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We predict the stabilities of \alpha-graphynes and their boron nitrideanalogues(\alpha-BNyne), which are considered as competitors of graphene andtwo-dimensional hexagonal BN. Based on first-principles plane wave method, weinvestigated the stability and structural transformations of these materials atdifferent sizes using phonon dispersion calculations and ab-initio finitetemperature, molecular dynamics simulations. Depending on the number ofadditional atoms in the edges between the corner atoms of the hexagons, n, both\alpha-graphyne(n) and \alpha-BNyne(n) are stable for even n, but unstable forodd n. \alpha-graphyne(3) undergoes a structural transformation, where thesymmetry of hexagons is broken. We present the structure optimized cohesiveenergies, electronic, magnetic and mechanical properties of stable structures.Our calculations reveal the existence of Dirac cones in the electronicstructures of \alpha-graphynes of all sizes, where the Fermi velocitiesdecrease with increasing n. The electronic and magnetic properties of thesestructures are modified by hydrogenation. A single hydrogen vacancy renders amagnetic moment of one Bohr magneton. We finally present the properties of thebilayer \alpha-graphyne and \alpha-BNyne structures. We expect that theselayered materials can function as frameworks in various chemical and electronicapplications.

Size dependence in the stabilities and electronic properties of \alpha -graphyne and its BN analogue