Low-Temperature Specific Heats of Silver-Zinc Alloys. The Effect of Lattice Dilatation

The specific heats of silver and six silver-sinc alloys covering the alpha phase were measured between 2 and 4°K with a relative precision of 0.2% or better. The purpose is to compare the effect of Zn as a solute with Cd and Sn, which have been shown to increase the electronic specific-heat coefficient $\gamma$ for silver as a function of electron concentration $\frac{e}{a}$ at the rate $\frac{d\left(\ln \gamma \right)}{d\left(\frac{e}{a}\right)}=0.2\mathrm{} \mathrm{to} 0.3$ in spite of their considerable difference in valence. The comparison should reveal the effect of atomic volume, since Zn contracts silver upon alloying, while Cd and Sn expand it at a constant rate per unit $\frac{e}{a}$. The result for Zn in Ag is $\frac{d\left(\ln \gamma \right)}{d\left(\frac{e}{a}\right)}=0.65\mathrm{}\pm 0.17$ (95% limit). The volume effect, although opposite in sign from that expected on the free-electron model, is shown to be consistent with the rigid-band model including—indeed, requiring—contact between the Fermi surface and the first zone boundary, as is well established on other evidence. We conclude that the sign of the above derivatives and the observed volume effect are most simply explained if the density of states in silver is an increasing function of energy at the Fermi level in spite of this contact. These results imply that the electronic-thermal-expansion coefficient of pure silver is negative. Experimental test of this prediction will constitute a sensitive test of the rigid-band model. The Debye temperatures of the $\mathrm{Ag}\mathrm{Zn}$ alloys do not differ from that of pure silver by more than 2°K, a slight negative trend being suggested. A significant $T^5$ component in the specific heat appears with Zn addition, growing from less than 0.0001 mJ ${\mathrm{mole}}^{-1\mathrm{}}$ °${\mathrm{K}}^{-6\mathrm{}}$ in pure Ag to 0.0005 units at 32 at.% Zn.