Preamble

The dilution refrigerator, to be dealt with in Chapter 3, can only be fully understood in terms of the properties of the two helium isotopes 3He and 4He and their mixtures. The purpose of this chapter is very briefly to review the relevant properties indicating, where necessary, sources giving more details. A useful general reference is by Wilks and Betts (1987) which also serves as an introduction to the research literature. As in the whole of this book, the reader is expected to derive at least as much information from the figures as from the minimal text.

Phase diagrams

The phase diagrams of 4He, 3He, and their mixtures are given below as Figures 2.1 and 2.2 respectively. Particular points of interest are discussed in the rubric and text following each figure.

Liquid 4He can be solidified by pressures above about 25 bar at temperatures below about 1 K. Higher pressures are needed at higher temperatures but below 1 K the melting pressure is nearly constant. The liquid phase is superfluid when the pressure is below the melting pressure and when in addition the temperature is below the lambda line (labelled in the figure) which runs from 2.17 K at p = 0 bar to 1.76 K at p = pmelt ≍ 30 bar. The superfluid phase is called He-II to distinguish it from normal He-I.

Liquid 3He has a pronounced minimum in its melting pressure of pmelt ≍ 29 bar at T ≍ 0.32 K and at lower temperatures pmelt rises to about 34 bar as T-→0 K. Normal (that is, non superfluid) liquid 3He persists down to a few millikelvin where it is well-described as a Fermi liquid.