Chapter IV Cryogenic Techniques: Generation and Measurement of Low Temperatures Chapter IV: Cryogenic Techniques Contents: 2013) - IV.1 Generation of Low Temperatures 2004 ( IV.1.1 Introduction IV.1.2 Expansion Machine Institut - IV.1.3 Regenerative Machine IV.1.4 Joule-Thomson Cooling Meißner - IV.1.5 Summary IV.1.6 Evaporation Cooling Walther © IV.1.7 Dilution Cooling IV.1.8 Pomeranchuk Cooling A. Marx , Marx, A. IV.1.9 Adiabatic Demagnetization and Gross IV.2 Thermometry R. IV.2.1 Introduction IV.2.2 Primary Thermometers IV.2.3 Secondary Thermometers Chapt. IV - 2 Chapter IV: Cryogenic Techniques Literature: 1. Tieftemperaturphysik 2013) - Enss, Hunklinger 2004 ( Springer (2000) Institut - 2. Matter and Methods at Low Temperatures F. Pobell Meißner - Springer, 2nd edition (1996) Walther © 3. Experimental Low-Temperature Physics Anthony Kent A. Marx , Marx, A. American Institute of Physics (1993) and Gross 4. Cryogenic Systems R. Randall F. Barron Oxford University Press, Oxford (1985) Chapt. IV - 3 IV.1 Generation of Low Temperatures IV.1.1 Introduction 9 10 center of hottest stars 108 center of the sun, nuclear energies 7 10 6 2013) - 10 5 2004 ( 10 electronic energies, chemical bonding 4 10 Institut - surface of sun, highest boiling temperatures 103 organic life Meißner 2 - background 10 liquid air temperature 1 Walther 10 liquid 4He © in universe 0 universe 10 (2.73 K) -1 electronic magnetism A. Marx , Marx, A. 10 and -2 temperature (K) temperature 10 Gross -3 3 superfluid He - R. 10 lowest temperature -4 10 superconductivity accessible in solids -5 10 nuclear (few µK) -6 magnetism 10 lowest temperatures of condensed matter 10-7 Chapt. IV - 4 IV.1 Generation of Low Temperatures IV.1.1 Introduction 2013) - low temperature record 2004 ( for nuclear spin system: Institut - • experimental setup Meißner according to Tauno Knuuttila (2000) - Walther • lowest temperature: about 100 pK © by demagnetization of Rhodium nuclei A. Marx , Marx, A. („temperature of nuclear spins“) and PhD Thesis, Gross Helsinki University of Technology R. (Espoo, Finland) • problem: spin temperature cannot be transferred to lattice of solid Chapt. IV - 5 IV.1 Generation of Low Temperatures IV.1.1 Introduction Generation of low temperatures by using cryo-liquids: 19th century: liquefaction of various gases by pressure except for “permanent gases” (O2, H2, He) 2013) - 1877: liquefaction of O2 by thermal expansion 2004 ( (L. Cailletet, C.R. Acad. Sci. Paris 85, 1213 (1877); R. Pictet, C.R. Acad. Sci. Paris 85, 1214 (1877)) 1884: liquefaction of H2 (precooling with liquid O2) Institut - (K. Olszewski, Ann. Phys. u. Chem. 31, 58 (1887)) 1898: significant amounts of lH for physical experiments Sir James Dewar, Meißner 2 - (1842-1923) (J. Dewar, Proc. R. Inst. Gt. Br. 15, 815 (1898)) Walther 1908: liquefaction of last “permanent gas” He by Kamerlingh Onnes © (H. Kammerlingh Onnes, Leiden Commun. 105, Proc. Roy. Acad. Sci. Amsterdam 11, 168 (1908)) 1922: Kammerlingh Onnes reaches T < 1K A. Marx , Marx, A. (H. Kammerlingh Onnes, Leiden Commun. 159, Trans. Faraday Soc. 18 (1922)) and 1926: adiabatic demagnetization of electron spins in Gross R. paramagnetic salts by Debye and independently (P. Debye, Ann. Phys. 81, 1154 (1926) 1927: by Giauque Heike Kammerlingh Onnes (W.F. Giauque, J. Am. Chem. Soc. 49, 1864 (1927) (1853 – 1926) since 1950th: 3He available Nobelpreis für Physik: 1913 3 He cryostat Peter J. Debye 3 4 He- He dilution refrigerator 1884 - 1966 Chapt. IV - 6 Low Temperature Technology in Germany 1861 study at Polytechnikum Zurich, teachers: Rudolf Clausius, Gustav Zeuner und Franz Reuleaux 1868 offer of chair at the Polytechnische Schule München (now TUM) 2013) - 1873 development of cooling machine allowing 2004 ( the temperature stabilization in beer Institut - brewing 21. 6. 1879 foundation of „Gesellschaft für Linde’s Meißner - Eismaschinen AG“ together with two Walther beer brewers and three other co-founders © 1892 - 1910 re-establishment of professorship A. Marx , Marx, A. 12.5.1903 and patent application: Gross R. „Lindesches Gegenstrom- verfahren“ liquefaction of oxygen (-182°C = 90 K) Carl Paul Gottfried von Linde * 11. Juni 1842 in Berndorf, Oberfranken † 16. November 1934 in Munich Chapt. IV - 7 R. Gross and A. Marx , © Walther-Meißner-Institut (2004 - 2013) IV.1.1 IV.1 Introduction Generation of Low Temperatures paramagnetic refrigeration paramagnetic Year nuclear demagnetization nuclear ultra-low temperatures low temperatures Chapt . IV - 9 IV.1 Generation of Low Temperatures IV.1.1 Introduction 2013) - temperature refrigeration technique available typical record 2004 ( range since Tmin Tmin Institut - Kelvin universe 2.73 K 4He evaporation 1908 1.3 K 0.7 K Meißner - 3He evaporation 1950 0.3 K 0.25 K Walther © Millikelvin 3He-4He dilution 1965 10 mK 2 mK Pomeranchuk cooling 1965 3 mK 2 mK A. Marx , Marx, A. and electron spin demagnetization 1934 3 mK 1 mK Gross R. Microkelvin nuclear spin demagnetization 1956 50 µK 100 pK Chapt. IV - 10 IV.1 Generation of Low Temperatures IV.1.1 Introduction cooling techniques: • expansion of an ideal gas 2013) - • expansion machine 2004 ( • regenerative machine Institut - work against outside world • expansion of a real gas Meißner - • Joule Thomson cooler Walther © work against internal interactions • evaporation of a real gas: A. Marx , Marx, A. and work against internal interactions Gross • dilution cooling (3He/4He) R. work against internal interactions • adiabatic demagnetization (electronic/nuclear moments) work against magnetic ordering Chapt. IV - 11 IV.1 Generation of Low Temperatures IV.1.1 Introduction 2013) - Liquefaction of gases three useful methods: 2004 ( Institut - 1. direct liquefaction by isothermal compression Meißner 2. letting the gas perform work against external forces at the expense of - Walther its internal energy © cooling and eventual liquefaction A. Marx , Marx, A. and 3. making the gas perform work against its own internal forces by Joule- Gross R. Kelvin or Joule-Thomson expansion cooling and eventual liquefaction Chapt. IV - 12 IV.1 Generation of Low Temperatures IV.1.1 Introduction direct liquefaction of gases by isothermal compression starting temperature must be smaller than critical temperature Tc 2013) p - melting curve 2004 ( solid Institut - liquid Meißner - boiling curve pc critical point Walther © triple point gas A. Marx , Marx, A. sublimation curve and T Tc Gross R. ammonia (NH3) 406 critical O2 154.5 temperatures Tc N2 126 in K of selected H2 33.2 liquid cryogens 4He 5.2 3He 3.32 Chapt. IV - 13 IV.1 Generation of Low Temperatures IV.1.1 Introduction p solid liquid 2013) - T , p T , p Cryogenic Liquids m m b b Tc , pc 1 at 2004 ( gas Ttr , ptr Institut - Tc T Meißner - Walther @ 1 bar © A. Marx , Marx, A. and Gross R. Chapt. IV - 14 IV.1 Generation of Low Temperatures IV.1.1 Introduction direct liquefaction of gases by expansion (Joule-Thomson-Effect) starting temperature must be smaller than inversion temperature 2013) - cryogen boiling liquefaction latent heat inversion 2004 ( point [K] [kJ/I] temp. [K] Institut - oxygen 90.2 1877: Cailletet and Pictet 240 762 Meißner - nitrogen 77.3 1883: Wroblewski and 160 625 Walther Olszewski © hydrogen 20.4 1898: Dewar 30 203 A. Marx , Marx, A. 4 and Helium 4.2 1908: Onnes 2.6 43.2 Gross 3 R. Helium 3.2 0.5 - • liquid oxygen and hydrogen have potential hazards • liquid nitrogen and 4He are the most widely used cryogens • liquid 3He is very expensive Chapt. IV - 15 IV.1 Generation of Low Temperatures IV.1.1 Introduction liquefaction of gases by performance of external work 2013) - 2004 ( Institut - Meißner - gas molecules are reflected at the moving piston-surface: Walther © incoming: laboratory system: 푣푀 A. Marx , Marx, A. piston system: 푣푀 − 푣퐾 and outgoing: piston system: − 푣푀 − 푣퐾 ′ Gross laboratory system: − 푣푀 − 푣퐾 + 푣퐾 = 2푣퐾 − 푣푀 = 푣푀 R. ′ i.e.: 푣푀 = 푣푀 − 2푣퐾 molecule is slower, i.e. colder average momentum transfer per time to piston = force, force · distance = work external work at the expense of internal energy cooling Chapt. IV - 16 IV.1 Generation of Low Temperatures IV.1.1 Introduction • Carnot process: - counterclockwise: heat pump (conversion of mechanical work into heat) - clockwise: heat engine (conversion of heat into mechanical work) 2013) - • pV diagram: 2004 ( expansion cooling: adiabats p 휅 dQ = 0 (adiabatic) (푝푉 = 푐표푛푠푡, 푑푄 = 0 Q12 Institut 1 - 푐푝 휅 = > 1) 퐶푉 Meißner - heat exchange: isotherms W41 2 T1 = const (푝푉 = 푐표푛푠푡, 푑푇 = 0) Walther (isothermic) © work per cycle: 4 W23 A. Marx , Marx, A. 푊 = ∮ 푝푑푉 = 퐚퐫퐞퐚 and dQ = 0 3 T2 = const Q34 Gross • efficiency: R. V W T thermodynamic definition of temperature Q T warm • Carnot process: technologically difficult to realize better: gas circulation, compressor and expansion machine are spatially separated Chapt. IV - 17 IV.1 Generation of Low Temperatures IV.1.2 Expansion Machine • medium: He gas Brayton method e.g. liquefaction of air: 2013) - - condensation on cold head 2004 ( - distillation in separation columns Institut N (77.4 K) cooling - 2 Ar (87.3 K) inert gas Meißner - O2 (90.2 K) welding Walther © (should not cause significant resistance • temperature reduction: for flowing gas e.g. A. Marx , Marx, A. concentric tubes) and Gross R. • efficiency: 휅 = 퐶푝/퐶푉 (= 5/3 for He) expansion from 100 bar to 1 bar results in T2 = 50 K T2 = 8 K can be reached in a 2 stage cycle Chapt. IV - 18 IV.1 Generation of Low Temperatures IV.1.1 Introduction • heat pumps: heating and refrigerating machines p - heat pump: 1 Q12 dQ = 0 2013) heat is generated by mechanical work - W 41 T = const 2004 1 - efficiency: ( 2 generated heat at T T1 Q1 Institut W - 4 23 h T = const performed work W dQ = 0 Q 3 2 Meißner 34 - V Walther © - ideal efficiency for reversible Carnot process: A. Marx , Marx, A. 1 T 1 hC 1 (increases with decreasing temperature difference T1 – T2) and C T1 T2 Gross R.