Phonon entropy of alloying and ordering of Cu-Au

Abstract

Inelastic neutron scattering spectra were measured with a time-of-flight spectrometer on six disordered Cu-Au alloys at 300 K. The neutron-weighted phonon density of states was obtained from a conventional analysis of these spectra. Several methods were developed to account for this neutron weighting and obtain the phonon entropy of the disordered alloys. The phonon entropies of formation of disordered fcc Cu-Au alloys obtained in this way were generally mutually consistent, and were also consistent with predictions from a cluster approximation obtained from ab-initio calculations by Ozoli\ifmmode \mbox{\c{n}}\else \c{n}\fi{}s\ifmmode \breve{}\else \u{}\fi{}, Wolverton, and Zunger. We estimate a phonon entropy of disordering of $0.15\ifmmode\pm\else\textpm\fi{}{0.05k}_{\mathrm{B}}/\mathrm{atom}$ in ${\mathrm{Cu}}_{3}\mathrm{Au}$ at 300 K. A resonance mode associated with the motions of the heavy Au atoms in the Cu-rich alloys was observed at 9 meV. An analysis of the resonance mode provided a check on the partial phonon entropy of Au atoms.