Structural and superconducting transitions in Mg_1-xAl_xB₂

From systematic ab initio calculations for the alloy system Mg_1-xAl_xB₂, we find a strong tendency for the formation of a superstructure characterized by Al-rich layers. We also present a simple model, based on calculated energies and an estimate of the configurational entropy, which suggests that the alloy has two separate concentration regimes of phase separation, with critical points near x=0.25 and x=0.75. These results, together with calculations of electronic densities of states in several ionic arrangements, give a qualitative explanation for the observed structural instabilities, as well as the x dependence of the superconducting T_c for x<0.6.