Effects of vacancies on phonon entropy of B2 FeAl

The phonon density of states (DOS) and phonon entropy of B2 FeAl were determined as functions of the Fe site vacancy concentration using several scattering techniques and were computed from first principles. Measurements at elevated temperature and pressure were performed to explore volume effects, test the usefulness of the quasiharmonic (QH) approximation, and provide comparison for the first-principles calculations. The average temperature and pressure dependencies of phonons were consistent with the QH model. The decrease in specific volume associated with the introduction of vacancies causes a stiffening of the DOS that was captured well with the experimentally determined Grüneisen parameter. Features associated with vacancies in the DOS are not well explained by this model, however, especially in the gap between the acoustic and optic branches. First-principles calculations indicated that these modes are primarily associated with vibrations of Al atoms in the first-nearest-neighbor shell of the vacancy, with some vibration amplitude also involving the second-nearest-neighbor Fe atoms. At the vacancy concentrations of study, the phonon entropy of vacancy formation was found to be approximately −1.7k_B/atom, about half as large and of opposite sign as the configurational entropy of vacancy formation