Specific Heats of Zirconium Alloys at Low Temperatures

Abstract

The specific heats of dilute alloys of silver, cadmium, indium, tin, and antimony in hexagonal zirconium have been measured from 1.2 to 4.5°K. For each alloy the specific heat obeys the relation $c=\gamma T+\beta T^3$ within the experimental error. All of these solutes increase $\gamma$ linearly with concentration and $\frac{d\gamma }{\mathrm{dx}}$ is linearly related to the chemical valence of the solute. The increase in $\gamma$ in the tin-zirconium alloys shows that all electrons outside closed shells cannot be treated as equivalent in the rigid band model of alloying. All of these solutes increase the density of states of zirconium, providing evidence for a zone overlap in the zirconium $d$ band and for a small number of electrons in a new band. All of the solutes increase the lattice specific heat and the Debye temperature is a linear function of solute concentration for each of these alloy systems. $\frac{d\theta }{\mathrm{dx}}$ is not simply related to the solute valence but shows a close correlation with the magnitude of the rate of change of the distance between atoms at (0,0,0) and ($\frac{1}{3}$, $\frac{2}{3}$, ½) of the hexagonal cell. Additions of tin to zirconium do not change the average interaction potential of the BCS theory appreciably.