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Thermometry Th att L Low T Temperatures t Temperature p is a thermodynamic y property p p y of f state It can be defined by a reversible cycle, like a carnot cycle l 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 p like the triple p p point of water and interpolation p like Pt-100 resistance thermometry or gas thermometry ITS-90 0.65 K to 1358 K PLTS-2000 PLTS 2000 0 9 mK to 1358 K 0.9 ITS-90 Substance and its state Defining point in Kelvins (range) Defining point in degrees Celsius (range) Vapor‐pressure / temperature relation (0.65 to 3.2) of helium‐3 (by equation) (−272.50 to −269.95) Vapor‐pressure / temperature relation of helium‐4 below its ((1.25 to 2.1768)) lambda point (by equation) ((−271.90 to −270.9732)) Vapor‐pressure / temperature relation of helium‐4 above its (2.1768 to 5.0) lambda point (by equation) a bda po t (by equat o ) (−270.9732 to −268.15) Vapor‐pressure / temperature relation (3 to 5) of helium (by equation) (−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 Triple point 234 3156 234.3156 −38 38.8344 8344 Triple point of water 273.16 0.01 Melting point1 of gallium 302.9146 29.7646 Freezing point1 of Indium 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 1234.93 961 78 961.78 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 p like the triple p p point of water and interpolation p like Pt-100 resistance thermometry and gas thermometry ITS-90 0.65 K to 1358 K PLTS-2000 PLTS 2000 0 9 mK to 1358 K 0.9 PLTS 2000 PLTS-2000 3He – melting curve PLTS 2000 PLTS-2000 3He – melting curve Fixed points of the PLTS‐2000 Fixed points p/MPa T2000 /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 g N.O. Pt NMR CMN Coulomb Gap Coulomb Gap Au:Er superconducting fixed points 3He MC He vapor pressure carbon & Ge resistors rhodium-Iron resistors Pt resistors 100 µK 1 mK 10 mK 100 mK 1K 10 K 100 K Primary thermometers 3He – melting curve Superconducting fix point devices Noise thermometry Coulomb blockade thermometry y Nuclear Orientation thermometry G thermometry Gas h Vapor pressure thermometry Mößbauer effect thermometry Osmotic pressure thermometry Superconducting p g Fixpoint p Devices Inductive measurement of the superconducting transition SRD 1000 SRM 767 and SRM 768 devices made by the NIST (formerly NBS) Superconducting p g Fixpoint p Devices SRD 1000 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 D SQUID DC D < 1 pA/√Hz /√H Finite Band width iwL: coil = one degree of freedom Inductively Read Out Noise Thermometer Noise source : Gold cylinder y ∅ 2 mm,, p purity y > 99,999%, , , RRR = 110 Kupfer cylinder, ∅ 2,5 mm, purity > 99,999%, RRR = 1000 Grenoble 21.09.07 ‐ 20 Frequency dependence Gold cylinder RRR = 110 Noise thermometer – Fixpoint device tmeas = 100 s Linear temperature dependence of the noise spectral power SΦ ~ T Copper & Gold 5 mK Copper‐Thermometer: pp Gold‐Thermometer: 100 mK RRR = 1000 RRR = 110 Deviations from expected linear Dependence small than 0,5 % Nuclear Orientation Thermometer example 60Co nuclear spin p 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 can be used between 50 mK and 30 K Secondary Thermometers Resistance Thermometer Susceptibility thermometers Thermo Couples Capacitance p Thermometers Pt-NMR Thermometry and d many more Resistance Thermometry AC Resistance Measurement Pt 100 - Thermometers Useful down to about 20 K Industrial standard Ge Thermometer Made specially Made specially for low temperature work Expensive Temperature range : 20 mK to 300 K Conduction Mechanism Variable Range Hopping Carbon Thermometers Mass production ‐‐ cheap Easy to make somewhat delicate to use RuO2-Thickfilm Thickfilm Thermometer Todays replacement of carbon resistors Magnetic Susceptibility Materials: CMN Au:Er Pd:Fe Inductance Measurement CMN C i Cerium-Magnesium-Nitrate M i Nit t Support en Araldite araldite 140 120 M-M0 [µH] M 100 M0/[µH] = 99.575 C/[µH/K] = 1682.8 Θ/[mK] = 0.49 Bobine secondary secondaire ±0.006 ±2 ±0.04 Bobine primary primaire coil coil Pastilles de CMN & CMN and silver Ag powder pads 80 Feuilles silver d'argent 60 foils Raccord en loaded Araldite araldite chargée 40 Support en copper cuivre 20 0 10 100 1000 T[mK] Problems: Slow, because of bad thermal contact can not be not be used in vacuum in vacuum … crystal crystal water is removed not easy to thermally contact Pd:Fe Pd:F A :E Au:Er Dielectric Capacity Thermocouples Seebeck effect Set‐up Thermocouples Pt NMR Thermometry Pt-NMR-Thermometry Pt NMR Thermometry Pt-NMR-Thermometry
