Skip to main content

Thank you for visiting 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.

Design and synthesis of multigrain nanocrystals via geometric misfit strain


The impact of topological defects associated with grain boundaries (GB defects) on the electrical, optical, magnetic, mechanical and chemical properties of nanocrystalline materials1,2 is well known. However, elucidating this influence experimentally is difficult because grains typically exhibit a large range of sizes, shapes and random relative orientations3,4,5. Here we demonstrate that precise control of the heteroepitaxy of colloidal polyhedral nanocrystals enables ordered grain growth and can thereby produce material samples with uniform GB defects. We illustrate our approach with a multigrain nanocrystal comprising a Co3O4 nanocube core that carries a Mn3O4 shell on each facet. The individual shells are symmetry-related interconnected grains6, and the large geometric misfit between adjacent tetragonal Mn3O4 grains results in tilt boundaries at the sharp edges of the Co3O4 nanocube core that join via disclinations. We identify four design principles that govern the production of these highly ordered multigrain nanostructures. First, the shape of the substrate nanocrystal must guide the crystallographic orientation of the overgrowth phase7. Second, the size of the substrate must be smaller than the characteristic distance between the dislocations. Third, the incompatible symmetry between the overgrowth phase and the substrate increases the geometric misfit strain between the grains. Fourth, for GB formation under near-equilibrium conditions, the surface energy of the shell needs to be balanced by the increasing elastic energy through ligand passivation8,9,10. With these principles, we can produce a range of multigrain nanocrystals containing distinct GB defects.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Epitaxially guided growth and gap closing of Mn3O4 grains on a Co3O4 nanocube.
Fig. 2: Extension of SK growth to 3D polyhedral substrates.
Fig. 3: GB defects in Co3O4/Mn3O4 nanocrystals.
Fig. 4: Strain tensor measurements of Co3O4/Mn3O4 nanocrystal.

Data availability

The data that produced and support the findings of this study are available from the corresponding author upon request.

Code availability

Strain and rotation mapping using real-space peak fitting, geometric phase analysis and other Fourier filtering measurements were performed using custom MATLAB scripts. The raw image data and analysis codes are available upon reasonable request.


  1. Siegel, R. W. & Thomas, G. J. Grain boundaries in nanophase materials. Ultramicroscopy 40, 376–384 (1992).

    Article  Google Scholar 

  2. Ovid’ko, I. A. Deformation of nanostructures. Science 295, 2386 (2002).

    Article  Google Scholar 

  3. Read, W. T. & Shockley, W. Dislocation models of crystal grain boundaries. Phys. Rev. 78, 275–289 (1950).

    Article  ADS  CAS  Google Scholar 

  4. Liu, H. H. et al. Three-dimensional orientation mapping in the transmission electron microscope. Science 332, 833–834 (2011).

    Article  ADS  CAS  Google Scholar 

  5. Feng, B. et al. Atomic structures and oxygen dynamics of CeO2 grain boundaries. Sci. Rep. 6, 20288 (2016).

    Article  ADS  CAS  Google Scholar 

  6. Lu, K. Stabilizing nanostructures in metals using grain and twin boundary architectures. Nat. Rev. Mater. 1, 16019 (2016).

    Article  ADS  CAS  Google Scholar 

  7. Klapper, H. & Rudolph, P. in Handbook of Crystal Growth 2nd edn 1093–1141 (Elsevier, 2015).

  8. Kwon, S. G. et al. Heterogeneous nucleation and shape transformation of multicomponent metallic nanostructures. Nat. Mater. 14, 215–223 (2015).

    Article  ADS  CAS  Google Scholar 

  9. Dixit, G. K. & Ranganathan, M. Consequences of elastic anisotropy in patterned substrate heteroepitaxy. Nanotechnology 29, 365305 (2018).

    Article  Google Scholar 

  10. Yang, B., Liu, F. & Lagally, M. G. Local strain-mediated chemical potential control of quantum dot self-organization in heteroepitaxy. Phys. Rev. Lett. 92, 025502 (2004).

    Article  ADS  Google Scholar 

  11. Oh, M. H. et al. Galvanic replacement reactions in metal oxide nanocrystals. Science 340, 964–968 (2013).

    Article  ADS  CAS  Google Scholar 

  12. Pan, A. et al. Insight into the ligand-mediated synthesis of colloidal CsPbBr3 perovskite nanocrystals: the role of organic acid, base, and cesium precursors. ACS Nano 10, 7943–7954 (2016).

    Article  CAS  Google Scholar 

  13. Tsivion, D., Schvartzman, M., Popovitz-Biro, R., von Huth, P. & Joselevich, E. Guided growth of millimeter-long horizontal nanowires with controlled orientations. Science 333, 1003–1007 (2011).

    Article  ADS  CAS  Google Scholar 

  14. Johnson, C. L. et al. Effects of elastic anisotropy on strain distributions in decahedral gold nanoparticles. Nat. Mater. 7, 120–124 (2008).

    Article  ADS  CAS  Google Scholar 

  15. Shklyaev, O. E., Beck, M. J., Asta, M., Miksis, M. J. & Voorhees, P. W. Role of strain-dependent surface energies in Ge/Si(100) island formation. Phys. Rev. Lett. 94, 176102 (2005).

    Article  ADS  CAS  Google Scholar 

  16. Chen, G. et al. Formation of Ge nanoripples on vicinal Si (1110): from Stranski–Krastanow seeds to a perfectly faceted wetting layer. Phys. Rev. Lett. 108, 055503 (2012).

    Article  ADS  CAS  Google Scholar 

  17. Sneed, B. T., Young, A. P. & Tsung, C.-K. Building up strain in colloidal metal nanoparticle catalysts. Nanoscale 7, 12248–12265 (2015).

    Article  ADS  CAS  Google Scholar 

  18. Foster, C. M., Pompe, W., Daykin, A. C. & Speck, J. S. Relative coherency strain and phase transformation history in epitaxial ferroelectric thin films. J. Appl. Phys. 79, 1405–1415 (1996).

    Article  ADS  CAS  Google Scholar 

  19. Sun, Y. et al. Ambient-stable tetragonal phase in silver nanostructures. Nat. Commun. 3, 971–976 (2012).

    Article  ADS  Google Scholar 

  20. Romanov, A. E. & Kolesnikova, A. L. Application of disclination concept to solid structures. Prog. Mater. Sci. 54, 740–769 (2009).

    Article  CAS  Google Scholar 

  21. Gránásy, L., Podmaniczky, F., Tóth, G. I., Tegze, G. & Pusztai, T. Heterogeneous nucleation of/on nanoparticles: a density functional study using the phase-field crystal model. Chem. Soc. Rev. 43, 2159–2173 (2014).

    Article  Google Scholar 

  22. Gaillac, R., Pullumbi, P. & Coudert, F. X. ELATE: An open-source online application for analysis and visualization of elastic tensors. J. Phys. Condens. Matter 28, 275201–275205 (2016).

    Article  Google Scholar 

  23. Ophus, C., Ciston, J. & Nelson, C. T. Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions. Ultramicroscopy 162, 1–9 (2016).

    Article  CAS  Google Scholar 

  24. Hu, H., Gao, H. J. & Liu, F. Theory of directed nucleation of strained islands on patterned substrates. Phys. Rev. Lett. 101, 216102 (2008).

    Article  ADS  Google Scholar 

  25. Zhong, Z. & Bauer, G. Site-controlled and size-homogeneous Ge islands on prepatterned Si (001) substrates. Appl. Phys. Lett. 84, 1922–1924 (2004).

    Article  ADS  CAS  Google Scholar 

  26. Damodaran, A. R. et al. New modalities of strain-control of ferroelectric thin films. J. Phys. Condens. Matter 28, 263001 (2016).

    Article  ADS  Google Scholar 

  27. Li, X., Wei, Y., Lu, L., Lu, K. & Gao, H. Dislocation nucleation governed softening and maximum strength in nano-twinned metals. Nature 464, 877–880 (2010).

    Article  ADS  CAS  Google Scholar 

  28. Mariano, R. G., Mckelvey, K., White, H. S. & Kanan, M. W. Selective increase in CO2 electroreduction activity at grain-boundary surface terminations. Science 358, 1187–1192 (2017).

    Article  ADS  CAS  Google Scholar 

  29. Fan, F. et al. Continuous-wave lasing in colloidal quantum dot solids enabled by facet-selective epitaxy. Nature 544, 75–79 (2017).

    Article  ADS  CAS  Google Scholar 

  30. Gao, P. et al. Atomic-scale mechanisms of ferroelastic domain-wall-mediated ferroelectric switching. Nat. Commun. 4, 2791 (2013).

    Article  ADS  Google Scholar 

Download references


Synthesis and image analysis of the nanocrystal samples were supported by the Research Center Program of IBS in Korea (IBS-R006-D1 to T.H.; IBS-R006-G1 to Y.-E.S. and K.K. The theoretical part of this work was also supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under contract number DE-AC02-05-CH11231 within the Physical Chemistry of Inorganic Nanostructures Program (KC3103 to A.P.A.). The computational work was supported by the Supercomputing Center/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2014-C3-037 to K.K.). Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231. Experiments at PLS-II were supported in part by MSIP and POSTECH.

Author information

Authors and Affiliations



M.H.O., M.G.C., A.P.A. and T.H. conceived the research. M.H.O. and M.G.C. designed and performed the experiments and analysed the results. I.P. and K.K. performed the density functional theory calculations and analysis. Y.P.K. and S.M. conducted the computer-vision-based image processing of HAADF-STEM images. C.O. conducted the strain tensor measurements for the HAADF-STEM micrographs. M.G.K. and B.J. contributed to the analysis of X-ray absorption spectroscopy and X-ray photoelectron spectroscopy data, respectively. D.Y.C., J.M.Y., D.K., X.W.G. and Y.-E.S. discussed and commented on the results. J.J. and J.H. prepared the samples for the TEM analysis. M.H.O., M.G.C., D.K., A.P.A. and T.H. wrote the manuscript. A.P.A. and T.H. supervised the project. All the authors commented on the manuscript.

Corresponding authors

Correspondence to A. Paul Alivisatos or Taeghwan Hyeon.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Laura Bocher, Yong Ding and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Discussion, Supplementary Figures 1–17, Supplementary Table 1 and References.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Oh, M.H., Cho, M.G., Chung, D.Y. et al. Design and synthesis of multigrain nanocrystals via geometric misfit strain. Nature 577, 359–363 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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.


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