Vibrational entropies of phases of Co3V measured by inelastic neutron scattering and cryogenic calorimetry

The difference in heat capacity of the L1(2) and hP24 phases of Co3V was measured by calorimetry at temperatures from 80 to 320 K. Inelastic neutron scattering measurements were performed on Co3V with the L1(2), hP24 and fcc phases at elevated temperatures, and the neutron-energy-loss spectra were converted into phonon density-of-states (DOS) curves. Heat capacities calculated from the L1(2) and hP24 DOS curves were approximately consistent with the calorimetry data. The phonon DOS curves showed a significant dependence on temperature, although not the temperature dependence of the simple Gruneisen approximation. The thermal expansion of the hP24 phase was measured and was interpreted adequately from the temperature dependence of the phonon DOS. By interpreting our cryogenic calorimetry data with a harmonic model, we estimate the difference in vibrational entropy of the L1(2) and hP24 phases to be (0.12 +/- 0.03)k(B) atom(-1) at low temperatures, with the L1(2) phase having the larger vibrational entropy. From the phonon DOS curves of the L1(2) phase at 898 K and the fcc phase at 1333 K, we found this difference in vibrational entropy to be (0.15 +/- 0.02)k(B) atom(-1). Phonon softening caused the entropy of the hP24 phase to increase by about 0.055 k(B) atom(-1) per 100 K.