Thermal expansion of copper, silver, and gold at low temperatures

Abstract

Improvements have been made in a differential dilatometer using the three-terminal capacitance detector. The dilatometer is of copper and has been calibrated from 1.5–34 K in an extended series of observations using silicon and lithium fluoride as low-expansion reference materials. The expansion of silver and gold samples has been measured relative to the dilatometer, while the calibrations themselves have been used to determine the expansion of copper relative to the reference materials. Analyses of six sets of observations indicate that below 12 K the linear expansion coefficient α of copper is represented by

$$10^{10} \alpha = (2.1_5 \pm 0.1){\rm T} + (0.284 \mp 0.005){\rm T}^3 + (5 \pm 3) \times 10^{ - 5} T^5 K^{ - 1} $$

corresponding to respective electronic and lattice Grüneisen parameters γ _e =0.9 ₃ and γ ₀ =γ ₁ =1.78. Measurements on oxygen-free silver yield

$$10^{10} \alpha = (1.9 \pm 0.2){\rm T} + (1.14 \mp 0.03){\rm T}^3 + (2 \pm 2) \times 10^{ - 4} T^5 K^{ - 1} $$

below 7 K, whence γ _e ≃ 0.9 ₇ , γ ₀ =γ ₁ =2.23. By contrast, silver containing ca. 0.02 at. % oxygen showed a much larger expansion at the lowest temperatures: below 7 K, 10¹⁰α ∼ 7T+1.19T ³. We have not been able to obtain an unambiguous representation for gold, but find a reasonable fit below 7 K to be

$$10^{10} \alpha \simeq (1 \pm 0.5){\rm T} + (2.44 \mp 0.05){\rm T}^3 - (5 \pm 1) \times 10^{ - 3} T^5 K^{ - 1} $$

with γ ₁ ≃ 2.94 and γ _e ≳ 0.7 (free-electron value).