Low-Temperature Specific Heats of Zr-Ti, Zr-Hf, and Zr-Sc Alloys

Abstract

The specific heats of hexagonal Zr-Ti, Zr-Hf, and Zr-Sc alloys were measured at 1.1 to 4.2°K. Maxima in both the electronic specific-heat coefficient $\gamma$ and the superconducting transition temperature $T_c$ were observed at 60 at.% Ti in the Zr-Ti system. No superconductivity was found in the Zr-Sc system, although $\gamma$ rose to high values for pure scandium, and a minimum in $\gamma$ occurred near 10 at.% Sc. In the Zr-Hf system $\gamma$ was nearly linear between pure element values. The Debye temperatures ${\Theta }_D$, after correction for atomic mass and volume, deviate negatively near 60 at.% Ti in Ti-Zr, positively near hafnium in Zr-Hf, and in an S-type manner in Zr-Sc. The effects of scandium in depressing $\gamma$ in the zirconium-rich region are in qualitative agreement with dependence on electron/atom ratio indicated by earlier $B$-subgroup solute effects in zirconium-rich alloys. The $\gamma$ for Zr-Sc alloys, after a correction for phonon enhancement and with the assumption of a rigid band in the alloys, correlates fairly well with the electronic density of states for pure zirconium, calculated by Loucks. The rigid-band approximation, on the other hand, cannot explain the maxima in $\gamma$ and $T_c$ in Zr-Ti alloys, which involve no change of electron/atom ratio. Rather the maximum may arise from differences in the relative energies of the third and fourth bands in titanium and zirconium, with a crossing of these bands in the alloys. The $\gamma$ and $T_c$ are related to both the density of states and the electron-electron interactions, and although a clear separation of the two factors is not possible, a reasonable interpretation can be made, assuming that the electron-phonon interaction is nearly constant.