The thermal expansion of copper at low temperatures

Abstract

Abstract The thermal expansion of copper has been determined at temperatures down to 2 °K by means of an electrical capacitance technique. By measuring three-terminal capacitances in a ratio-transformer bridge length changes smaller than 10-9 cm can be detected in the capacitor-expansion cell. Below 10 °K, the linear expansion coefficient, α, may be represented by α = (1·45 ± 0·15) x 10-10T + (2·8 ± 0·1) x 10-11T3 per degK. These terms, identified respectively as electronic (e) and lattice (l) in origin, lead to the following values of the Grüneisen parameter: γe = 0·63 ± 0·06, γl = 1·72 ± 0·03 ( = γo). γe is compared with a theoretical free-electron value of 2/3, and the low temperature value of γl is compared with values of 1·75 to 1·77 calculated from elastic constants. At room temperature γ(≈ γ∞) is 2·00, so that γ∞ – γ0≈ 0·28, which agrees well with the theoretical estimates of Barron for a close-packed cubic lattice.