (SIAM, Philadelphia, 2001)

  40. 40.

    , & Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects. J. Opt. Soc. Am. A 15, 1662–1669 (1998)

  41. 41.

    , , & Beyond crystallography: diffractive imaging using coherent X-ray light sources. Science 348, 530–535 (2015)

  42. 42.

    Electron Tomography: Methods for Three-Dimensional Visualization of Structures in the Cell (Springer, 2010)

  43. 43.

    Iterative methods for the three-dimensional reconstruction of an object from projections. J. Theor. Biol. 36, 105–117 (1972)

  44. 44.

    , & Equally sloped tomography with oversampling reconstruction. Phys. Rev. B 72, 052103 (2005)

  45. 45.

    & Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm. Ultrason. Imaging 6, 81–94 (1984)

  46. 46.

    et al. Crystallography & NMR System: a new software suite for macromolecular structure determination. Acta Crystallogr. D54, 905–921 (1998)

  47. 47.

    Advanced Computing in Electron Microscopy 2nd edn (Springer Science & Business Media, 2010)

  48. 48.

    , & Theoretical study of antiphase boundaries in fcc alloys. Phys. Rev. Lett. 65, 1016–1019 (1990)

  49. 49.

    & Lattice Monte Carlo simulations of FePt nanoparticles: influence of size, composition, and surface segregation on order-disorder phenomena. Phys. Rev. B 72, 094203 (2005)

  50. 50.

    A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proc. 14th Int. Joint Conf. on A.I. Vol. 2, 1137–1143 (Morgan Kaufmann, San Francisco, 1995)

  51. 51.

    & Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45, 566–569 (1980)

  52. 52.

    & From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999)

  53. 53.

    Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994)

  54. 54.

    et al. Order-N multiple scattering approach to electronic structure calculations. Phys. Rev. Lett. 75, 2867–2870 (1995)

  55. 55.

    , , & Magnetic anisotropy of monoatomic iron chains embedded in copper. Phys. Rev. B 65, 144424 (2002)

  56. 56.

    et al. On calculating the magnetic state of nanostructures. Prog. Mater. Sci. 52, 371–387 (2007)

Download references


We thank J. Shan, J. A. Rodriguez, M. Gallagher-Jones and J. Ma for help with this project. This work was primarily supported by the Office of Basic Energy Sciences of the US DOE (DE-SC0010378). This work was also supported by the Division of Materials Research of the US NSF (DMR-1548924 and DMR-1437263) and DARPA (DARPA-BAA-12-63). The chemical ordering analysis and ADF-STEM imaging with TEAM I were performed at the Molecular Foundry, Lawrence Berkeley National Laboratory, which is supported by the Office of Science, Office of Basic Energy Sciences of the US DOE (DE-AC02-05CH11231). M.E. (DFT calculations) was supported by the US DOE, Office of Science, Basic Energy Sciences, Material Sciences and Engineering Division. DFT calculations by P.K. were conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. This research used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science of the US DOE (DE-AC05-00OR22725).

Author information

Author notes

    • Yongsoo Yang
    • , Chien-Chun Chen
    • , M. C. Scott
    •  & Colin Ophus

    These authors contributed equally to this work.


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

    • Yongsoo Yang
    • , Chien-Chun Chen
    • , M. C. Scott
    • , Rui Xu
    • , Alan Pryor
    • , Li Wu
    • , Jihan Zhou
    •  & Jianwei Miao
  2. Department of Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

    • Chien-Chun Chen
  3. National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • M. C. Scott
    • , Colin Ophus
    •  & Peter Ercius
  4. Department of Physics, University at Buffalo, the State University of New York, Buffalo, New York 14260, USA

    • Fan Sun
    •  & Hao Zeng
  5. Nanoscale Physics Research Laboratory, School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

    • Wolfgang Theis
  6. National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    • Markus Eisenbach
  7. Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    • Paul R. C. Kent
  8. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    • Paul R. C. Kent
  9. Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182, USA

    • Renat F. Sabirianov


  1. Search for Yongsoo Yang in:

  2. Search for Chien-Chun Chen in:

  3. Search for M. C. Scott in:

  4. Search for Colin Ophus in:

  5. Search for Rui Xu in:

  6. Search for Alan Pryor in:

  7. Search for Li Wu in:

  8. Search for Fan Sun in:

  9. Search for Wolfgang Theis in:

  10. Search for Jihan Zhou in:

  11. Search for Markus Eisenbach in:

  12. Search for Paul R. C. Kent in:

  13. Search for Renat F. Sabirianov in:

  14. Search for Hao Zeng in:

  15. Search for Peter Ercius in:

  16. Search for Jianwei Miao in:


J.M. directed the project; F.S. and H.Z. prepared the samples; M.C.S., W.T., P.E. and J.M. discussed and/or acquired the data; Y.Y., C.-C.C., R.X., A.P.J., L.W., J.Z. and J.M. conducted the image reconstruction and atom tracing; C.O., Y.Y., H.Z., P.E., W.T., R.F.S., M.C.S. and J.M. analysed and interpreted the results; M.E., P.R.C.K., R.F.S., Y.Y., H.Z., C.O., W.T. and J.M. discussed and performed the DFT calculations; J.M., Y.Y., H.Z., P.E., C.O., W.T., M.E., P.R.C.K., R.F.S. wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Jianwei Miao.

Reviewer Information Nature thanks M. Farle and A. Kirkland for their contribution to the peer review of this work.

Extended data

Supplementary information


  1. 1.

    Progressive orthoslices along the [010] direction (y-axis), showing the 3D reconstructed intensity from 68 experimental ADF-STEM images.

    Each orthoslice integrates the intensity of a 1.86-Å-thick layer and individual Fe and Pt atoms can be clearly distinguished from their intensity contrast.

  2. 2.

    3D visualization of the different phases in the FePt nanoparticle.

    The nanoparticle consists of two large L12 FePt3 grains and seven smaller grains located between them, including three L12 FePt3 grains, three L10 FePt grains and a Pt-rich A1 grain.

About this article

Publication history






Further reading


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.