Structural and superconducting transitions in Mg1ÀxAlxB2

From systematic ab initio calculations for the alloy system Mg12xAlxB2, 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 x50.25 and x50.75. 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 Tc for x,0.6.