Vibrational entropy of spinodal decomposition in FeCr

Inelastic neutron-scattering spectra were measured on stoichiometric Fe0.50Cr0.50 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. M\"ossbauer spectrometry was used to characterize the extent of decomposition after annealing. A neutron-weight correction was performed, using results from the M\"ossbauer spectra and recent data on inelastic nuclear resonant scattering from ⁵⁷Fe-Cr. The vibrational entropy of decomposition was found to be -0.17±0.01kB∕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 Fe0.50Cr0.50.