Inelastic neutron-scattering spectra were measured on stoichiometric ${\mathrm{Fe}}_{0.50}{\mathrm{Cr}}_{0.50}$ prepared as a body-centered-cubic (bcc) solid solution, and after increasing amounts of chemical unmixing on the bcc lattice induced by annealing the solid solution at 773 K. These spectra were reduced by a conventional procedure to a neutron-weighted vibrational density of states. Mössbauer spectrometry was used to characterize the extent of decomposition after annealing. A neutron-weight correction was performed, using results from the Mössbauer spectra and recent data on inelastic nuclear resonant scattering from ${}^{57}\mathrm{Fe}\text{−}\mathrm{Cr}$. The vibrational entropy of decomposition was found to be $-0.17\pm 0.01k_{\mathrm{B}}∕\mathrm{atom}$, nearly equal to the change in configurational entropy after spinodal decomposition. Effects of vibrational entropy on the thermodynamics of unmixing are analyzed, showing a large effect on the free energy with the formation of Cr-rich zones, and a large effect on the critical temperature for spinodal decomposition for equiatomic ${\mathrm{Fe}}_{0.50}{\mathrm{Cr}}_{0.50}$.

• Received 2 February 2005

DOI:https://doi.org/10.1103/PhysRevB.72.024305