Charge Redistribution and Phonon Entropy of Vanadium Alloys

The effects of alloying on the lattice dynamics of vanadium were investigated using inelastic neutron scattering. Phonon densities of states were obtained for bcc solid solutions of V with 3d, 4d, and 5d transition metal solutes, from which vibrational entropies of alloying were obtained. A good correlation is found between the vibrational entropy of alloying and the electronegativity of transition metal solutes across the 3d row and down columns of the periodic table. First-principles calculations on supercells matching the experimental compositions predicted a systematic charge redistribution in the nearest-neighbor shell around the solute atoms, also following the Pauling and Watson electronegativity scales. The systematic stiffening of the phonons is interpreted in terms of the modified screening properties of the electron density around the solutes

Negative Entropy of Mixing for Vanadium-Platinum Solutions

The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born–von Kármán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius

The Phonon Entropy of Transition Metals and Alloys: Effects of Impurities and of a Martensitic Phase Transition

For a fixed configuration of ions on a given crystalline lattice, low energy excitations around the static average configuration can be thermally activated and will contribute to the entropy of the system. As such, phonons, spin-waves or electronic excitations have their own entropic contribution. This thesis investigates the entropic effects of lattice vibrations in transition metal alloys, both from experimental and computational points of view. Using inelastic neutron scattering, it is shown that a few percent of substitutional impurities from the transition metal series strongly affect the phonon density of states (DOS) of pure vanadium. Alloying with 6% Pt solutes produces a strong stiffening of the phonon DOS, inducing a large and negative vibrational entropy of mixing, which overcomes the increase in configurational entropy. A systematic study of chemical trends for different transition metal impurities was conducted. A previously unknown correlation is established between the vibrational entropy of alloying and the difference in electronegativity of the solute and the host. Density-functional theory calculations were conducted and confirmed the occurrence of systematic charge-transfers correlating with the electronegativity, which affect the interatomic force-constants and the phonons. The effect of impurities on the anomalous temperature-dependence of phonons in vanadium is investigated. It is found that the solutes which affect the phonon density of states most strongly at room temperature also suppress the anomalous temperature behavior. Electron-phonon and phonon-phonon couplings are examined as potential sources of this effect, through a careful accounting of their contributions to the heat capacity, based on inelastic neutron scattering experiments, calorimetry measurements and electronic structure calculations. Finally, the changes in the phonon DOS and the vibrational entropy across the low-temperature martensitic phase transformation in Fe71Ni29 are investigated. The respective contributions of the phonons and magnetism to the entropy of the direct and reverse transformation are evaluated from neutron scattering and differential scanning calorimetry measurements. A significant magnetic entropy is found in the reverse transformation, which is not present in the direct transformation. This result stresses the necessity to account for the respective contributions of all microscopic degrees of freedom in evaluating entropy changes in solid-solid phase transitions.</p

Neutron scattering measurements of phonons in nickel at elevated temperatures

Measurements of elastic and inelastic neutron scatterings from elemental nickel were made at 10, 300, 575, 875, and 1275 K. The phonon densities of states (DOSs) were calculated from the inelastic scattering and were fit with Born–von Kármán models of the lattice dynamics. With ancillary data on thermal expansion and elastic moduli, we found a small, negative anharmonic contribution to the phonon entropy at high temperature. We used this to place bounds on the magnetic entropy of nickel. A significant broadening of the phonon DOS at elevated temperatures, another indication of anharmonicity, was also measured and quantified

Phonons in aluminum at high temperatures studied by inelastic neutron scattering

Inelastic neutron scattering measurements on aluminum metal were performed at temperatures of 10, 150, 300, 525, and 775 K using direct-geometry Fermi chopper spectrometers. The temperature dependent phonon density of states (DOS) was determined from the scattering, and was used to fit Born–von Kármán models of lattice dynamics. The shifts in the phonon frequencies with increasing temperature were largely explained by the softening of the longitudinal force constants out to third nearest neighbors. A significant broadening of the phonon spectra at high temperatures was also measured. The phonon DOS was used to determine the vibrational contributions to the entropy of aluminum as a function of temperature. All other contributions to the entropy of aluminum were calculated or assessed, and the total entropy was in excellent agreement with the NIST-JANAF compilation [M. W. Chase, J. Phys. Chem. Ref. Data Monogr. 9, 59 (1998)]. Anharmonic effects were attributed to phonon-phonon interactions. The quasiharmonic approximation was generally successful, but its weaknesses are discussed

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