  The structural stability and electronic properties of the ternary
intermetallic compounds NiSnM (M = Ti, Zr, Hf) and the closely related Heusler
compounds Ni$_2$SnM are discussed using the results of ab initio
pseudopotential total energy and band-structure calculations performed with a
plane wave basis set using the conjugate gradients algorithm. The results
characterize the lowest energy phase of NiSnM compounds, with a SnM rocksalt
structure sublattice, as narrow gap semiconductors with indirect gaps near 0.5
eV. Two other atomic arrangements for NiSnM in the MgAgAs structure result in
energetically unfavorable compounds that are metallic. The gap formation in the
lowest energy structure of NiSnZr and relative stability of the three atomic
arrangements are investigated within a tight-binding framework and by
considering the decompositions of each ternary compound into a binary
substructure plus a third element sublattice. The stabilization of the lowest
energy phase of NiSnZr is found to be mainly due to the relative stability of
the SnZr rocksalt substructure, while the opening of the gap induced by the
addition of the symmetry-breaking Ni sublattice makes a relatively minor
contribution. From analysis of structural and chemical trends, CoVSn is
predicted to be a new semiconducting intermetallic in the MgAgAs structure with
a 0.8 eV indirect gap.
