Adiabatic Electron-Phonon Interaction and High-Temperature Thermodynamics of A15 Compounds

Inelastic neutron scattering was used to measure the phonon densities of states of the A15 compounds V_3Si, V_3Ge, and V_3Co at temperatures from 10 to 1273 K. It was found that phonons in V_3Si and V_3Ge, which are superconducting at low temperatures, exhibit an anomalous stiffening with increasing temperature, whereas phonons in V_3Co have a normal softening behavior. First-principles calculations show that this anomalous increase in phonon frequencies at high temperatures originates with an adiabatic electron-phonon coupling mechanism. The anomaly is caused by the thermally induced broadening of sharp peaks in the electronic density of states of V_3Si and V_3Ge, which tends to decrease the electronic density at the Fermi level. These results show that the adiabatic electron-phonon coupling can influence the phonon thermodynamics at temperatures exceeding 1000 K

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

Inelastic neutron scattering was used to measure the phonon densities of states (DOSs) for pure V and solid solutions of V with 6 to 7at% of Co, Nb, and Pt, at temperatures from 10 K to 1323 K. Ancillary measurements of heat capacity and thermal expansion are reported on V and V-7at%Co and used to help identify the different sources of entropy. Pure V exhibits an anomalous anharmonic stiffening of phonons with increasing temperature. This anharmonicity is suppressed by Co and Pt, but not by isoelectronic Nb solutes. The changes in phonon frequency with alloying and with temperature both correlate to the decrease in electron density of states (DOS) at the Fermi level as calculated using density functional theory. The effects of both temperature and alloying can be understood in terms of an adiabatic electron-phonon interaction (EPI), which broadens sharp features in the electron DOS. These results show that the adiabatic EPI can influence the phonon thermodynamics at temperatures exceeding 1000 K, and that thermal trends of phonons may help assess the strength of the EPI

Phonon self-energy and origin of anomalous neutron scattering spectra in SnTe and PbTe thermoelectrics

The anharmonic lattice dynamics of rock-salt thermoelectric compounds SnTe and PbTe are investigated with inelastic neutron scattering (INS) and first-principles calculations. The experiments show that, surprisingly, although SnTe is closer to the ferroelectric instability, phonon spectra in PbTe exhibit a more anharmonic character. This behavior is reproduced in first-principles calculations of the temperature-dependent phonon self-energy. Our simulations reveal how the nesting of phonon dispersions induces prominent features in the self-energy, which account for the measured INS spectra and their temperature dependence. We establish that the phase-space for three-phonon scattering processes, rather than just the proximity to the lattice instability, is the mechanism determining the complex spectrum of the transverse-optical ferroelectric mode

Nonharmonic phonons in MgB_2 at elevated temperatures

Inelastic neutron scattering was used to measure phonon spectra in MgB_2 and Mg_(0.75)Al_(0.25)B_2 from 7 to 750 K to investigate anharmonicity and adiabatic electron-phonon coupling. First-principles calculations of phonons with a linear response method were performed at multiple unit cell volumes, and the Helmholtz free energy was minimized to obtain the lattice parameters and phonon dynamics at elevated temperature in the quasiharmonic approximation. Most of the temperature dependence of the phonon density of states could be understood with the quasiharmonic approximation, although there was also significant thermal broadening of the phonon spectra. In comparison to Mg_(0.75)Al_(0.25)B_2, in the energy range of 60 to 80 meV the experimental phonon spectra from MgB_2 showed a nonmonotonic change with temperature around 500 K. This may originate from a change with temperature of the adiabatic electron-phonon coupling

Phonon density of states and heat capacity of La_(3−x)Te_4

The phonon density of states (DOS) of La_(3−x)Te_4 compounds (x=0.0,0.18,0.32) was measured at 300, 520, and 780 K, using inelastic neutron scattering. A significant stiffening of the phonon DOS and a large broadening of features were observed upon introduction of vacancies on La sites (increasing x). Heat-capacity measurements were performed at temperatures 1.85 ≤ T ≤ 1200 K and were analyzed to quantify the contributions of phonons and electrons. The Debye temperature and the electronic coefficient of heat capacity determined from these measurements are consistent with the neutron-scattering results, and with previously reported first-principles calculations. Our results indicate that La vacancies in La_(3−x)Te_4 strongly scatter phonons and this source of scattering appears to be independent of temperature. The stiffening of the phonon DOS induced by the introduction of vacancies is explained in terms of the electronic structure and the change in bonding character. The temperature dependence of the phonon DOS is captured satisfactorily by the quasiharmonic approximation

Effects of chemical composition and B2 order on phonons in bcc Fe–Co alloys

The phonon density of states (DOS) gives insight into interatomic forces and provides the vibrational entropy, making it a key thermodynamic function for understanding alloy phase transformations. Nuclear resonant inelastic x-ray scattering and inelastic neutron scattering were used to measure the chemical dependence of the DOS of bcc Fe–Co alloys. For the equiatomic alloy, the A2→B2 (chemically disordered→chemically ordered) phase transformation caused measurable changes in the phonon spectrum. The measured change in vibrational entropy upon ordering was −0.02±0.02 k_B/atom, suggesting that vibrational entropy results in a reduction in the order–disorder transition temperature by 60±60 K. The Connolly–Williams cluster inversion method was used to obtain interaction DOS (IDOS) curves that show how point and pair variables altered the phonon DOS of disordered bcc Fe–Co alloys. These IDOS curves accurately captured the change in the phonon DOS and vibrational entropy of the B2 ordering transition

Temperature and Pressure Dependence of the Fe-specific Phonon Density of States in Ba(Fe(1-x)Co(x))2As2

The {57}Fe-specific phonon density of states of Ba(Fe(1-x)Co(x))2As2 single crystals (x=0.0, 0.08) was measured at cryogenic temperatures and at high pressures with nuclear-resonant inelastic x-ray scattering. Measurements were conducted for two different orientations of the single crystals, yielding the orientation-projected {57}Fe-phonon density of states (DOS) for phonon polarizations in-plane and out-of-plane with respect to the basal plane of the crystal structure. In the tetragonal phase at 300 K, a clear stiffening was observed upon doping with Co. Increasing pressure to 4 GPa caused a marked increase of phonon frequencies, with the doped material still stiffer than the parent compound. Upon cooling, both the doped and undoped samples showed a stiffening, and the parent compound exhibited a discontinuity across the magnetic and structural phase transition. These findings are generally compatible with the changes in volume of the system upon doping, increasing pressure, or increasing temperature, but an extra softening of high-energy modes occurs with increasing temperature. First-principles computations of the phonon DOS were performed and showed an overall agreement with the experimental results, but underestimate the Grueneisen parameter. This discrepancy is explained in terms of a magnetic Grueneisen parameter, causing an extra phonon stiffening as magnetism is suppressed under pressure

Temperature and pressure dependence of the Fe-specific phonon density of states in Ba(Fe_(1−x)Co_x)_2As_2

The ^(57)Fe-specific phonon density of states (DOS) of Ba(Fe_(1−x)Co_x)_2As_2 single crystals (x=0.0,0.08) was measured at cryogenic temperatures and at high pressures with nuclear-resonant inelastic x-ray scattering. Measurements were conducted for two different orientations of the single crystals, yielding the orientation-projected ^(57)Fe-phonon density of states for phonon polarizations in-plane and out-of-plane with respect to the basal plane of the crystal structure. In the tetragonal phase at 300 K, a clear stiffening was observed upon doping with Co. Increasing pressure to 4 GPa caused a marked increase of phonon frequencies, with the doped material still stiffer than the parent compound. Upon cooling, both the doped and undoped samples showed a stiffening and the parent compound exhibited a discontinuity across the magnetic and structural phase transitions. These findings are generally compatible with the changes in volume of the system upon doping, increasing pressure, or increasing temperature, but an extra softening of high-energy modes occurs with increasing temperature. First-principles computations of the phonon DOS were performed and showed an overall agreement with the experimental results, but underestimate the Grüneisen parameter. This discrepancy is explained in terms of a magnetic Grüneisen parameter, causing an extra phonon stiffening as magnetism is suppressed under pressure