Ultra-Low-Temperature Refrigerators

In 1951, H. London made the suggestion to use a solution of the rarer isotope He in the more common isotope He to obtain low temperatures. In any dilute solution, the solute molecules can be considered to behave like a 

The density of He is less than that of He. Therefore, at temperatures below 0.87 K, solutions of He and He exist in two liquid phases with the He rich phase residing above the He phase. The migration of He atoms across the liquid-liquid interface is similar to evaporation in that the He atoms exert no drag force on the He atoms. Since the osmotic pressure of the He dilute phase extrapolates to about 0.0023 MPa at 0 K instead of 0 MPa, it suggests that, near absolute zero, a stable solution of these isotopes should contain about 6.4% He. During the phase transition of He into the He solution at constant temperature, the entropy increases and heat is absorbed by the He to increase its enthalpy. This is the driving force behind the dilution cycle. 

The refrigeration effect for the dilution refrigerator can be determined by an energy balance around the mixing chamber 

The simplest dilution refrigerator may be operated as a single cycle. The He- He mixture is condensed into the mixing chamber, precooled, and then circulated. Temperatures of 4-5 mK have been obtained with such a device since heat is not added continuously with the liquid feed.  

A method for achieving temperatures around 2 mK by using the properties of solid He was originally proposed in 1950 by Pomeranchuk and subsequently developed in 1969 by Wheatley. Pure liquid He will not solidify at 0 K unless a pressure of about 3.5 MPa is applied to the liquid. The melting curve has a minimum at 0.3 K for which the required pressure is close to 3 MPa. Below 0.3 K, the solid has a higher molar entropy than the liquid. In fact, at 20 mK the molar entropy of the liquid is only 1/7 that of the solid. This implies that a substantial cooling effect could be gained by adiabatic solidification under compression at these low temperatures. However, for this 

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