Structural stability of Ni-containing half-Heusler compounds

Half-Heusler compounds containing Ni of the form NiMP, where M is a trivalent (Sc) or tetravelent (Ti, Zr, Hf) ion and P is a pnictide or stannide ion (Sb, Sn), are known to form semiconducting phases for $M=\mathrm{Sc}$ and $P=\mathrm{Sb}$ as well as when M=Ti,Zr,Hf and $P=\mathrm{Sn}.$ However, the electronic structure of these compounds depends sensitively on the relative arrangements of the atoms within the unit cell, changing from a narrow-gap semiconductor to a zero-gap semiconductor to a metal, depending on which of the three atoms lies in the octahedrally coordinated pocket of the NaCl substructure formed by the other two atoms. We have carried out extensive calculations of the total energy for these systems using an all-electron, full-potential method within density-functional theory [using both the local-density approximation and the generalized gradient approximation] to clarify some of the conflicts in earlier calculations using pseudopotential and linear muffin-tin orbital–atomic-sphere approximation methods. The minimum-energy configuration for each of these systems occurs when the Ni atom occupies the octahedrally coordinated pocket formed by the other two elements MP. By comparing the energies of the binary compounds arising from different arrangements of the atoms within the unit cell, we find that the stability of the lowest-energy configuration of the ternary system derives from the energy gained from two sources. The largest source is MP forming in the NaCl substructure rather than a diamond substructure, in agreement with the previous pseudopotential calculations of Ogut and Rabe. Also important are the Ni atoms lying in the octahedrally coordinated pockets and bonding with four M and four P nearest-neighbor atoms rather than forming a part of the NaCl substructure itself. The energies of antisite defects have been investigated by studying the supercell $(\mathrm{Ni}\mathit{MP}{)}_4$ formed in the simple cubic structure with individual atoms moved from their ideal positions. We find that the idealized half-Heusler structure (formed by three interpenetrating fcc lattices) has the lowest energy ${(E}_0)$ while structures where Ni atoms move out of a fcc arrangement, but remain within the octahedrally coordinated pockets of MP, have energies of 0.5-eV/unit cell higher than $E_0,$ while structures with disorder in the MP NaCl substructure have energies about 1.5-eV/unit cell higher than $E_0.$ Since the MP disorder and not the Ni disorder is seen experimentally at low temperatures, this Ni disorder may be annealed out while the MP disorder is quenched.