Missing links towards understanding the equilibrium shapes of hexagonal boron nitride: algorithm, hydrogen passivation, and temperature effects.

There is a large discrepancy between the experimental observations and the theoretical predictions in the morphology of hexagonal boron nitride (h-BN) nanosheets. Theoretically predicted hexagons terminated by armchair edges are not observed in experiments; and experimentally observed triangles terminated by zigzag edges are found theoretically unstable. There are two key issues in theoretical investigations, namely, an efficient and accurate algorithm of the absolute formation energy of h-BN edges, and a good understanding of the role of hydrogen passivation during h-BN growth. Here, we first proposed an efficient algorithm to calculate asymmetric edges with a self-consistent accuracy of about 0.0014 eV Å-1. This method can also serve as a standard approach for other two-dimensional (2D) compound materials. Then, by using this method, we discovered that only when edges are passivated by hydrogen atoms and temperature effects are taken into account can experimental morphology be explained. We further employed the Wulff construction to obtain the equilibrium shapes of H-passivated h-BN nanosheets under their typical growth conditions at T = 1300 K and p = 1 bar, and found out that the equilibrium shapes are sensitive to hydrogen passivation and the growth conditions. Our results resolved long-standing discrepancies between experimental observations and theoretical analysis, explaining the thermodynamic driving force of triangular, truncated triangular, and hexagonal shapes, and revealing the key role of hydrogen in h-BN growth. These discoveries and the advancement in the algorithm may open the gateway towards the realization of 2D electronic and spintronic devices based on h-BN.