Production of Very Low Temperatures with the Dense Phases of Helium Three

Abstract

The melting anomaly of ${\mathrm{He}}^{3}$ enables one to produce very low temperatures through adiabatic solidification. Exchange effects in the solid are expected to prevent the reaching of temperatures very much below the one defined by the exchange-energy parameter, where the melting anomaly should cease. Relaxation-time measurements in the solid define this parameter within the limitations of the assumed exchange-interaction scheme, as well as of those of the formalism which connects the coupling scheme with the relaxation times. With the empirical exchange parameter, the entropy of the solid at melting can be obtained down to quite low temperatures. This entropy combined with that of the liquid, available from an earlier theory of this phase, enables one to calculate the melting-pressure line, essentially from fundamentals. The agreement between the theoretical melting-pressure line and the available data at low and medium temperatures is satisfactory. The theoretical melting line has an inflection point, outside the range of measurements, due to the magnetic ordering process imposed by the assumed interaction scheme. The most promising way of verifying this prediction, at temperatures well above the ordering temperature, appears to be through the observation of the crossing of the heat-capacity curves of the liquid and solid at or near melting. The theoretical entropies of the two phases suggest that in starting with liquid ${\mathrm{He}}^{3}$ at saturation and at an easily accessible temperature, adiabatic compression alone ensures, in principle, the reaching of quite low temperatures. This process is discussed in detail, and its use toward reaching temperatures in the millidegree range will be described. An analysis of the thermal anomalies of low-pressure solid ${\mathrm{He}}^{3}$ due to the assumed exchange coupling will be presented. At melting these anomalies should extend up to near 0.25\ifmmode^\circ\else\textdegree\fi{}K. The solid at and near melting is shown to exhibit a narrow entropy wedge over a fairly wide pressure range around the melting-line minimum. With its spin entropy being practically complete at 0.1\ifmmode^\circ\else\textdegree\fi{}K, solid ${\mathrm{He}}^{3}$ should have very small derivative thermal properties, expansion coefficient, and heat capacity over a fairly wide temperature and pressure range. The expansion coefficient at or near melting is estimated to vanish, and to become negative, somewhat below 0.25\ifmmode^\circ\else\textdegree\fi{}K. This technically difficult region of the thermal properties extends down to a few hundredths of a degree, below which the thermal anomalies of the low-pressure solid should increase rapidly to become more accessible to observations and measurements.