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Ab initio determination of solid-state nanostructure


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.

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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.


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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.

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Correspondence to S. J. L. Billinge.

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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)

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Juhás, P., Cherba, D., Duxbury, P. et al. Ab initio determination of solid-state nanostructure. Nature 440, 655–658 (2006).

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