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renewable sourcesolar sun wind flow inside of the book their is bhoot which will kill you no body save you please be aware of this book it is not a book it is presentation i was kidding tell me about your self how the things are going on all are wright keep it up go and achieve your goal do not waste yor time wake up man and go solar sun wind flow inside of the book their is bhoot which will kill you no body save you please be aware of this book it is not a book it is presentation i was kidding tell me about your self it is presentation i was kidding tell me about your self how the things are going on all are wright keep it up go and achieve your goal do not waste yor time wake up man and go solar sun wind flow inside of the book their is bhoot which will kill you no body save you please be aware of this book it is not a book it is presentation i was kidding tell me about your self renewable sourcesolar sun wind flow inside of the book their is bhoot which will kill you no body save you please be aware of this book it is not a book it is presentation i was kidding tell me about your self how the things are going on all are wright keep it up go and achieve your goal do not waste yor time wake up man and go solar sun wind flow inside of the book their is bhoot which will kill you no body save you please be aware of this book it is not a book it is presentation i was kidding tell me about your self it is presentation i was kidding tell me about your self how the things are going on all are wright keep it up go and achieve your goal do not waste yor time wake up man and go solar sun wind flow inside of the book their is bhoot which will kill you no body save you please be aware of this book it is not a book it is presentation i was kidding tell me about your self
Citation preview
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 K)
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:
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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 fr Physik: 1913
Sir James Dewar, (1842-1923)
Peter J. Debye 1884 - 1966
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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 Mnchen (now TUM)
1873 development of cooling machine allowing the temperature stabilization in beer brewing
21. 6. 1879 foundation of Gesellschaft fr Lindes 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 (-182C = 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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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 K 100 pK
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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:
work against internal interactions
dilution cooling (3He/4He)
work against internal interactions
adiabatic demagnetization (electronic/nuclear moments)
work against magnetic ordering
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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: piston system: outgoing: piston system:
laboratory system: + = 2 =
i.e.: = 2 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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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 ( = , = 0
=
> 1)
heat exchange: isotherms ( = , = 0)
work per cycle:
= =
warmT
T
Q
W
thermodynamic definition of temperature
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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:
= / (= 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
IV.1 Generation of Low Temperatures IV.1.1 Introduction
(decreases with increasing temperature difference T1 T2)
Chapt. IV - 20
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Wikimedia Commons
IV.1 Generation of Low Temperatures IV.1.1 Introduction
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
IV.1 Generation of Low Temperatures IV.1.2 Expansion Machine
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
IV.1 Generation of Low Temperatures IV.1.2 Expansion Machine
(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
IV.1 Generation of Low Temperatures IV.1.2 Expansion Machine
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 = =
- 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
T2 = const V = const
Q23
Q41 1
2
4
3
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
3 4 4 1 1 2 2 3
T2
T1
Chapt. IV - 26
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(beta) Stirling machine:
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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.
Chapt. IV - 27
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(alpha) Stirling machine:
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
pressure wave from valve
hot
cold
regenerator
switching valve
cycle:
V
p Q12
Q34
V = const
T1 = const
T2 = const V = const
Q23
Q41 1
2
4
3
Chapt. IV - 32
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Gifford-McMahon cycle:
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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. 5357
suggested to be used to liquefy oxygen on Mars
Chapt. IV - 34
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IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
Chapt. IV - 39
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pulse tube refrigerator for studies of liquefying oxygen on
Mars (580 mm total length)
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.3 Regenerative Machines
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
IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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 ( 43/3): excluded volume per particle Van der Waals equation:
IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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
En
erg
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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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
interaction potential: Epot
r
repulsive attractive
p
repulsive attractive
U (p,T)
T = const.
minimum
with
Chapt. IV - 46
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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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
> 0: cooling on expansion
< 0: heating on expansion
Chapt. IV - 47
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ideal gas: 0
JT
p T
V
p
R
T
VRTpV
IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
0 .2
5
2
3),(
T
JTBBBp
HconstTNkTNkTNkpVUpTH
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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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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
JT > 0 for T < 2a/bR cooling on expansion
JT < 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
Chapt. IV - 49
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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
areas of H = const.
lines of intersection with H = const.
inversion curve
Chapt. IV - 50
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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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 JT = 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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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
experimental data for N2:
H
JTp
T
slope of isenthalps
repulsion
attraction
Chapt. IV - 52
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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
IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
vdW gas can be liquefied only for T < Tinv !!!
Chapt. IV - 53
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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
Lindesche Gasverflssigungsanlage (1895)
Chapt. IV - 55
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Professor Dr. Carl Paul Gottfried von Linde (* 11. Juni 1842 in Berndorf, Oberfranken; 16. November 1934 in Mnchen) war ein deutscher Ingenieur, Erfinder und Grnder eines heute internationalen Konzerns, der Linde AG. Linde begann 1861 ein Studium am Polytechnikum Zrich, 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 Mnchen zog, um als Konstrukteur bei der Lokomotivenfabrik Krauss zu arbeiten. 1866 heiratete er Helen Grimm: aus der 53-jhrigen Ehe folgten sechs Kinder. 1868 folgte er einem Ruf der Polytechnischen Schule Mnchen, wo er zunchst - mit erst 26 Jahren - auerordentlicher Professor, 1872 dann ordentlicher Professor fr Maschinenbau wurde. Am Polytechnikum richtete Linde ein Maschinenlabor ein, an dem unter anderem Rudolf Diesel ausgebildet wurde. 1871 verffentlichte Linde einen Aufsatz ber verbesserte Kltetechnikverfahren. Viele Brauereien interessierten sich dafr, und bald versorgte Linde sie mit den neuen Maschinen, an denen er stndig arbeitete. Linde schuf wesentliche Grundlagen der modernen Kltetechnik. 1871 konzipierte er eine mit Methylether arbeitende Kltemaschine, die er in der Maschinenfabrik Augsburg (heute MAN AG) herstellen lie. Die zweite, 1876 folgende Generation von Khlmaschinen arbeitete mit Ammoniak. Das Prinzip der Abkhlung von Gas, das vorher mechanische Arbeit geleistet hatte, war beiden gemeinsam. Ein Preisausschreiben fr eine Khlanlage zum Auskristallisieren von Paraffin war 1873 fr den Hochschullehrer der Anreiz zum Bau einer Khlmaschine, die beim Bierbrauen die Grung bei konstanter Temperatur zulie. Brauereien in ganz Europa (so Dreher in Triest, die Mainzer Actien-Bierbrauerei, Spaten in Mnchen, Heineken in den Niederlanden, Carlsberg in Dnemark) interessierten sich prompt fr die neue Kltetechnik. Am 21. Juni 1879 gab der Erfinder sein Lehramt auf und rief mit zwei Brauern und drei anderen Grndern die "Gesellschaft fr Lindes Eismaschinen AG" ins Leben (heute Linde AG). Nach relativ kurzer Zeit war das Unternehmen in Europa fhrend auf kltetechnischem Gebiet, auch begnstigt durch einen milden Winter 1883/1884. Es kam deshalb zu einer Knappheit bei Natureis, das zum Khlen des Gerstensaftes in Bierkellern eingesetzt wurde. Bisherige Vorbehalte der Brauer gegen das Kunsteis schmolzen dahin, Khlmaschinen waren pltzlich gefragt und Linde lieferte umgehend. Khlhuser fr Lebensmittel und mehrere Eiswerke lie Linde nach und nach sogar selbst bauen. Doch auch auf Eislaufbahnen, in Molkereien und bei der Verflssigung von Chlor und Kohlensure war sein Verfahren gefragt. Die Firma florierte, 1890 zog sich Linde aus dem operativen Geschft in den Aufsichtsrat seiner Aktiengesellschaft zurck. 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 Einfhrung des Gegenstromverfahrens konnte Linde 1895 erstmals grere Mengen Luft verflssigen (Linde-Verfahren). Damit schuf er die Mglichkeiten fr 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 gehrte er dem Kuratorium der Physikalisch-Technischen Reichsanstalt und der Bayerischen Akademie der Wissenschaften an. Er wurde vom bayerischen Knig Ludwig II in den nicht erblichen Adelsstand erhoben. Linde war 1916 der erste Preistrger des Siemens-Rings. Ab 1910 zog sich Linde als Direktor seiner inzwischen ungeheuer erfolgreichen Aktiengesellschaft zurck und reichte sie an seinen Shne 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.
IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
Chapt. IV - 56
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IV.1 Generation of Low Temperatures IV.1.4 Joule-Thomson Cooling
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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IV.1 Generation of Low Temperatures IV.1.5 Summary
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
IV.1 Generation of Low Temperatures IV.1.5 Summary
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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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
Chapt. IV - 65
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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
www.mallister.com/graphics/vapor3.jpg
Chapt. IV - 67
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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 0.8 @ 0.6K
explained by a two-fluid model
density 125 kg/m3
IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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
IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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
IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
He-bath cryostat
Chapt. IV - 71
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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
He-gas flow cryostat
Chapt. IV - 72
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no liquid Nitrogen required radiation shield cooled by cold helium return gas
IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
He-gas flow cryostat (II)
Chapt. IV - 73
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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]
NAEbinding: 90 J/mole for 4He
IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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)
IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
Chapt. IV - 76
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IV.1 Generation of Low Temperatures IV.1.6 Evaporation Cooling
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
Chapt. IV - 77
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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
Chapt. IV - 79
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bonding:
>1
2 + complete miscibility (e.g. water and alcohol)
1
2 + > 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: 3, = 3
=3,
3, = chemical potential of pure (concentrated) liquid
(ii) single 3He atom in liquid 4He:
binding energy for single 3He atom: 3,(3 0) =3, 30
3, = chemical potential of dilute phase 3, 0 > 3, 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 |3, 0 | > |3,|
corresponds to case >1
2 + complete miscibility expected,
why miscibility only up to 6.5% ??
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling revision of I.6
Chapt. IV - 81
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Questions:
why cant we dissolve more than 6.5% of 3He in 4He at T = 0 ? two effects: (i) 3He forms degenerate Fermi liquid increases with 3 for 3 > 6.5%, the Fermi energy exceeds the gain in binding energy
(ii) 3, 3 > 3,(3 = 0) effective attraction between two He atoms (magnetic and volume effect)
why dont 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
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling revision of I.6
Chapt. IV - 82
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x3
0.065
3,(0)
3,
+
0 gaseous He
pure liquid He
He diluted in 4He
= + =
for 3 > 6.5%: + > , = = + =
separation of pure He
energy
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling revision of I.6
Chapt. IV - 83
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for Fermi liquid: Cconcentrated < Cdiluted (x3 = 0.065) ( /,
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 !
He/4He dilution refrigerator
operation principle: remove He atoms from the dilute phase below Tk = 0.87 K
transport of He atoms across phase boundary to maintain equilibrium concentration corresponds to evaporation of He from concentrated phase cools as the latent heat of evaporation is removed
concentrated (lighter)
diluted,6.5% (heavier)
He
U
T
Uconcentrated
Udiluted
He
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling revision of I.6
Chapt. IV - 84
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assumption: one mole of He 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)
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling revision of I.6
Chapt. IV - 85
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IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling revision of I.6
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
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling
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)
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling
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
= 8.31 J/mole K
Chapt. IV - 88
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mixing
chamber
heat
exchangers
still
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling
Chapt. IV - 89
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JANIS Model JDR-500 Dilution Refrigerator
IV.1 Generation of Low Temperatures IV.1.7 Dilution Cooling
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 He Pomeranchuk effect
Isaak Jakowlewitsch Pomeranschuk
( ; 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
Chapt. IV - 91
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IV.1 Generation of Low Temperatures IV.1.8 Pomeranchuk Cooling
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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IV.1 Generation of Low Temperatures IV.1.8 Pomeranchuk Cooling
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
Chapt. IV - 93
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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
Chapt. IV - 94
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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
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 + Tad). 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:
Chapt. IV - 95
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adiabatic
=
=
experiment: use of copper: Bi = 3 T, Bf = 0.3 mT, Ti = 10 mK Tf 1K
IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
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
Chapt. IV - 96
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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
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 gBB
Chapt. IV - 97
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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
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
Chapt. IV - 98
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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
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 K problem: transfer of spin temperature to lattice long spin-lattice relaxation time other materials: 141PrNi5 (L=5/2),
195Pt (L=1/2)
Chapt. IV - 99
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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 K
lowest reported experimental temperature
demagnetization of Pt: Teq = 2 K (F. Pobell et al., (1996))
0 nT
T
nucleare
T
T
electron dTcdTceq
f
eq
i
IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
Chapt. IV - 100
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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
R. Gloss et al.,
J. Low Temp. Phys. 73, 101 (1988)
Cu demagnetization stage (length: 525 mm, diameter: 78 mm)
Chapt. IV - 101
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K 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 K. The red line depicts the calculated course of temperature for the thermodynamically optimized demagnetization function. heat leak: below 1.5 nW.
IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
Chapt. IV - 102
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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.
IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
Chapt. IV - 104
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IV.1 Generation of Low Temperatures IV.1.9 Adiabatic demagnetization
Continuous Adiabatic Demagnetization Refrigerator (CADR) under development at NASAs 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 Q incident on the system during an infinitesimal quasi-static transformation, and the variation S 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 = - 273.15C 1 K = 1C
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)
IV.2 Thermometry IV.2.1 Introduction
Chapt. IV - 108
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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 (Comit 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.
IV.2 Thermometry IV.2.1 Introduction
Chapt. IV - 109
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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 (0.01C)
solid
liquid
gaseous
critical point
triple point
(0.01C, 603 Pa)
273.15 K
(374C, 21800 kPa)
273.16 K
IV.2 Thermometry IV.2.1 Introduction
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
IV.2 Thermometry IV.2.1 Introduction
Chapt. IV - 111
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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
IV.2 Thermometry IV.2.1 Introduction
Chapt. IV - 112
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T(K)
typical temperature range of some thermometers
IV.2 Thermometry IV.2.1 Introduction
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 /K @ 4.2K,
self-heating around 10A) 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
IV.2 Thermometry IV.2.1 Introduction
Chapt. IV - 114
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magnetic suceptibility thermometer
T
C
B
M 0Curies law:
Cerium magnesium nitrate (CMN) useful from 1K - 10mK low temperature limit set by magnetic ordering at 1mK
0 fmm mutual inductance between two coils:
most common thermometers for T < 1K
T < 1mK: Nuclear Magnetic Resonance (NMR) thermometer
temperature dependence of spin relaxation platinum ideal choice for NMR thermometry
M: magnetization B: applied magnetic field C: Curie constant
resistance thermometers
IV.2 Thermometry IV.2.1 Introduction
Chapt. IV - 115
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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 - 116
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IV.2 Thermometry IV.2.2 Primary Thermometers
gas thermometers
ideal gas would be a perfect thermometer:
nRTpV measure pressure at constant volume
32 )()()( TTdTTcpTbRTnpV
virial coefficients (tabulated ITS-90 values)
systematic errors: dead volumes thermal expansion of cell, elastic deformation of cell adsorption and desorption from walls mainly used in calibration laboratories !
for real gases life is more complicated deviations from ideal behavior
Chapt. IV - 117
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in practice, a set of secondary vapour pressure scales is used: ITS-90: with 3He and 4He: ITS defined down to 0.65 K
vapour pressure thermometry
Clausius-Clapeyron equation:
for ideal gas (pV = RT):
if Hvap(T) is known determine T of liquid (e.g. He) via measurement of He pressure above liquid
TV
TH
TVV
TL
dT
dp
gas
vap
liquidgas
)(
)(
)(
dTTTH
constpRvap
2
)(.ln
i
i
iC
BpAT
)(ln (in principle no primary
thermometer !!)
limited T range
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 118
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values of the constants for the helium vapour-pressure, and the temperature range for which each equation, identified by its set of constants, is valid (see http://www.its-90.com).
3He
0.65K to 3.2K
4He 1.25K to 2.1768K
4He 2.1768K to 5.0K
A0 1.053 447 1.392 408 3.146 631
A1 0.980 106 0.527 153 1.357 655
A2 0.676 380 0.166 756 0.413 923
A3 0.372 692 0.050 988 0.091 159
A4 0.151 656 0.026 514 0.016 349
A5 -0.002 263 0.001 975 0.001 826
A6 0.006 596 -0.017 976 -0.004 325
A7 0.088 966 0.005 409 -0.004 973
A8 -0.004 770 0.013 259 0
A9 -0.054 943 0 0
B 7.3 5.6 10.3
C 4.3 2.9 1.9
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 119
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vapour pressure thermometry
4He
3He
4He
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 120
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www.mallister.com/graphics/vapor3.jpg
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 121
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vapour pressure thermometry
www.bm-industries.com
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 122
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3He melting curve thermometry
use of melting curve of 3He to define PLTS-2000 temperature scale down to 0.9 mK
polynom for melting curve: coefficients given by PLTS-2000 also use of 4 fix points (minimum of melting curve, transition temperatures to A and B phase and afm order of nuclear spins in solid 3He)
9
3i
i
iTp
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 123
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3He melting curve thermometry
melting curve of 3He
Source: R.L. Rusby et al. (2001)
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 124
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noise thermometry
Nyquist theorem:
valid only in the low frequency limit f
Chapt. IV - 125
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superconducting fix point thermometers
based on the precise measurement of the transition temperatures of superconductors
available from NIST at Boulder
ITS-90 NIST fixpoint device
IV.2 Thermometry IV.2.2 Primary Thermometers
Chapt. IV - 126
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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 - 127
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IV.2 Thermometry IV.2.3 Secondary Thermometers
Chapt. IV - 128
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resistance thermometers
required: well established relation between resistance and temperature, sufficiently large dR/dT
advantage: resistance easy to measure resistance thermometry very popular
fact: temperature variation of resistance may have very different physical origin
commonly used: Pt resistors (PT-100, PT-1000) RhFe resistors carbon resistors (Speer, Allen-Bradley) carbon glass resistors Ge resistors RuO2 resistors
IV.2 Thermometry IV.2.3 Secondary Thermometers
Chapt. IV - 129
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Platinum resistors
Source: Lake Shore Cryotronics, Inc.
The platinum resistance thermometer (PRT) is very widely used below 500 C as a thermometric sensor. There is a wide range of quality of PRT available, from the standard instrument (SPRT) of the ITS-90 to some industrial types (IPRT) that are accurate only to within a few tenths of a kelvin or, perhaps, even a kelvin or more. The major difference of the industrial type of fabrication from the standard type is not just the purity of platinum, but also the less strain-free mounting of the film or wire which is embedded (partially or totally) in a cement (glass or refractory). Furthermore, in most cases, the thermometer body is not hermetically sealed.
IV.2 Thermometry IV.2.3 Secondary Thermometers
Chapt. IV - 130
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W(29.7646 C) 1.118 07 W(-38.8344 C) 0.844 235
Platinum resistors
ITS-90 requirement for Pt resistance thermometer (PRT)
W(T90) = R(T90)/R(0.01 C)
industrial PRT
IV.2 Thermometry IV.2.3 Secondary Thermometers
for 0 < T < 100C R = R0 (1 + a T) a = 3.85 10-3 / K
allowed errors in C: classA: dT = (