3He-4He Dilution Explanation

Parts of the cryostat cool down to such cryogenic temperatures as 20 milliKelvin (0.02 K) using a technique called "3Helium - 4Helium Dilution." For this reason another name for the cryostat is "dilution refrigerator." This process relies on certain thermodynamic characteristics of 3He (a rare helium isotope with 1 neutron) and 4He (the most abundant helium isotope, which has 2 neutrons). The 3He-4He dilution has the following phase diagram:

     

    3He-4He Phase Diagram(1)
    The phase of 3He-4He mixture depends on the fraction of He3

  • At temperatures below the triple point , the 3He-4He mixture will separate into two liquid phases, divided by a phase boundary.
    • One phase we'll call the 3He rich phase, because it contains mostly 3He. This corresponds to a point in the diagram below and to the right of the triple point, along the equilibrium line.
    • The second phase we'll call the 4He rich phase, because it is mostly 4He -- it will, however, always be composed of at least 6% 3He, no matter what temperature. This corresponds to a point in the diagram below and to the left of the triple point, along the equilibrium line.
  • The two phases are maintained in liquid-vapor form. Since there is a boundary between both phases, extra energy is required for particles to go from one phase to another.
  • A good example of this state would be what happens when you mix together oil and water. If you maintain the mixture at a high temperature they will stay mixed. But, if you were to lower the temperature (this effect can be seen at room temperature) the oil would separate from the water and float to the top, giving you two different phases in the liquid mixture. Not only that, but if you were to take a sample of the oil you would find a small amount of water present and vice-versa.

When you pump (we use a rotary pump) on the 4He rich phase you will remove mostly 3He (a move to the left off the equilibrium line in the diagram), destroying the equilibrium. To restore equilibrium, 3He will have to cross the phase boundary from the 3He rich side to the 4He rich side. However, it needs energy to get past the boundary. The 3He rich phase will provide the 3He and get the energy in the form of heat, from the walls of the mixing chamber; the walls are in thermal contact with whatever you're trying to cool down. Then the 3He will cross the phase boundary and join the 4He rich phase, restoring equilibrium. Finally, the atoms lost by the 3He rich phase are replenished by a constantly circulating flow of 3He.

Another way of thinking about this process is in terms of expansion. 4He is inert, in that it does not react with other molecules and thermodynamically can be thought of as a vacuum in some situations. Thus when the 3He moves from the 3He rich phase to the 4He rich phase, it expands into an almost vacuum. This expansion takes heat out of the walls of the mixing chamber, reducing the temperature of whatever you're trying to cool.


Credits:

Comments: jrembaum@cosmology.berkeley.edu
Updated: (JDR) 05/24/02

 
 
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