Melting Pressure Thermometry of the Saturated Helium Mixture at Millikelvin Temperatures

The melting pressure of a ³ He–⁴He mixture has a very simple quadratic temperature dependence below some tens of mK, determined by the entropy of the ³ He component in the liquid mixture. For undersaturated mixtures, the melting pressure also depends on the ³ He concentration x, which may vary in the course of the experiment as ⁴ He transfers between the liquid and the solid phases. On the other hand, if the mixture is saturated, the system is in a univariant state with a melting pressure that depends uniquely on temperature and, thus, offers a thermometric standard. However, the univariant state includes a pure liquid ³ He phase, which complicates the temperature dependence around its superfluid transition temperature T_c. In this paper, we analyze the melting pressure of the saturated mixture in simple terms and find an expression that is in good agreement with our experimental data, and is applicable across T_c down to very low temperatures. The obtained derivatives of the melting pressure with respect to the square of temperature are 0.92 Pa·mK⁻² above T_c and 1.52 Pa·mK⁻² in the zero-temperature limit.