TlmKJ

-~

i

-0 L.{')

.

.

11

-I

;.· 1.·

v.·.

-

⁰ I

-I

I

I

lt

.

/

. . ^.

/

.

/

.

/

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I

0

-~

I

I _. . . .

. . . .

I I I

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I~E

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-co.

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c.D o·

N

d

N 0

~-in which Tph<Tm~-in,i and Tx=O>Tm~-in,i (figure 3.5.a). In a heigh mix~-ing chamber, one has to be carefull in interpreting the measuring results in order to determine the low-temperature limit.

In a flat mixing chamber none of the mentioned difficulties show up. Since there is a far smaller heat content of the concentrated phase during continuous operation, during a single cycle the cooling rateis more or less the same as intheideal situation (figure 3.5.b).

At lower temperature (T<8 mK) the influence of the dilute-exit tube becomes noticable, leading to a smaller temperature reduction then.

As can be seen from the figure, after the phase boundary has

reached x/h=0.6 no noticable cooling takes place anymore. In this quasi-stationary state all temperatures in the mixing chamber range from

4.8-5.4 mK. So from the point the cooling stopped, the intrinsic low-temperature limit can be determined within an accuracy of a few thenths of á millikelvin.

In conclusion, the flat mixing chamber is appropriate for

experimental determination of the fundamental low-temperature--limit.

The lower the Peelet number (Pe=e2), the better single-cycle properties are. In an infinitely flat mixing chambertherewould be no temperature gradient, and the temperature reduction would be the same as calculated for the ideal situation in the last paragraph. In an infinitely heigh mixing chamber there would be no cooling of the phase boundary al all!

In this chapter the design and construction of a new m1x1ng chamber are discussed. The calculations presented before led to the conclusion that a relatively flat mixing chamber would be promissing for determining the intrinsic low-temperature limit.

After presenting the design and construction of the mixing chamber in sectien 4.1, the measuring devices installed will be discussed in sectien 4.2.

4.1 The Mixing Chamber

From the considerations presented in the last chapter, it can be concluded that the new designed mixing chamber should have a large surface area and possibly minimum height. We expected that during a single cycle, in such mixing chamber sufficiently low temperatures would be reached, and therefore far-reaching features like a two-compartment mixing chamber (Severijns et al., 1978) could be avoided.

The height of the mixing chamber was chosen 30 mm, for reasens of the measuring devices, which had to fit easily. The total volume of the mixing chamber was determined in such a way that the mixing chamber could be completely filled with concentrated 3He befere the single

cycle was started. Considering the amount of 3He we have at our disposal, a surface area of about 28 cm2 resulted (diameter=60 mm).

In figure 4.1 a drawing of the mixing chamber is given. It was constructed out of stainless steel and consists of a flange and a cylindrical chamber, bolted tagether by 12 screws, with indium 0-ring

·sealing. The flange is suspended to the heat-exchanger cold plate by means of copper-nickel tubes (measures are indicated in figure 4.1).

The entrance tube and the 3He exhaust tube were placed apart as much as possible, in order to avoid an eventual 3He shunt stream, which causes an ineffective dilution of the 3He during continuous operation. The entrance of the dilute-exit channel was constructed in a way that a variety of flow impedances couldbe attached.

1001

I i I

I

t

80

5

30

C~1N thermometer para 11 e 1 tube flow resistance

, ...

'

60

heat exchanger cold plate

cupper-nickel tubes (o.d 5;

i .d 4.6 mm)

---di lute-exi t channe 1 / entrance tube

flange

~

phase boundary level detector (capacitor)

figure 4.1. Scheme of the single-cycle mixing chamber and the devices installed.

Attention was paid to the construction of the feed-through for the electrical wires from the mixing chamber to the vacuum jacket.

Normally we use a plug introducer with rather large volume. Since we wanted to avoid a big dead volume on top of the mixing chamber, the use of the plug introducer was prohibited. The feed-through was made according to figure 4.2.

superconducting wire copper-nickel

tube

Stycast~

silver solder tin solder

flange of the mixing chamber

figure 4.2. Feed-through for the eLectricaL wires from the mixing chamber to the vacuum jacket.

The electrical wires (20x50 pm Niomax superconducting wire) were pulled through a copper-nickel tube with inner diameter 2.7 mm, silver soldered to a support cap. After intensive cleaning, the wires were

~ositioned bufilling the tube with Stycast 2850GT, using the elevated temperature harder Catalyst 11. The Stycast completely surrounded one end of the tube (figure 4.2). After soft-soldering the construction

to the flange of the mixing chamber, the seal appeared to be leak-thight.

4.2 Measuring Devices

In the mixing chamber several measuring devices were installed,

20mm

which will be discussed below.

Level Measuring Capacitor

The height of the phase boundary inside the mixing chamber is measured by a capacitive method. The capacitor consists of two

concentric metal cylinders, with a 0.3 mm anular space. In the direction along the axis of the cylinders a slit has been cut, allowing the

liquid to stream freely into and out of the capacitor (figure 4.3). The capacitor¹S height is 20 mm, covering the biggest part of the total height of the mixing chamber.

I _~ 06 mm

é ^{516 mm} i! 5 mm

' I

'

I I

;; ^I

I I

I I I _I

I I

I I

~O.Smm

figure 4.3 Capacitor consisting of 2 concentria metal cylinders.

The capacitor is used for measuring the level of the phase boundary inside the mixing chamber.

The capacity C is a function of the 3He concentratien of the mixture inside the capacitor:

(4.1)

where EO is the dielectrical constant of vacuum

Erd is the relative dielectrical constant of the diluted mixture

Ere is the relative dielectrical constant of the concentrated phase

Ac is the surface area of one cylinder

de is the mutual distance between the cylinders.

The dependenee of the capacity on the level of the phase boundary hph can be determined bath from calculations (eq. (4.1)) and measurements (Keltjens, 1983), leading to

dC/dhph

= 6.1

.fF/mm

^(4.2)

In this way, height differences of about 10 wm can be measured.

The capacitor, determining the level of the phase boundary, can serve for measuring the 3He flow rate

n

₃ as well. Normally this flow rateis measured by a molar flow meter at room temperature. In- many

situations not only 3He, but also a certain amount of 4He is circulating.

The flow meter does not distinguish between the two He-isotopes, and measures the total helium flow. However, by determining the rate at which the height of the phase boundary changes, an accurate value for the net 3He flow is obtained.

The total number of moles (n3) of 3He inside the mixing chamber is given by

n

3 ::.

A ( h - h pn)

⁺

A h P~

v3

^v3d.

( 4.3).

n3 was defined as the rate at which the 3He is exhausted from the mixing chamber. Using

n -

-dn3 - -dn3

3

-d\: d hph

the 3He flow rate equals

dhph. _d_C

d( clt

n~

⁼

^{A (}

^V1

3

_

'~

^..

..~

^{) 1 dG}

'~:)\.\ dC

I

d

hpn

oH ..

(4.4).

The term dC/dhph is known from calibration (cf. eq. (4.2)); the 3He flow rate can be determined by measuring dC/dt.

Thermometers

For temperature measurements we used carbon resistors and a CMN thermometer.

The resistance thermometers we used were 220~ Speer resistors.

The resistance was determined using a resistance bridge*) with excitation voltages of 30 or 100 ~v, depending on the prevalent resistance value. The thermometers were calibrated by the use of

a superconducting fixed point device from Nss**). This device contains 5 different materials with the normal to superconducting transition at specific temperatures in the region from 15 to 205 mK.

Inside the mixing chamber two carbon resistors were placed. One was fixed at the top of the mixing chamber in the neighbourhood of the 3He-inlet tube. The other one was situated near the bottorn of the mixing chamber. In this way an eventual temperature gradient in the mixing chamber could be measured.

Resistance thermometers have a number of practical advantages, such as high sensitivity, fast response, and of course the ease with which an electrical resistance can be measured. A disadvantage is that the accuracy of the resistor declines a great deal at temperatures below 12 mK. Furthermore response times are getting noticable in this temperature region (Lounasmaa, 1973).

In order to measure temperatures below 12 mK, a CMN thermometer

·(coops, 1981) was mounted inside the mixing chamber. Cerous Magnesium Nitrate is a paramagnetic salt following the Curie law down toa few millikelvin. The CMN is powdered and pressed in the shape of a cylinder with length equal to the diameter. In this configuration the deviation from Curie law is the smalle-st (Webb et al., 1978). The magnetic

susceptibility of the salt is measured by the mutual inductance of two

"') type: IT -VS2

**) type: SRM768

coils using a lock-in amplifier*). The CMN thermometer, containing 78.0 mg of the salt, was calibrated against the lower Speer resistor, situated in the mixing chamber at the same height as the CMN thermo-meter.

Although the 01N thermometer is accurate for temperatures down toa few mK (9curie~2 mK), time constants are rather large in this temperature region. Because the processes during single cycle are time dependent, it is necessary to estimate these time constants.

CMN CMN ^mixture

spins phonons phonons

'a

^'ph

Ts Cs Tph cph Tm

figure 4.4. The three baht model representing the CMN saZt in thermaZ contact with the diZuted mixture.

Following Stoneham, 1965, we consicter the three bath system in figure 4.4. It is assumed that the CMN, in thermal contact with the 3He4He mixture, may be thought of as consisting of three parts -the CMN electron spins, -the CMN phonon system and -the mixture in

which the phonons are supposed to interact with the 3He quasiparticles without noticable relaxation. Each of the three parts has a specific temperature: the spin temperature Ts' the phonon temperature Tph and the mixture at Tm. The time constants involved are the spin-lattice

!elaxation time 'o and the time constant 'ph for the interaction between the two phonon systems.

In the system under investigation the rate-determining process is some process in the phonon system rather than the transfer of energy from the spins to the lattice: 'ph>><o (Chapellier, 1978).

The temperature of the spin system can be described by one differential equation:

~} type: PAR124A

ei T~

= __

^{1 _ ( T} ~ ^_ T ~) d 1: l:ob~

(4.5) where 'obs='o+'ph.C

5

^/Cph~'ph.C5^/Cph: the time constant

for the total system, being a function of temperature Cs is the heat capacity of the CMN spin system

Cph is the heat capacity of the CMN phonon system.

Usually it is assumed that

T 'V l

'-ph

-V

where v is a characteristic velocity of the phonon 21 is the average dimension of the CMN grain.

(4.6)

For :our applications CMN grain sizes less than 50 ~m were used.

'obs was measured by Chapellier, 1978 for somewhat larger grain sizes, resulting in larger values, according to equation (4.6).

For a rough estimate it is sufficient to approximate the time dependenee of a single cycle by an exponential:

( 4. 7)

where Tm is the temperature of the mixing chamber befare

*

a single cycle

'se is a typical time constant of the temperature decay in the mixing chamber during single-cycle operation.

Tsc for instanee can be estimated from figure 3.3.

A salution of eq. (4.5) reads

T.* 1

T!l (

t.)

= '""

^1.₆^{c. e.xp (-}\:.h:~J

"'C.~c. -Lob~

ar

T~(t.)-Tm{l)

⁼

T;

^{Lob: ('-}

exp(-ch:!)J)

l~~- Lob~

( 4.8).

The temperature difference between the CMN spin system and the

temperature of the mixing chamber is small in cases

<< 1 (4.9).

At temperatures above 8 mK, Tobs is measured to be less than 102

sec (Chapellier, 1978), whereas Tsc typically is of the order of 103 sec (see figure 3.5.a,b).

At lower temperatures Tobs becomes more and more significant (5 mK:Tobs=103 sec). However, in our system in this temperature region the cooling is slowed down, because the tube impedance has such

dimensions that heat conduction becomes noticable (figure 3.3). As a result, in the temperature region below 5 mK Tsc increases rapidly and for not too width impedances condition (4.9) is satisfied.

In conclusion, the CMN thermometer is appropriate for measuring temP.eratures during single-cycling, since condition (4.9) commonly is satisfied.

CHAPTER 5: RESULTS

In this chapter the measurements of temperature profiles in the mixing chamber during both continuous and single-cycle operatien are reported. Since at the time of report the experiment was not completed, the results have a preliminar character.

5.1 Temperature Profile during Continuous Operatien

The design of the single-cycle mixing chamber had to satisfy the condition that during continuous operation, the temperatures in the mixing chamber should be as homogenuous as possible. We calculated the temperature profiles {section 3.1), and measured temperatures in the mixing chamber at various heights with respect to the phase boundary.

In order to obtain large temperature gradients, the measurements were -performed in a mixing chamber with height larger than diameter (h=7 cm>Dmc=3 cm). Since there was no phase boundary level detector, the

position of the phase boundary could not be measured directly. Therefore, we used the following procedure.

By admitting or removing a definite amount of 3Hefrom the refrigerating system, we could fix the phase boundary at a specific level in the mixing chamber. First, the phase boundary was located as low as possible, by admitting the maximum amount of 3

He. In the stationary state, the temperature of a CMN thermometer, positioned high in the mixing chamber, was determined.

By the remaval of a known amount of 3

He from the refrigerating system, the phase boundary could be raised a definite distance. By 'repeating this procedure, the CMN thermometer determined temperature

at various distances from the phase boundary. The phase boundary temperature T h was determined as that temperature, which did nat

p 3

alter after removing more He.

The results of the measurements are shown in figure 5.1, and compared with calculated temperature profiles for the corresponding flow rates. We fitted the temperature profiles, calculated according to equation (3.4), to the measurements at the highest temperature points.

40

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30 _{ri •.}

_4~

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/ _,../ ^,../

20

^I _{I /}

/

^{... /}

--""'

I~ ---o/

Al ,...W

~-A_-_.!/-~

----~+9

10

^I _I

I

0

-2~----~0---~2----~4--~ ^I

In document Eindhoven University of Technology MASTER The intrinsic minimum temperature of a 3He circulating dilution refrigerator Keusters, H.W.M.P.M. (pagina 44-57)