The thermal expansion of copper at low temperatures

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 = (1·4 5 ± 0·1 5 ) x 10 -10 T + (2·8 ± 0·1) x 10 -11 T 3 per degK. These terms, identified respectively as electronic ( e ) and lattice ( l ) in origin, lead to the following values of the Grüneisen parameter: γ e = 0·63 ± 0·06, γ l = 1·72 ± 0·03 ( = γ o ). γ e is compared with a theoretical free-electron value of 2/3, and the low temperature value of γ l 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 ∞ – γ 0 ≈ 0·28, which agrees well with the theoretical estimates of Barron for a close-packed cubic lattice.