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| [[File:Helium phase diagram.svg|250px|thumb|Phase diagram of liquid <sup>3</sup>He–<sup>4</sup>He mixtures showing the phase separation.]]
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| [[File:Dilution refrigerator01.jpg|250px|thumb|Schematic diagram of a standard, or wet, dilution refrigerator]]
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| [[Image:Cold part of dilution refrigerator.jpg|250px|thumb|Schematic diagram of the low-temperature part of a dilution refrigerator.]]
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| [[File:Helium dilution cryostat.jpg|250px|thumb|The inside of a helium dilution refrigerator, with the vacuum cans removed.]]
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| [[Image:Helium dilution refrigerator.jpg|250px|thumb|Gas control system for a helium dilution refrigerator]] | |
| [[File:Dilution refrigerator03.jpg|250px|thumb|Schematic diagram of a cryogen-free, or dry, dilution refrigerator precooled by a two-stage [[pulse tube refrigerator]], indicated by the dotted rectangle.]]
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| A '''<sup>3</sup>He/<sup>4</sup>He dilution refrigerator''' is a [[cryogenics|cryogenic]] device that provides continuous cooling to temperatures as low as 2 [[Kelvin|mK]], with no moving parts in the low-temperature region.<ref>O.V. Lounasmaa, Experimental Principles and Methods Below 1 K, (Academic, London 1974).</ref> The cooling power is provided by the [[heat of mixing]] of the [[Helium-3]] and [[Helium-4]] isotopes. It is the only continuous refrigeration method for reaching temperatures below 0.3 K.<ref>F. Pobell, Matter and Methods at Low Temperatures, (Springer-Verlag, Berlin, 2007)</ref>
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| The dilution refrigerator was first proposed by [[Heinz London]] in the early 1950s, and was experimentally realized in 1964 in the Kamerlingh Onnes Laboratorium at [[Leiden University]].<ref>P. Das, R. de Bruyn Ouboter, and K.W. Taconis, "A realization of a London-Clarke-Mendoza type refrigerator" Proc. LT9, Columbus Ohio (1964), (Plenum Press, New York, 1965) pp1253-1255</ref>
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| == Theory of operation ==
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| The refrigeration process uses a mixture of two [[isotope]]s of [[helium]]: [[helium-3]] and [[helium-4]]. When cooled below approximately [[Orders of magnitude (temperature)|870]] [[Kelvin|millikelvin]], the mixture undergoes spontaneous phase separation to form a <sup>3</sup>He-rich phase (the concentrated phase) and a <sup>3</sup>He-poor phase (the dilute phase). As shown in the phase diagram, at very low temperatures the concentrated phase is essentially pure <sup>3</sup>He, while the dilute phase contains about 6.6% <sup>3</sup>He and 93.4% <sup>4</sup>He. The working fluid is <sup>3</sup>He, which is circulated by vacuum pumps at room temperature.
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| The <sup>3</sup>He enters the cryostat at a pressure of a few hundred [[Bar (unit)|millibar]]. In the classic dilution refrigerator (known as a ''wet dilution refrigerator''), the <sup>3</sup>He is precooled and [[Cold trap|purified]] by [[liquid nitrogen]] at 77 K and a <sup>4</sup>He bath at 4.2 K. Next, the <sup>3</sup>He enters a vacuum chamber where it is further cooled to a temperature of 1.2–1.5 K by the "1 K bath", a pumped <sup>4</sup>He bath (as decreasing the pressure of the helium reservoir depresses its boiling point). The 1 K bath liquifies the <sup>3</sup>He gas and removes the [[heat of condensation]]. The <sup>3</sup>He then enters the main impedance, a capillary with a large flow resistance. It is cooled by the still (described below) to a temperature 500–700 mK. Subsequently the <sup>3</sup>He flows through a secondary impedance and one side of a set of counterflow heat exchangers where it is cooled by a cold flow of <sup>3</sup>He. Finally, the pure <sup>3</sup>He enters the mixing chamber, the coldest area of the device.
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| In the mixing chamber, two phases of the <sup>3</sup>He–<sup>4</sup>He mixture, the concentrated phase (practically 100% <sup>3</sup>He) and the dilute phase (about 6.6% <sup>3</sup>He and 93.4% <sup>4</sup>He), are in equilibrium and separated by a phase boundary. Inside the chamber, the <sup>3</sup>He is diluted as it flows from the concentrated phase through the phase boundary into the dilute phase. The heat necessary for the dilution is the useful cooling power of the refrigerator, as the process of moving the <sup>3</sup>He through the phase boundary is endothermic and removes heat from the mixing chamber environment. The <sup>3</sup>He then leaves the mixing chamber in the dilute phase. On its way up, the cold, dilute <sup>3</sup>He cools the downward flowing <sup>3</sup>He via the heat exchangers until it enters the still. In the still, the <sup>3</sup>He flows through [[superfluid]] <sup>4</sup>He which is at rest.<ref>A.Th.A.M. de Waele and J.G.M. Kuerten, Thermodynamics and hydrodynamics of <sup>3</sup>He–<sup>4</sup>He mixtures, Progress in Low Temperature Physics, XIII, 167-218 (1992)</ref> The pressure in the still is kept low (about 10 Pa) by the pumps at room temperature. The vapor in the still is practically pure <sup>3</sup>He, which has a much higher partial pressure than <sup>4</sup>He at 500–700 mK. The pump therefore creates an [[osmotic pressure]] difference, which drives more <sup>3</sup>He from the concentrated to dilute phases in the mixing chamber, and then up from the mixing chamber to the still. Heat is supplied to the still to maintain a steady flow of <sup>3</sup>He. The pumps compress the <sup>3</sup>He to a pressure of a few hundred millibar and feed it back into the cryostat, completing the cycle.
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| == Cryogen-free dilution refrigerators ==
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| Modern dilution refrigerators can precool the <sup>3</sup>He with a [[cryocooler]] in place of liquid nitrogen, liquid helium, and a 1 K bath.<ref>A.T.A.M. de Waele, Basic operation of cryocoolers and related thermal machines, Review article, Journal of Low Temperature Physics, Vol.164, pp. 179-236, (2011), {{DOI|10.1007/s10909-011-0373-x}}</ref> No external supply of cryogenic liquids is needed in these "dry cryostats" and operation can be highly automatized. However, dry cryostats have high energy requirements and are subject to mechanical vibrations, such as those produced by [[pulse tube refrigerator]]s. The first experimental machines were built in the 1990s, when (commercial) [[cryocooler]]s became available, capable of reaching a temperature lower than that of [[liquid helium]] and having sufficient cooling power (on the order of 1 watt at 4.2 K).<ref>K. Uhlig and W. Hehn, ''Cryogenics'' '''37''', 279 (1997).</ref> [[Pulse tube refrigerator|Pulse tube coolers]] are commonly used cryocoolers in dry dilution refrigerators.
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| Dry dilution refrigerators generally follow one of two designs. One design incorporates an inner vacuum can, which is used to initially precool the machine from room temperature down to the base temperature of the pulse tube cooler (using heat-exchange gas). However, every time the refrigerator is cooled down, a vacuum seal that holds at cryogenic temperatures needs to be made, and low temperature vacuum feed-throughs must be used for the experimental wiring. The other design is more demanding to realize, requiring heat switches that are necessary for precooling, but no inner vacuum can is needed, greatly reducing the complexity of the experimental wiring. The latter type is used for the SCUBA-2 sub-millimetre camera on the [[James Clerk Maxwell Telescope]].
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| ==Cooling power==
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| At not too low temperatures the cooling power at the mixing chamber is approximately given by
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| : <math>\dot Q_m =\dot n_3(12T_i^2-96T_m^2)</math> | |
| where <math>\dot n_3</math> is the <sup>3</sup>He molar circulation rate, ''T''<sub>m</sub> is the mixing-chamber temperature, and ''T''<sub>i</sub> the temperature of the <sup>3</sup>He entering the mixing chamber. In the case of zero heat load there is a fixed ratio between the two temperatures
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| : <math>T_m =\frac{T_i}{2.8}.</math> | |
| From this relation it is clear that a low ''T''<sub>m</sub> can only be reached if ''T''<sub>i</sub> is low. In dilution refrigerators ''T''<sub>i</sub> is reduced by using heat exchangers as shown in the schematic diagram of the low-temperature region above. However, at very low temperatures this becomes more and more difficult due to the so-called [[Kapitza resistance]]. This is a heat resistance at the surface between the helium liquids and the solid body of the heat exchanger. It is inversely proportional to ''T''<sup>4</sup> and the heat-exchanging surface area ''A''. In other words: to get the same heat resistance one needs to increase the surface by a factor 10,000 if the temperature goes down by a factor 10. In order to get a low thermal resistance at low temperatures (below about 30 mK) a large surface area is needed. The lower the temperature, the larger the area. In practice one uses very fine silver powder.
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| ==Limitations==
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| There is no fundamental limiting low temperature of dilution refrigerators. Yet the temperature range is limited to about 2 mK for practical reasons. At very low temperatures both the viscosity and the thermal conductivity of the circulating fluid become larger if the temperature is lowered. To reduce the viscous heating the diameters of the inlet and outlet tubes of the mixing chamber must go as ''T''<sub>m</sub><sup>−3</sup> and to get low heat flow the lengths of the tubes should go as ''T''<sub>m</sub><sup>−8</sup>. That means that, to reduce the temperature by a factor 2, one needs to increase the diameter by a factor 8 and the length by a factor 256. Hence the volume should be increased by a factor 2<sup>14</sup>=16384. In other words: every cm<sup>3</sup> at 2 mK would become 16.384 liter at 1 mK. The machines would become very big and very expensive. Fortunately there is a very powerful alternative for cooling below 2 mK and that is [[Magnetic_refrigeration#Nuclear_demagnetization|nuclear demagnetization]].
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| ==See also==
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| * [[Adiabatic demagnetization]]
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| * [[Magnetic refrigeration]].
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| * [[Dry dilution refrigerator]]
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| * [[Helium-3 refrigerator]]
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| * [[Refrigerated transport Dewar]]
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| * [[Timeline of low-temperature technology]]
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| ==References==
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| {{Reflist}}
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| *{{cite journal|authors=H. E. Hall, P. J. Ford, and K. Thomson|title=A helium-3 dilution refrigerator|journal=Cryogenics|volume=6|pages=80–88|year=1966}}
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| *{{cite journal|authors=J. C. Wheatley, O. E. Vilches, and W. R. Abel|title=Principles and methods of dilution refrigeration|journal=Journal of Low Temperature Physics|volume=4|pages=1–64|year=1968}}
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| *{{cite journal|authors=T. O. Niinikoski|title=A horizontal dilution refrigerator with very high cooling power|journal=Nuclear Instruments and Methods|volume=97|pages=95–101|year=1971|doi=10.1016/0029-554X(71)90518-0}}
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| *{{cite journal|authors=G. J. Frossati|title=Experimental techniques: methods for cooling below 300 mK|journal=Journal of Low Temperature Physics|volume=87|pages=595–633|year=1992}}
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| ==External links==
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| *[http://www.magnet.fsu.edu/education/tutorials/magnetacademy/lowtemperaturephysics/ Low Temperature Physics: The What, the How, the Why] - The National High Magnetic Field Laboratory
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| *[http://cdms.berkeley.edu/UCB/75fridge/inxsrc/dilution/ 3He-4He Dilution Explanation]
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| *[http://www.lancs.ac.uk/depts/physics/research/condmatt/ult/tech.html Lancaster University, Ultra Low Temperature Physics] - Description of dilution refrigeration.
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| *[http://users.physics.harvard.edu/~coldwell/marcus/how_to/Fridge.pdf Harvard University, Marcus Lab] - Hitchhiker's Guide to the Dilution Refrigerator.
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| :
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| [[Category:Cryogenics]]
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| [[Category:Cooling technology]]
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