Vibrational entropy differences in materials

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. An investigation has been made into the differences in vibrational entropy between two states of a material. These vibrational entropy differences have been measured experimentally by low-temperature calorimetry for several alloy systems. The results from the calorimetry experiments have been compared with phonon densities of states (DOS) for the two states of the material obtained from inelastic neutron scattering data. The systems which have been examined are [...], and nanophase [...]. The difference in vibrational entropy between chemically disordered and [...]-ordered [...] was measured by calorimetry to be [...] /atom at high temperatures, with the ordered alloy having the lower vibrational entropy. Analysis of the vibrational modes of the ordered and disordered alloys with a Born-von Karman model showed that the lower vibrational entropy of the ordered alloy originates from high-frequency optical modes involving large-amplitude vibrations of the aluminum-rich sublattice. Inelastic neutron scattering measurements were performed on powdered [...]. The alloy was prepared in two states of chemical order: 1) with equilibrium [...] order, and 2) an fcc solid solution prepared by high- energy ball milling. The main difference in the phonon DOS of the ordered and disordered alloys occurs near 39 meV, the energy of a peak arising from optical modes in the ordered alloy. These high-frequency optical modes involve primarily the vibrations of the aluminum-rich sublattice. The difference in vibrational entropy of disordered and ordered [...] kB/atom at high temperatures. The difference in heat capacity of chemically disordered and [...] ordered [...] was measured by calorimetry from 70 K - 300 K. By comparing these measured results to a harmonic heat capacity calculated with a Born-von Karman model, we estimate the difference in vibrational entropy between disordered and ordered Cu3Au to be [...] kg/atom at high temperatures. Samples of [...] were prepared with two microstructures: 1) with equilibrium [...] order, and 2) with partial disorder (having a large [...] chemical order parameter, but without the tetragonality of the unit cell). We measured the difference in their heat capacities from 60 K to 325 K and inelastic neutron scattering spectra at four values of Q at 11 K and at 300 K. We describe a microstructural contribution to the anharmonic heat capacity that originates with the anisotropy of the [...] structure. We estimate the difference in vibrational entropy between partially-disordered and ordered [...] to be [...] kg/atom at high temperature. The elastic energy stored in the microstructure is about 60 J/mole at low temperatures. The difference in vibrational entropy between fcc disordered and hexagonal ordered [...] was measured by calorimetry to be [...] /atom at high temperatures, with the ordered alloy having the lower vibrational entropy. Neutron diffraction data revealed that the observed L12 region of the phase diagram does not exist, but is a state that can be obtained in quenched alloys. Neutron energy loss spectra were measured for two states of nanophase Fe: 1) as-milled, with a characteristic nanocrystallite size of 12 nm, and 2) annealed, with a characteristic crystallite size of 28 nm. The longitudinal peak in the phonon DOS of the nanophase Fe was broadened compared to that of the annealed material. We attribute this broadening to short phonon lifetimes in nanocrystals. The nanophase material also showed an enhanced density of states at low energies below 15 meV, which may indicate the presence of inter-crystallite vibrations. These differences in phonon DOS should have only a small effect on the difference in vibrational entropy of n.anocrystalline and larger-grained [...]. The vibrational entropy differences that have been measured are large enough in comparison to 0.56 [...]/atom, the maximum possible difference in configurational entropy for a 3:1 atomic ratio, to make a significant contribution to the alloy thermodynami