Phonon modes and vibrational entropy of mixing in Fe-Cr

Abstract

Results from neutron inelastic-scattering experiments on Fe, Cr, and three bcc Fe-Cr alloys were analyzed with a Born--von K\'arm\'an model to obtain phonon density-of-states (DOS) curves. We compared the phonon DOS of the bcc Fe-Cr alloys to the composite phonon DOS from appropriate fractions of the phonon DOS of the pure metals Fe and Cr. In the high-temperature limit, we obtained the vibrational entropy of mixing of Fe and Cr to be 0.141, 0.201, and 0.214 ${\mathit{k}}_{\mathit{B}}$/atom for alloys of ${\mathrm{Fe}}_{70}$${\mathrm{Cr}}_{30}$,${\mathrm{Fe}}_{53}$${\mathrm{Cr}}_{47}$, and ${\mathrm{Fe}}_{30}$${\mathrm{Cr}}_{70}$, respectively, with the disordered solid solution having the larger vibrational entropy. Some expected effects of vibrational entropy on the chemical unmixing transformation in Fe-Cr are discussed.