Polymorphism of two-dimensional boron.

The structural stability and diversity of elemental boron layers are evaluated by treating them as pseudoalloy B(1-x)[hexagon](x), where [hexagon] is a vacancy in the close-packed triangular B lattice. This approach allows for an elegant use of the cluster expansion method in combination with first-principles density-functional theory calculations, leading to a thorough exploration of the configurational space. A finite range of compositions x is found where the ground-state energy is essentially independent of x, uncovering a variety of stable B-layer phases (all metallic) and suggesting polymorphism, in stark contrast to graphene or hexagonal BN.