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.

Ab initio determination of solid-state nanostructure

Nature volume 440, pages 655–658 (2006)Cite this article

Abstract

Advances in materials science and molecular biology followed rapidly from the ability to characterize atomic structure using single crystals1,2,3,4. Structure determination is more difficult if single crystals are not available5. Many complex inorganic materials that are of interest in nanotechnology have no periodic long-range order and so their structures cannot be solved using crystallographic methods6. Here we demonstrate that ab initio structure solution of these nanostructured materials is feasible using diffraction data in combination with distance geometry methods. Precise, sub-ångström resolution distance data are experimentally available from the atomic pair distribution function (PDF)6,7. Current PDF analysis consists of structure refinement from reasonable initial structure guesses6,7 and it is not clear, a priori, that sufficient information exists in the PDF to obtain a unique structural solution. Here we present and validate two algorithms for structure reconstruction from precise unassigned interatomic distances for a range of clusters. We then apply the algorithms to find a unique, ab initio, structural solution for C60 from PDF data alone. This opens the door to sub-ångström resolution structure solution of nanomaterials, even when crystallographic methods fail.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

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

Figure 1: Reconstruction of an LJ-88 cluster from unlabelled distances using the Liga algorithm.
Figure 2: Structure solution of fullerene from neutron PDF data.
Figure 3: Illustration of the Liga algorithm for an octahedron.

References

  1. Friedrich, W., Knipping, P. & Laue, M. Interference appearances in x-rays. Ann. Phys.(Berlin) 41, 971–988 (1913); reprinted from Sitzb. K. Bayer. Akad. Wiss. 303–322 (1912).

  2. Bragg, W. H. & Bragg, W. L. The reflection of x-rays by crystals. Proc. R. Soc. Lond. A 88, 428–438 (1913)

    Article  ADS  CAS  Google Scholar 

  3. Perutz, M. F. et al. Structure of haemoglobin: a three-dimensional Fourier synthesis at 5.5?Å resolution, obtained by x-ray analysis. Nature 185, 416–422 (1960)

    Article  ADS  CAS  Google Scholar 

  4. Kendrew, J. B. et al. Structure of myoglobin: a three-dimensional Fourier synthesis at 2?Å resolution. Nature 185, 422–427 (1960)

    Article  ADS  CAS  Google Scholar 

  5. David, W., Shankland, K., McCusker, L. & Baerlocher, C. (eds) Structure Determination from Powder Diffraction Data (Oxford Univ. Press, Oxford, UK, 2002)

  6. Billinge, S. J. L. & Kanatzidis, M. G. Beyond crystallography: the study of disorder, nanocrystallinity and crystallographically challenged materials. Chem. Commun., 749–760 (2004)

  7. Egami, T. & Billinge, S. J. L. Underneath the Bragg Peaks: Structural Analysis of Complex Materials (Pergamon, Oxford, UK, 2003)

    Book  Google Scholar 

  8. 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 

  9. Millis, A. J. Lattice effects in magnetoresistive manganese perovskites. Nature 392, 147–150 (1998)

    Article  ADS  CAS  Google Scholar 

  10. Zhang, H. Z., Gilbert, B., Huang, F. & Banfield, J. F. Water-driven structure transformation in nanoparticles at room temperature. Nature 424, 1025–1029 (2003)

    Article  ADS  CAS  Google Scholar 

  11. Clore, G. M. & Gronenborn, A. M. Determining the structures of large proteins and protein complexes by NMR. Trends Biotechnol. 16, 22–34 (1998)

    Article  CAS  Google Scholar 

  12. Nilges, M. & O'Donoghue, S. I. Ambiguous NOEs and automated NOE assignment. Prog. Nucl. Magn. Reson. Spectrosc. 32, 107–139 (1998)

    Article  CAS  Google Scholar 

  13. Wright, A. Diffraction studies of glass structure: the first 70 years. Glass Phys. Chem. 24, 148–179 (1998)

    CAS  Google Scholar 

  14. Gilbert, B., Huang, F., Zhang, H., Waychunas, G. & Banfield, J. Nanoparticles: Strained and stiff. Science 305, 651–654 (2004)

    Article  ADS  CAS  Google Scholar 

  15. Page, K. et al. Direct observation of the structure of gold nanoparticles by total scattering powder neutron diffraction. Chem. Phys. Lett. 393, 385–388 (2004)

    Article  ADS  CAS  Google Scholar 

  16. Chupas, P. J. et al. Rapid acquisition pair distribution function analysis (RA-PDF). J. Appl. Crystallogr. 36, 1342–1347 (2003)

    Article  CAS  Google Scholar 

  17. Petkov, V. et al. Structure of nanocrystalline materials using atomic pair distribution function analysis: study of LiMoS2 . Phys. Rev. B 65, 092105 (2002)

    Article  ADS  Google Scholar 

  18. McGreevy, R. L. & Pusztai, L. Reverse Monte Carlo simulation: a new technique for the determination of disordered structures. Mol. Simul. 1, 359–367 (1988)

    Article  Google Scholar 

  19. Soper, A. K. Empirical potential Monte Carlo simulation of fluid structure. Chem. Phys. 202, 295–306 (1996)

    Article  CAS  Google Scholar 

  20. Biswas, P., Tafen, D. & Drabold, D. A. Experimentally constrained molecular relaxation: The case of glassy GeSe2 . Phys. Rev. B 71, 054204 (2005)

    Article  ADS  Google Scholar 

  21. Crippen, G. M. & Havel, T. F. Distance Geometry and Molecular Conformation (Wiley & Sons, New York, 1988)

    MATH  Google Scholar 

  22. Hendrickson, B. The molecule problem—exploiting structure in global optimization. SIAM J. Optimiz. 5, 835–857 (1995)

    Article  MathSciNet  Google Scholar 

  23. Deaven, D., Tit, N., Morris, J. & Ho, K. Structural optimization of Lennard-Jones clusters by a genetic algorithm. Chem. Phys. Lett. 256, 195–200 (1996)

    Article  ADS  CAS  Google Scholar 

  24. Wales, D. J. & Scheraga, H. A. Review: Chemistry - global optimization of clusters, crystals, and biomolecules. Science 285, 1368–1372 (1999)

    Article  CAS  Google Scholar 

  25. Cai, W. S. & Shao, X. G. A fast annealing evolutionary algorithm for global optimization. J. Comput. Chem. 23, 427–435 (2002)

    Article  CAS  Google Scholar 

  26. Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  27. Hartke, B. Global cluster geometry optimization by a phenotype algorithm with niches: Location of elusive minima, and low-order scaling with cluster size. J. Comput. Chem. 20, 1752–1759 (1999)

    Article  CAS  Google Scholar 

  28. Thorpe, M. F., Levashov, V. A., Lei, M. & Billinge, S. J. L. in From Semiconductors to Proteins: Beyond the Average Structure (eds Billinge, S. J. L. & Thorpe, M. F.) 105–128 (Kluwer/Plenum, New York, 2002)

    Book  Google Scholar 

  29. Deaven, D. M. & Ho, K. M. Molecular-geometry optimization with a genetic algorithm. Phys. Rev. Lett. 75, 288–291 (1995)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank A. P. Ramirez and R. C. Haddon for supplying the C60 sample. P.J. appreciates discussions with J. Bloch and E. S. Božin. P.M.D. acknowledges support from the Department of Energy (DOE) and S.J.L.B. from the NSF NIRT programme. Neutron data were collected at the GLAD instrument IPNS, which is funded by DOE.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy,

    P. Juhás, P. M. Duxbury & S. J. L. Billinge

  2. Department of Computer Science and Engineering, Michigan State University, Michigan, 48824, East Lansing, USA

    D. M. Cherba & W. F. Punch

Authors
  1. P. Juhás
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. M. Cherba
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. M. Duxbury
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. F. Punch
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. J. L. Billinge
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. J. L. Billinge.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Movie 1

Reconstruction of 88-atom Lennard-Jones cluster from unlabelled pair distances. The movie shows reconstruction of LJ-88 cluster from unlabelled pair distances using the Liga algorithm. The procedure starts by building up partial clusters using only allowed distances. Growth from defective subclusters leads to appearance of high-error (red) atoms. Badly placed atoms are removed allowing convergence to the correct structure. (MPG 2866 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Juhás, P., Cherba, D., Duxbury, P. et al. Ab initio determination of solid-state nanostructure. Nature 440, 655–658 (2006). https://doi.org/10.1038/nature04556

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature04556

This article is cited by

Comments

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.

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