Structure, bonding, and stability of topologically close-packed intermetallic compounds

An orthogonalized-plane-wave-based first-principles pseudopotential method is presented for calculating the crystal structure, lattice constants, enthalpy, and volume of formation of binary intermetallic compounds and alloys. The pseudopotential is optimized specifically for the case of binary systems. The Xα method is used to construct the electron-ion potential. The theory is applied to investigate the random binary alloys and ordered intermetallic compounds between alkali metals. The crystal structure of the intermetallic phases (Na₂K, Na₂Cs, K₂Cs, and K₇{Cs}₆$) which belong to the type of topologically close-packed (Frank-Kasper) phases is successfully explained in terms of a delicate balance between electrostatic and band-structure forces. The enthalpies and volumes of formation and the range of stability of these phases are calculated with good accuracy---with the exception of Na₂Cs, however. It is argued that s-d hybridization is vital for the formation of Na₂Cs. The physical principle governing the bonding is shown to be close-packing, described in terms of soft interionic potentials.