The Art of Cryogenics This page intentionally left blank The Art of Cryogenics Low-Temperature Experimental Techniques Guglielmo Ventura and Lara Risegari Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Elsevier Linacre House, Jordan Hill, Oxford OX2 8DP, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA First edition 2008 Copyright © 2008 Elsevier Ltd. All rights reserved The right of Guglielmo Ventura and Lara Risegari to be identified as the authors of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-08-044479-6 For information on all Elsevier publications visit our web site at books.elsevier.com Printed and bound in Great Britain 0708091010987654321 Working together to grow libraries in developing countries www.elsevier.com | www.bookaid.org | www.sabre.org Contents Preface xiii PART I 1 1 Vacuum Techniques 3 1.1 Introduction 3 1.2 Vapour pressure 5 1.3 Mean free path and viscosity 6 1.4 Gas flow 7 1.4.1 Conductance of an orifice and of a pipe for molecular flow 9 1.4.2 Conductance of an orifice and of a pipe for viscous flow 10 1.5 Evacuation of a lumped volume 11 1.6 Vacuum pumps 12 1.6.1 Rotary vane oil-sealed mechanical pump 13 1.6.2 Booster pumps 14 1.6.3 Scroll pumps 15 1.6.4 Sorption pumps 17 1.6.5 Oil diffusion pumps 17 1.6.6 Turbomolecular pumps 20 1.6.7 Molecular drag pumps 22 1.7 Other vacuum components 23 1.8 Pressure gages 26 1.8.1 Total-pressure gages 26 1.8.2 McLeod gage 27 1.8.3 Bourdon gage 28 1.8.4 Diaphragm gage 28 1.8.5 Thermal conductivity gages 29 1.8.6 Hot cathode ionization gage 29 1.8.7 Cold cathode gage 31 1.9 Measurement of partial pressures 32 1.9.1 Leak detectors 32 References 33 v vi Contents PART II 35 2 Cryoliquids 37 2.1 Cryogenics: Introduction and history 37 2.2 Cryoliquids 40 2.2.1 Liquid oxygen and hydrogen 40 2.2.2 Liquid nitrogen 42 2.2.3 Liquid helium 43 2.2.4 Helium physics properties 45 2.2.4.1 Helium vapour pressure and latent heat of evaporation 45 2.2.4.2 Helium specific heat 47 2.2.4.3 Transport properties of liquid 4He: thermal conductivity and viscosity 51 References 53 3 Properties of Solids at Low Temperature 55 3.1 Introduction 55 3.2 Specific heat 56 3.3 Lattice specific heat 56 3.4 Electronic specific heat 58 3.5 Electronic specific heat in superconducting materials 59 3.6 Magnetic specific heat 62 3.7 Specific heat due to the amorphous state 66 3.8 Data of specific heat 69 3.9 Thermal expansion 71 3.10 Thermal conductivity 73 3.10.1 Phonons 75 3.10.2 Electron thermal conductivity 77 3.11 Superconducting metals 80 3.12 Data of low-temperature thermal conductivity 81 3.13 The Wiedemann–Franz law 83 References 84 4 Heat Transfer and Thermal Isolation 89 4.1 Introduction 89 4.2 Selection of materials of appropriate thermal conductivity 89 4.3 Heat switches 91 4.3.1 Gas heat switches 91 4.3.2 Superconducting heat switches 92 4.3.3 Other heat switches 93 4.4 Contact thermal resistance 94 References 100 Contents vii PART III 103 5 Cooling Down to 0.3K 105 5.1 Introduction 106 5.2 Transport and storage vessels 106 5.3 Liquid 4He in the cryostats 107 5.3.1 Cool-down period 108 5.3.2 Constant temperature period 108 5.3.2.1 Heat conduction 108 5.3.2.2 Heat radiation 108 5.3.2.3 Conduction by gas particles 110 5.3.2.4 Thermoacoustic oscillations 111 5.4 4He cryostats 111 5.4.1 Cryostats for T>42 K 111 5.4.2 Cryostats for 13K<T<42 K 112 5.5 3He cryostats 114 5.5.1 3He refrigerator with internal pump 115 5.6 Accessories 117 5.6.1 N2 transfer tubes 117 5.6.2 4He transfer tubes 117 5.6.3 Liquid-level detectors 119 5.7 Mechanical refrigerators 120 5.7.1 Introduction 120 5.7.2 Coolers using counterflow heat exchangers 121 5.7.2.1 Pressure drop 121 5.7.2.2 Heat transfer 121 5.7.2.3 Efficiency and length 122 5.7.2.4 Construction 123 5.7.2.5 Other liquefier details 124 5.7.3 The Collins helium liquefier 125 5.7.4 Klimenko cycle 125 5.7.5 Coolers using turbo-expanders 126 5.7.6 Brayton cycle 127 5.7.7 Coolers using regenerative heat exchangers 128 5.7.8 Philips Stirling cycle 128 5.7.9 Gifford–McMahon 130 5.8 Pulse tube refrigerators 131 5.8.1 Introduction 131 5.8.2 Two compression methods for the PTR 133 5.8.3 Simplified operation principle of PTRs 135 5.8.4 Cooling power 137 5.8.5 Multistage PTRs 139 References 139 viii Contents 6 Dilution Refrigerators 143 6.1 Introduction 143 6.2 Properties of 3He–4He liquid mixture 144 6.3 The classic DR 147 6.4 The J–T DR 153 6.5 Practical operations with a DR 156 6.6 DR in high magnetic fields 157 6.7 Dry DR 158 6.8 No-gravity dilution 158 References 160 7 Other Refrigerators 163 7.1 Introduction 163 7.2 Pomeranchuck refrigerator 163 7.2.1 The strange behaviour of 3He 164 7.3 Adiabatic demagnetization refrigerator 167 7.4 Adiabatic nuclear demagnetization 169 7.5 Electronic refrigeration 170 References 170 PART IV 173 8 Temperature Scales and Temperature Fixed Points 175 8.1 Introduction 175 8.2 Reference fixed points 176 8.3 The ITS 90 178 8.4 The provisional Low-Temperature Scale 2000 181 8.5 NBS-SRM 767a, 768 and SRD 1000 fixed point devices 184 8.6 APPENDIX: Superconductive transitions and influence of purity and magnetic fields 187 References 190 9 Low-Temperature Thermometry 193 9.1 Introduction 193 9.2 Gas thermometry 194 9.2.1 Constant volume gas thermometry 195 9.2.2 Acoustic gas thermometry 196 9.2.3 Dielectric constant gas thermometry 197 9.3 Vapour pressure thermometry 198 9.4 3He melting curve thermometry 199 9.5 Thermocouples 200 Contents ix 9.6 Resistance thermometry 202 9.6.1 Metal thermistors 202 9.6.2 Semiconductors, carbon and metal oxide thermistors 203 9.6.2.1 Doped germanium resistors 204 9.6.2.2 Carbon resistors 205 9.6.2.3 Thick-film RuO2 resistors 206 9.6.2.4 Zirconium oxinitride 207 9.6.2.5 Junction diodes 208 9.6.3 Traps in resistance thermometry 208 9.7 Noise thermometry 211 9.8 Dielectric constant thermometry 212 9.9 Paramagnetic salt thermometry 215 9.10 Nuclear orientation thermometry 216 9.11 Magnetic thermometry with nuclear paramagnets 219 9.12 Coulomb blockade thermometry 219 References 221 10 Instrumentation for Cryogenics 225 10.1 Magnets 225 10.1.1 Superconducting magnets 225 10.1.2 Magnet wires 226 10.1.3 Magnet specifications 226 10.1.4 Persistent mode 227 10.1.5 Power supplies for magnets 228 10.2 Radio frequency shielding and filtering 228 10.2.1 Electric and magnetic fields 228 10.2.2 Superconducting shields 229 10.2.3 Electromagnetic interference filtering 229 10.3 Bridges 231 10.4 The synchronous demodulator (lock-in) 232 10.5 Temperature control 237 10.6 Low-noise cold amplifiers 238 References 240 PART V 243 11 Measurement of the Properties of Solids at Low Temperature 245 11.1 Introduction 245 11.2 Measurement of the thermal conductivity 246 11.3 Measurement of the thermal conductivity of A6061-T6 and A1050 between 4.2 and 77 K 249 11.3.1 Introduction 249 11.3.2 Experiment and results 249 x Contents 11.4 Thermal conductivity of copper at very low temperatures 252 11.4.1 Introduction 252 11.4.2 Experiment 253 11.4.3 Results 255 11.5 Measurement of the thermal conductivity of Torlon 257 11.5.1 Introduction 257 11.5.2 Thermal conductivity of Torlon 4203 in the 0.08–5 K temperature range 257 11.5.3 Thermal conductivity of Torlon 4203 between 4.2 and 300 K 259 11.5.3.1 Comparison among the power passing through the sample and the spurious power contributions 263 11.5.3.2 Thermal contacts to the sample 263 11.5.3.3 Error budget 264 References 264 12 Measurements of Heat Capacity 267 12.1 Introduction 267 12.2 Measurement methods 268 12.2.1 Heat pulse technique 268 12.2.2 AC calorimetry 270 12.2.3 Time constant (relaxation) method 270 12.2.4 Dual slope method 270 12.2.5 Thermal bath modulation 271 12.2.6 Measurement constrains 271 12.3 Example of ‘classical’ set up for the measurement of heat capacities 271 12.4 Heat capacity of a TeO2 single crystal between 0.06 and 0.28 K 272 12.4.1 Thermal conductance of the sample to the thermal bath 274 12.4.2 Measurement of the heat capacity 275 12.4.3 Results 276 12.5 Measurement of the specific heat of Torlon between 0.15 and 4.2 K 277 12.5.1 Experimental technique 277 12.5.2 Results 279 12.5.3 Discussion 280 12.6 Measurement of heat capacity of NTD Ge thermistors 282 12.6.1 Introduction 282 12.6.2 NTD process and realization of thermistors 282 12.6.3 Experimental technique 283 12.6.4 Results 284 12.6.5 Discussion 285 References 287 Contents xi 13 Measurements of Thermal Expansion 289 13.1 Introduction 289 13.2 A simple interferometric dilatometer 290 13.3 Thermal expansion of Torlon between 4.2 and 295 K 292 References 295 PART VI 297 14 Practical, Industrial and Space Applications