Sensitive Dilatometer for Low Temperatures and the Thermal Expansion of Copper below 10 K

Abstract

We describe a dilatometer which is an improved version of the one previously used in this laboratory. It consists of a doubly twisted strip of beryllium copper with a mirror attached to its central region. This system is immersed in liquid helium II. Dilations of the sample are sensed by this system via a thin diaphragm, causing rotations of the mirror, which is detected by an external optical lever. The system has a sensitivity to relative length changes Δl/l of 10⁻¹¹. Copper has been used as the test material to evaluate the performance of the instrument. It has been possible to make direct measurements of α, the coefficient of linear thermal expansion, down to 2 K for ΔT=0.2 deg. These results yield α=1.3×10⁻¹⁰ T+2.7×10⁻¹¹ T³ deg⁻¹. The ratio of these terms is much more accurately known than the absolute values because of uncertainty in the absolute calibration. The linear term leads to an electronic Grüneisen γ of 0.57. This value is compared with recent theoretical and experimental values.