First-principle studies of Ca-X (X=Si,Ge,Sn,Pb) intermetallic compounds

The structural properties, elastic properties, heats of formation, electronic structures, and densities of states of 20 intermetallic compounds in the Ca-X (X=Si, Ge, Sn, Pb) systems have been systematically investigated by using first-principle calculations. Our computational results indicated that with increasing atomic weight of X, the bulk modulus of Ca-X intermetallic compounds decreases gradually. It was also found that Ca₃₆Sn₂₃ and CaPb are mechanically unstable phases. Results on the electronic energy band and densities of states also indicated that Ca₃Si₄ is an indirect band gap semiconductor with a band gap of 0.598 eV, and Ca₂Si, Ca₂Ge, Ca₂Sn, and Ca₂Pb are direct band gap semiconductors with band gaps of 0.324, 0.265, 0.06, and 0.07 eV, respectively. In addition, it is found that the absolute values of heats of formation for all Ca-X intermetallics are larger than 30 kJ/mol atom.