Statistical Physics of Crystals and Liquids

Electron-phonon interactions and high-temperature thermodynamics of vanadium and its alloys

“…͑2͒ is still valid for the case of anharmonic vibrations, and that the full phonon entropy is obtained by using the experimental high-temperature phonon DOS measured by INS. 9 The effect of lattice dilation on the total entropy, S D , can be obtained from…”

“…A deeper argument is that the adiabatic EPI ͑which accounts for how nuclear displacements alter the energies of the electron eigenstates and vice versa͒ should be of negligible thermodynamic importance because the EPI accounts for little change in the electron energy levels. 9 ͑This argument is probably more relevant for the nonadiabatic EPI, which is understood as a phonon coupling of unperturbed electron states across the Fermi surface.͒ Nevertheless, the importance of the EPI for the high-temperature thermodynamics of metals remains controversial. Quantitative calculations for nearly-free electron metals have predicted a significant contribution to the free energy from the adiabatic component of the EPI at temperatures up to melting.…”

“…9,12 At high temperature, the extra vibrational entropy associated with softer ͑lower energy͒ phonon modes favors the expansion of the lattice. In the standard quasiharmonic model ͑QH͒, the rate of softening of the average phonon energy ͗E͘ is related to the rate of change in volume V of the crystal as:…”

“…9 In most materials, ␥ Ͼ 0, and phonons soften upon thermal expansion. Microscopically, this thermal expansion and the associated shifts and broadenings of phonon frequencies stem from the anharmonic components in interatomic potentials, which are responsible for the PPI ͑scattering between harmonic phonon quasiparticles͒.…”

The role of correlation entropy in nuclear fusion in liquid lithium, indium and mercury

“…Only the one-body S 1 and two-body correlation S 2 entropies are large and need to be considered for our scope. In fact, Wallace [25,40,41] has calculated S 2 for many liquid metals as the difference between the experimental value of the total entropy and the one-body term S 1 , disregarding corrections from the smaller terms. In turns, the difference between the one-body entropy in the two phases is easily determined [25] and it cannot influence the two-body reaction rate: only the two-body correlation entropy S 2 needs to be considered to explain the different fusion rates in liquid relative to solid metals.…”