The Mixing Chamber
The mixing chamber is where helium-3 crosses the phase boundary from the concentrated to the dilute phase, absorbing heat and producing the coldest point in a dilution refrigerator.
The cold heart of the fridge
The mixing chamber is the lowest-temperature stage of a dilution refrigerator and the component to which the experiment is thermally anchored. Inside it sit two coexisting liquid phases: an upper concentrated phase that is essentially pure helium-3, and a lower dilute phase of helium-3 dissolved in superfluid helium-4. A sharp phase boundary separates them.
Where the cooling comes from
Helium-3 in the concentrated phase behaves like a Fermi liquid with one enthalpy; helium-3 dissolved in the dilute phase has a higher enthalpy per atom. When an atom is pulled across the boundary into the dilute phase it must absorb heat from its surroundings to make up the difference. Because the dilute phase retains a finite helium-3 concentration all the way to zero temperature, this quasi-evaporation never stops.
The cooling power scales roughly with the helium-3 circulation rate and with the square of the mixing-chamber temperature. A useful approximation is that the heat absorbed per mole of circulating helium-3 is proportional to the temperature difference in enthalpies, giving cooling power on the order of 84 times the circulation rate times T squared, with T in kelvin. This T-squared dependence is why base temperature is set by residual heat leaks and the limits of the heat exchangers.
Design considerations
Good thermal contact between the incoming helium-3 stream and the chamber is critical. At millikelvin temperatures the Kapitza boundary resistance between liquid helium and solid surfaces grows sharply, so mixing chambers use sintered silver or copper powder to expose enormous surface area, often tens of square meters packed into a small volume.
- Contains the coexisting concentrated and dilute phases
- Coldest point; the sample platform bolts here
- Cooling power proportional to circulation rate and T squared
- Uses sintered metal to defeat Kapitza resistance