Helium-3 / Helium-4 Phase Diagram
The phase diagram of liquid helium-3 and helium-4 mixtures shows the tricritical point and the phase-separation curve that make dilution refrigeration possible.
Reading the diagram
Plot temperature against the fraction of helium-3 in a liquid helium-3 / helium-4 mixture and a rich structure appears. At high temperatures the two isotopes mix in all proportions. As the mixture is cooled, a line marks where superfluidity of the helium-4 component sets in, and at lower temperatures a dome-shaped region marks where the liquid spontaneously separates into two phases.
The tricritical point
The superfluid transition line meets the phase-separation curve at the tricritical point, near 0.87 kelvin and about 67 percent helium-3. Below this temperature a mixture in the two-phase region splits into a concentrated phase, nearly pure helium-3, and a dilute phase of helium-3 in superfluid helium-4. The concentrated phase is less dense and floats on top.
The finite zero-temperature solubility
The single most important feature for cryogenics is the left edge of the two-phase region as temperature goes to zero. Rather than the dilute phase becoming pure helium-4, helium-3 remains soluble in superfluid helium-4 up to about 6.6 percent even at absolute zero. This nonzero residual solubility is what allows the mixing chamber to keep cooling all the way down, and it is the physical basis of the dilution refrigerator.
Why helium-3 dissolves at all
Helium-3 atoms are fermions and are lighter than helium-4. In dilute solution they behave as a nearly ideal Fermi gas of quasiparticles moving through the superfluid background, with an effective mass a few times the bare mass. Their binding to the superfluid is energetically favorable enough that a finite fraction stays dissolved even at zero temperature.
- Tricritical point near 0.87 K and 67 percent helium-3
- Below it the liquid separates into concentrated and dilute phases
- Helium-3 remains about 6.6 percent soluble at absolute zero
- Dilute helium-3 acts as a Fermi gas of quasiparticles