Concentration susceptibility of 3He-4He mixtures near the superfluid transition

Abstract

Measurements of the concentration susceptibility % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabiqaaiaacaGaaeqabaWaaeaaeaaakeaacuaHhpWygaacai% abg2da9iabgkGi2kaadIfacaGGVaGaeyOaIyRaeuiLdqKaaiykamaa% BaaaleaacaWGubaabeaaaaa!3C99!\[\tilde \chi = \partial X/\partial \Delta )_T \] are reported for 3He-4He mixtures at saturated vapor pressure and at constant mole fraction X(3He) as a function of temperature. Here δ is the isotopic difference in chemical potentials. The mixtures cover the range from X = 0.60 to X = 0.677. Particular emphasis is given to the region near the lambda line for three mixtures and to the region close to the tricritical point. The method makes use of the vertical concentration gradient induced in the mixture by gravity. This difference δX is measured via the dielectric constant over a height of 2 mm using a capacitance technique. The predicted peak of the susceptibility at the superfluid transition is observed and as the tricritical point is approached, this peak is progressively broadened by gravity effects. The data are compared with those from other methods and also with estimations based on calorimetric data for more dilute mixtures. The susceptibility data are transformed into results along a path at constant chemical potential δ. Sufficiently close to T λ, these can be fitted to an expression with a weakly singular term, which is consistent with the predictions on the grounds of universality. These predictions are based on the calorimetric data of more dilute mixtures. The width of this critical region is found to be consistent with theoretical estimations by Riedel, Meyer, and Behringer. The tricritical scaling scheme by these authors is tested by the new data and the resulting scaling curve is found to be in reasonable agreement with that obtained from earlier data by Goellner, Behringer, and Meyer, except in the region closest to the tricritical point. There the new data appear to be more consistent with measurements from light scattering. In addition, the concentration susceptibility for more dilute mixtures (0.05 < X < 0.4) is calculated both from calorimetric data and from saturated vapor pressure measurements and the results are found to be internally consistent.