  The stabilities of $(BN)_x(C_2)_{1-x}$ alloys and related superlattices are
investigated by ab initio pseudopotential calculations. We find that the
$(BN)_1/(C_2)_1$ superlattices in (111) orientations have the lowest formation
energy among many short-range ordered $BNC_2$ structures due to the smallest
number of B-C and C-N bonds. Based on the calculated formation energies at
several compositions and for various ordered structures and assuming
thermodynamic equilibrium, the solid solution phase diagram of
$(BN)_x(C_2)_{1-x}$ alloys is constructed. We find that the complete
miscibility of $(BN)_x(C_2)_{1-x}$ alloys is possible, which is in contrast
with previous theoretical predictions but in agreement with experimental
reports.
