  We predict the stabilities of \alpha-graphynes and their boron nitride
analogues(\alpha-BNyne), which are considered as competitors of graphene and
two-dimensional hexagonal BN. Based on first-principles plane wave method, we
investigated the stability and structural transformations of these materials at
different sizes using phonon dispersion calculations and ab-initio finite
temperature, molecular dynamics simulations. Depending on the number of
additional 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 for
odd n. \alpha-graphyne(3) undergoes a structural transformation, where the
symmetry of hexagons is broken. We present the structure optimized cohesive
energies, electronic, magnetic and mechanical properties of stable structures.
Our calculations reveal the existence of Dirac cones in the electronic
structures of \alpha-graphynes of all sizes, where the Fermi velocities
decrease with increasing n. The electronic and magnetic properties of these
structures are modified by hydrogenation. A single hydrogen vacancy renders a
magnetic moment of one Bohr magneton. We finally present the properties of the
bilayer \alpha-graphyne and \alpha-BNyne structures. We expect that these
layered materials can function as frameworks in various chemical and electronic
applications.
