Specific Heats of Copper, Silver, and Gold below 30°K

The specific heats of pure copper, silver, and gold have been measured in the range 3 to 30°K. Gold has also been measured in the range 0.4 to 1.5°K. The ${{\Theta }_0}^c$ and $\gamma$ values are estimated as 345.6±1.0°K and 166.3±1.3 μcal °${\mathrm{K}}^{-2\mathrm{}}$ ${\mathrm{}\left(\mathrm{g}\mathrm{atom}\right)\mathrm{}}^{-1\mathrm{}}$ for copper, 226.6±1.0°K and 154.4±1.0 μcal °${\mathrm{K}}^{-2\mathrm{}}$ ${\mathrm{}\left(\mathrm{g}\mathrm{atom}\right)\mathrm{}}^{-1\mathrm{}}$ for silver, and 162.4±2.0°K and 174.1±4.3 μcal °K ${\mathrm{}\left(\mathrm{g}\mathrm{atom}\right)\mathrm{}}^{-1\mathrm{}}$ for gold. The ${{\Theta }_0}^c$ values are in good agreement with the most recent estimates for ${{\Theta }_0}^{\mathrm{el}}$, the Debye temperature computed from the zero-temperature elastic constants. However, the lattice specific heat of gold is anomalous in that, on increasing the temperature from zero temperature, a maximum is first observed in the value of ${\Theta }^c$. The maximum is followed by the usual minimum on further increase of temperature. The results are discussed in terms of models due to Blackman and to Bhatia and Horton. The paper includes some remarks on thermometry below 30°K.