Cryogenic Techniques: Generation and Measurement of Low … · 2013. 7. 18. · (H. Kammerlingh...

Chapter IV

Cryogenic Techniques: Generation and Measurement of

Low Temperatures

Chapt. IV - 2

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Chapter IV: Cryogenic Techniques

Contents: IV.1 Generation of Low Temperatures IV.1.1 Introduction IV.1.2 Expansion Machine IV.1.3 Regenerative Machine IV.1.4 Joule-Thomson Cooling IV.1.5 Summary IV.1.6 Evaporation Cooling IV.1.7 Dilution Cooling IV.1.8 Pomeranchuk Cooling IV.1.9 Adiabatic Demagnetization

IV.2 Thermometry IV.2.1 Introduction IV.2.2 Primary Thermometers IV.2.3 Secondary Thermometers

Chapt. IV - 3

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Literature: 1. Tieftemperaturphysik

Enss, Hunklinger Springer (2000)

2. Matter and Methods at Low Temperatures F. Pobell Springer, 2nd edition (1996)

3. Experimental Low-Temperature Physics Anthony Kent American Institute of Physics (1993)

4. Cryogenic Systems Randall F. Barron Oxford University Press, Oxford (1985)

Chapter IV: Cryogenic Techniques

Chapt. IV - 4

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IV.1 Generation of Low Temperatures IV.1.1 Introduction

background temperature in universe

(2.73 K)

lowest temperature accessible in solids

(few µK)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

tem

per

atu

re (

K)

center of hottest stars

center of the sun, nuclear energies

electronic energies, chemical bonding

surface of sun, highest boiling temperatures

organic life

liquid air

liquid 4He universe

superfluid 3He

lowest temperatures of condensed matter

elec

tro

nic

m

ag

net

ism

nu

clea

r-

ma

gn

etis

m

sup

erco

nd

uct

ivit

y

Chapt. IV - 5

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• experimental setup according to Tauno Knuuttila (2000)

• lowest temperature: about 100 pK

by demagnetization of Rhodium nuclei („temperature of nuclear spins“)

PhD Thesis,

Helsinki University of Technology (Espoo, Finland)

• problem: spin temperature cannot be transferred to lattice of solid

low temperature record for nuclear spin system:


Chapt. IV - 6

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Generation of low temperatures by using cryo-liquids:

19th century: liquefaction of various gases by pressure except for “permanent gases” (O2, H2, He)

1877: liquefaction of O2 by thermal expansion (L. Cailletet, C.R. Acad. Sci. Paris 85, 1213 (1877); R. Pictet, C.R. Acad. Sci. Paris 85, 1214 (1877)) 1884: liquefaction of H2 (precooling with liquid O2) (K. Olszewski, Ann. Phys. u. Chem. 31, 58 (1887)) 1898: significant amounts of lH2 for physical experiments (J. Dewar, Proc. R. Inst. Gt. Br. 15, 815 (1898)) 1908: liquefaction of last “permanent gas” He by Kamerlingh Onnes (H. Kammerlingh Onnes, Leiden Commun. 105, Proc. Roy. Acad. Sci. Amsterdam 11, 168 (1908)) 1922: Kammerlingh Onnes reaches T < 1K (H. Kammerlingh Onnes, Leiden Commun. 159, Trans. Faraday Soc. 18 (1922)) 1926: adiabatic demagnetization of electron spins in paramagnetic salts by Debye and independently (P. Debye, Ann. Phys. 81, 1154 (1926) 1927: by Giauque (W.F. Giauque, J. Am. Chem. Soc. 49, 1864 (1927) since 1950th: 3He available 3He cryostat 3He-4He dilution refrigerator

Heike Kammerlingh Onnes

(1853 – 1926)

Nobelpreis für Physik: 1913

Sir James Dewar, (1842-1923)

Peter J. Debye 1884 - 1966


Chapt. IV - 7

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Carl Paul Gottfried von Linde * 11. Juni 1842 in Berndorf, Oberfranken

† 16. November 1934 in Munich

Low Temperature Technology in Germany

1868 offer of chair at the Polytechnische Schule München (now TUM)

1873 development of cooling machine allowing the temperature stabilization in beer brewing

21. 6. 1879 foundation of „Gesellschaft für Linde’s Eismaschinen AG“ together with two beer brewers and three other co-founders

1892 - 1910 re-establishment of professorship

12.5.1903 patent application: „Lindesches Gegenstrom- verfahren“ liquefaction of oxygen (-182°C = 90 K)

1861 study at Polytechnikum Zurich, teachers: Rudolf Clausius, Gustav Zeuner und Franz Reuleaux

Chapt. IV - 9

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Year

low

te

mp

era

ture

s

ult

ra-l

ow

te

mp

era

ture

s

paramagnetic refrigeration

nuclear demagnetization


Chapt. IV - 10

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temperature range

refrigeration technique available since

typical

Tmin

record

Tmin

Kelvin universe 4He evaporation 3He evaporation

1908

1950

1.3 K

0.3 K

2.73 K

0.7 K

0.25 K

Millikelvin 3He-4He dilution

Pomeranchuk cooling

electron spin demagnetization

1965

1965

1934

10 mK

3 mK

3 mK

2 mK

2 mK

1 mK

Microkelvin nuclear spin demagnetization 1956 50 µK 100 pK


Chapt. IV - 11

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cooling techniques:

• expansion of an ideal gas

• expansion machine

• regenerative machine

work against outside world

• expansion of a real gas

• Joule Thomson cooler

work against internal interactions

• evaporation of a real gas:


• dilution cooling (3He/4He)


• adiabatic demagnetization (electronic/nuclear moments)

work against magnetic ordering


Chapt. IV - 12

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Liquefaction of gases three useful methods:

1. direct liquefaction by isothermal compression

2. letting the gas perform work against external forces at the expense of

its internal energy

cooling and eventual liquefaction

3. making the gas perform work against its own internal forces by Joule-

Kelvin or Joule-Thomson expansion

cooling and eventual liquefaction


Chapt. IV - 13

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direct liquefaction of gases by isothermal compression starting temperature must be smaller than critical temperature Tc

ammonia (NH3) 406

O2 154.5

N2 126

H2 33.2 4He 5.2 3He 3.32

critical temperatures Tc in K of selected liquid cryogens

melting curve

sublimation curve

critical point

triple point

solid

liquid

gas

T

p

Tc

boiling curve pc


Chapt. IV - 14

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@ 1 bar

Cryogenic Liquids

Ttr , ptr

solid liquid

gas

T

p

Tc

1 at Tc , pc

Tm , pm Tb , pb


Chapt. IV - 15

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cryogen boiling point [K]

liquefaction latent heat [kJ/I]

inversion temp. [K]

oxygen 90.2 1877: Cailletet and Pictet 240 762

nitrogen 77.3 1883: Wroblewski and Olszewski

160 625

hydrogen 20.4 1898: Dewar 30 203

4Helium 4.2 1908: Onnes 2.6 43.2

3Helium 3.2 0.5 -

• liquid oxygen and hydrogen have potential hazards

• liquid nitrogen and 4He are the most widely used cryogens

• liquid 3He is very expensive


direct liquefaction of gases by expansion (Joule-Thomson-Effect) starting temperature must be smaller than inversion temperature

Chapt. IV - 16

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gas molecules are reflected at the moving piston-surface:

incoming: laboratory system: 𝑣𝑀 piston system: 𝑣𝑀 − 𝑣𝐾 outgoing: piston system: − 𝑣𝑀 − 𝑣𝐾

laboratory system: − 𝑣𝑀 − 𝑣𝐾 + 𝑣𝐾 = 2𝑣𝐾 − 𝑣𝑀 = 𝑣𝑀′

i.e.: 𝑣𝑀′ = 𝑣𝑀 − 2𝑣𝐾 molecule is slower, i.e. colder

liquefaction of gases by performance of external work

average momentum transfer per time to piston = force, force · distance = work

external work at the expense of internal energy cooling


Chapt. IV - 17

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• efficiency: • Carnot process: technologically difficult to realize better: gas circulation, compressor and expansion machine are spatially separated

• Carnot process: - counterclockwise: heat pump (conversion of mechanical work into heat) - clockwise: heat engine (conversion of heat into mechanical work)

• pV diagram: expansion cooling: adiabats (𝑝𝑉𝜅 = 𝑐𝑜𝑛𝑠𝑡, 𝑑𝑄 = 0

𝜅 =𝑐𝑝

𝐶𝑉> 1)

heat exchange: isotherms (𝑝𝑉 = 𝑐𝑜𝑛𝑠𝑡, 𝑑𝑇 = 0)

work per cycle:

𝑊 = ∮ 𝑝𝑑𝑉 = 𝐚𝐫𝐞𝐚

warmT

T

Q

W

thermodynamic definition of temperature


V

p

Q12

Q34

dQ = 0 (adiabatic)

T1 = const (isothermic)

T2 = const dQ = 0

W23

W41

1

2

4

3

Chapt. IV - 18

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IV.1 Generation of Low Temperatures IV.1.2 Expansion Machine

• medium: He gas

Brayton method

e.g. liquefaction of air:

- condensation on cold head

- distillation in separation columns

N2 (77.4 K) cooling

Ar (87.3 K) inert gas

O2 (90.2 K) welding

• temperature reduction:

𝜅 = 𝐶𝑝/𝐶𝑉 (= 5/3 for He)

expansion from 100 bar to 1 bar

results in T2 = 50 K

T2 = 8 K can be reached in a 2 stage cycle

(should not cause

significant resistance

for flowing gas e.g.

concentric tubes)

• efficiency:

Chapt. IV - 19

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• heat pumps: heating and refrigerating machines

- heat pump: heat is generated by mechanical work

- efficiency:

W

Q TT h

11

work performed

at heat generated

- ideal efficiency for reversible Carnot process:

11

21

1

TT

Th

C

C (increases with decreasing temperature difference T1 – T2)

- refrigerating machine: removing heat (generating cold) by mechanical work

01work performed

at heat removed

21

22

TT

Th

TTk CC

V

p Q12

Q34

dQ = 0

T1 = const

T2 = const dQ = 0

W23

W41 1

2

4

3


(decreases with increasing temperature difference T1 – T2)

Chapt. IV - 20

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Wikimedia Commons


Schematic diagram of a heat pump's vapor-compression refrigeration cycle: 1) condenser, 2) expansion valve, 3) evaporator, 4) compressor.

e.g. air conditioning e.g. heating of swimming pool

Chapt. IV - 21

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realizations of expansion machines:

• piston-cylinder machine

similar to automobile engine

crankshaft, camshaft, valve

brake on turbine axis

controls rotational speed,

annihilates performed work,

use of gas bearings


• cooling turbine commercially relevant

higher efficiency for larger throughput

principle:

Chapt. IV - 22

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turbine cooler

(Sulzer machine)

turbine wheel

and nozzle ring


(Source: Linde Cryogenics Ltd.)

Chapt. IV - 23

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conclusions:

• expansion machines are technologically simple

• multi-stage arrangements for lower temperatures

almost down to 4.2 K

• but:

efficiency only acceptable for cooling turbines

• no direct liquefaction of gas (mechanical problems)

liquefaction by Joule-Thomson stage

• for small-scale facilities:

regenerative machines better suited


Chapt. IV - 24

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IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines

• regenerator replaces heat exchanger

column with staple of fine

metal meshes (Cu, Pb)

low flow resistance

high heat capacity

low longitudinal heat conductivity

cold gained in step 2 →3 has to be stored and provided in step 4 → 1

• alternating gas flow:

cold gas upward

cooling of meshes

warm gas downward

cooling of gas

• used in Stirling process

V

p Q12

Q34

V = const

T1 = const

T2 = const V = const

Q23

Q41 1

2

4

3

Stirling process (heat engine):

Chapt. IV - 25

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• Stirling machine: (heat engine)

- periodic expansion and compression of gas along two isotherms and two isochors

- 1 2: isothermal expansion, Q12 is added - 2 3: isochoric cooling, Q23 is removed - 3 4: isothermal compression, Q34 is removed - 4 1: isochoric warming, Q41 is added

- for isochoric steps there is no mechanical work 𝑸𝟐𝟑 = −𝑸𝟒𝟏 = 𝑪𝑽𝚫𝑻

- goal: intermediate storage of Q23 in regenerator to be able to add it again in step 4 1 use of two pistons with phase shift V

p Q12

Q34

V = const

T1 = const


Q23

Q41 1

2

4

3


3 – 4 4 – 1 1 – 2 2 – 3

T2

T1

Chapt. IV - 26

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• (beta) Stirling machine:


Power piston (dark grey) has

compressed the gas, the displacer piston (light grey) has moved so that most of the gas is

adjacent to the hot heat exchanger

The heated gas increases in

pressure and pushes the power

piston to the farthest limit of the

power stroke.

The displacer piston now moves,

shunting the gas to the cold end of the

cylinder.

The cooled gas is now compressed by

the flywheel momentum. This takes less energy, since when it is

cooled its pressure dropped.

http://en.wikipedia.org/wiki/File:Beta_Stirling_frame_12.pnghttp://en.wikipedia.org/wiki/File:Beta_Stirling_frame_16.pnghttp://en.wikipedia.org/wiki/File:Beta_Stirling_frame_4.pnghttp://en.wikipedia.org/wiki/File:Beta_Stirling_frame_8.pnghttp://en.wikipedia.org/wiki/File:Stirling_Animation.gifhttp://upload.wikimedia.org/wikipedia/commons/c/c7/Beta_Stirling_frame_12.pnghttp://upload.wikimedia.org/wikipedia/commons/f/f1/Beta_Stirling_frame_16.pnghttp://upload.wikimedia.org/wikipedia/commons/1/1b/Beta_Stirling_frame_8.pnghttp://upload.wikimedia.org/wikipedia/commons/4/4e/Stirling_Animation.gif

Chapt. IV - 27

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• (alpha) Stirling machine:


http://upload.wikimedia.org/wikipedia/commons/0/06/Alpha_Stirling_frame_16.pnghttp://upload.wikimedia.org/wikipedia/commons/e/ea/Alpha_Stirling_frame_4.png

Chapt. IV - 30

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conclusions (Stirling machine):

•advantages:

high efficiency

well-suited for small systems, especially small coolers

cryocooler

not realizable with turbines

•disadvantages:

mechanically complicated

piston (compressor) at low temperature

•more simple:

Gifford-McMahon machine

but: lower efficiency


Chapt. IV - 31

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Gifford-McMahon machine: uses compressor with switching valve instead of piston

1. warm compression: 2 1 2. isochoric cooling: 1 4 3. expansion in cylinder: 4 3 4. isochoric regeneration: 3 2 5. warm compression: 2 1


pressure wave from valve

hot

cold

regenerator

switching valve

cycle:

V

p Q12

Q34

V = const

T1 = const


Q23

Q41 1

2

4

3

Chapt. IV - 32

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Gifford-McMahon cycle:


Chapt. IV - 33

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3) • the pulse tube refrigerator (PTR) or pulse tube cryocooler is based on operation

principle of Stirling cooler • PTR is made without moving parts in the low temperature part (in contrast with

other cryocoolers, e.g. Stirling cryocooler and Gifford-McMahon cooler) • compact design possible suitable for a wide variety of applications • minimum temperature about 2.5 K (with 4He) and 1.3 K (with 3He)

Pulse – Tube – Refrigerator


applications: • industrial applications such as semiconductor fabrication (e.g. cryopumps) • cooling of infrared sensors • cooling of astronomical detectors (e.g. Atacama Cosmology Telescope or the QUBIC

experiment (an interferometer for cosmology studies) • precoolers of dilution refrigerators

Kurt Uhlig (WMI), “Dry” dilution refrigerator with pulse-tube precooling, Cryogenics 44, (2004), pp. 53–57

• suggested to be used to liquefy oxygen on Mars

Chapt. IV - 34

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Pulse – Tube – Refrigerator Stirling Cooler

regenerator regenerator

2-1

1-4

4-3

displacer piston

work piston

second (displacer) piston is replaced by pulse tube (gas piston)

3-2

motion of gas volume element equivalent to motion of „displacer piston“

90° phase shift between motion of „displacer piston“ and „work piston“ realized by buffer volume

90° phase shift required for finite heat transport

buffer volume

acoustic impedance

coldest spot between regenerator and pulse tube

regenerator

regenerator

regenerator

regenerator

regenerator

regenerator

Q34

Q12

work piston

Chapt. IV - 36

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Qc

QH

Qc

QH

Qc: removed heat, QH: generated heat

Pulse – Tube – Refrigerator Stirling Cooler


almost sinusoidal motion, phase difference of 90°

Chapt. IV - 38

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principle

Pulse – Tube – Refrigerator (realizations)

commercially available

pulse tube refrigerator

with GM drive

0.5 W @ 4.2 K Tmin = 2.3 K (2-stage)

www.cryomech.com


Chapt. IV - 39

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pulse tube refrigerator for studies of liquefying oxygen on

Mars (580 mm total length)


Chapt. IV - 40

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conclusion (pulse tube refrigerator):

•presently very active development

•no moving parts at low temperatures

long endurance

mobile base stations and satellite applications

(e.g. for superconductive microwave filters)

•almost no vibrations

•efficiency lower than for displacer

•only one simpler method:

Joule-Thomson cooling


Chapt. IV - 41

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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling

William Thomson (Lord Kelvin) Born: 26 June 1824, Belfast, Northern Ireland Died: 17 December 1907, Netherhall, Largs Ayrshire, Scotland

Chapt. IV - 43

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principle:

• gas performs work against its

own internal attractive forces

• working medium/gas (V1) flows

through impedance and

expands to V2

1122

0

0

1122

2

1

VpVpdVpdVpV

V

WQU

12 UU

111222 VpUVpU


1st law of thermodynamics:

= 0 (adiabatic)

this means: process with constant enthapy: .constpVUH

- for ideal gas: p1V1 = p2V2 and hence U1 = U2 resp. T1 = T2 no cooling !!

Chapt. IV - 44

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weak long-range attraction: tends to keep molecules closer together, same effect as additional compression of the gas. a is a measure of the long-range attraction strong short-range repulsion: molecules are rigid: p as soon as the molecules “touch” each other. b (≈ 4𝜋𝜎3/3): “excluded volume” per particle Van der Waals equation:


Epot(r)

short-distance repulsion

long-distance attraction

-3

-2

-1

0

1

2

3

4

1.5 2.0 2.5 3.0 3.5 4.0

distance

Energ

y

r

real gas: transformation of gas into liquid on decreasing T and (or) increasing p due to work against attractive interaction between the molecules

2V

appeff

bVVeff expansion (decrease of pressure): low pressure: attraction costs work cooling of gas high pressure: repulsion provides work heating of gas RTbV

V

ap m

m

2

Chapt. IV - 45

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interaction potential: Epot

r

repulsive attractive

p

repulsive attractive

U (p,T)

T = const.

minimum

with

Chapt. IV - 46

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0

p

p

HT

T

HH

Tp

• more detailed analysis of Joule-Thomson process (isenthalpic expansion):

pp

HTCC

T

H

T

pp

p

JT

HTpp

T

p

H

C

1

Vp

ST

p

HpVSTH

TT

pTT

V

p

S

V

T

VT

Cp

H

Cp

T

ppTpH

JT

11

Joule-Thomson coefficient

with

with

𝜇𝐽𝑇 > 0: cooling on expansion

𝜇𝐽𝑇 < 0: heating on expansion

Chapt. IV - 47

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ideal gas: 0

JT

p T

V

p

R

T

VRTpV


0 .2

5

2

3),(

T

JTBBBp

HµconstTNkTNkTNkpVUpTH

equipartition theorem for monoatomic gas

ideal gas law

areas of H = const.

lines of intersection with H = const.

@ T = const

Chapt. IV - 48

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real gas: RTbVV

ap m

m

2

at low densities: we use approximation and obtain bVV

ap ,

2

pT

RTpbV

apV ...,

2

2,

V

ap

R

T

VR

T

V

V

a

T

Vp

ppp

b

RT

a

Cp

T

PH

JT 21

μJT > 0 for T < 2a/bR cooling on expansion

μJT < 0 for T > 2a/bR heating on expansion inversion temperature:

bR

aTinv

2

.),(2

5),( constTpUTNkpVUpTH B

V

T

VT

Cp

H

Cp

T

ppTpH

JT

11

insert into

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areas of H = const.

lines of intersection with H = const.

inversion curve

Chapt. IV - 50

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Joule-Thomson coefficient (without approx.):

22

121

)1)(2(

VbVRTaC

bVbRTa

p

JT

large volume (p >> a/V2, V >> b) :

b

RT

a

CPJT 2

1

inversion curve: points where µJT = 0

vdW gas: (2a/RT)(1-b/V)2 = b

inversion temperature Tinv: 2

12

V

b

bR

aTinv

equation of state gives Tinv(p,T)

maximum inversion temperature: bR

aTinv

2

maximum inversion

temperature

Chapt. IV - 51

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experimental data for N2:

H

JTp

T

slope of isenthalps

repulsion

attraction

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gas maximum inversion temperature [K]

Helium-3 (23)

Helium-4 45

Hydrogen 205

Neon 250

Nitrogen 621

Air 603

Carbon monoxide 652

Argon 794

Oxygen 761

Methane 939

Carbon dioxide 1500

Ammonia 1994


vdW gas can be liquefied only for T < Tinv !!!

Chapt. IV - 53

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closed cycle cooling:

• gas is cooled by JT-expansion until liquid drops out the impedance

Carl von Linde (1842 – 1934)

“Linde-process”

(Source: PTB Braunschweig)

• patent application by Carl von Linde on May 12, 1903 (liquefaction of oxygen)

Chapt. IV - 54

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Lindesche Gasverflüssigungsanlage (1895)

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Professor Dr. Carl Paul Gottfried von Linde (* 11. Juni 1842 in Berndorf, Oberfranken; † 16. November 1934 in München) war ein deutscher Ingenieur, Erfinder und Gründer eines heute internationalen Konzerns, der Linde AG. Linde begann 1861 ein Studium am Polytechnikum Zürich, wo Rudolf Clausius, Gustav Zeuner und Franz Reuleaux seine Lehrer waren. 1864 beendete er sein Studium. Reuleaux vermittelte ihm eine Lehrstelle in der Baumwollfabrik Kottern in Berlin, die er im selben Jahr antrat. Es war aber nur kurze Zeit, bevor er nach München zog, um als Konstrukteur bei der Lokomotivenfabrik Krauss zu arbeiten. 1866 heiratete er Helen Grimm: aus der 53-jährigen Ehe folgten sechs Kinder. 1868 folgte er einem Ruf der Polytechnischen Schule München, wo er zunächst - mit erst 26 Jahren - außerordentlicher Professor, 1872 dann ordentlicher Professor für Maschinenbau wurde. Am Polytechnikum richtete Linde ein Maschinenlabor ein, an dem unter anderem Rudolf Diesel ausgebildet wurde. 1871 veröffentlichte Linde einen Aufsatz über verbesserte Kältetechnikverfahren. Viele Brauereien interessierten sich dafür, und bald versorgte Linde sie mit den neuen Maschinen, an denen er ständig arbeitete. Linde schuf wesentliche Grundlagen der modernen Kältetechnik. 1871 konzipierte er eine mit Methylether arbeitende Kältemaschine, die er in der Maschinenfabrik Augsburg (heute MAN AG) herstellen ließ. Die zweite, 1876 folgende Generation von Kühlmaschinen arbeitete mit Ammoniak. Das Prinzip der Abkühlung von Gas, das vorher mechanische Arbeit geleistet hatte, war beiden gemeinsam. Ein Preisausschreiben für eine Kühlanlage zum Auskristallisieren von Paraffin war 1873 für den Hochschullehrer der Anreiz zum Bau einer Kühlmaschine, die beim Bierbrauen die Gärung bei konstanter Temperatur zuließ. Brauereien in ganz Europa (so Dreher in Triest, die Mainzer Actien-Bierbrauerei, Spaten in München, Heineken in den Niederlanden, Carlsberg in Dänemark) interessierten sich prompt für die neue Kältetechnik. Am 21. Juni 1879 gab der Erfinder sein Lehramt auf und rief mit zwei Brauern und drei anderen Gründern die "Gesellschaft für Linde’s Eismaschinen AG" ins Leben (heute Linde AG). Nach relativ kurzer Zeit war das Unternehmen in Europa führend auf kältetechnischem Gebiet, auch begünstigt durch einen milden Winter 1883/1884. Es kam deshalb zu einer Knappheit bei Natureis, das zum Kühlen des Gerstensaftes in Bierkellern eingesetzt wurde. Bisherige Vorbehalte der Brauer gegen das Kunsteis schmolzen dahin, Kühlmaschinen waren plötzlich gefragt und Linde lieferte umgehend. Kühlhäuser für Lebensmittel und mehrere Eiswerke ließ Linde nach und nach sogar selbst bauen. Doch auch auf Eislaufbahnen, in Molkereien und bei der Verflüssigung von Chlor und Kohlensäure war sein Verfahren gefragt. Die Firma florierte, 1890 zog sich Linde aus dem operativen Geschäft in den Aufsichtsrat seiner Aktiengesellschaft zurück. In den Jahren 1892 bis 1910 nahm er seine Professur wieder auf. Auf der Grundlage der Arbeiten von James Prescott Joule, Sir William Thomson (Lord Kelvin of Largs) und der Einführung des Gegenstromverfahrens konnte Linde 1895 erstmals größere Mengen Luft verflüssigen (Linde-Verfahren). Damit schuf er die Möglichkeiten für physikalische Tieftemperaturuntersuchungen und zur Trennung der Luftbestandteile durch fraktionierte Destillation. 1901 folgte die Errichtung einer Anlage zur Gewinnung von Sauerstoff und (ab 1903) Stickstoff. Linde war Mitglied wissenschaftlicher und Ingenieurvereinigungen, unter anderem gehörte er dem Kuratorium der Physikalisch-Technischen Reichsanstalt und der Bayerischen Akademie der Wissenschaften an. Er wurde vom bayerischen König Ludwig II in den nicht erblichen Adelsstand erhoben. Linde war 1916 der erste Preisträger des Siemens-Rings. Ab 1910 zog sich Linde als Direktor seiner inzwischen ungeheuer erfolgreichen Aktiengesellschaft zurück und reichte sie an seinen Söhne Friedrich und Richard weiter. Die Weltwirtschaftskrise von 1929 versetzte der Linde AG einen starken Schlag; das Unternehmen erholte sich aber, und die Gewinne fingen schon wieder an zu steigen, bevor Linde 1934 im Alter von 92 Jahren starb.


http://de.wikipedia.org/wiki/11._Junihttp://de.wikipedia.org/wiki/1842http://de.wikipedia.org/wiki/Berndorfhttp://de.wikipedia.org/wiki/Oberfrankenhttp://de.wikipedia.org/wiki/16._Novemberhttp://de.wikipedia.org/wiki/1934http://de.wikipedia.org/wiki/M%C3%BCnchenhttp://de.wikipedia.org/wiki/Linde_AGhttp://de.wikipedia.org/wiki/Eidgen%C3%B6ssische_Technische_Hochschule_Z%C3%BCrichhttp://de.wikipedia.org/wiki/Eidgen%C3%B6ssische_Technische_Hochschule_Z%C3%BCrichhttp://de.wikipedia.org/wiki/Eidgen%C3%B6ssische_Technische_Hochschule_Z%C3%BCrichhttp://de.wikipedia.org/wiki/Rudolf_Julius_Emanuel_Clausiushttp://de.wikipedia.org/wiki/Rudolf_Julius_Emanuel_Clausiushttp://de.wikipedia.org/wiki/Gustav_Anton_Zeunerhttp://de.wikipedia.org/wiki/Gustav_Anton_Zeunerhttp://de.wikipedia.org/wiki/Franz_Reuleauxhttp://de.wikipedia.org/wiki/Franz_Reuleauxhttp://de.wikipedia.org/w/index.php?title=Kottern&action=edithttp://de.wikipedia.org/wiki/Berlinhttp://de.wikipedia.org/wiki/M%C3%BCnchenhttp://de.wikipedia.org/wiki/Krausshttp://de.wikipedia.org/w/index.php?title=Polytechnische_Schule_M%C3%BCnchen&action=edithttp://de.wikipedia.org/wiki/Maschinenbauhttp://de.wikipedia.org/wiki/Rudolf_Dieselhttp://de.wikipedia.org/wiki/K%C3%A4ltemaschinehttp://de.wikipedia.org/wiki/K%C3%A4ltetechnikhttp://de.wikipedia.org/wiki/MAN_AGhttp://de.wikipedia.org/wiki/K%C3%BChlschrankhttp://de.wikipedia.org/wiki/Ammoniakhttp://de.wikipedia.org/wiki/Gashttp://de.wikipedia.org/wiki/Arbeit_(Physik)http://de.wikipedia.org/wiki/Paraffinhttp://de.wikipedia.org/wiki/1873http://de.wikipedia.org/wiki/G%C3%A4runghttp://de.wikipedia.org/wiki/Mainzer_Aktien_Bierbrauerei_AGhttp://de.wikipedia.org/wiki/Mainzer_Aktien_Bierbrauerei_AGhttp://de.wikipedia.org/wiki/Mainzer_Aktien_Bierbrauerei_AGhttp://de.wikipedia.org/wiki/Mainzer_Aktien_Bierbrauerei_AGhttp://de.wikipedia.org/wiki/Heinekenhttp://de.wikipedia.org/wiki/Carlsberghttp://de.wikipedia.org/wiki/21._Junihttp://de.wikipedia.org/wiki/1879http://de.wikipedia.org/wiki/Linde_AGhttp://de.wikipedia.org/wiki/K%C3%A4ltetechnikhttp://de.wikipedia.org/wiki/Chlorhttp://de.wikipedia.org/wiki/Kohlens%C3%A4urehttp://de.wikipedia.org/wiki/1890http://de.wikipedia.org/wiki/Operatives_Gesch%C3%A4fthttp://de.wikipedia.org/wiki/Aufsichtsrathttp://de.wikipedia.org/wiki/1892http://de.wikipedia.org/wiki/1910http://de.wikipedia.org/wiki/James_Prescott_Joulehttp://de.wikipedia.org/wiki/William_Thomson,_1._Baron_Kelvinhttp://de.wikipedia.org/w/index.php?title=Gegenstromverfahren&action=edithttp://de.wikipedia.org/wiki/Linde-Verfahrenhttp://de.wikipedia.org/wiki/Linde-Verfahrenhttp://de.wikipedia.org/wiki/Linde-Verfahrenhttp://de.wikipedia.org/wiki/Tieftemperaturphysikhttp://de.wikipedia.org/wiki/Fraktionierte_Destillationhttp://de.wikipedia.org/wiki/Sauerstoffhttp://de.wikipedia.org/wiki/Stickstoffhttp://de.wikipedia.org/wiki/Physikalisch-Technische_Bundesanstalthttp://de.wikipedia.org/wiki/Physikalisch-Technische_Bundesanstalthttp://de.wikipedia.org/wiki/Physikalisch-Technische_Bundesanstalthttp://de.wikipedia.org/wiki/Bayerische_Akademie_der_Wissenschaftenhttp://de.wikipedia.org/wiki/Bayernhttp://de.wikipedia.org/wiki/Ludwig_II._(Bayern)http://de.wikipedia.org/wiki/Adelhttp://de.wikipedia.org/wiki/1916http://de.wikipedia.org/wiki/Werner-von-Siemens-Ringhttp://de.wikipedia.org/wiki/Werner-von-Siemens-Ringhttp://de.wikipedia.org/wiki/Werner-von-Siemens-Ringhttp://de.wikipedia.org/wiki/1910http://de.wikipedia.org/wiki/Weltwirtschaftskrisehttp://de.wikipedia.org/wiki/1929http://de.wikipedia.org/wiki/1934

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schematics of a Helium liquefier

Chapt. IV - 57

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IV.1 Generation of Low Temperatures IV.1.5 Summary

Chapt. IV - 58

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Chapt. IV - 59

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specification for cryocooler: • 1 Watt of cooling @ 80 K, rejecting heat at 300 K • 10 year life • 230 K to 340 K survival temperature • survival of launch vibration (non-operating) • low exported vibration • high efficiency • no maintenance possible oil-free

Northrop Grumman's HEC cryocooler


Stirling cycle miniature cryocooler: - lightweight cooler, ideal for cooling of sensors and other electronics when low power consumption is important - mean time before failure of 24,000 hours - cooling capacity of 1 W @ 80 K - power consumption of only 55 W.

Sumitomo Heavy Industries

Chapt. IV - 60

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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling

Chapt. IV - 61

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• everyday experience: sweating, wind direction, cooling of coffee, …

moisten finger, evaporation cooling

• microscopically:

• evaporation: work required to overcome binding forces

only the fastest molecules will do it

high-energy particles are lost

liquid cools down

Chapt. IV - 62

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• limit of evaporation cooling: kBT becomes too small compared to Hvap

(heat of evaporation)

• Hvap should be small to reach large cooling power at low temperatures

• numbers: about 1 K can be reached with 4He, about 0.3 K with 3He

• boiling point can be calculated by using the Clausius-Clapeyron equation, if heat of vaporization and the vapor pressure of the liquid at a certain temperature is known

Chapt. IV - 63

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Clausius-Clapeyron equation:

Hvap: molar latent heat [J/mole]

• approximate expression using pV = RT (ideal gas):

• integration yields (assuming that Hvap is constant over the considered T range):

≈ 90 J/mole

for 4He

• normal boiling temperature: pressure above liquid

boiling temperature at p0

(boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the surrounding environmental pressure)

Chapt. IV - 64

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Chapt. IV - 65

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www.mallister.com/graphics/vapor3.jpg

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liquid 4He (c.f. chapter II)

• boson

• liquid down to 0 K (@ 1 atm)

• superfluid 4Helium at 2.17 K

– Bose condensation: macroscopic number of atoms in ground state

– very low viscosity

– very high heat conduction

– strange thermomechanical effects

– creeping on vertical surfaces

– vortex core with radius 0.8Å @ 0.6K

– explained by a two-fluid model

• density 125 kg/m3


Chapt. IV - 68

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Liquid Helium cryostats:

• LHe has small latent heat

good thermal insulation by vacuum

LHe container of poor thermal conductivity, glass or stainless steel

thermal radiation shield at liquid Nitrogen temperature to reduce black-body radiation


bath cryostat - sample is immersed in the LHe

gas flow cryostat - sample is located in cold He gas

Chapt. IV - 69

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LHe


Liquid Helium container

vacuum radiation shields

narrow neck to minimize - heating by radiation - heating by thermal conduction

typical losses

- 1 l of LHe / day

Chapt. IV - 70

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He-bath cryostat

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He-gas flow cryostat

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• no liquid Nitrogen required • radiation shield cooled by cold helium return gas


He-gas flow cryostat (II)

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bath of 4Helium

• temperature down to 1.2 K at pumping speed of 10 m3/h

Hvap: molar latent heat [J/mole]

≈ NA∙Ebinding: 90 J/mole for 4He


Liquid 4He temperature < 4.2 K Clausius-Clapeyron equation:

cooling power:

RT

HpHnQ

vapvapgas

exp

rate of atoms going to gas phase up to 10 mW cooling power @ 1.2K

Chapt. IV - 75

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Liquid 3Helium (c.f. chapter II):

• fermion

• superfluid at 2.5mK

– formation of weakly bound fermions: Cooper pairs

• density 59 kg/m3

• higher vapour pressure than 4He due to smaller latent heat: Hvap = 40 J/mole cooling power ≈ 80mW @ 1.2K and 10 m

3/h pumping speed

• 0.3 K by pumping 3He vapour

– some cm3

– 0.1mW cooling power @ 0.3K

• 3He obtained by nuclear reactions

• extremely expensive

• 1 liter of 3He gas costs about US $5.000 (2012)


Chapt. IV - 76

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Liquid 3He cryostat

4He

3He ≈ 0.3 K

4He pump

3He pump

3He backflow

4He impedance 4He bath 4.2 K

vacuum

condensation of backflowing 3He gas

latent heat of 3He: Hvap = 40 J/mole as compared to 90 J/mole for 4He larger cooling power

≈ 80mW @ 1.2 K for 3He as compared to ≈ 10mW @ 1.2 K for 4He

minimum temperature: ≈ 300 mK (cooling power ≈ 0.1 mW)

≈ 1.2K

flow restriction for condensed 3He

RT

HpHnQ

vapvapgas

exp

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IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling

makes use of miscibility gap of 3He/4He mixtures (compare section I.6)

revision of some facts on 3He/4He mixtures cf. chapter I.6

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• bonding:

• 𝑉𝐴𝐵 >1

2𝑉𝐴𝐴 + 𝑉𝐵𝐵 complete miscibility (e.g. water and alcohol)

• 1

2𝑉𝐴𝐴 + 𝑉𝐵𝐵 > 𝑉𝐴𝐵 phase separation (e.g. water and petrol)

A A A B B B

VAA VAB VBB

critical point

miscibility gap

increasing mixing with increasing T:

F = U – TS min

binding energy

thermal motion

optimization of binding energy complete phase separation @ T = 0

minimization of free energy

IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling – revision of I.6

Chapt. IV - 80

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• binding energy of 3He in 3He (V33) and 4He (V34):

(i) 3He in 3He: binding energy is given by the latent heat of evaporation L3:

binding energy for single 3He atom: 𝜖3,𝑐 = −𝐿3

𝑁𝐴=

𝜇3,𝑐

𝑁𝐴

𝜇3,𝑐 = chemical potential of pure (concentrated) liquid

(ii) single 3He atom in liquid 4He:

binding energy for single 3He atom: 𝜖3,𝑑(𝑥3 → 0) =𝜇3,𝑑 𝑥3→0

𝑁𝐴

𝜇3,𝑑 = chemical potential of dilute phase

• 𝜖3,𝑑 0 > 𝜖3,𝑐 or vice versa ? 3He has smaller mass larger zero point fluctuations occupies larger volume binding of 3He is larger in 4He than in 3He due to larger density of 4He |𝜖3,𝑑 0 | > |𝜖3,𝑐|

corresponds to case 𝑉𝐴𝐵 >1

2𝑉𝐴𝐴 + 𝑉𝐵𝐵 complete miscibility expected,

why miscibility only up to 6.5% ??


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Questions:

• why can‘t we dissolve more than 6.5% of 3He in 4He at T = 0 ? two effects: (i) 3He forms degenerate Fermi liquid 𝑇𝐹 increases with 𝑥3 for 𝑥3 > 6.5%, the Fermi energy exceeds the gain in binding energy

(ii) 𝜖3,𝑑 𝑥3 > 𝜖3,𝑑(𝑥3 = 0) effective attraction between two ³He atoms (magnetic and volume effect)

• why don‘t we have a complete phase separation into 3He and 4He at T = 0 ? results in finite disorder, violation of 3. law of thermodynamic ? no: we have degenerate Fermi gas, ordering in k-space


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x3

0.065

−𝜖3,𝑑(0)

−𝜖3,𝑐

𝑬𝐩𝐨𝐭 𝒙𝟑 + 𝒌𝐁𝑻𝐅 𝒙𝟑

0 gaseous ³He

pure liquid ³He

³He diluted in 4He

𝑬𝐩𝐨𝐭 𝒙𝟑 = 𝟏 + 𝒌𝐁𝑻𝐅 𝒙𝟑 = 𝟏

for 𝑥3 > 6.5%: 𝑬𝐩𝐨𝐭 𝒙𝟑 + 𝒌𝐁𝑻𝐅 𝒙𝟑 > 𝝐𝟑,𝒄 = 𝑬𝐩𝐨𝐭 𝒙𝟑 = 𝟏 + 𝒌𝑩𝑻𝐅 𝒙𝟑 = 𝟏

separation of pure ³He

energy

𝑬𝐩𝐨𝐭 𝒙𝟑


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• for Fermi liquid: Cconcentrated < Cdiluted (x3 = 0.065) (𝐶𝑉 ∝ 𝑇/𝑇𝐹, 𝑇𝐹 ∝ 𝑛

2/3)

• with we therefore obtain:

Uconcentrated (T) < Udiluted (T) • on transition across phase boundary: F ≈ U = const increase of U results in decrease of temperature !

³He/4He dilution refrigerator

• operation principle: remove ³He atoms from the dilute phase below Tk = 0.87 K

transport of ³He atoms across phase boundary to maintain equilibrium concentration corresponds to evaporation of ³He from concentrated phase cools as the latent heat of evaporation is removed

concentrated (lighter)

diluted,6.5% (heavier)

³He

U

T

Uconcentrated

Udiluted

³He


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• assumption: one mole of ³He crosses boundary

• removed heat depends on enthalpy difference between concentrated and dilute phase

• cooling power

• since there is no volume change

• with and

we obtain the entropy

(standard expressions for Fermi liquid)


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3He, concentrated

3He, diluted

Fermi sphere

large 3He density large Fermi sphere high TF

small 3He density small Fermi sphere low TF

fraction of thermally excited 3He atoms increases ( T/TF) entropy increases going from concentrated to diluted phase removed heat: dQ = TdS

thermally excited 3He atoms

plausibility consideration kBT

kBT

Fermi sphere

Chapt. IV - 86

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• large cooling power requires large throuphput


23 84 TnQ

> 90% 3He

3He pump

from ≈ 1.2 K 3He condenser

heat exchangers < 1% 3He

still (≈ 0.7 K)

flow impedance

concentrated phase

dilute phase

6.5% 3He

100% 3He

heater to allow for effective pumping of 3He

mixing chamber (≈ 0.01 K)

dilute phase

concentrated phase

pumping of 3He generates osmotic pressure 3He flows from mixing chamber to still only possible if 3He atoms cross phase boundary cooling

minimum temperature: ≈ 1.5 mK

Chapt. IV - 87

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• numbers: vapor pressure of 3He at 0.7 K: 0.0828 mbar = 8.28 Pa @ 300 K we obtain:

large 3He pump is required

• what is the required pumping speed ??

we assume that 3He is an ideal gas (R = 8.31 J / mole K)


• example: desired cooling power: 10-5 W still temperature: 0.7 K mixing chamber temperature: 10 mK

s /mole 0012.0)10(84

1022

5

3

n

pRTnV /3

l/s 360 s/m 0.363 28.8/30031.80012.0 3 V

23 84 TnQ

𝑅 = 8.31 J/mole K

Chapt. IV - 88

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mixing

chamber

heat

exchangers

still


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JANIS Model JDR-500 Dilution Refrigerator


Chapt. IV - 90

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3He shows minimum in melting curve at T = 0.32 K (compare I.5.2) can be used for cooling of ³He Pomeranchuk effect

Isaak Jakowlewitsch Pomeranschuk

(Исаак Яковлевич Померанчук;

born: 20. Mai 1913 at Warschau;

died: 14. Juli 1966 at Moscow)

Russian physicist.

IV.1 Generation of Low Temperatures IV.1.8 Pomeranchuk Cooling

0.1 1 1010

1

102

103

104

p (

bar

)

T (K)

phase diagram of 4He and 3He

3He

4He hcp

bcc

liquid

hcp

liquid

bcc

fcc

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F

liquidsolidT

TTRSSTnQ

2-ln2) -(

2

3

• explanation: solid phase: atoms are ordered,

spins are disordered and determine entropy: Ssolid = R ln2 at low T: antiparallel ordering of spins, S decreases towards zero liquid phase: atoms are spatially disordered, but ordering in k-space (Fermi liquid) entropy of Fermi liquid:

• Clausius-Clapeyron equation:

• always: Vsol < Vliq

• for T < 0.32 K: disorder larger in solid than in liquid phase !!

S

lnT

R ln2

0

liquid

solid

320 mK

• cooling power:

Chapt. IV - 92

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stamp stainless steel bellow

liquid

solid pressure cell

• precooling to T < Tmin

• adiabatic compression solidification and cooling • lowest T: ≈ 1.5 mK limitation due to antiparallel

spin ordering in solid 3He

10-3

10-2

10-1

100

2.8

2.9

3.0

3.1

3.2

3.3

3.4

p (

MP

a)

10-3

10-2

10-1

100

0.0

0.2

0.4

0.6

0.8

S /

R

T (K)

liquid

solid

liquid

solid

Tmin

ln 2

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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization

magnetic refrigeration: based on the magnetocaloric effect

magnetocaloric effect: - magneto-thermodynamic phenomenon - reversible change in temperature is caused by exposing a material to a changing magnetic field - also known as adiabatic demagnetization

http://upload.wikimedia.org/wikipedia/commons/0/08/Magnetocaloric_effect1_04a.svg

Chapt. IV - 94

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Adiabatic magnetization: - substance is placed in an insulated environment - increasing external magnetic field (+H) causes magnetic ordering reduction of magnetic entropy and heat capacity - overall energy is not lost and therefore total entropy is not reduced (T + ΔTad). Isomagnetic enthalpic transfer: - added heat is removed by coupling to heat sink (-Q) - magnetic field is held constant - after heat removal, magnetocaloric material and the coolant are separated (H = 0). Adiabatic demagnetization: - the substance is decoupled from heat sink no heat exchange with environment entropy stays constant - magnetic field is decreased, the thermal energy causes the magnetic moments to overcome the field, and thus the sample cools energy (and entropy) transfers from thermal entropy to magnetic entropy (disorder of the magnetic dipoles). Isomagnetic entropic transfer: - the magnetic field is held constant to prevent the material from heating up - the material is brought in thermal contact with the environment being refrigerated cooling effect - magnetic materials heats up (+Q)

thermodynamic cycle:

http://upload.wikimedia.org/wikipedia/en/c/cb/MCE.gif

Chapt. IV - 95

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• adiabatic 𝑆𝐵𝑖

𝑇𝑖= 𝑆

𝐵𝑓

𝑇𝑓 𝑇𝑓 = 𝑇𝑖 ⋅

𝐵𝑓

𝐵𝑖

• experiment: use of copper: Bi = 3 T, Bf = 0.3 mT, Ti = 10 mK Tf ≈ 1μK


• generation of temperatures below 1 mK

• dQ = TdS = dU – dW = dU + pdV – B dM ≈ dU – B dM (for solid: pdV small)

• adiabatic cooling: dQ = 0 dU = B dM

– step1: magnetize sample with field B, work must be done on sample and heat is released to thermal bath at Ti

– step2: thermally isolated sample and remove magnetic field B, sample uses internal energy to demagnetize and temperature falls to Tf < Ti

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more detailed discussion:

• which amount of heat Qspin can be absorbed by the spin systems ?

i

f

i

f

T

TB

spinT

Tspinspin dT

T

STdTCBQ )0(

2

2int

2

2

22

6

)1()12ln(

T

BB

k

JJgJNkS

B

BB

2int

2

2int

2

BB

BBTT

i

f

if

remaining internal field due to finite magnetic interactions (should be as small as possible)

(cooling capacity)

• entropy of spin system with spin quantum number J for gµBB

Chapt. IV - 97

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Ti Tf

Bf = 0 Bi = 5T en

tro

py

S

1

2

1 switch on magnetic field at constant Ti (coupling to heat sink)

2 switch off magnetic field for thermally isolated sample cooling to Tf

i

f

i

f

T

TB

spinT

Tspinspin dT

T

STdTCBQ )0(

)12ln( JNkB

0 0

medium

heat sink

heat switch

T

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• paramagnetic salts: e.g MAS = MnSO4 · (NH4)2SO4 · 6H2O cooling of electron spins material with large entropy S/R but large Bint lowest temperatures Tf ≈ 100 mK large cooling capacity

e.g CMN = 2Ce(NO3)3 · 2Mg(NO3)2 · 24H2O cooling of electron spins material with small entropy S/R but small Bint lowest temperatures Tf ≈ 2 mK small cooling capacity • nuclear demagnetization: e.g 63Cu (L = 3/2) or 65Cu (L = 3/2) (Bint ≈ 0.3 mT, Ti ≈ 10 mK, Bi ≈ 3 T) cooling of nuclear spins Tf (Bf = 0) ≈ 1 µK problem: transfer of spin temperature to lattice long spin-lattice relaxation time other materials: 141PrNi5 (L=5/2),

195Pt (L=1/2)

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• spin-lattice coupling cools the lattice

– metals: ≈ 1000 s (hyperfine interaction: t = CKorringa/Te, Korringa relation) – non-metals: ≈ hours to several days

• spin-lattice coupling: spin temperature increases and lattice temperature decreases

in thermal equilibrium

• calculation of equilibrium temperature for copper: (Bint ≈ 0.3 mT, Ti ≈ 10 mK, Bi ≈ 3 T)

Teq = 1.03 μK

• lowest reported experimental temperature

demagnetization of Pt: Teq = 2 μK (F. Pobell et al., (1996))

0 nT

T

nucleare

T

T

electron dTcdTceq

f

eq

i


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R. Gloss et al.,

J. Low Temp. Phys. 73, 101 (1988)

Cu demagnetization stage (length: 525 mm, diameter: 78 mm)

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µK facility of PTB Berlin: Lattice temperatures measured on the 105-mol-copper stage of the Berlin microkelvin facility with Pt-NMR. The achieved minimal temperature was 23.3 µK. The red line depicts the calculated course of temperature for the thermodynamically optimized demagnetization function. heat leak: below 1.5 nW.


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Cryogen-free Two Stage Adiabatic Demagnetization Refrigerator from Janis

A cryogen-free two stage adiabatic demagnetization refrigerator using a 4 K pulse tube cryocooler. Gallium Gadolinium Garnet (GGG) and Ferric Ammonium Alum (FAA) paramagnetic pills were used for the first and second stage of the ADR, with Kevlar string supports for each stage. The FAA stage reaches a base temperature below 50 mK, and remains below 100 mK for more than two days.


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Continuous Adiabatic Demagnetization Refrigerator (CADR) under development at NASA´s Goddard Space Flight Center - CADR to cool from below 5K to ≈ 35 mK - advantage: no stored cryogens maximizing the lifetime/mass ratio for the instrument

Chapt. IV - 105

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Contents: IV.1 Generation of Low Temperatures IV.1.1 Introduction IV.1.2 Expansion Machine IV.1.3 Regenerative Machine IV.1.4 Joule-Thomson Cooling IV.1.5 Summary IV.1.6 Evaporation Cooling IV.1.7 Dilution Cooling IV.1.8 Pomeranchuk Cooling IV.1.9 Adiabatic Demagnetization

IV.2 Thermometry IV.2.1 Introduction IV.2.2 Primary Thermometers IV.2.3 Secondary Thermometers

Chapt. IV - 106

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IV.2 Thermometry IV.2.1 Introduction

temperature and temperature scales

• temperature of a system in thermodynamic equilibrium: defined as the relation between the amount of heat δQ incident on the system during an infinitesimal quasi-static transformation, and the variation δS of its entropy during this transformation: for reversible Carnot process (dS = 0):

S

QT

T

Q0

Kelvin scale Celsius scale (1742)

see http://www.its-90.com

• Lord Kelvin (1854): there is an absolute zero of temperature scale T0 = 0 K = - 273.15°C 1 K = 1°C

http://www.its-90.com/http://www.its-90.com/http://www.its-90.com/http://www.its-90.com/

Chapt. IV - 107

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William Thomson (Lord Kelvin)

http://br.geocities.com/saladefisica3/fotos/kelvin.gif

Lord Kelvin by Hubert von Herkomer

Born 26 June 1824(1824-06-26) Belfast, Co. Antrim, Ireland

Died 17 December 1907 (aged 83)[1] Largs, Ayrshire, Scotland [1]

Residence Cambridge, England Glasgow, Scotland

Nationality United Kingdom of Great Britain and Ireland

Institutions University of Glasgow

Alma mater Glasgow University Peterhouse, Cambridge

A variety of physical phenomena and concepts with which Thomson is associated are named Kelvin: • Kelvin material • Kelvin water dropper • Kelvin wave • Kelvin-Helmholtz instability • Kelvin-Helmholtz mechanism • Kelvin-Helmholtz luminosity • The SI unit of temperature, kelvin • Kelvin transform in potential theory • Kelvin's circulation theorem • Kelvin-bridge (also known as Thomson-bridge)


http://en.wikipedia.org/wiki/June_26http://en.wikipedia.org/wiki/1824http://en.wikipedia.org/wiki/Belfasthttp://en.wikipedia.org/wiki/County_Antrimhttp://en.wikipedia.org/wiki/Irelandhttp://en.wikipedia.org/wiki/December_17http://en.wikipedia.org/wiki/1907http://en.wikipedia.org/wiki/Largshttp://en.wikipedia.org/wiki/Ayrshirehttp://en.wikipedia.org/wiki/Scotlandhttp://en.wikipedia.org/wiki/Cambridgehttp://en.wikipedia.org/wiki/Englandhttp://en.wikipedia.org/wiki/Glasgowhttp://en.wikipedia.org/wiki/Scotlandhttp://en.wikipedia.org/wiki/United_Kingdom_of_Great_Britain_and_Irelandhttp://en.wikipedia.org/wiki/United_Kingdom_of_Great_Britain_and_Irelandhttp://en.wikipedia.org/wiki/University_of_Glasgowhttp://en.wikipedia.org/wiki/Alma_materhttp://en.wikipedia.org/wiki/Glasgow_Universityhttp://en.wikipedia.org/wiki/Peterhouse,_Cambridgehttp://en.wikipedia.org/wiki/Peterhouse,_Cambridge

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• SI temperature scale - the SI temperature scale is the Kelvin scale. It defines the triple point of water as the numerical value of 273.16, i.e., 273.16 K. The unit of temperature in this scale is the Kelvin (K).

• Celsius scale: the Celsius scale has units of °C (degrees Celsius) with the size of the unit equal to 1 Kelvin.

T(°C) = T(K) – 273.15

• agreement of bureaus of standards:

ITS-90 temperature scale for T > 0.65 K (Comité International des Poids et Messures 1990) - the ITS-90 is defined by 17 fixed points and 4 defining instruments. It spans a temperature range from 0.65 K to 10 000 K. For cryogenic purposes the three defining instruments are helium vapor pressure thermometry, gas thermometry, and platinum resistance thermometry.

PLTS-2000 for lower T (Provisonal Low Temperature Scale, melting curve of 3He ) - the PLTS-2000 is defined by a polynomial, relating the melting pressure of 3He to temperature from the range 0.9 mK to 1 K. The pressure to temperature relationship

is based on primary thermometers such as Johnson noise and nuclear orientation.


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The Water Triple Point The triple point of water is the most important defining thermometric fixed point used in the calibration of thermometers to the International Temperature Scale of 1990 (ITS-90). It is the sole realizable defining fixed point common to the Kelvin Thermodynamic Temperature Scale (KTTS) and the ITS-90; the assigned value on these scales is 273.16 K (0.01°C)

solid

liquid

gaseous

critical point

triple point

(0.01°C, 603 Pa)

273.15 K

(374°C, 21800 kPa)

273.16 K


Chapt. IV - 110

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Defining Fixed Points of the ITS-90

Number Temperature Substance a State b Wr (T90)

T90/K t90/°C

1 3 to 5 -270.15 to -268.15 He V

2 13.8033 -259.3467 e-H2 T 0.001 190 07

3 ~17 ~-256.15 e-H2 (or He) V (or G)

4 ~20.3 -252.85 e-H2 (or He) V (or G)

5 24.5561 -248.5939 Ne T 0.008 449 74

6 54.3584 -218.7916 O2 T 0.091 718 04

7 83.8058 -189.3442 Ar T 0.215 859 75

8 234.3156 -38.8344 Hg T 0.844 142 11

9 273.16 0.01 H20 T 1.000 000 00

10 302.9146 29.7646 Ga M 1.118 138 89

11 429.7485 156.5985 In F 1.609 801 85

12 505.078 231.928 Sn F 1.892 797 68

13 692.677 419.527 Zn F 2.568 917 30

14 933.473 660.323 Al F 3.376 008 60

15 1234.93 961.78 Ag F 4.286 420 53

16 1337.33 1064.18 Au F

17 1357.77 1084.62 Cu F

a All substances except 3He are of natural isotopic composition, e-H2 is hydrogen at the equilibrium concentration of the ortho- and para-molecular forms. b V: vapour pressure point; T: Triple Point (temperature at which the solid, liquid and vapour phases are in equilibrium); G: gas thermometer point; M,F melting point, freezing point (temperature, at a pressure of 101 325 Pa, at which the solid and liquid phases are in equilibrium)

see http://www.its-90.com


http://www.its-90.com/http://www.its-90.com/http://www.its-90.com/http://www.its-90.com/

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temperature measurement

• definition of temperature via reversible Carnot process is not well suited for establishing useful measuring methods

• in practice: use of fixpoints and interpolation polynoms

• primary thermometers: measured quantity is related directly to temperature (in a theoretically predictably way) no calibration is required

• secondary thermometers: measured quantity varies with temperature in a reproducible way must be calibrated using a primary thermometer

• requirements for temperature measurement: good thermal contact between thermometer and sample low self-heating fast response to temperature changes


Chapt. IV - 112

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T(K)

typical temperature range of some thermometers


Chapt. IV - 113

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most common thermometers for 1K < T < 300K

• gas thermometer: p = p(T) – Helium gas ≈ ideal gas down to 10K:

• vapour pressure thermometer: Tliquid = f(pvapor) – pressure of 10 Pa corresponds to 0.4K for 3He

• thermocouples: Vth = Vth(T)

• resistance thermometry: R = R(T) – 1K - 300K – semiconductors (e.g. Ge doped with Arsenic has 100-500 Ω/K @ 4.2K,

self-heating around 10μA) – p-n junction diode (problem with high bias current self heating)

• capacitance thermometry: C = C(T) – based on temperature change of dielectric properties – virtually no magnetic field-induced errors

• noise thermometer: S = S(T) – Johnson noise in resistor: SV = 4kBTR – like gas thermometer, but with electrons – with SQUID measurements: 0.1% @ 1K


Chapt. IV - 114

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• magnetic suceptibility thermometer

T

C

B

M 0Curie’s law:

Ce

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Cryogenic Techniques: Generation and Measurement of Low … · 2013. 7. 18. · (H. Kammerlingh...

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