4He, 3He, and 3He-4He dilution refrigerator
Physics 590 B, Spring 2014 4He, 3He, and 3He-4He dilution refrigerator
Instrument Gas handling system Still pumping line Magnet power supply Dil fridge Dump (mixture storage) Pump room 3He pumping Oxford 14 T cryostat
LN 2 trap
LHe Dewar
LN 2 Dewar
Vacuum pump Turbo pump Rotary pump Computer-data acquisition
Typical dil-fridge room 4He, 3He, and 3He-4He dilution refrigerator
Instrument Gas handling system Still pumping line Dil fridge Magnet powersupply Dump (mixture storage) Pump room 3He pumping Oxford 14 T cryostat
LN 2 trap
LHe Dewar
LN 2 Dewar
Vacuum pump Turbo pump Rotary pump Computer data acquisition
Typical dil-fridge room DON’T 4He, 3He, and 3He-4He dilution refrigerator measurements Instrument Gas handling system Still pumping line March 10-14 March 3-7 Dil fridge Magnet powersupply Dump (mixture storage) Pump room 3HeKaminski pumping Oxford 14 T cryostat
LN 2 trap
LHecryogens Dewar
cryogensLN 2 Dewar
MarchVacuum 3-7 pump Turbo pump RotaryKaminski pump Computer data acquisition
How to cool below 4 K 4He, 3He, and 3He-4He dilution refrigerator 4He
Phase diagram Cryostat Cooling power Pressure, thermometer 3He
Isotopes of Helium Phase diagram Cooling power Refrigerator- closed system with charcoal, measurements in liquid Thermometer 3He-4He Mixture
Phase diagram of mixture Properties of mixture Cooling power of mixture Operation Cryogen free system Thermometer
Very nice reference book: Matter and Methods at Low Temperatures, 2 nd Edition, F.Pobell Cryogenic systems 4He Phase Diagram
Critical point 5.19 K Triple point ~ 2.17 K at 1 atm Boiling point 4.222 K (0.22746 MPa)
• 4He has no spin, Boson • No solid phase (1 atm) due to weak van der Waals inter-atomic interactions, large quantum mechanical-zero-point energy due to small mass (high kinetic energy and low Potential energy), Bose-Einstein condensate instead of a solid
• Helium-4 : triple point involving two different fluid phase. The λ(lamda)-point is the temperature below which normal fluid helium transition to superfluid helium. 4He Cryostat
4He pumping Sample holder
Sample space Vacuum sapce
LN 2
LHe Base temperature 4.2 K at 1 atm
Cool below 4.2 K Reduce pressure – pumping cryostat down to ~ 1K Reality! 1.5 ~ 2 K Sample Cooling power is proportional to vapor pressure. space
Cryostat design magnetic field – March 10-14 4He Cryostat with 1 K pot
1K pot pumping Needle valve
Sample space
Capillary flow (impedances)
Cool down sample stage by 1 K pot or use VTI
Save Helium! Save money! Efficient! 1K pot
Difficult to cool down below 1.5 K Sample should be called 2 K pot? space 4He Cryostat with 1 K pot
1K pot pumping Needle valve
Sample space
reach ~0.9 K and sample in liquid Small volume with low impedance: easy to reach low pressure He gas Sample space pumping below 1 K
Small He bath/VTI pumping < 2K 1K pot
Liquid He Sample inside liquid sample High vacuum
charcoal Cooling power of evaporative cooling
dP S − S L LP = gas liq ~ = dT V −V TV RT 2 gas liq gas latent heat of 3He and 4He V >> V L ~ TdS Assuming gas liq and using
Latent heat L ~ independent of temperature 4He dP L dT = (J/mol) P R T 2 L
L 3 P ∝ − He exp( ) Latent heat RT Cooling power: proportional to vapor pressure and exponentially small with temperature Temperature (K) Pressure
Pressure ranges of vacuum -details March 3-7 low pressure, vacuum generation and gauge (Kaminski) Torr Vacuum gauge pump
Atmospheric 760
Low vacuum 25 ~ 1 X 10 -3 Pirani gauge (0.5 ~ 10 -4 Torr) Rotary pump
High vacuum 1 X 10 -3 ~ 1 X 10 -9 Ionization gauge (10 -3 ~ 10 -10 Torr) Turbo pump, diffusion pump, Penning gauge (10 -3 ~ 10 -13 Torr) cryopump (charcoal) -9 -12 Ultra high vacuum 1 X 10 ~ 1 X 10 Inverted magnetrons (~ 1 X 10 -12 ) Outer space 1 X 10 -6 < 3 X 10 -17
U-Tube Manometer Perfect vacuum 0 Bourdon Tube
Capacitance Manometer
Themocouple
McLeod
1 atm Schulz-Phelps IG = 1.01325 X 10 5 Pascal (Pa) Bayert-Alpert IG Pirani gauge = 1.01325 Bar (bar) Cold Cathode IG Penning gauge
= 760 Torr (mm Hg ) Mass Spectrometer (RGA) = 14.69595 Pound per square inch (psi) 10 -13 10 -11 10 -9 10 -7 10 -5 10 -3 10 -1 10 1 10 3 Pressure in Torr 4He thermometer January 22-24 measuring temperature (Prozorov)
Cernox™ sensors can be used from 100 mK to 420 K with good sensitivity over the whole range. They have a low magnetoresistance, and are the best choice for applications with magnetic fields up to 30 T (for temperatures greater than 2 K). Cernox™ are resistant to ionizing radiation, and are available in robust mounting packages and probes. Because of their versatility, they are used in a wide variety of cryogenic applications, such as particle accelerators, space satellites, MRI systems, cryogenic systems, and research science. From Lakeshore.com CX-1050 -SD/BC X00000 : good sensitivity and stability
Response time 1.5ms CX-1050 for 4He CX-1030 for 3He
Response time 15ms
Time related measurements such as AC heat capacity Consider response time BC: 1.5 ms at 4.2 K, 50 ms at 77 K, 135 ms at 273 K SD: 15 ms at 4.2 K, 0.25 s at 77 K, 0.8 s at 273 K I2R AA: 0.4 s at 4.2 K, 2 s at 77 K, 1.0 s at 273 K Low current or voltage (~2mV): Joule heating Isotopes of Helium
3He 4He Parent isotopes 3H (beta decay of tritium) Neutron 1 2 proton 2 2
Isotope (atomic) mass (m a/u) 3.016 4.002 Nuclear spin (I) 1/2 0
Magnetic Moment (µ/µN) -2.127 0 Half life Stable stable Natural abundance (atom %) on Earth 0.000137 99.99986 Boiling point at 1atm 3.19 K 4.23 K Critical point 3.35 K 5.19 K (0.22746 MPa) Triple point 2.177 K (5.043 kPa) Density of liquid at boiling point 0.059 g/mol 0.12473 g/mol Latent heat of vaporization 0.26 kJ/mol 0.0829 kJ/mol Molar heat capacity 5/2 R = 20.768 J/mol Other isotopes, He-5, He-6 He-7 … extremely short half-life The shortest-lived heavy helium isotope is He-5 with a half-life of 7.6×10−22 s. He-6 decays by emitting a beta particle and has a half-life of 0.8 second. He-7 also emits a beta particle as well as a gamma ray. He-7 and He-8 are created in certain nuclear reactions. He-6 and He-8 are known to exhibit a nuclear halo. C. A. Hampel (1968). The Encyclopedia of the Chemical Elements. pp. 256–268. 3He Phase Diagram
Critical point 3.35 K Boiling point 3.19 K Triple point 3.05
• 3He: Nuclear spin I = ½, Fermion, Pauli principle. • Superfluid phases: Bose-Einstein condensate of pairs, spins in the liquid state are indistinguishable. • Diamagnetic: levitation under high magnetic field
PS) Supersolid state of 3He or 4He? A supersolid is a spatially ordered material with superfluid properties. Superfluidity; a special quantum state of matter, substance is flowing without viscosity. Quantum magnet in triangular angular lattice; breaking translational and rotational symmetry. 3He cooling power
Cooling Power proportional to Vapour Pressure
L P ∝ exp(− ) RT
Latent heat 4He ~90 J/mol Latent heat 3He ~40 J/mol
Cooling power: exponentially small at low temperature Pumping on 4He T~1 K (normally down to 1.8 K) Pumping on 3He T~0.26 K (down to 0.3 K) 3He Refrigerator
• Sample in vacuum configuration, only few places operate sample in liquid 3He • Operation one-shot mode: keep base temperature 10-60 hours continuous mode: forever? ~very long time • 3He is stored in a sealed space (closed system) to avoid loss, keep low pressure (<1atm) • 3He pump: sealed (tight, casted) pump or charcoal pump
One-shot mode Continuous mode Pumping Pumping (gas) (gas)
1 K 3He Refrigerator operation
Reach 0.3 K base temp: Clean gas => Make liquid 3He => Reduce pressure
Needle valve 1K pot pumping 4 pumping
condensing Sample space 3He operation 1) Cleaning gas through LN 2 trap or use cryopump 2) Condense by heat exchange with 1 K pot 3) Cool condensate to 1.5 K (below 2 K) 4) Start pumping to reach 1 base temperature 1K 2 pot
3He 3 pot 3He Storage LN 2 trap cleaning gas 3He Refrigerator operation: closed system
Charcoal Charcoal is a light black residue consisting of carbon and any remaining ash, obtained by removing water and other volatile constituents from animal and vegetation substances.
Cryopumps are often combined with sorption pumps by coating the cold head with highly adsorbing materials such as activated charcoal or a zeolite. As the sorbent saturates, the effectiveness of a sorption pump decreases, but can be recharged by heating the zeolite material (preferably under conditions of low pressure) to outgas it. The breakdown temperature of the zeolite material’s porous structure may limit the maximum temperature that it may be heated to for regeneration. from Wikipedia
Activate ~ 40 K, control with heater and thermometer 3He Refrigerator operation: closed system
Needle valve 1K pot pumping 3He operation 3He gas storage 1)Cleaning gas cryopump (charcoal) – at 4 K all gases inside charcoal sorption pump 2)Release gas by heating up to 40 K 3)Condense by heat exchange with 1 K pot Sample 4)Cool condensate to 1.5 K (below 2 K) in space He-3 pot 5)Start pumping to reach base temperature using sorption pump-set 4 K Charcoal Sorption pump
1K pot
3He pot 3He Refrigerator operation: closed system
3He storage vessel
1 2 3
4 K 40 K 4 K Charcoal Sorption pump
1K pot
3He pot 3He Refrigerator operation: sample in liquid Top loading: measurements inside 3He liquid )
Sample holder O-ring seal
Vacuum line Knife gate valve (KF)
3He gas handling system
vacuum Rotator Electrical transport
3 4 Resistivity He He 300 kHz 50 µA, 500 µA ? 3He thermometer
10 10 8
) 6
Ω at 14 Tesla: 0.14 K shift 4
1 (k R 2 )
Ω H = 0 0.4 0.6 0.8 1.0 1 T 3 T T R (k R (K) 5 T 7 T 0.1 9 T 14 T
1 10 100 T (K)
Cernox CX-1030 - negative magnetoresistance (MR) < 10 K MR effect can be ignored T > 30 K Below 0.3 K ?
Cooling Power proportional to Vapour Pressure
L P ∝ exp(− ) RT
How cool below 0.2 K? How can exponentially small vapor pressure be overcome?
Oxford dil 3He and 4He Mixture
The working fluid mixture of the dilution refrigerator: phase separation into 3He rich (concentrated) and 3He poor (dilute) phase below 800 mK (NOT PURE 3He and 4He).
Fermi liquid 3He 4 in superfluid He Phase separation starts T = 800 mK
Temperature (K) Temperature x = 0.675
Phase separation
3He concentration x 3He and 4He Mixture
3He and 4He mixtures as Fermi Liquid • 4He: Nuclear spin I = 0, Bose static. At low temp Bose liquid under Bose condensation in momentum space (correspond to transition to super-liquid for 4He). • At T < 0.5 K 4He condensed into quantum mechanical ground state, no excitation (phonon) • In mixture: 4He acts as inert superfluid background contributes to the volume and to the dissolved isotope 3He. • 3He: Nuclear spin I = ½ , Fermion, Pauli principle. • In analogy to conduction electrons, the specific heat of liquid 3He behaves as: Fermi degenerate or Classical; π 2 T Fermi degenerate:C = R → at → T < TF 2 TF 5 Classical: C = R → at → T > TF → P = const ⋅ tan t 2
• Behavior is classical-gas-like at : T > 1 K • Behavior is Fermi-gas-like at : T << 0.1 K • 3He-4He mixture can be described by the law of an interacting Fermi gas 3He and 4He Mixture
Finite solubility of 3He in 4He • 3He in pure 3He: The chemical potential of pure liquid 3He is given by the latent heat of evaporation, corresponding to the binding energy. • One 3He atom in liquid 4He: Identical chemical structure of the He isotopes-van der Walls force. The liquid phase 4He atoms occupy a smaller volume than 3He atoms. Its binding energy, due to the smaller distance or larger density, is stronger if it is in 4He that it would be in 3He. • Many 3He atoms in liquid 4He: attractive interaction between the 3He atoms and in liquid 4He, due to i)magnetic interaction due to the nuclear magnetic moments of 3He as in pure 3He ii)density effect • Pauli principle: the energy states up to the Fermi energy are filled with two 3He atoms of opposite nuclear spin EF = kB TF. • Result: The binding energy of the 3He atoms has to decrease, due to their Fermi character, if their number is increased.
Phase separation: purely quantum effect (classical liquids separate into pure components), the Fermi statistics 3He and Bose statistics 4He 3He and 4He Mixture
The cooling capacity is the heat mixing of the two isotopes. The cooling power of an evaporating cryogenic liquid; Q = n∆H = nL Make use of the latent heat L of evaporation, pumping with a pump of constant volume rate V on 3He and 4He bath with vapour pressure; Q = VP(T )L(T) 3He-4He dilution refrigeration: use the difference of the specific heats of the two phases (the enthalpy of mixing); ∆H ∝ ∫ ∆CdT => Q ∝ x∆H ∝ T 2
Dilution refrigerator cooling power:~ T 2 3He-4He Dilution Refrigerator
Reach base temp: Clean gas => Make liquid 3He-4He => pumping 3He (circulation)
Needle valve 1K pot pumping
3He-4He operation pumping 1) Cleaning mixture through LN 2 and LHe trap condensing Sample 2) Condensing mixture space through 1 K pot 3) 3He circulation 3He circulation
sorption 1K trubo pump vs 0.02 K cryopump still
concent dilute Dump LN 2 trap Mixing chamber 3He- 3He Storage cleaning gas Keep always low pressure P < 1 atm to avoid loss of mixture 3He-4He Dilution Refrigerator
• Evaporation: depends on the classical heat of evaporation for cooling • Dilution refrigeration: depends on the enthalpy of mixing of two quantum liquid, the different zero- point motions of the two Heluim isotopes and the different statistics
Evaporation Dilution
Pumping 3He Still-evaporates 3He from mixture (gas) pump
1 K 1 K
Vapour 3He -4He Mixing Chamber Liquid 3He Phase separation line 3He-4He Dilution Refrigerator
From Makariy note 3He-4He Dilution Refrigerator: liquid operation
Sample holder O-ring seal ~3m long
Vacuum line
Knife gate valve (KF)
1 K pot
still
Mixing Sample in liquid chamber Cryogen free 3He-4He Dilution Refrigerator
Base temperature limit Oxford triton • Radiation – shield • Ground loop - !!! • RF heating – proper shielding • Vibration – rigid tail Pulse tube CCR - Unltra low vibration - absolute cryocooler vibration amplitudes less than 100 nm
With cryogen free magnet High efficient Heat exchange
Still
Mixing chamber
NO 1 K POT: by driving condensation at higher pressures, higher condensation temperatures are possible Ruthenium Oxide (ROx) Thermometer Ruthenium Oxide (ROx) Thermometer
20 ~10 mK shift at 13 T 20 18 18 (due to positive MR)
16 ) Ω 14 16
12 (k R 14 10 H=0T 12 8 H=1T 0.05 0.06 0.07 0.08 0.09 0.10
) H=2T T (K)
Ω 6
H=3T H=4T H=5T R R (k 4 H=7T H=9T H=11T H=13T 2 0.1 1 T (K)