Structure and Energetics of Fragments of the Planar α and β Boron Sheets

Large scale first principles calculations based on density functional theory and using hybrid exchange-correlation functionals have been performed in order to study the structural properties and the relative stability of fragments of the planar α and β boron sheets. Based on the considered structures, we show that, in contrast to the fragments of the α -sheet, all the fragments of the β -sheet, having more than ≈30 atoms, are fully planar regardless of their shape. We conclude that the β -sheet is the only planar boron sheet reported so far that retains planarity even if it is reduced to relatively small fragments.