  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/{\AA}. This method can also potentially 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 Wulff construction to obtain the
equilibrium shapes of H-passivated h-BN nanosheets under its 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 the
triangular, truncated triangular, and hexagonal shapes, and revealing the key
role of hydrogen in h-BN growth. These discoveries and the advancement in
algorithm may open the gateway towards the realization of 2D electronic and
spintronic devices based on h-BN.
