Method for extrapolating the compressibility data of solids from room to lower temperatures

Abstract

Around room temperature, the elastic constants of solids can be measured comfortably applying commercial equipment, e.g., resonant ultrasound spectroscopy devices, whereas at low temperatures special efforts are necessary. To decrease the effort, a method has been developed and tested for extrapolating data on the compressibility of solids to lower temperatures. The method is based on well-known approximate relations between the thermodynamic properties of solids, the derivation of which was pioneered by Gruneisen, and the measurement of quantities, which are easier accessible experimentally than the elastic constants (thermal expansion, specific heat). In essence, the extrapolation uses data for the thermal expansion. The applicability of the method has been tested for copper, the properties of which are documented comprehensively in literature even at low temperatures. In a second step, the method has been applied to extrapolate the compressibility data of a copper-beryllium-cobalt alloy from near room temperature down to about 80 K with a relative uncertainty of order 0.1%. This extrapolation is needed for and verified by dielectric-constant gas thermometry, a special kind of primary thermometry for determining thermodynamic temperatures. For such gas-thermometry experiments cylindrical capacitors, the electrodes of which have been made from the investigated copper beryllium alloys, are used.