<b><i>Ab initio</i></b>studies of the (111) and ( 1¯ 1¯ 1¯) surfaces of cubic BN: Structure and energetics

We present ab initio local-density-functional investigations of the (111) and $(1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{})$ surfaces of cubic BN. We give a detailed geometrical analysis of different reconstructions, namely, the (1\ifmmode\times\else\texttimes\fi{}1), the (2\ifmmode\times\else\texttimes\fi{}1), and several (2\ifmmode\times\else\texttimes\fi{}2) patterns. We compare the stability of models with different stoichiometries as a function of the chemical potential. Stable phases as a function of nitrogen chemical potential are predicted for both surfaces. In a B-rich environment the N-adatom and in a N-rich environment the nitrogen-triangle patterns are realized on the (111) surface. We predict two phase transitions on the $(1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{})$ surface: as the N chemical potential increases, the boron-triangle, the (2\ifmmode\times\else\texttimes\fi{}1), and the nitrogen-triangle reconstructions are realized.