  First principles calculations of the vibrational, thermodynamic and
mechanical properties of the Ni-Ti-Sn Heusler and half-Heusler compounds have
been performed. First, we have calculated the Raman and infrared spectra of
NiTiSn, providing benchmark theoretical data directly useful for the
assignments of its experimental spectra and clarifying the debate reported in
the literature on the assignment of its modes. Then, we have discussed the
significant vibrational density-of-states of Ni2TiSn at low-frequencies. These
states are at the origin of (i) its smaller free energy, (ii) its higher
entropy, and (iii) its lower Debye temperature, with respect to NiTiSn.
Finally, we have reported the mechanical properties of the two compounds. In
particular, we have found that the half-Heusler compound has the largest
stiffness. Paradoxically, its bulk modulus is also the smallest. This unusual
behavior has been related to the Ni-vacancies that weaken the structure under
isostatic compression. Both compounds show a ductile behavior.
