Elements of Cryogenics

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Elements of Cryogenics
Øyvind Haugen 19.04.2005
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Outline

• Temperatures 300K-1K
• Liquid cryogens
• Helium properties
• Helium cryostat
• Liquefaction of gases
• Temperatures 1K-1mK
• Dilution refrigerator
• Temperatures 1mk-pK
• Magnetic cooling
• Thermometer
• Resistance thermometer
• Magnetic susceptibility thermometer
• Heat transfer
• conduction
• convection
• radiation
• Vacuum technique
• rotary vacuum pump
• Turbomolecular pump

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300K-1KLiquid cryogens

• Liquid Oxygen and hydrogen has potential hazards
• Liquid Nitrogen and 4Helium are the most widely
  used cryogens
• Liquid 3Helium very expensive

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Liquid 4He

• Boson
• Liquid to 0K (_at_ 1 atm)
• Superfluid Helium-II at 2.17K
• Bose condensation Macroscopic number of atoms in
  ground state
• very low viscosity
• very high heat conduction
• strange thermomechanical effect
• creeping on vertical surfaces
• vortice core with radius 0.8Å _at_ 0.6K
• explained by a two-liquid model
• Density 125 kg/m3
• Refractive index

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Helium cryostats

• Helium has small latent heat
• Thermal insulation by vacuum
• LHe container of poor thermal conductivity, glass
  or stainless steel
• Thermal radiation shield at liquid Nitrogen
  temperature reduce black-body radiation
• Bath cryostat - Sample is immersed in the LHe
• Gas flow cryostat

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Bath cryostat
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Gas flow cryostat
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Gas flow cryostat (II)
No liquid Nitrogen Radiation shield cooled by
helium return gas
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Liquid 4He Temperature below 4.2K

• Reducing the vapour pressure over bath of 4Helium
• Temperature down to 1.2K is possible at pumping
  speed 10 m3/h

up to 10mW cooling power _at_ 1.2K
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Liquid 3Helium

• Fermion
• Superfluid at 2.5mK
• formation of weakly bound fermions cooper pairs
• Densit 59 kg/m3
• Higher vapour pressure than 4He -gt 80mW cooling
  power _at_ 1.2K
• 0.3K by pumping 3He vapour
• some cm3
• 0.1mW cooling power _at_ 0.3K
• Generated by nuclear reactions
• Extremely expensive
• 1 liter of liquid 3He sells for about 100.000

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Liquefaction of gases

• 3 methods
• Direct liquefaction by isothermal compression
• Making the gas perform work against external
  forces at the expense ot its internal energy,
  leading to cooling and eventual liquefaction
• Making the gas perform work against its own
  internal forces by Joule-Kelvin expansion

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1. Direct liquefaction by isothermal compression
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2. Making the gas perform work against external
forces
A. Stirling refrigerator
Specific heat capacity of the regenerator limits
the temperature to 10K
P-V diagram
Schematic stirling refrigerator
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2. Making the gas perform work against external
forces (II)

• B. Gifford-McMahon refrigerator
• Substanially heavier than Stirling
• 1/3 of Stirlings efficiency
• More robust
• Compressor can be placed far from cold head
• easy to multi-stage
• established as standard coolers lt30K
• 0.5 - 3 W cooling power _at_ 4.2 K at an input power
  of 1 -12 kW.

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3. Joule-Thomson effect Making the gas perform
work against its own internal forces
Adiabatic process Q0 -gt H1H2 -gt
E1p1V1E2p2V2 Effectiveness described by
Joule-Thomson coefficient
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1K-1mKThe 3He-4He dilution refrigerator

• Maximum 6.5 3He in superfluid 4He
• Adding more 3He creates consentrated 3He
• Pumping 3He from mixture makes the concentrated
  3He evaporize into mixture cooling of
  concentrated 3He.
• 6.5 3He in superfluid 4He constant
• 1µW cooling power at 10mK

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Dilution refrigerator from Janis
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1mK-pKAdiabatic demagnetisation

• dQdE-BdM
• Adiabatic cooling dQ0 -gt dEBdM
• step1 Magnetise sample with field B, work must
  be done on sample and heat is released to thermal
  bath at Ti
• step2 Thermally isolated, remove magnetic field
  B from sample, sample use internal energy to
  demagnetise and temperature fall to TfltTi
• Adiabatic -gt S(Bi/Ti)S(Bf/Tf) -gt TfTiBf/Bi
• Ex Copper, Bi3T, Bf0.3mT, Ti10mK -gt Tf1µK

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Adiabatic demagnetisation (II)

• Spin-lattice coupling cools the lattice
• metals 1000s
• non-metals hours to several days
• Thermal energy
• Equilibrium temperature Teq (ex. 1.03µK)

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Thermometers
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Thermometers 300K-1K

• Gas thermometer
• Helium gas appr. ideal gas to 10K
• Vapour pressure thermometer
• lower pressure of 10 Pa -gt 0.4K for 3He
• Thermocouples
• Resistance thermometry
• 1K-300K
• Semiconductor ( Ge doped with Arsenic has 100-500
  O/K _at_ 4.2K, self-heating around 10µA)
• p-n junction diode ( Problem with high bias
  current -gt self heating)
• Capacitance thermometry
• Virtually no magnetic field-induced errors
• Noise thermometer
• Johnson noise in resistor
• Like gas thermometer, but with electrons
• With SQUID measurements 0.1 _at_ 1K

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Thermometers lt1K

• 1K-1mK Magnetic suceptibility thermometer

Curies law
Mutual inductance between coils

• Cerium magnesium nitrate (CMN) useful from
  1K-10mK
• Low temperature limit set by magnetic ordering at
  1mK
• lt 1mK Nuclear Magnetic Resonans (NMR)
  thermometer
• Temperature dependence of spin relaxation
• Platinum ideal choise for NMR thermometry

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Heat transfer

• Conductive heat transfer
• Transfer by molecular action
• Convective heat transfer
• Transfer by fluid motion
• Radiative heat transfer
• Transfer by EM-radiation

hc function of Re and Pr
Emissivity e

• Aluminium, higly polished 0.04
• Gold, polished 0.02
• Stainless steel 0.1
• Copper, oxide layer 0.78
• Black-body 1

For low temperature we normally use vacuum
isolation and neglect convective heat transfer
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Thermal conductivity
300K-1K
1K-30mK
A Aluminium B Copper C Quartz crystal D
Brass E Stainless steel F Silica
Metals kaT dielectrics k bT3
http//fy.chalmers.se/delsing/LowTemp/
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Vacuum technique

• Rotary vacuum pumps
• 1 bar-10-7 bar (10-2 Pa)
• 10-10.000 liter/s
• Vapour diffusion pumps
• down to 10-11 bar (10-6 Pa)
• 50-50.000 liter/s
• inlet less than 0.1mBar
• Turbomolecular pumps
• down to 10-13 bar (10-8 Pa)
• 100-1.000 liter/s
• inlet less than 1mBar
• gas compressed by turbine blades
• Cryopumps
• down to 10-15 Bar (10-10 Pa)
• 5.000 liter/s
• single shot

http//www.schoonoverinc.com/PDFs/fundamen.pdf