Thermometry at Low and Ultra-low Temperatures

Temperature is a thermodynamic property of state It can be defined by a reversible cycle, like a carnot cycle but this is not very practical

General Considerations determination of temperature is often as difficult as the experiment itself as thermometer anything can be used which has a temperature dependence temperature is by far the most uncertain scale compare it to time Primary thermometers: can be used without any prior calibration Secondary thermometers: must be calibrated again an other thermometer the distinction is often somewhat arbitrary examples will be given

Temperature Scales Defined by Comité International des Poids et Messures based on fixpoints like the triple point of water and interpolation like Pt-100 resistance thermometry or gas thermometry ITS-90 0.65 K to 1358 K PLTS-2000 0.9 mk to 1358 K

ITS-90 Substance and its state Defining point in Kelvins (range) Defining point in degrees Celsius (range) Vapor-pressure / temperature relation of helium-3 (by equation) Vapor-pressure / temperature relation of helium-4 below its lambda point (by equation) Vapor-pressure / temperature relation of helium-4 above its lambda point (by equation) (0.65 to 3.2) ( 272.50 to 269.95) (1.25 to 2.1768) ( 271.90 to 270.9732) (2.1768 to 5.0) ( 270.9732 to 268.15) Vapor-pressure / temperature relation of helium (by equation) (3 to 5) ( 270.15 to 268.15) Triple point of hydrogen 13.8033 259.3467 Triple point of neon 24.5561 248.5939 Triple point of oxygen 54.3584 218.7916 Triple point of argon 83.8058 189.3442 Triple point of mercury 234.3156 38.8344 Triple point of water 273.16 0.01 Meltingpoint 1 ofgallium 302.9146 29.7646 Freezingpoint 1 ofindium 429.7485 156.5985 Freezing point of tin 505.078 231.928 Freezing point of zinc 692.677 419.527 Freezing point of aluminum 933.473 660.323 Freezing point of silver 1234.93 961.78 Freezing point of gold 1337.33 1064.18 Freezing point of copper 1357.77 1084.62

Difference between ITS-90 and ITS-68

Temperature Scales Defined by Comité International des Poids et Messures based on fixpoints like the triple point of water and interpolation like Pt-100 resistance thermometry and gas thermometry ITS-90 0.65 K to 1358 K PLTS-2000 0.9 mk to 1358 K

PLTS-2000 3 He melting curve

Fixed points of the PLTS-2000 Fixed points p/mpa T 2000 /mk Minimum 2.93113 315.24 A 3.43407 2.444 A-B 3.43609 1.896 Néel 3.43934 0.902

Overview noise gas thermometer N.O. Pt NMR CMN Coulomb Gap Au:Er superconducting fixed points 3 He MC He vapor pressure carbon & Ge resistors rhodium-iron resistors Pt resistors 100 µk 1 mk 10 mk 100 mk 1 K 10 K 100 K

Primary thermometers 3 He melting curve Superconducting fix point devices Noise thermometry Coulomb blockade thermometry Nuclear Orientation thermometry Gas thermometry Vapor pressure thermometry Mößbauer effect thermometry Osmotic pressure thermometry

Superconducting Fixpoint Devices Inductive measurement of the superconducting transition SRD 1000 W.A. Bosch, Hightech Development Leiden SRM 767 and SRM 768 devices made by the NIST (formerly NBS)

Superconducting Fixpoint Devices SRD 1000

Ir AuAl 2 AuIn 2 Cd

W Be Ir 80 Rh 20 Ir 92 Rh 08

Noise Thermometry

Johnson & Nyquist (1928) Thermal Fluctuations of the voltage across a conductor quantum corrections: can be neclegted since (T > 100 mk, f < 1 khz)

Current Noise Current noise if shorted Sensitivity of a current sensing DC SQUID < 1 pa/ Hz finite band width iwl: coil = one degree of freedom

Current Sensing Noise Thermometer first suggested by R.A. Webb, et al. JLTP 13, 383 (1973) C. Lusheret al., Meas. Sci. Technol. 12, 1-15 (2001) Gainesville 6.11.08-20

Current Noise Spectrum C. Lusheret al., Meas. Sci. Technol. 12, 1-15 (2001) Cut off at Temperature determination from plateau value Gainesville 6.11.08-21

Comparison to PLTS 2000 C. Lusher et al., Meas. Sci. Technol. 12, 1-15 (2001) 3 He melting curve thermometer (PTB) and calibrated resistance thermometers averaging per Point t meas = 160 s expected resolution 1% Gainesville 6.11.08-22

Performance at Ultralow Temperatures lowest noise power corresponds to: T = 300 µk C. Lusheret al., Meas. Sci. Technol. 12, 1-15 (2001)

Inductively Read Out Noise Thermometer Noise source : Gold cylinder 2 mm, purity > 99,999%, RRR = 110 Kupfer cylinder, 2,5 mm, purity > 99,999%, RRR = 1000

Frequency dependence Gold cylinder RRR = 110

Noise thermometer Fixpoint device t meas = 100 s Linear temperature dependence of the noise spectral power S ~ T Φ

Copper & Gold 5 mk 100 mk Deviations from expected linear Dependence smaller than 0,5 % Copper-Thermometer: RRR = 1000 Gold-Thermometer: RRR = 110

Gainesville 6.11.08-28 Commercial Product

Nuclear Orientation Thermometer example 60 Co nuclear spin I magnetic field: splitting into (2I+1) sublevels

Nuclear Orientation Thermometer

Coulomb Blockade Thermometer Conductance through an array of tunnel junctions

Coulomb Blockade Thermometer

Coulomb Blockade Thermometer canbeusedbetween50 mkand30 K

Secondary Thermometers Resistance Thermometer Susceptibility thermometers Thermo Couples Capacitance Thermometers Pt-NMR Thermometry and many more

Resistance Thermometry

AC Resistance Measurement

Pt 100 - Thermometers Useful down to about 20 K Industrial standard

Made specially for low temperature work Expensive Temperaturerange: 20 mkto300 K Ge Thermometer

Conduction Mechanism Variable Range Hopping

Carbon Thermometers Mass production -- cheap Easy tomake somewhat delicate to use

New Carbon Thermometers Little Demon of the Ohmite Manufacturing J Low Temp Phys (2010) 160: 246 253

RuO 2 -Thickfilm Thermometer Todays replacement of carbon resistors

Magnetic Susceptibility Materials: CMN Au:Er Pd:Fe

Inductance Measurement

CMN Cerium-Magnesium-Nitrate 140 Support en araldite Araldite M-M 0 [µh] 120 100 80 60 40 M 0 /[µh] = 99.575 ±0.006 C/[µH/K] = 1682.8 ±2 Θ/[mK] = 0.49 ±0.04 Bobine secondaire secondary coil primary coil Bobine primaire Pastilles de CMN & Ag CMN and silver powder pads Feuilles d'argent silver foils Raccord en araldite chargée loaded Araldite 20 copper Support en cuivre 0 10 100 1000 T[mK] Problems: Slow, because of bad thermal contact cannot beusedin vacuum crystalwaterisremoved not easy to thermally contact

Pd:Fe

Au:Er

Dielectric Capacity

Thermocouples Seebeck effect Set-up

Thermocouples

Pt-NMR-Thermometry