Journal of Physics E: Scientific Instruments

REVIEW ARTICLE

Dilution refrigerationTo cite this article: O V Lounasmaa 1979 J. Phys. E: Sci. Instrum. 12 668

 

View the article online for updates and enhancements.

Related contentUltralow temperatures-how and whyW J Huiskamp and O V Lounasmaa

-

Microkelvin physicsG R Pickett

-

Frozen spin polarised deuteron target 60cm3 in volumeN S Borisov, E I Bunyatova, M Yu Liburget al.

-

Recent citationsDilution refrigerator for muon spinrelaxation experimentsW. A. Steyert et al

-

Very low temperatures and theirapplications in nuclear orientationEska, G.

-

Low temperature irradiation equipment formeasurements down to 150 mKW. Bauriedl et al

-

This content was downloaded from IP address 103.100.150.2 on 09/09/2018 at 07:13

J. Phys. E: Sci. Instrum., Vol. 12, 1979. Printed in Great Britain

REV1 E W A RTI C L E

D i I uti on ref rig erat i on

0 V Lounasmaa Low Temperature Laboratory, Helsinki University of Technology, SF-02150 Espoo 15, Finland

Abstract In the first part of this review the theory and operation of a conventional dilution refrigerator are explained in simple terms. The discussion of heat exchangers is, however, somewhat more detailed. In the second part several of the latest machines are discussed, including a refrigerator which reaches 2.0 mK and another which operates by an unconventional gas circulation cycle.

2 Operating principles and theory 2.1 Liquid mixtures of 3He and 4He The operating principle of the dilution refrigerator is based on the peculiar properties exhibited by mixtures of 3He and *He at low temperatures. Below about 0.8 K a liquid mixture of these two isotopes spontaneously separates into two components, one of the phases being rich in 3He and the other rich in "e. Because of its lower density, the 3He-rich phase floats on top of the 4He-rich phase. This is schematically illustrated on the right in figure 1. As the temperature is lowered further, the relative amounts of 3He and 4He in the

1 Introduction 3He/4He dilution refrigerators have been in general use for more than a decade. During this time their cooling power has increased by a factor of 100 and the low-temperature limit has been pushed from 10 to 2mK. Successful commercial machines are available. The dilution refrigerator has already fully established itself as the most important tool for research at ultra-low temperatures, replacing adiabatic demagnetisation of paramagnetic salts. Many experiments which earlier would have been difficult or impossible below 0.3 K are now per- formed routinely with dilution refrigerators. Anyone with some knowledge of low-temperature techniques can easily learn to operate a cryostat of this type.

In this review, written mainly for the non-expert, the working principle of the dilution refrigerator will first be explained in simple terms. For more information the reader is referred to the books of Betts (1976) and Lounasmaa (1974). Our discussion on heat exchangers is a little more detailed because they are the most important constructional details of a successful cryostat. The second part of this review will be devoted to descriptions of the latest machine built by Frossati et al (1977: Frossati 1978), reaching 2 m K in continuous operation, of the Leiden refrigerator (Pennings 1976, Pennings et a1 1976), of the horizontal machine by Niinikoski (1976), and of a special refrigerator by Roubeau (1976; Roubeau et a1 1978).

The principle of the dilution refrigerator was originally suggested by London in 1951 and by London, Clarke and Mendoza in 1962, and the first cryostat of this type, reaching 0.22 K, was built by Das, de Bruyn Ouboter and Taconis in 1965. Machines cooling to much lower temperatures were constructed the next year by Neganov, Borisov and Liburg and by Hall, Ford and Thompson. A considerable amount of development work was later done by Wheatley (1970), among others. Extensive bibliographies can be found from the references cited in the present review.

t:::. ~, ; , , , , , : ;;,. 1.; ..................... 1. . . . , , . , . , . . , , . . . . ::::. . . , , , . . . ....................... . . . . . , . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . , . . . .

Figure 1 refrigerators. 3He flows in the direction of the arrows and cooling is produced when the phase boundary is crossed. Concentrations refer to right-hand figure.

Comparison of the evaporation and dilution

two phases change; below about 40mK the upper, con- centrated phase is practically pure 3He and the lower, dilute phase is made of 6.4 a t% of 3He and 93.6% of *He. The possibility to dissolve 6.4% of 3He in liquid 4He even at absolute zero is of paramount importance for the success of the dilution refrigerator.

There is, indeed, a remarkable difference at low tempera- tures between the thermal properties of liquid 4He and liquid 3He. Because of its zero nuclear spin and superfluid properties, liquid *He is, below 0.5 K, effectively in its quantum mecha- nical ground state. Very few phonons are excited and the liquid is thermally inert. The light isotope We, with a nuclear spin I= +, behaves very differently. Its heat capacity, approxi- mately a linear function of temperature T, is rather high in the whole temperature range which is of interest in dilution refrigeration. As a result we may describe *He in the dilute phase as a 'supporting medium' or 'mechanical vacuum' for the active 3He atoms.

0022-3735/79/080668+08 $01.00 1979 The Institute of Physics

Dilution refrigcrutiorr

2.2 The principle of dilution the mixing chamber. The process can be made continuous by The principle of the dilution process can now be explained by circulating 3He in the system by a pumpat room temperature. comparing it with ordinary evaporation. The concentrated Incoming gas is first pre-cooled and liquefied in the condenser, phase in the dilution refrigerator, where the active 3He atoms which is attached to the 4He pot, at about 1.1 K. The 3He are close to one another, corresponds to the liquid phase in then enters the still heat exchanger at about 0.7 K and passes the evaporation refrigerator (cf figure 1). Similarly, the dilute through a tubular heat exchanger and three successive units of phase, with only 6.4% of the atoms being of the active 3He the main heat exchanger before entering the mixing chamber. type, corresponds to the vapour phase in the evaporation After crossing the phase boundary there, 3He atoms, driven refrigerator. The positions of the ‘liquid’ and the ‘vapour’ by an osmotic pressure gradient, proceed in reverse order have thus been changed in the two systems. When molecules through the heat exchangers, along an unbroken column of the move upward from the liquid to the vapour phase in the dilute superfluid phase, to the still where the liquid column evaporation refrigerator the temperature is lowered because ends. energy is needed to overcome the interatomic forces. Similarly, Vapour is removed from the still by pumping, and this is when 3He atoms move downward, from the concentrated to where 3He is separated from 4He. If a suiiable orifice for the dilute phase, cooling results. reducing the 4He film flow is installed, more than 95%

It is now easy to see the importance of the 6.4% solubility of the outcoming gas is 3He because the vapour pressure of of 3He into 4He. In an ordinary evaporation refrigerator the 4He is almost negligible even at 0.7 K. vapour phase becomes depleted of molecules rather soon, The operating procedure for a dilution refrigerator is because the vapour pressure decreases exponentially with briefly as follows. After the temperature of the 4He pot has temperature, whereas in the dilution refrigerator the con- been reduced to 1 . 1 K the 3He/4He gas mixture is condensed centration of 3He atoms in the ‘vapour’, or dilute, phase and passed to the refrigerator. The quantity of 3He needed remains constant at 6.4% as the temperature is lowered below can be calculated from the known volumes of the heat 40mK. Therefore, the number of 3He atoms that cross the phase boundary per unit time is, in the latter case, inde- pendent of temperature.

2.3 The dilution refrigerator The principal parts of a conventional dilution refrigerator are illustrated in figure 2. Cooling is achieved in a container called

Figure 2 A schematic illustration of a conventional dilution refrigerator. To increase the thermal contact area the main heat exchangers of the step type are filled with a sintered copper or silver sponge, with clear holes in the middle for an unimpeded flow of 3He. The condenser at 1.1 K and the still heat exchanger at 0.7 K are also filled with sinter.

Figure 3 built in the author’s laboratory (G J Ehnholm, J P Ekstrom, 0 T lkkala and M T Loponen) for pre-cooling a two-stage adiabatic nuclear demagnetisation cryostat. The dilution unit is about 80 mm wide and 200 mm high. It has one tubular and 14 sintered-copper-type step heat exchangers, 12 smaller ones on the upper level and two large units below. The gas flow rate is 0.3 mmol s-l. The body of the mixing chamber reaches 7 mK in continuous operation without a load and IO mK during experiments with the nuclear refrigerator in place.

Photograph of a dilution refrigerator recently

669

0 VLounasmaa

exchangers and the mixing chamber. Gas circulation is then started with a rotary pump which causes further cooling. After the still pressure becomes low enough a diffusion pump is switched on. The dilution refrigerator then cools to about 0.8 K, with the mixing chamber being the warmest and the still the coldest part.

After the phase separation has occurred, as indicated by a sudden cooling of the mixing chamber, the temperature gradient in the refrigerator changes sign. External heating is then supplied to the still to increase the gas circulation rate. The various parts of the apparatus reach their equilibrium temperatures in 1-2 h. Figure 3 is a photograph of a dilution refrigerator recently built in the author’s laboratory.

2.4 Enthalpy considerations We shall next derive some simple expressions which are necessary for a quantitative understanding of the dilution process, In the concentrated phase the thermodynamic functions can be calculated from experimental measurements of the specific heat of pure liquid 3He. Below 40 mK, C3 = 25 T J K-2 mol-1, whereby we find for entropy and enthalpy

^ -

SC = fi (C3/T) dT= 25 T J K-2 mol-l,

HC = io Cs d T= 12.5 T2 J K-2 mol-l.

(I)

(2 ) T

In the dilute phase the specific heat is sufficiently accurately given by that of an ideal Fermi gas, whose density is the same as the density of 3He in the dilute solution. Therefore, at T< TF, we find, per mole of 3He in the solution, C D = r2RT/ ~ T F = 107 TJ K-2 mol-l, with the Fermi temperature TF= 0.383 K. We then obtain

T SD = io (CD/T) d T= 107 T J K-‘ mol-l. ( 3 )

In the mixing chamber, under equilibrium conditions, the chemical potentials p c and p~ of 3He in the concentrated and dilute phases respectively are equal, i.e.

H c - TSc = HD - TSD. (4 )

We thus find, using equations (l-4),

H D = HC + T(SD - Sc) = 94.5 T2 J K-2 mol-1. (5)

The fact that the numerical value of H D is much larger than that of HC is, of course, the basic reason that cooling is produced in the mixing chamber.

In the heat exchangers, on the other hand, T

HD = 1, C D dT= 53.5 T2 J KW2 mol-l. ( 6 )

We next assume that the dilution refrigerator has reached a steady state, the temperature of the mixing chamber being constant at Thf . We further make the simplifying assumptions that only 3He is circulated and that frictional heating can be ignored, and calculate the cooling power and ultimate temperature of a refrigerator under these idealised conditions.

External heating of the mixing chamber is caused by the heat leak e and by the incoming liquid 3He which must be cooled from the temperature Tx, at which it leaves the last heat exchanger, to TPI. Cooling is simultaneously produced by dilution at the rate A~(HD( T N ) - Hc( T3r)): here A 3 = dns/dt is the molar circulation rate of 3He. In equilibrium

0 + fi3(Hc( TK) - Hc( Tx ) ) = AB(HD( Tx) - Hc( Tx)) , (7)

(8)

which gives, by applying equations (2) and (5 ) ,

0 = A 3 (94.5 TM* - 12.5 TI?) J K-2 mol-l.

The cooling power is thus proportional to the 3He circulation rate, provided that we ignore the dependence of TX on htg (cf equation (18) later).

If the external heat leak is zero we find, according to equation (8),

(9) TM = 0.36 Tx.

For a perfect exchanger, i.e. when T ~ I = T K , we obtain from equation (8)

T M ~ = Q i 8 2 A 3 K2 mol J-l. (10)

When the dilution refrigerator is run in the single-cycle mode, i.e. when the 3He input is cut off, the situation is the same as for a perfect exchanger. The cooling power is then proportional to the square of the mixing chamber temperature (cf equation (10)). This is why the external heat leak eventually catches up and further cooling stops, even though the constant 6.4”/, solubility of 3He into liquid 4He ensures that A 3 is not a function of TM.

2.5 Theory of heat exchangers The success of a particular dilution refrigerator depends critically on the construction of its heat exchangers (Niinikoski 1976, Frossati et a1 1977, Frossati 1978). Two basically different kinds have been employed.

In the continuous-counterflow type the temperature varies over the length of the exchanger body and heat is transferred between the two liquid streams across a wall. The simplest exchanger of this type is made of two concentric tubes as illustrated in figures 2 and 4. The incoming 3He flows down- wards in the inner tube whereas the outgoing 3He moves upwards through the dilute mixture confined in the annular space between the two tubes. This type of exchanger, often the only one used in a dilution refrigerator, is normally employed

H o t e n d A

, I

Figure 4 Analysis of a tubular continuous-counterflow heat exchanger. Details are given in the text. Usually the inner tube is coiled to a spiral.

670

Dilution refrigeration

immediately below the still to lower the temperature from 0.7 K to 50 mK or even less. Typically the tubular exchanger is 0.50-1.0 m long with 1 and 4 mm diameter tubes.

The temperature is approximately constant throughout the copper body of a discrete or step heat exchanger. Even though this type has been used in most dilution refrigerators built so far (cf figures 2 and 3), we shall not discuss it in detail because a continuous-counterflow exchanger, on which we shall focus our attention, is the better type.

Our presentation is simplified from discussions given by Niinikoski (1976) and by Frossati et a1 (1977; Frossati 1978). We shall analyse the performance of a perfect tubular exchanger (cf figure 4) between the still and the mixing chamber. We thus assume that all heat given up by the incoming concentrated 3He flows radially across the wall of the inner tube and is taken up by the outgoing 3He, i.e.

We ignore viscous heating and also vertical conduction along the exchanger body and the liquid columns.

Heat flow from the concentrated to the dilute side is determined by the Kapitza thermal boundary resistance (cf Lounasmaa 1974, $9.6). That is, referring to the surface element dA = 2.xrdz of figure 4,

d Q = a2nr dz( Tc4 - T D ~ ) % a: dA 4 7 3 d T, (12)

where c1 is the heat transfer constant and is related to the Kapitza resistivity RK = dA d Tido by

CY = 1/4 Rx T3. (1 3)

In passing through the volume element d d z of figure 4

(14)

We have assumed that a : ~ = a : ~ .

the enthalpy of incoming 3He is reduced by

dHc = 25 TC d TC J K-* mol-1

and that of the dilute side increased by

dHD = 107 TD d TD J mol-I, (1 5)

where we have employed equations ( 2 ) and (6). By combining ( l l ) , (14) and (15), and by integrating, we obtain

1 2 , 5 T ~ ~ = 5 3 , 5 T ~ ~ . (1 6)

We have ignored Ts2 in comparison with Tc2 and T d in comparison with T D ~ .

By equating d e from equation (12) with AsdHc, and by using equation (16) for eliminating TD, we find

25ri3(dTc/Tc3) J K-* mol-l=oldA[l-(12~5/53~5)2]

When we integrate from the cold bottom of the tubular heat exchanger ( z = 0, TC = TN) to the hot top end ( z= L, TC = Ts; L is the total length of the exchanger and TS is the temperature of the still) we find

12.5ri3/T~* J K-2 mol-1 = 0,95a:A, (18)

where A is the total surface area of the inner tube and we have ignored the small quantity l/Tsz in comparison with l/Tx2.

Finally, by employing equations (8), (13) and (18) we obtain the important expression relating the mixing chamber temperature to the properties of the continuous heat exchanger :

where T L ~ is expressed in kelvins if RK is given in m2 K W-I, r i 3

in mol s-1, A in m2, and 0 in watts.

2.6 Heat leaks and ultimate temperature The optimum flow rate for a given heat exchanger construction can now be found from equation (19) by writing d T5l2/dri3 = 0, which yields

(20)

T>r(min)= 0 * 7 4 ( e R ~ T ~ / A ) ~ ; ~ . (21)

A3 (opt) = (QA/660 RK T3)1/2 K2 mol J-1.

By inserting this expression back into equation (19) we obtain

For Q = 30 nW and R K T ~ = O . ~ m* K4 W-l, which are reasonable values, we obtain TN(min) = 2 mK with A = 160 m2 and r i 3 (opt) = 0.1 5 mmol s-l. Frossati et a1 (1977 ; Frossati 1978) have used exchangers with sintered sponges made of very fine silver powder of 70 nm average diameter. For this material A = 1.8 m2 8-l and, by assuming a 50 % packing factor for the powder, the volume of 3He in the voids becomes approximately 20 cm3. This is a very reasonable quantity of liquid 3He.

The heat leak Q can approximately be divided into two components: a background and a flow-dependent part. The first term is caused by the remaining exchange gas in the space surrounding the dilution refrigerator, by mechanical \ ibrations of the cryostat, by heat conduction along supports and along the liquid helium columns in the tubes, and by slow cooling of poorly conducting epoxy parts. This source of heat usually decreases with time and can be made as small as 10nW, although a considerably larger value is more common.

The flow-dependent part of 0 is roughly proportional to r i3 . This term, which usually becomes important below 10 mK, can be attributed to viscosity which impedes the flow of 3He, and to conduction along the length of the exchanger and the liquid columns themselves. Since viscous heating is propor- tional to LID4 and conduction to D2/L, where L is the length of the tube and D its diameter, the flow-dependent heat leak can always be minimised by increasing both L and D . A practical limit is set, of course, by the volume of the liquid and by the available space.

The discussion and numerical calculations in this section show that a final mixing chamber temperature of 2.0 mK is possible, provided that sufficiently fine powder is employed for making the sintzred sponge in the heat exchangers. How this is done in practice will be explained briefly in the next section,

3 Examples of dilution refrigerators 3.1 The Grenoble refrigerator Frossati et ul (1977; Frossati 1978) have recently built a refrigerator which actually reaches 2.0 mK in continuous operation; this is the lowest temperature so far produced by the dilution method. The Grenoble group has for many years worked to improve the performance of dilution refrigerators; for more details the original publications should be consulted.

The apparatus is, in principle, rather similar to that shown schematically in figure 2. The secret of success is, in accordance with $2.6, in the heat exchanger construction; an illustration is shown in figure 5. The liquid flows along square channels, whereas the heat exchange takes place between the silver sinter and the stationary liquid in the pores. Thermal conductivity of 3He is sufficient to assure equilibrium between the moving and stationary liquid. This principle of exchanger construction has been employed in many cryostats over the past years but the Grenoble group is responsible for several crucial improve- ments, including the efficient use of very fine powder.

The heat exchanger of figure 5 is made as follows: 70 nm diameter silver powder is first sintered to a 1-2 mm thick layer on both sides of a 0.1 mm thick silver-plated CuNi foil which is 15-30 mm in width and 250 mm long. This assembly is then placed between two CuNi pieces of the profile shown in

671

0 V Lounasmaa

tures, perhaps in the vicinity of 1 mK. These include the use of finer powder for making the silver sponge, ‘direct‘ heat transfer (cf 83.2) in the exchangers to avoid the Kapitza resistance, and a multiple-mixing-chamber construction. Some important data on their new refrigerator are given in table 1.

3.2 The Leiden refrigerator Development work on a rather different dilution refrigerator has been done at Leiden for many years (Pennings 1976, Pennings et a1 1976). In this machine 4He, instead of 3He, is circulated. Figure 6 is a schematic illustration of the apparatus.

v 1)‘ Cold end

Figure 5 The heat exchanger construction of Frossati et a1 (1977). Concentrated 3He enters through the smaller square channel (Ac = D c ~ ) at the hot end and leaves by the cold end. 3He in the dilute mixture moves in the opposite direction along the larger square channel (AD = DD”. Because the speed of 3He flow is 15 times higher on the dilute side and because viscous heating is proportional to 1/04, one should make DDIDc = 2.

OD

r figure 5. Next, the unit is twisted to make a helix and welded. Inlet and outlet tubes are then soldered to both ends. The exchanger is approximately of the continuous-counterflow type analysed in $2.5, because heat conduction over its length is small. Five units, with progressively larger channel sizes towards the low-temperature end, are then fitted in series. A tubular continuous exchanger (cf figure 2) is mounted between the still and the first sintered exchanger.

The still and the mixing chamber are of standard con- struction. Their design is not critical for reaching the lowest temperatures, except that the inlet and outlet tubes in the mixer must be large enough, about 5 and 13 mm in diameter respectively, to reduce viscous heating.

Frossati et a1 (1977; Frossati 1978) suggest in their paper several possible improvements to reach even lower tempera-

Table 1 Some constructional and performance data for the heat exchanqers of figure 5 ( L = 250 mm. r i3 = 0.2 mmol s-l, 0 = 30 nW).

Exchanger D o DC A TD Tc TD Tc number (mm) (mm) (m2) (hot) (hot) (cold) (cold)

(mK) (mK) (mK) (mK)

1 4.0 1 .6 29 25 70 6 .5 17 2 658 2.8 29 6 . 5 17 4.0 10 3 8 .2 3 .4 58 4.0 10 2 .7 6.6 4 10 4.2 58 2 . 7 6 . 6 2.2 5 . 0 5 12 5 .0 58 2 - 2 5.0 2 .0 4 .3

Demixing chawber

Figure 6 A schematic diagram of the Leiden dilution refrigerator, which is explained in the text.

The refrigerator works as follows. The system is first filled with the 3He/4He mixture in such a way that the boundary between the concentrated and dilute phases is in the demixing chamber, which is pre-cooled to 0.6 K by a 3He refrigerator. The mixing chamber above is thus filled, at first, with the concentrated phase. Superfluid 4He, which carries no heat, is then continuously supplied to the mixing chamber through a tube filled with fine powder; this tube acts as a superleak admitting only “e. The concentrated 3He in the mixing chamber is diluted by the incoming “e whereby cooling results, as explained in 82.2.

The dilute mixture then falls through the central tube to the demixing chamber while concentrated 3He simultaneously rises, through the same tube, from the demixing to the mixing chamber. This tube thus acts as a continuous-counterflow heat exchanger: the cold dilute mixture descends and the relatively warm 3He ascends due to effects of gravity. Finally, 4He is separated from the dilute phase in the demixing chamber by a second superleak tube through which 4He is extracted. The heat of demixing is absorbed by the 3He refrigerator, which is in good thermal contact with the demixing chamber. Con- tinuous flow of “e in the dilution machine is maintained by a pump at room temperature.

672

Dilution refrigeration

The Leiden cycle has certain advantages over the conven- tional dilution process. The machine of figure 6 needs no heat exchangers of large surface area because heat is transferred directly between the two counterflowing liquid phases in the same tube between the mixing and demixing chambers. The Kapitza thermal boundary resistance between the two liquid streams is, therefore, eliminated. Another advantage is that the refrigerator can work at any pressure up to solidification; this might be very important in some applications. It is, furthermore, possible to confine the 4He circulation entirely to the low-temperature part of the apparatus by making use of the fountain pressure in superfluid “e. The 3He refrigerator may be used for absorbing most of the external heat leak; in the conventional dilution machine the still can be employed for the same purpose.

An analysis shows that it should be possible to reach 5 mK with the Leiden refrigerator. So far the lowest temperature has been 7.9 mK, which is rather high when compared with the best conventional dilution refrigerators. Until now the Leiden refrigerator has had only a few practical applications but it has potential to become useful in the future for special purposes.

3.3 A horizontal refrigerator Dilution cryostats can easily be adapted to various experi- mental needs. A good example is the horizontal refrigerator built by Niinikoski (1976); the unusual construction was dictated by the geometry of magnet pole pieces and by the counting arrangements to be used during actual experiments on spin-frozen, polarised proton targets. Figure 7 is an illustration of the apparatus.

For many experiments a high cooling power is more impor- tant than a very low temperature. Since 0 is proportional to 113 (equation (8)) it is then necessary to design heat exchangers which allow a high circulation rate for 3He. Typically for 113 = 0.5 mmol s-1 and TM= 10 mK, the cooling power is 0.5-2 pW. Niinikoski’s refrigerator is much bigger. When run at k3=7 mmol s-1 it delivers 10 mW at 200 mK; at 123=25 mmol s-1 and T>f= 500 mK, = 150 mW. For details the reader is referred to figure 7 and to original publications.

3.4 A refrigerator with easy access Roubeau (1976; Roubeau et a1 1978) has designed a refri- gerator in which the specimen and the thermometer are put directly into the mixing chamber to ensure thermal equilibrium. For quick access the whole dilution unit can easily be lifted out of the cryostat; it simply fits inside a 35 mm diameter tube at the centre of the apparatus. This tube serves, at the Same time, as the still pumping line.

Counter current heat exchanger

Figure 7 The horizontal dilution refrigerator of Niinikoski (1976).

Pre-cooling of the incoming 3He to 2.17 K (the h point) is achieved by pumping the main 4He bath at its bottom by means of a small container into which “e first enters from the bath via a calibrated leak and is then pumped away through a separate tube. By working in this fashion the top of the *He bath remains at 4.2 K and at atmospheric pressure whereby transfer of liquid during an experiment is made simple.

The dilution unit is illustrated in figure 8. Incoming 3He, at 2.2 K and at 20 kPa, is expanded when it leaves the upper

Upper constriction

L mm constriction .- - -. - .- - - , . . . . . . . . . . . , . . , . . . . . . . . , . , . . . . . . . . . , . . . . . . . . . . . Liquid level

. , . . . I . . . . .

0 . L mm tube

Lower constriction

0.3 mm tube

Phase boundary

3He inlet tube

,Mixing chamber

-Dilute phase out I et tube

Figure 8 The special dilution refrigerator of Roubeau (1 976).

constriction and enters a 0.4 mm diameter tube wound around an evacuated container. The temperature at the end of this tube is about 200mK. Next, 3He passes through the lower constriction and then through a 0.3 mm tube which is coiled and immersed in the dilute phase.

The mixing chamber is a bell-shaped, thin-walled stainless steel container, insulated by the sole action of the Kapitza thermal boundary resistance. The temperature of 3He, when it enters the mixer, is about 100 mK.

The still is an inverted copper can, open at its lower end. It is connected to the pumping tube via a 4 m m diameter constriction. The amount of 3He/“e mixture condensed into the refrigerator is adjusted so that the liquid level, both inside and outside the still, is in the middle. The dilute phase above the mixing chamber communicates with the still through the annular space between the 35 mm tube and the evacuated container ; this arrangement provides sufficiently good heat exchange between the incoming and outgoing 3He.

A 4He film creeps along the wall of the 35 mm tube and evaporates between 1 and 2 K. Most of the vapour is prevented from being pumped away by the close fit between the tube and the pre-cooler and it condenses on the outside top of the still. Without this arrangement the quantity of 4He in the outgoing

3* 673

0 V Lounasmaa

gas would increase markedly with adverse effects on the per- formance of the refrigerator. Condensation Of 4He evaporates 3He inside, whereby electrical heating of the still can be reduced.

The minimum temperature obtained in this cryostat is 40 mK in continuous operation. With A3=0.3 mmol s-1 the cooling power at 50mK is IOpW. At T ~ = 1 0 0 m K and rtn=0.5 mmol s-1, Q=0.2 mW.

3.5 Commercial dilution refrigerators SHE 422 6.0 0.10 4.5 135

commercial machines have been available for many years; SHE 434 4.5 0.10 17 600

Table 2 Performance of Some commercial dilution refrigemtors.

Model 8 at

(PW) (PW)

T M (min) A3 (opt) 8 at (mK) (mmol s-l) 20mK 0.1 K

A clear sign of the success of dilution refrigerators is that SHE 433 4.5 0.10 IO 300

over 200 units have already been sold. Many of them have OXF 100pW 5 0.09 2 100 successfully been operated by persons who are not experts in OXF 300pW 5 0.3 10 300 low-temperature techniques. The customer may purchase just OXF 1 O00pW 5 0.6 20 IO00 the dilution refrigerator itself or the complete cryogenic installation, including thermometers, pumps and gas-handling systems.

Commercial refrigerators are offered in many sizes and they can usually be adapted to particular needs at little or no extra cost. Prices range from El 500 for a 'minifridge' dilution unit to E50 OOO for a complete high-power installation. Commercial 4 Conc1usion machines reaching 4.5 mK have recently been introduced; they Low-temPeratUre physics has recently entered, once again, a employ heat exchangers of the type discussed in $3.1. new and exciting era. I n this development an important role

Table 2 gives some performance data on commercial has been played by new cooling methods, i.e. by dilution refrigerators. For complete details the manufacturerst should refrigeration, adiabatic nuclear demagnetisation and by he contacted. Figure 9 is a photograph of an SHE refrigerator. FYn-"nnchuk cooling (Huiskamp and Lounasmaa 1973). The

temperature range from 2 to 3°K may be covered by dilution, while nuclear demagnetisation is employed for cooling below 2 mK. Many new types of experiment, requiring complicated installations, can now be performed at very low temperatures. No one whose research would benefit from extending it below 0.3 K should hesitate using a dilution refrigerator, which is a very versatile machine, adaptable to different needs, both large and small.

SHE: SHE Corporation; OXF: Oxford Instruments Ltd.

Acknowledgments Helpful criticism and comments by G Frossati, 0 Ikkala, T 0 Niinikoski, P Roubeau and K W Taconis are gratefully acknowledged. This work was financially supported by the Academy of Finland.

References Betts D S 1976 Refrigeration and Thermometry Below One Kelcin (Brighton: Sussex University Press) Frossati G 1978 Obtaining ultra-low temperatures by dilution of 3He into 4He J . Physique C 39 1578 Frossati G, Godfrin H, Hebral B, Schumacher G and Thoulouze D 1977 Conventional cycle dilution refrigeration down to 2.0 mK Physics at Ultralow Temperatures: Proc. Hakone Int . Symp. (Tokyo: Physical Society of Japan) p 205 Huiskamp W J and Lounasmaa 0 V 1973 Ultra-low temperatures - how and why Rep. Prog. Phys. 36 423 Lounasmaa 0 V 1974 Experimental Principles and Methods Below I K (New York: Academic) Niinikoski T 0 1976 Dilution refrigeration: new concepts Proc. 6th Int. Cryogenic Engineering Conf. (Guildford : IPC) p 102 Pennings N H 1976 The Leiden dilution refrigerator Thesis University of Leiden

Figure 9 Photograph of a commercial dilution refrigerator which reaches 4 3 mK with a gas circulation rate of 0.1 mmol s-l. At IO mK the cooling power is 2 pW (SHE Corporation).

t Oxford Instruments Ltd, Osney Mead, Oxford OX2 ODX, UK and SHE Corporation, 4174 Sorrento Valley Boulevard, San Diego, California 92121, USA.

674

Dilution refrigeration

Pennings N H, de Bruyn Ouboter R and Taconis K W 1976 On the lowest temperature which can be achieved in the Leiden dilution refrigerator Physica B 84 249 Roubeau P 1976 A dilution refrigerator for neutron experiments Proc. 6th Znt. Cryogenic Engineering ConS. (Guildford: IPC)

Roubeau P, Roinel Y , Bouffard V and Avenel 0 1978 A He-3 dilution refrigerator for neutron diffraction study of nuclear antiferromagnetic order J. Physique C 39 1146 Wheatley J C 1970 Experimental properties of pure 3He and dilute solutions of 3He in superfluid *He at very low temperatures. Application to dilution refrigeration Prog. Low Temp. Phys. 6 77

P 99

675