Vibrational entropy of spinodal decomposition in FeCr

Abstract

Inelastic neutron-scattering spectra were measured on stoichiometric Fe 0.50 Cr 0.50 prepared as a bodycentered-cubic ͑bcc͒ 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 Fe-Cr. The vibrational entropy of decomposition was found to be −0.17± 0.01k B / 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 Fe 0.50 Cr 0.50 .

Vibrational entropy near glass transition in a chalcogenide glass and supercooled liquid

“…This observation is particularly interesting since recent studies have shown that besides thermal expansion effects, phonons often soften for other reasons such as electron-phonon coupling or internal structural rearrangements [17,[21][22][23]. Although phonon softening via electron-phonon coupling is likely to be dominant primarily in metals, such softening via changes in the structural rearrangements in the supercooled liquid state would be quite likely in glass-forming liquids.…”

Mössbauer spectrometry of near equiatomic Fe–Cr alloys: Phase separation at high temperature?

“…2) which are discussed in Ref. [28], none shows the features expected for phase-separated alloys [20][21][22][23][24][25][26][27]. In that case, P(B) would reveal a main peak due to the Fe-rich Fe-Cr bcc phase, centered at a field ranging Table 1 Average hyperfine magnetic fields and the associated standard deviations of the HMFDs of between ∼26 T (x = 0.25) and ∼27 T (x = 0.20) for T a ∼ 1200 • C according to the phase diagram proposed in Refs.…”

“…Mössbauer studies of bcc Fe-Cr alloys ( [4,[20][21][22][23][24][25][26][27][28] and references therein) were and are still most often performed on as-cast alloys which are first cold-rolled, are then annealed for homogenization and to remove strain and are generally quenched. Various small angle neutron scattering experiments evidenced no signs of unmixing in alloys quenched in rather standard conditions.…”

“…The purpose of the present work was to check for the existence of an eventual high-temperature phase separation by Mössbauer spectrometry at RT which is a well-established technique of investigation of such a phenomenon in Fe-Cr alloys [4,[20][21][22][23][24][25][26][27]. vacuum in sealed quartz tubes and quenched into water.…”

Miscibility gap and phonon thermodynamics of Fe-Au alloys studied by inelastic neutron scattering and nuclear-resonant inelastic x-ray scattering

“…A recent computational study of the compositional trends in the NiCu system found the vibrational entropy of mixing to be negative, favoring chemical un-mixing [9]. Other phenomena in segregating systems where S vib is chief include the spinodal decomposition in FeCr [10] and the retrograde solubility in several dilute vanadium alloys [11]. Fe and Au are of major importance in industry and technology and the scientific literature on the Fe-Au system is vast, but bulk mixtures of Au and Fe atoms are largely immiscible at low temperatures.…”