Thermometry at Low and Ultra-low Temperatures
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1 Thermometry at Low and Ultra-low Temperatures
2 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
3 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
4 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 K to 1358 K PLTS mk to 1358 K
5 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) ( to ) (1.25 to ) ( to ) ( to 5.0) ( to ) Vapor-pressure / temperature relation of helium (by equation) (3 to 5) ( to ) Triple point of hydrogen Triple point of neon Triple point of oxygen Triple point of argon Triple point of mercury Triple point of water Meltingpoint 1 ofgallium Freezingpoint 1 ofindium Freezing point of tin Freezing point of zinc Freezing point of aluminum Freezing point of silver Freezing point of gold Freezing point of copper
6 Difference between ITS-90 and ITS-68
7 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 K to 1358 K PLTS mk to 1358 K
8 PLTS He melting curve
9 PLTS He melting curve
10 Fixed points of the PLTS-2000 Fixed points p/mpa T 2000 /mk Minimum A A-B Néel
11 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
12 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
13 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)
14 Superconducting Fixpoint Devices SRD 1000
15 Ir AuAl 2 AuIn 2 Cd
16 W Be Ir 80 Rh 20 Ir 92 Rh 08
17 Noise Thermometry
18 Johnson & Nyquist (1928) Thermal Fluctuations of the voltage across a conductor quantum corrections: can be neclegted since (T > 100 mk, f < 1 khz)
19 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
20 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
21 Current Noise Spectrum C. Lusheret al., Meas. Sci. Technol. 12, 1-15 (2001) Cut off at Temperature determination from plateau value Gainesville
22 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
23 Performance at Ultralow Temperatures lowest noise power corresponds to: T = 300 µk C. Lusheret al., Meas. Sci. Technol. 12, 1-15 (2001)
24 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
25 Frequency dependence Gold cylinder RRR = 110
26 Noise thermometer Fixpoint device t meas = 100 s Linear temperature dependence of the noise spectral power S ~ T Φ
27 Copper & Gold 5 mk 100 mk Deviations from expected linear Dependence smaller than 0,5 % Copper-Thermometer: RRR = 1000 Gold-Thermometer: RRR = 110
28 Gainesville Commercial Product
29 Nuclear Orientation Thermometer example 60 Co nuclear spin I magnetic field: splitting into (2I+1) sublevels
30 Nuclear Orientation Thermometer
31 Coulomb Blockade Thermometer Conductance through an array of tunnel junctions
32 Coulomb Blockade Thermometer
33 Coulomb Blockade Thermometer canbeusedbetween50 mkand30 K
34 Secondary Thermometers Resistance Thermometer Susceptibility thermometers Thermo Couples Capacitance Thermometers Pt-NMR Thermometry and many more
35 Resistance Thermometry
36 AC Resistance Measurement
37 Pt Thermometers Useful down to about 20 K Industrial standard
38 Made specially for low temperature work Expensive Temperaturerange: 20 mkto300 K Ge Thermometer
39 Conduction Mechanism Variable Range Hopping
40 Carbon Thermometers Mass production -- cheap Easy tomake somewhat delicate to use
41 New Carbon Thermometers Little Demon of the Ohmite Manufacturing J Low Temp Phys (2010) 160:
42 RuO 2 -Thickfilm Thermometer Todays replacement of carbon resistors
43 Magnetic Susceptibility Materials: CMN Au:Er Pd:Fe
44 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.](/docs-images/90/103514911/images/45-0.jpg "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")
45 CMN Cerium-Magnesium-Nitrate 140 Support en araldite Araldite M-M 0 [µh] M 0 /[µh] = ±0.006 C/[µH/K] = ±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 T[mK] Problems: Slow, because of bad thermal contact cannot beusedin vacuum crystalwaterisremoved not easy to thermally contact
46 Pd:Fe
47 Au:Er
48 Dielectric Capacity
49 Thermocouples Seebeck effect Set-up
50 Thermocouples
51 Pt-NMR-Thermometry
52 Pt-NMR-Thermometry
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