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Three-dimensional mapping of a deformation field inside a nanocrystal

Abstract

Coherent X-ray diffraction imaging is a rapidly advancing form of microscopy: diffraction patterns, measured using the latest third-generation synchrotron radiation sources, can be inverted to obtain full three-dimensional images of the interior density within nanocrystals1,2,3. Diffraction from an ideal crystal lattice results in an identical copy of this continuous diffraction pattern at every Bragg peak. This symmetry is broken by the presence of strain fields, which arise from the epitaxial contact forces that are inevitable whenever nanocrystals are prepared on a substrate4. When strain is present, the diffraction copies at different Bragg peaks are no longer identical and contain additional information, appearing as broken local inversion symmetry about each Bragg point. Here we show that one such pattern can nevertheless be inverted to obtain a ‘complex’ crystal density, whose phase encodes a projection of the lattice deformation. A lead nanocrystal was crystallized in ultrahigh vacuum from a droplet on a silica substrate and equilibrated close to its melting point. A three-dimensional image of the density, obtained by inversion of the coherent X-ray diffraction, shows the expected facetted morphology, but in addition reveals a real-space phase that is consistent with the three-dimensional evolution of a deformation field arising from interfacial contact forces. Quantitative three-dimensional imaging of lattice strain on the nanometre scale will have profound consequences for our fundamental understanding of grain interactions and defects in crystalline materials4. Our method of measuring and inverting diffraction patterns from nanocrystals represents a vital step towards the ultimate goal of atomic resolution single-molecule imaging that is a prominent justification for development of X-ray free-electron lasers5,6,7.

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Figure 1: Schematic diagram of the coherent X-ray diffraction experiment.
Figure 2: Two perpendicular views of the three-dimensional reconstruction of the magnitude of the nanocrystal's complex density function.
Figure 3: Phase maps cutting through the crystal at three parallel planes.
Figure 4: Phase interpretation.

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Acknowledgements

This research was funded by the NSF Division of Materials Research and the EPSRC. The UNICAT facility at the APS and the APS itself are supported by the US Department of Energy, the former through the Frederick Seitz Materials Research Laboratory.

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Correspondence to Ian K. Robinson.

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Supplementary information

Supplementary Figure 1

Animation showing the main result of the 3D visualisation of a strain field inside a Pb nanocrystal. This is a moving rendition of Fig 3(a) rotating about the substrate normal. A single isosurface of the phase and the best fit are superimposed on an image of the crystal density. The point defect lines used to generate the fit (dots) and the direction of Q (arrow) are also illustrated. (MPG 2140 kb)

Supplementary Figure 2

Raw coherent X-ray diffraction data measured for the Pb nanocrystal studied in this work. (PDF 391 kb)

Supplementary Figure 3

Isosurface views of the nanocrystal density, before (left column) and after (middle and right) performing the geometric correction. (PDF 47 kb)

Supplementary Figure 4

Sections of the real space density map of the crystal. (PDF 332 kb)

Supplementary Figure 5

Least-square fits of the shape of the boundary of the real space density map of the crystal. (PDF 765 kb)

Supplementary Figure 6

Sections of the real space phase map of the crystal. (PDF 16 kb)

Supplementary Figure 7

Plots of the density variation across rounded portions of the crystal (a), and across planar boundaries of the crystal (b-d). (PDF 793 kb)

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Pfeifer, M., Williams, G., Vartanyants, I. et al. Three-dimensional mapping of a deformation field inside a nanocrystal. Nature 442, 63–66 (2006). https://doi.org/10.1038/nature04867

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  • DOI: https://doi.org/10.1038/nature04867

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