Vibrational thermodynamics of vanadium and dilute vanadium alloys
Using inelastic neutron scattering, we measured the phonon densities of states for pure vanadium and solid solutions of vanadium with 6 to 7at% of Co, Ni, Pd, Pt, at temperatures up to 1273 K for the alloys and 1673 K for pure vanadium. At room temperature, 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 at 293 K exceeds the conventional positive chemical entropy of mixing. At elevated temperatures, the vanadium phonon DOS shows a pronounced anharmonic behavior, with minimal softening occurring up to 1273 K. On the other hand, the alloy V-7%Co showed the more expected trend of softening between 293 K and 1273 K, in good agreement with classical thermal expansion arguments. As a result, the vibrational entropy of alloying becomes less negative with higher temperatures for this solute. The consequences of vibrational entropy on the phase-diagrams and in particular on the bcc solvus line are discussed.
