Thermal expansion of copper, silver, and gold below 30 K

Abstract

A variable transformer technique has been used to determine the linear thermal expansion coefficients of the noble metals from 4 to 30 K. The precision of the data initially was ±0.04 A, and this was later increased to ±0.015 A, resulting in a sensitivity of approximately 2×10−11 for relative length changes of a 10-cm-long sample. The results agree at all temperatures (to better than 5%) with those of White and Collins who used a differential capacitor technique. The differences are 2% or less above 20 K for Cu, above 8 K for Ag, and at all temperatures for Au. The differences between the two sets of data for the three metals are not systematic (αWC greater for Cu, less for Ag) and may be due to differences in sample purity since much larger low-temperature anomalies were found within each set for certain samples of Cu and Ag. The resulting electronic Gruneisen parameters γe and theT=0 lattice Gruneisen parameters γ0 are as follows: $$\begin{gathered} copper \gamma _{\text{e}} = 0.91 \pm 0.05 \gamma _{\text{0}} = 1.67 \pm 0.02 \hfill \\ silver \gamma _{\text{e}} = 1.18 \pm 0.15 \gamma _{\text{0}} = 2.29 \pm 0.03 \hfill \\ gold \gamma _{\text{e}} = 1.6 \pm 0.5 \gamma _{\text{0}} = 2.96 \pm 0.04 \hfill \\ \end{gathered} $$ The values of γ0 are in reasonable (5% at worst) agreement with elastic constant values.