4He, 3He, and 3He-4He

Physics 590 B, Spring 2014 4He, 3He, and 3He-4He dilution refrigerator

Instrument handling system Still pumping line Magnet supply Dil fridge Dump ( storage) 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 , thermometer 3He

Isotopes of diagram Cooling power Refrigerator- with charcoal, measurements in Thermometer 3He-4He Mixture

Phase diagram of mixture Properties of mixture Cooling power of mixture Operation Cryogen free system Thermometer

Very nice reference book: and Methods at Low , 2 nd Edition, F.Pobell Cryogenic systems 4He Phase Diagram

Critical point 5.19 K ~ 2.17 K at 1 atm point 4.222 K (0.22746 MPa)

• 4He has no spin, Boson • No phase (1 atm) due to weak van der Waals inter-atomic interactions, large quantum mechanical-zero-point due to small (high and low ), Bose-Einstein condensate instead of a solid

• Helium-4 : triple point involving two different fluid phase. The λ(lamda)-point is the 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 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 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 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( ) 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 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 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): heating

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 ( %) on Earth 0.000137 99.99986 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) of liquid at boiling point 0.059 g/mol 0.12473 g/mol Latent heat of 0.26 kJ/mol 0.0829 kJ/mol 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) state of 3He or 4He? A supersolid is a spatially ordered material with superfluid properties. ; a special quantum , 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 and other volatile constituents from animal and vegetation substances.

Cryopumps are often combined with sorption 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 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 mixture of the dilution refrigerator: 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 x 3He and 4He Mixture

3He and 4He as Fermi Liquid • 4He: Nuclear spin I = 0, Bose static. At low temp Bose liquid under Bose 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 of 3He in 4He • 3He in pure 3He: The of pure liquid 3He is given by the latent heat of , 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 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 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 : use the difference of the specific of the two phases (the 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 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 , 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)