Phonon contributions to the entropies of hP24 and fcc Co3V

Inelastic neutron-scattering spectra and neutron-diffraction patterns were measured on the alloy Co3V at temperatures from 1073-1513 K, where the hP24 (ordered hexagonal) and fee structures are the equilibrium states of the alloy. Phonon density of states (DOS) curves were calculated from the inelastic-scattering spectra, allowing estimates of the vibrational entropy in the harmonic and quasiharmonic approximations. The vibrational entropy of the hP24-fcc phase transition at 1323 K was found to be 0.07k(B)/atom. The anharmonic contributions to the entropy over a temperature range of 100 K were comparable to the vibrational entropy of this phase transition. The anharmonic softening of the phonon DOS was only slightly larger for the hP24 than the fee phase, however, so the anharmonic effects contribute only slightly to the difference in entropy of the two phases. The simple Gruneisen approximation was inadequate for predicting the thermal softening of the phonon DOS.