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Rice, ORNL team shows growing 2D sheets on cones allows control of defects to optimize properties

Researchers at Rice University and their colleagues at Oak Ridge National Laboratory (ORNL) have learned to manipulate two-dimensional materials to design in defects that enhance the materials’ properties. Combining theory and experimentation, they showed it’s possible to give 2D materials specific defects—especially atomic-scale seams called grain boundaries. These boundaries may be used to enhance the materials’ electronic, magnetic, mechanical, catalytic and optical properties.

The key is introducing curvature to the landscape that constrains the way defects propagate. The researchers call this “tilt grain boundary topology,” and they achieve it by growing their materials onto a topographically curved substrate—in this case, a cone. The angle of the cone dictates if, what kind and where the boundaries appear. The research is the subject of a paper in the journal ACS Nano.

Grain boundaries are the borders that appear in a material where edges meet in a mismatch. These boundaries are a series of defects; for example, when two sheets of hexagonal graphene meet at an angle, the carbon atoms compensate for it by forming nonhexagonal (five- or seven-member) rings.

Rice theoretical physicist Boris Yakobson and his team have already demonstrated that these boundaries can be electronically significant. They can, for instance, turn perfectly conducting graphene into a semiconductor. In some cases, the boundary itself may be a conductive subnanoscale wire or take on magnetic properties.

But until now researchers had little control over where those boundaries would appear when growing graphene, molybdenum disulfide or other 2-D materials by chemical vapor deposition.

The theory developed at Rice showed growing 2-D material on a cone would force the boundaries to appear in certain places. The width of the cone controlled the placement and, more importantly, the tilt angle, a crucial parameter in tuning the materials' electronic and magnetic properties, Yakobson said.

Experimental collaborators from Oak Ridge led by co-author David Geohegan provided evidence backing key aspects of the theory. They achieved this by growing tungsten disulfide WS2) onto small cones similar to those in Rice’s computer models. The boundaries that appeared in the real materials matched those predicted by theory.

(a) A triangular WS2 crystal flake. (b) Modeled time progression of crystal growth on a flat surface (formally a cone with 2a = π). (c) Experimental SEM image of WS2 crystal grown on flat substrate. (d) Modeled progression of crystal growth on a conical surface with 2a = 19.2° (or Δ = π/3). (e) Experimental image of WS2 crystal grown on a conical substrate. (f) Simulations of crystal growth for a series of different cones, with 2a = 19.2°, 28.9°, 38.9°, 47.2°, 60°. (g) Color-coded plot of the orientation field θ for (f). Blue represents φ = 1(grain), and white represents φ = 0 (substrate); in (g) cyan represents substrate. Credit: ACS, Yu et al. Click to enlarge.

The nonplanar shape of the substrate forces the 2-D crystal to grow in a curved non-Euclidian space>. This strains the crystal, which occasionally yields by giving a way to the seams, or grain boundaries. It’s no different from the way a tailor would add a seam to a suit or a dress to fit a curvy customer.

—Boris Yakobson

Modeling cones of different widths also revealed a “magic cone” of 38.9 degrees upon which growing a 2-D material would leave no grain boundary at all.

The Rice team extended its theory to see what would happen if the cones sat on a plane. They predicted how grain boundaries would form over the entire surface, and again, Oak Ridge experiments confirmed their results.

Yakobson said both the Rice and Oak Ridge teams were working on aspects of the research independently.

It was slow going until we met at a conference in Florida a couple of years back and realized that we should continue together. It was certainly gratifying to see how experiments confirmed the models, while sometimes offering important surprises. Now we need to do the additional work to comprehend them as well.

—Boris Yakobson

Rice graduate students Henry Yu and Nitant Gupta are co-lead authors of the paper. Co-authors are former Rice postdoctoral researcher Zhili Hu, now at Nanjing University of Aeronautics and Astronautics, and researchers Kai Wang, Bernadeta Srijanto and Kai Xiao of Oak Ridge National Laboratory. Geohegan is the functional hybrid nanomaterials group leader at Oak Ridge’s Center for Nanophase Materials Sciences. Yakobson is the Karl F. Hasselmann Professor of Materials Science and NanoEngineering and a professor of chemistry.

The US Department of Energy Basic Energy Sciences and its Center for Nanophase Materials Sciences and the Office of Naval Research supported the research.

Computer resources were provided by the Night Owls Time-Sharing Service and its National Science Foundation-supported DAVinCI supercomputer, both administered by Rice’s Center for Research Computing; the resources were procured in partnership with Rice’s Ken Kennedy Institute for Information Technology.


  • Henry Yu, Nitant Gupta, Zhili Hu, Kai Wang, Bernadeta R. Srijanto, Kai Xiao, David B. Geohegan, and Boris I. Yakobson (2017) “Tilt Grain Boundary Topology Induced by Substrate Topography” ACS Nano Article doi: 10.1021/acsnano.7b03681


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