Abstract:Previous studies have indicated that the figure of merit (ZT) of half-Heusler (HH) alloys with composition MNiSn (M = Ti, Zr, or Hf) is greatly enhanced when the alloys contain a nano-scale full-Heusler (FH) MNi 2 Sn second phase. However, the formation mechanism of the FH nano-structures in the HH matrix and their vibrational properties are still not well understood. We report on first principles studies of thermodynamic phase equilibria in the MNiSn-MNi 2 Sn pseudo-binary system as well as HH and FH vibrational properties. Thermodynamic phase diagrams as functions of temperature and Ni concentration were developed using density functional theory (DFT) combined with a cluster expansion and Monte Carlo simulations. The phase diagrams show very low excess Ni solubility in HH even at high temperatures, which indicates that any Ni excess will decompose into a two-phase mixture of HH and FH. Vibrational properties of HH and FH alloys are compared. Imaginary vibrational modes in the calculated phonon dispersion diagram of TiNi 2 Sn indicate a dynamical instability with respect to cubic [001] transverse acoustic modulations. Displacing atoms along unstable vibrational modes in cubic TiNi 2 Sn reveal lower energy structures with monoclinic symmetry. The energy of the monoclinic structures are found to depend strongly on the lattice parameter. The origin of the instability in cubic TiNi 2 Sn and its absence in cubic ZrNi 2 Sn and HfNi 2 Sn is attributed to the small size of the Ti 3d shells compared to Zr and Hf atoms. Lattice constants and heat capacities calculated by DFT agree well with experiment.