Phonon densities of states and vibrational entropies of ordered and disorderedNi3Al

We performed inelastic neutron-scattering measurements on powdered ${\mathrm{Ni}}_3$Al. The alloy was prepared in two states of chemical order: (1) with equilibrium L$1_2$ order, and (2) with disorder (the material was a fcc solid solution prepared by high-energy ball milling). Procedures to convert the energy loss spectra into approximate phonon density of states (DOS) curves for ${\mathrm{Ni}}_3$Al in the two states of chemical order were guided by Born–von Kármán analyses with force constants obtained from previous single-crystal experiments on L$1_2$-ordered ${\mathrm{Ni}}_3$Al and fcc Ni metal. The main difference in the phonon DOS of the ordered and disordered alloys occurs near 39 meV, the energy of a peak arising from optical modes in the ordered alloy. These high-frequency optical modes involve primarily the vibrations of the aluminum-rich sublattice. The disordered alloy, which does not have such a sublattice, shows much less intensity at this energy. This difference in the phonon DOS around 39 meV is the main contributor to the difference in vibrational entropy of disordered and ordered ${\mathrm{Ni}}_3$Al, which we estimate to be ${\mathit{S}}_{\mathrm{vib}}^{\mathrm{dis}}$-${\mathit{S}}_{\mathrm{vib}}^{\mathrm{ord}}$=(+0.2±0.1)${\mathit{k}}_{\mathit{B}}$/atom at high temperatures.