Phase Transformations and Entropy of Non-Equilibrium Materials

Abstract

Time-resolved vibrational spectra through the glass transition in the bulk metallic glass CuZr were acquired with inelastic neutron scattering. Vibrational density of states (DOS) in ranges as small as 4K were extracted from continuous heating through the glass transition. For each temperature interval, the vibrational entropy is calculated from the DOS. This provides a detailed characterization of how the vibrational entropy contributes to the large jump in heat capacity that characterizes the glass transition in amorphous materials. This change in heat capacity has been attributed to combinations of configurational and vibrational entropy. However, the role of vibrational entropy in this transition has never been demonstrated for all vibrational modes in an amorphous material. This work provides the first experimental measurement of the change in vibrational entropy through the glass transition. We found the unique contributions of both the vibrational and configurational entropy and find that the change in vibrational entropy can be bound at less than 0.01 kB per atom. By elimination, this means that the configurational entropy is dominant, putting to rest a controversial debate over the role of entropy through the glass transition. The changes in vibrational entropy during the early stages of chemical unmixing was studied in a nanocrystalline fcc solid solution of 6%-Fe in Cu. Material prepared by high-energy ball milling was annealed at temperatures from 200 to 360°C to induce chemical unmixing. Nuclear resonant inelastic x-ray scattering spectra yield the phonon partial density of states (pDOS) of 57Fe. The pDOS of the as-prepared material is that of an fcc crystal. In the earliest stages of unmixing, the features of the pDOS broaden, with only small changes in average phonon frequencies, until the bcc phase begins to form. The chemical state of the material was characterized by three-dimensional atom probe microscopy, Mӧssbauer spectrometry, and x-ray powder diffractometry. The unmixing was heterogeneous, with iron atoms forming iron-rich zones that thicken with further annealing. The vibrational entropy calculated from the pDOS underwent little change during the early stage of unmixing, but decreased rapidly when the bcc phase formed in the material. Electrochemical cycling of lithium ion batteries causes fundamental structural changes and the formation of new phases in cathode materials. The reversibility of these transitions is often critical to the viability of cathode materials for long-term performance. The cycle lives for cathodes of nanocrystalline iron trifluoride (FeF3) were measured in rechargeable lithium batteries at different depths of discharge. When the discharge was limited to less than one Li+ ion per FeF3, both the cycle life and energy efficiency were considerably greater than when converting FeF3 into Fe and LiF in deep discharge. An in situ X-ray diffractometry (XRD) study of the FeF3 cathode during its initial discharge to LiFeF3 showed a continuous change of the FeF3 diffraction pattern, indicating Li+ insertion into the rhombohedral FeF3 causing distortion of its lattice parameters. Electrochemical cycling is most reversible when this mechanism occurs in the absence of other changes in the crystal structure.