Electrons and phonons in the ternary alloy CaAl_{2–x}Si_{x} as a function of composition

We report a detailed first-principles study of the structural, electronic, and vibrational properties of the superconducting C32 phase of the ternary alloy CaAl2?xSix, both in the experimental range 0.6x1.2, for which the alloy has been synthesized, and in the theoretical limits of high aluminum and high silicon concen- tration. Our results indicate that, in the experimental range, the dependence of the electronic bands on com- position is well described by a rigid-band model, which breaks down outside this range. Such a breakdown, in the theoretical limit of high aluminum concentration, is connected to the appearance of vibrational instabili- ties and results in important differences between CaAl2 and MgB2. Unlike MgB2, the interlayer band and the out-of-plane phonons play a major role on the stability and superconductivity of CaAlSi and related C32 intermetallic compounds.