Missing links towards understanding 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 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. This method can also potentially serve as a standard approach for other two-dimensional (2D) compound materials. Based on this algorithm, we constructed Wulff plot and discovered that only when edges are passivated by hydrogen atoms and temperature effects are taken into account can experimental morphology be explained.