THERMOELECTRIC REFRIGERATION

Transcription

1 THERMOELECTRIC REFRIGERATION

2 THE INTERNATIONAL CRYOGENICS MONOGRAPH SERIES Volumes in preparation Very High Magnetic Fields Superconductivity for Engineers Cryogenic Laboratory Equipment Superconductivity in Elements, Alloys, and Compounds Specific Heats at Low Temperatures The Electrical Resistivity of Metals at Low Temperatures D. H. Parkinson and B. Mulhall I. L. Olsen and S. Gygax A. I. Croft and P. V. E. McClintock G. K. Gauze E. S. Raja Gopal G. T. Meaden

3 General Editors Dr. K. Mendelssohn, F.R.S. The Clarendon Laboratory Oxford, England Dr. K. D. Timmerhaus University of Colorado Boulder, Colorado THERMOELECTRIC REFRIGERATION H. J. Goldsmid, B.Sc., Ph.D., F.Inst.P. The General Electric Company Limited Wembley, England Springer Science+Business Media, LLC 1964

4 Library of Congress Catalog Card Number Springer Science+ Business Media New York Originally published by Plenum Press in Softcover reprint of the hardcover 1st edition 1964 ISBN ISBN (ebook) DOI /

5 PREFACE During the nineteen-fifties, while rapid progress was being made on the development of the alloys of bismuth telluride as thermoelectric materials, there were forecasts that Peltier cooling might replace the conventional methods of refrigeration. This state of affairs has not come about and is unlikely to do so in the future. In the last three or four years there have been virtually no improvements in the figures of merit of thermoelectric materials for use at ordinary temperatures. While there is hope that better figures of merit will result from solid state research, it is difficult to see how thermoelectric cooling units can ever be as efficient as compressor units when the required cooling capacity is large. Thus, we must regard thermoelectric refrigeration, not as a competitor of the conventional methods, but rather as a complementary technique. It is particularly important for small-scale applications, and it is obvious that its potentialities in this field have not yet been fully exploited. One of the objectives of this book is, therefore, to encourage the more widespread use of thermoelectric refrigeration, in the applications for which it is most suitable, through a proper understanding of its limitations as well as its advantageous features. I have attempted to cover the whole subject, from the physics of thermoelectric materials to the engineering of devices, at a level that is appropriate for the nonspecialist reader. In spite of the intensive basic research that has been carried out, there is still plenty of scope for the discovery of new and better compounds and alloys, especially for use at low temperatures. The scientist who wishes to undertake research in this field should find the book useful as an introduction to the fundamental principles. It is with a view primarily to future prospects that I have included a chapter on the thermomagnetic effects, since Ettingshausen cooling at low temperatures seems to show great promise. The engineer or technologist who is responsible for the development and application of cooling units should find all aspects of his work dealt with in the second half of the book. I have deliberately limited my discussion of the construction of cooling units and their uses so as to illustrate the basic principles rather than to provide an exhaustive catalogue. v

6 vi Preface I am very grateful to the members of the Heat Group at the Hirst Research Centre who have spent much of their time discussing the engineering of thermoelectric devices with me. In particular, I must mention Mr. L. J. C. Connell, Mr. P. B. Curtis, and Mr. R. W. Dudding, as well as Mr. D. H. Bridges of the Patent Department of the General Electric Company Ltd. My own work on the physics of the subject has been stimulated by Prof. R. W. Douglas, Prof. D. A. Wright, Dr. J. R. Drabble, Mr. R. T. Delves, and many other members of the Solid Physics Group of these Laboratories. Finally, I wish to thank Dr. J. H. Ashby and Mr. A. W. Penn of De La Rue Frigistor Ltd. for their most helpful comments on the manuscript. The General Electric Company Ltd. Hirst Research Centre Wembley, Middlesex England March 1964 H. J. GOLDSMID

7 CONTENTS Chapter 1 Basic Principles 1.1. The Thermoelectric Effects Simple Theory of Thermoelectric Refrigeration Chapter 2 Transport Processes in Metals and Semiconductors 2.1. The Crystal Lattice Chemical Bonds Lattice Vibrations Heat Conduction by the Lattice Electrons and Holes The Free Electron Theory of Metals Energy Bands Insulators, Semiconductors, and Metals Scattering of the Charge Carriers Transport in a Single Band General Expressions for the Thermoelectric Parameters Nondegenerate Semiconductors Degenerate Conductors Bipolar Effects Chapter 3 Selection of Materials 3.1. Metals Prediction and Optimisation of the Figure of Merit Extrinsic Semiconductors-Classical Statistics Extrinsic Semiconductors-Fermi-Dirac Statistics Mixed and Intrinsic Semiconductors 53 vii

8 viii Contents 3.3. Factors Relating to the Choice of Semiconductor Mobility and Effective Mass Lattice Scattering Scattering by Static hnperfections Complex Band Structures Lattice Thermal Conductivity Pure Elements and Compounds Semiconductor Alloys Thermoelectric Cooling at Low Temperatures Temperature Dependence of the Figure of Merit The Phonon-Drag Effect Chapter 4 Effects in a Magnetic Field 4.1. The Thermomagnetic Effects The Thermomagnetic Figure of Merit Thermomagnetic Cooling Using Extrinsic Semiconductors Thermomagnetic Cooling Using Intrinsic Semiconductors and Semimetals Thermoelectric Refrigeration in a Magnetic Field Chapter 5 Properties and Performance of Specific Materials 5.1. Bismuth Telluride and Its Alloys General Properties of Bismuth Telluride Band Structure of Bismuth Telluride Electrical and Thermal Properties of Bismuth Telluride Electrical Conductivity Hall Coefficient Seebeck Coefficient Thermal Conductivity Figure of Merit Bismuth Telluride Alloys Band Structure Electrical and Thermal Properties Figure of Merit

9 Contents ix 5.2. Bismuth-Antimony Alloys Band Structure and Thermoelectric Properties of Bismuth and Antimony Thermoelectric Properties of Bismuth- Antimony Alloys Thermomagnetic Effects in Bismuth- Antimony Alloys Lead Telluride and Related Compounds and Alloys The IV-VI Compounds Silver Antimony Telluride Alloys Based on the IV-VI Compounds An Upper Limit to the Thermoelectric Figure of Merit Chapter 6 Measurement of Thermoelectric Parameters 6.1. Seebeck Coefficient Electrical Conductivity Thermal Conductivity Static Methods Dynamic Methods Direct Measurement of the Figure of Merit Simple Theory of the Corrections Experimental Arrangement Measurement of the Thermomagnetic Effects Chapter 7 Design Theory 7.1. Multistage Thermoelectric Units Thermomagnetic Cascades Temperature-Dependent Thermoelectric Parameters Simple Treatment of the Thomson Effect Precise Calculation of the Coefficient of Performance with Temperature- Dependent Parameters Design of an Ideal Cooling Unit Nonideal Thermoelectric Cooling Units Contact Resistance Thermal Resistance Between the Cooling Unit and the Source and Sink

10 X Contents 7.6. Nonsteady Currents Effect of Current Ripple Transient Behaviour Chapter 8 Chapter 9 Appendixes References Preparation of Thermoelements and Construction of Cooling Units 8.1. Tolerance on the Properties of Thermoelements Spread of Electrical Conductivity about the Optimum Value Departure of the Mean Conductivity from the Optimum Value Tolerance on the Dimensions Methods of Preparation Directional Freezing and Zone Melting Crystal Pulling Sintered Thermoelements Cutting and Tinning Construction of Cooling Units Heat Transfer to and from Cooling Units Applications of Thermoelectric Refrigeration 9.1. Control of Temperature Cooling of Instruments and Electronic Equipment Medical and Biological Applications Air Conditioning... A. Table of Fermi-Dirac Integrals.... B. Effect of Small Changes in the Figure of Merit on the Coefficient of Performance.... C. Circuit for the Thermoelectric Temperature Controller.... D. List of Symbols Subject Index