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 materials^1,2 is well known. However, elucidating this influence experimentally is difficult because grains typically exhibit a large range of sizes, shapes and random relative orientations^3-5. 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 passivation^8-10. With these principles, we can produce a range of multigrain nanocrystals containing distinct GB defects.