Vibrational entropy of L12 Cu3Au measured by inelastic neutron scattering

The phonon density of states of elemental Au, Cu, and Cu3Au with L12 chemical order were measured by inelastic neutron scattering and used to calculate the vibrational entropy of formation of the ordered compound from the elemental metals. A vibrational entropy of formation of (0.06±0.03) kB/atom at 300 K was obtained, with the vibrational entropy of the ordered alloy being larger than that of the elemental metals. The phonon DOS of the disordered Cu3Au was simulated by adding the phonon DOS curves of fcc Cu, L12 Cu3Au, and fcc Au to match the numbers of first-nearest-neighbor pairs in a disordered alloy. The vibrational entropy obtained with this simulated DOS disagrees with calorimetric data and theoretical estimates, indicating that the phonon DOS of disordered Cu3Au depends on chemical order at spatial lengths larger than is set by first-nearest-neighbor pairs

Phonon entropy of alloying and ordering of Cu-Au

Inelastic neutron scattering spectra were measured with a time-of-flight spectrometer on six disordered Cu-Au alloys at 300 K. The neutron-weighted phonon density of states was obtained from a conventional analysis of these spectra. Several methods were developed to account for this neutron weighting and obtain the phonon entropy of the disordered alloys. The phonon entropies of formation of disordered fcc Cu-Au alloys obtained in this way were generally mutually consistent, and were also consistent with predictions from a cluster approximation obtained from ab-initio calculations by Ozolin[underaccent cedilla [below] s-breve, Wolverton, and Zunger. We estimate a phonon entropy of disordering of 0.15±0.05kB/atom in Cu3Au at 300 K. A resonance mode associated with the motions of the heavy Au atoms in the Cu-rich alloys was observed at 9 meV. An analysis of the resonance mode provided a check on the partial phonon entropy of Au atoms

Temperature dependence of the phonon entropy of vanadium

The phonon density-of-states (DOS) of elemental vanadium was measured at elevated temperatures by inelastic neutron scattering. The phonon softening predicted by thermal expansion against the bulk modulus is much larger than the measured shifts in phonon energies. We conclude that the phonon anharmonicities associated with thermal expansion are largely canceled by effects from phonon-phonon scattering. Prior measurements of the heat capacity and calculations of the electronic entropy of vanadium are assessed, and consistency requires an explicit temperature dependence of the phonon DOS. Using data from the literature, similar results are found for chromium, niobium, titanium, and zirconium

Using bond-length dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys

A model is tested to rapidly evaluate the vibrational properties of alloys with site disorder. It is shown that length-dependent transferable force constants exist, and can be used to accurately predict the vibrational entropy of substitutionally ordered and disordered structures in Au-Cu, Au-Pd, and Cu-Pd. For each relevant force constant, a length- dependent function is determined and fitted to force constants obtained from first-principles pseudopotential calculations. We show that these transferable force constants can accurately predict vibrational entropies of L1$_{2}$-ordered and disordered phases in Cu$_{3}$Au, Au$_{3}$Pd, Pd$_{3}$Au, Cu$_{3}$Pd, and Pd$_{3}$Au. In addition, we calculate the vibrational entropy difference between L1$_{2}$-ordered and disordered phases of Au$_{3}$Cu and Cu$_{3}$Pt.Comment: 9 pages, 6 figures, 3 table

The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics

A longstanding limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty to account for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the impact of lattice vibrations on phase stability indicates that this effect can be substantial. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2 k_B/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693 k_B/atom). This paper describes the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for lattice vibrations. We overview the various techniques allowing the theoretical calculation and the experimental determination of phonon dispersion curves and related thermodynamic quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and volume change arguments. Vibrational entropy change can be attributed to the changes in chemical bond stiffness associated with the changes in bond length that take place during a phase transformation. This so-called ``bond stiffness vs. bond length'' interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.Comment: Submitted to Reviews of Modern Physics 44 pages, 6 figure