Quasicrystalline nanocrystal superlattice with partial matching rules


Expanding the library of self-assembled superstructures provides insight into the behaviour of atomic crystals and supports the development of materials with mesoscale order1,2. Here we build on recent findings of soft matter quasicrystals3,4,5,6 and report a quasicrystalline binary nanocrystal superlattice that exhibits correlations in the form of partial matching rules reducing tiling disorder. We determine a three-dimensional structure model through electron tomography7,8 and direct imaging of surface topography. The 12-fold rotational symmetry of the quasicrystal is broken in sublayers, forming a random tiling of rectangles, large triangles and small triangles with 6-fold symmetry. We analyse the geometry of the experimental tiling and discuss factors relevant for the stabilization of the quasicrystal. Our joint experimental–computational study demonstrates the power of nanocrystal superlattice engineering and further narrows the gap between the richness of crystal structures found with atoms and in soft matter assemblies.

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Figure 1: Self-assembled binary NC superlattices with quasiperiodic and periodic order.
Figure 2: Tomographic reconstruction and SEM imaging reveal the three-dimensional structure of the superlattices.
Figure 3: Three-dimensional structure model of the quasicrystal and geometric tiling analysis.
Figure 4: Stabilization and growth of the quasicrystal.


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X.Y. and C.B.M. were supported by the US Department of Energy Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award No. DE-SC0002158. J.C. and C.B.M. received support from NSF MRSEC under Award No. DMR-1120901. M.E.I., M.E. and S.C.G. were supported by the US Army Research Office under Award No. W911NF-10-1-0518 and by the Assistant Secretary of Defense for Research and Engineering, US Department of Defense under Award No. N00244-09-1-0062. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the DOD/ASD(R&E). S.C.G. was partially supported by a Simons Investigator award from the Simons Foundation. A.D. was supported by the National Basic Research Program of China (2014CB845602) and the Natural National Science Foundation of China (21373052). We thank B. Schultz for providing image analysis code. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant number ACI-1053575, XSEDE award DMR 140129. Additional computational resources and services were supported by Advanced Research Computing at the University of Michigan, Ann Arbor.

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X.Y., J.C. and C.B.M. conceived and designed the experiments. X.Y. and J.C. carried out nanocrystal syntheses and self-assembly, and carried out TEM imaging and electron tomography reconstruction. X.Y., J.C. and A.D. performed SEM imaging. M.E.I., M.E. and S.C.G. planned and discussed theoretical analysis and computer simulations. M.E.I. performed analysis and simulations. M.E., S.C.G. and C.B.M. supervised the project. All authors discussed the results and commented on the manuscript.

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Correspondence to Sharon C. Glotzer or Christopher B. Murray.

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Ye, X., Chen, J., Eric Irrgang, M. et al. Quasicrystalline nanocrystal superlattice with partial matching rules. Nature Mater 16, 214–219 (2017). https://doi.org/10.1038/nmat4759

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