CINDAS Data Series on Material Properties Volume 1-2

SPECIFIC HEAT OF SOLIDS Edited by

С Y. Ho Director, Center for Information and Numerical Data Analysis and Synthesis

Purdue University

Authored by

Ared Cezairliyan

Senior Author and Volume Coordinator

and

A. C. Anderson, D. W. Bonnell, С R. Brooks, M. G. Chasanov, D. A. Ditmars, D. F. Fischer, R. K. Kirby, Ya. A. Kraftmakher, L. Leibowitz, С Loriers-Susse,

J. L. Margrave, D. L. Martin, A. P. Müller, R. L. Montgomery, S. C. Mraw, E. E, Stansbury, B. Stephenson, P. C. Sundareswaran, and E. F. Westrum, Jr.

О HEMISPHERE PUBLISHING CORPORATION

A member of the Taylor & Francis Group

New York Washington Philadelphia London

Contents

Foreword to the Series, David R. Lide, Jr. xix

Preface to the Series, Y. S. Touloukian xxi

Introduction xxiii

Chapter 1. Theory of Specific Heat of Solids 1 : J

1.1. Introduction 1

1.1.1., Definition of Specific Heat 2 1.1.2. Relation of Specific Heat to Other Thermodynamic

Quantities 3 1.1.3. Historical Background 6

1.2. Lattice Specific Heat 7

1.2.1. The Einstein Model 8 1.2.2. The Debye Model 10 1.2.3. Theory of Harmonic Lattice Dynamics 16

1.2.3.1. Dynamics of a One-Dimensional Diatomic Lattice 16

1.2.3.2. Dynamics of a Three-Dimensional Lattice 18

1.2.4. Determination of Phonon Dispersion Relations 22 1.2.5. Calculation of Vibrational Frequency Spectra 24 1.2.6. Thermodynamic Properties in the Harmonic

Approximation 25 1.2.7. Thermodynamic Properties of Lattice Vibrations in

Anharmonic Crystals 28

1.2.7.1. Quasiharmonic and Explicitly Anharmonic Contributions 28

1.2.7.2. Total (Harmonic Plus Anharmonic)

Contribution 31

1.2.8. Contribution of Lattice Vacancies 32

1.3. Electronic Specific Heat 34

1.3.1. Statistics of an Electron Fermi Gas 34 1.3.2. Specific Heat of Electrons in Normal Metals 35

1.3.2.1. The Free Electron Model 36 1.3.2.2. Experimental Specific Heat at Low

Temperatures 38 1.3.2.3. The Effect of Electron Band Structure and

Many-Body Enhancement 40

vii

CONTENTS

1.3.2.4. The Rigid-Band Model 43 1.3.3. Specific Heat of Superconductors 44

1.3.3.1. Specific Heat According to Classical Thermodynamics 44

1.3.3.2. Thermodynamic Properties According to BCS Theory 48

1.3.3.3. Specific Heat of Type II Superconductors 50 1.4. Magnetic Specific Heat 52

1.4.1. Spin-Wave Specific Heat 53 1.4.1.1. Ferromagnetic and Ferrimagnetic Systems 57 1.4.1.2. Antiferromagnetic Systems 58

1.4.2. Specific Heat in the Critical Temperature Region 60 1.4.2.1. Approximate Methods: The Weiss Molecular

Field Model 61 1.4.2.2. Statistical Methods: The Heisenberg and

Ising Models 63 1.4.3. The Schottky Anomaly 64

1.4.3.1. Schottky Specific Heat in Paramagnetic Systems 67

1.4.3.2. Nuclear Specific Heat 68 1.4.4. Other Magnetic Contributions to Specific Heat 69

1.4.4.1. Spin Fluctuations 69 1.4.4.2. The Kondo or Single-Impurity Effect 70 1.4.4.3. The Spin-Glass Effect 70

1.5. Summary 71 1.6. Appendix: Estimation and Correlation of Specific Heat 72

1.6.1. Specific Heat at Low Temperatures 76 1.6.2. Specific Heat at Moderate Temperatures 77 1.6.3. Specific Heat at High Temperatures 80

1.7. References 82

Chapter 2. Calorimetry Below 1 К 91

2.1. Introduction 91 2.2. Problems Encountered in the Temperature Range 0.01-1 К 92

2.2.1. Refrigeration 92 2.2.2. Temperature Scale and Standards 92 2.2.3. Thermometry 93 2.2.4. Thermal Isolation 94 2.2.5. Thermal Contact 95 2.2.6. Application of Heat 95 2.2.7. Sample Characteristics 96

2.3. Calorimetric Technique 97 2.3.1. Adiabatic Calorimetry 97 2.3.2. Continuous-Heating Calorimetry 101 2.3.3. Transient Calorimetry 102 2.3.4. a.c. Calorimetry 106

CONTENTS

2.3.5. Miscellaneous Examples of Low-Temperature Calorimetry 108

2.4. Summary 109 2.5. Acknowledgement 109 2.6. References 110

Chapter 3. Calorimetry in the Range 0 . 3 - 3 0 К 113

3.1. Introduction 113 3.2. Cryostats 114

3.2.1. Location of Cryostat 114 3.2.1.1. Minimization of Vibrational Heating 114 3.2.1.2. Minimization of Radio-Frequency Heating 114

3.2.2. Refrigerants Used in Cryostat 115 3.2.3. Cryostat Design 115 3.2.4. Cryostat Construction 116

3.3. Thermometry 116 3.3.1. Review of Temperature Scales in the Range

0.3-30 К 116 3.3.2. Conversion Between Temperature Scales 117 3.3.3. Secondary Thermometers 117 3.3.4. Thermometer Calibration Points 118

3.3.4.1. Vapor Pressure Thermometry 118 3.3.4.2. Superconducting Transition Points 119

3.3.5. Thermometer Calibration 119 3.3.6. Measuring Thermometer Resistance 120 3.3.7. Checking or Extrapolating a Thermometer Calibration

Using Specific Heat Measurements 120 3.3.8. Note on Thermocouples 120

3.4. Calorimeter Design 121 3.4.1. Thermal Contact Between the Sample and Calorimeter 121

3.4.1.1. The 'Tray' Technique 122 3.4.1.2. The 'Copper Stud' Technique 122 3.4.1.3. The 'Differential Contraction' Technique 122 3.4.1.4. The 'Differential Expansion' Technique 122 3.4.1.5. The 'Clamp' Technique 123 3.4.1.6. The 'Spring Loaded Foot' Technique 123 3.4.1.7. The'Plug'Technique 123 3.4.1.8. The 'Loose Powder' Technique 123 3.4.1.9. Compressed Powder Techniques 123 3.4.1.10. The Heat Exchange Medium Technique 123

3.4.2. Calorimeter Thermometer 124 3.4.3. Calorimeter Heater 124 3.4.4. Thermal Isolation of the Calorimeter 125

3.4.4.1. Radiation 125 3.4.4.2. High Vacuum 125 3.4.4.3. Conduction 126

3.4.5. Cooling the Calorimeter. Thermal Switches 126

CONTENTS

3.4.5.1. To Rely on Thermal Conduction Through Leads 126

3.4.5.2. To Use a Vapor Pressure 'Pot' on the Calorimeter 126

3.4.5.3. Mechanical Heat Switch 126 3.4.5.4. Superconducting Heat Switch 127

3.4.6. Checking the Thermometer Calibration 'In Situ' 127 3.4.7. Checking the Calorimeter Operation. Standard Sample 128 3.4.8. Note on Differential Calorimeters 128 3.4.9. Note on Measuring Condensed Gases 129 3.4.10. Note on Measurements at High Pressure 129 3.4.11. Note on Measurements in Magnetic Field 130 3.4.12. Heat Capacity of Materials Used in Calorimeter

Construction 130 3.5. Isoperibol Calorimeters 131 3.6. Adiabatic Calorimeters 132 3.7. Continuous Heating Calorimeters 133 3.8. Novel Techniques 133

3.8.1. 'Traditional' Methods Adapted for Small Sample 134 3.8.2. Steady-State a.c. Temperature Calorimetry 134 3.8.3. Temperature Wave Method 134 3.8.4. Diffuse Temperature Pulse Method (sometimes called

Heat Pulse Technique) 135 3.8.5. Temperature Relaxation Methods 135 3.8.6. Resistive SQUID Calorimetry 135 3.8.7. Differential Calorimetry with Small Samples 136 3.8.8. Novel Techniques with Larger Samples 136

3.8.8.1. Large Sample Weakly Coupled to Heat Sink 136 3.8.8.2. Cooling Curve Method 137

3.9. Special Situations 137 3.9.1. Short Time-Scale Experiments 137 3.9.2. Annealing Experiments 137 3.9.3. Thin Film Experiments 137 3.9.4. Small Particle Experiments 138 3.9.5. Experiments on Radioactive Materials 138

3.10. Automated Calorimetry in the 0.3-30 К Temperature Range 139 3.10.1. The Development of Automation 139 3.10.2. Self-Balancing Instruments 139 3.10.3. Some General Considerations 140 3.10.4. Some Typical Systems 140

3.10.4.1. 'Off-Line' Systems 141 3.10.4.2. 'On-Line' Systems 141 3.10.4.3. 'On-Line' Systems for 'Novel'

Techniques 141 3.11. Analysis of Data. Accuracy 141

3.11.1. Reduction of Observations to Molar Specific Heat 141 3.11.2. The Various Contributions to Specific Heat 142

3.11.2.1. Lattice Specific Heat 142 3.11.2.2. Electronic Specific Heat 143 3.11.2.3. Nuclear Specific Heat 143

CONTENTS

3.12.

3.11.2.4. Magnetic Specific Heat 3.11.2.5. Superconducting Transition 3.11.2.6. Impurities

3.11.3. Analysis and Presentation of Results 3.11.4. Accuracy References

143 144 144 144 145 146

Chapter 4. Calorimetry in the Range 5 - 3 0 0 К 153

4.1. 4.2.

4.3.

4.4.

4.5. 4.6. 4.7.

4.8.

Introduction Cryostat Design 4.2.1. Immersion or Not ?

4.2.2. 4.2.3.

4.2.1.1. Immersion in a Refrigerant Bath 4.2.1.2. Aneroid-Type Cryostat Cooling and/or Quenching Adiabatic Technique 4.2.3.1. Aneroid-Type Adiabatic Cryostat 4.2.3.2. Immersion-Type Adiabatic Cryostat 4.2.3.3. Combination Immersion-Aneroid-Type

Adiabatic Cryostat 4.2.3.4. Filling-Tube-Type Cryostat 4.2.3.5. Control of Heat Exchange with the

Calorimeter 4.2.4. Isoperibol Technique

4.2.4.1 Typical Isoperibol Cryostats Calorimeter Design 4.3.1. General Considerations 4.3.2. Calorimeter with Internal Thermometer and Heater 4.3.3. Calorimeter with Thermometer-Heater on Outer

Surface Calorimeter for Liquids and Condensable Gases Special Calorimeters Calculations Involved in Calorimetric Operation

Thermometry and Temperature Scales 4.4.1. Thermometric Sensors 4.4.2. Thermometer Calibration and Thermometric Scales 4.4.3. Temperature Calibration and Thermometric Scales

4.4.3.1. Special Thermometers 4.4.3.2. Thermocouples and Thermels

The Trend Toward Automation in Data Acquisition The Trend Toward Smaller Samples Measurement Techniques and Adjuvant Circuitry 4.7.1. Energy Circuitry A .1.2. Resistance Thermometry Circuitry 4.7.3. Adiabatic Jacket Control Circuitry Special Techniques 4.8.1. Inverse Temperature Drop-Calorimetry 4.8.2. Calorimetry at High Pressures

4.3.4 4.3.5 4.3.6

153 154 155 155 156 156 157 157 160

160 160

161 163 164 165 165 165

167 167 168 168 169 169 169 170 170 170 170 171 172 172 173 173 174 175 175

CONTENTS

4.8.3. Calorimetry in Magnetic Fields 175 4.8.4. Calorimetry by the Thermal Relaxation Method 175 4.8.5. Laser-Flash Calorimetry 176 4.8.6. High-Resolution Heat Capacity Calorimeter 111 4.8.7. Flow Calorimetry 178

4.9. Transitions—Phase and Otherwise 178 4.10. Reference Standards for Thermophysical Calorimetry 178 4.11. Procedures for Data Handling and Presentation 179

4.11.1 Calculation of Cp ° and Other Thermophysical Properties 179 4.11.1.1. General Principles 179 4.11.1.2. Derived Quantities 180

4.11.2. The Extrapolation to Zero Kelvin 180 4.11.2.1. Conduction Electron and Debye

Contributions 180 4.11.2.2. The Zero Point Entropy 181

4.11.3. Other Matters of Calculational Relevance 181 4.11.3.1. Routine Details 181 4.11.3.2. Errors Associated with Thermophysical

Data 181 4.11.3.3. The Lattice Heat Capacity 183

4.12. Comparison of DSC and Adiabatic Approaches 183 4.13. Concluding Remarks 185 4.14. Acknowledgement 185 4.15. References 185

Chapter 5. Adiabatic Calorimetry Above 300 К 191

5.1. 5.2.

5.3.

5.4.

5.5.

5.6.

Introduction 191 The Principle of Adiabatic Calorimetry 192 5.2.1. Continuous Heating 192 5.2.2. Discontinuous Heating 194 5.2.3. Nonadiabatic Conditions 194 General Design and Operation 194 5.3.1. Design 195 5.3.2. Operation—Continuous Heating 196 5.3.3. Operation—Discontinuous Heating 197 Adiabatic Shield and Calorimeter Cell and Sample Design 198 5.4.1. Radiation Shields 198 5.4.2. Conduction Shields 203 5.4.3. Sample and Cell Heater Design 206 Temperature Measurements in High-Temperature Calorimetry 210 5.5.1. Resistance Thermometry 211 5.5.2. Thermocouple Thermometry 213 5.5.3. Thermocouple Errors 214 5.5.4. Factors Governing the Use of Thermocouples in

High-Temperature Adiabatic Calorimetry 220 Corrections to the Measured Specific Heat 221

CONTENTS XIII

5.6.1. Correction for the Sample Heater 222 5.6.2. Correction for Heat Leakage from the

Sample—Continuous Heating 223 5.6.3. Corrections for Heat Leakage from the

Sample—Discontinuous Heating 228 5.6.4. Corrections Using a Cell 229

229 230 232 232 234 237 237 237 238 239

Chapter 6. Drop Calorimetry Above 300 К 243

5.7.

5.8. 5.9.

5.10. 5.11. 5.12. 5.13.

Errors and Accuracy of Specific Heat Measurements 5.7.1. Systematic Errors 5.7.2. Random Errors 5.7.3. Accuracy of Specific Heat Measurements Computer Operation of Calorimeters Survey of Adiabatic Calorimeters Closure Acknowledgements Bibliography References

6.1. 6.2.

6.3.

6.4. 6.5.

Chapter 7.

Introduction Fundamental Concepts and Relationships in Drop Calorimetry 6.2.1. Ideal Drop-Calorimetric Experiment 6.2.2. Real Drop-Calorimetric Experiment; Some Error

Sources 6.2.2.1. Sample 6.2.2.2. Sample Temperature 6.2.2.3. Sample Heat Loss; Encapsulation

Classification and Description of Drop-Calorimetric Apparatus 6.3.1. Furnaces 6.3.2. Calorimeters

6.3.2.1. Liquid-Bath Type 6.3.2.2. Metal-Block Type 6.3.2.3. Adiabatic-Receiving Type 6.3.2.4. Phase-Change (Isothermal) Type

Analysis and Presentation of Drop-Calorimetric Data References

Levitation Calorimetry

243 244 244

246 246 247 247 248 248 249 249 249 252 254 257 261

265

7.1. Introduction 265 7.2. Levitation Methods 266

7.2.1. Electromagnetic Levitation 266 7.2.2. Laboratory Levitation Systems 268 7.2.3. Design of Levitation Coils 271

7.3. Calorimeter Designs 275 7.3.1. The Rice University Levitation Calorimeter 276

7.3.1.1. The Levitation Chamber 276 7.3.1.2. The Radiation Gate 277 7.3.1.3. Calorimeter Block and Jacket Assembly 278

XFV CONTENTS

7.3.1.4. Isothermal Bath and Controls 280 7.3.1.5. Flow Gas Purification 280 7.3.1.6. The Quartz Thermometer 281

7.4. Optical Pyrometry 281 7.5. Data Reduction 283

7.5.1. Enthalpy Determination 284 7.5.2. Temperature Determination 287 7.5.3. Radiation Loss Correction 287 7.5.4. Conduction Loss Correction 289 7.5.5. The Enthalpy Function 290

7.6. Enthalpies and Heat Capacities of Liquid Metals 290 7.7. Acknowledgements 294 7.8. References 294 7.9. Appendix: Nomenclature 297

Chapter 8. Modulation Calorimetry 299

8.1. Introduction 299 8.2. Theory of Modulation Calorimetry 300 8.3. Modulation of Heating Power 303

8.3.1. Direct Heating 303 8.3.2. Electron-Bombardment Heating 303 8.3.3. Use of Electrical Heaters 303 8.3.4. Modulated-Light Heating 304 8.3.5. Induction Heating 304

8.4. Measurement of Temperature Oscillations 305

8.4.1. Methods Based on the Temperature Dependence of Sample Resistance 305

8.4.1.1. Supplementary-Current Method 305 8.4.1.2. Third-Harmonic Method 305 8.4.1.3. Equivalent-Impedance Method 305

8.4.2. Photoelectric Detectors 307 8.4.3. Thermocouples and Resistance Thermometers 308 8.4.4. Use of Phase-Locked Detectors 308

8.5. Measurements at High Modulation Frequencies 309 8.6. Accuracy of Modulation Measurements 310 8.7. Applications of Modulation Calorimetry 313

8.7.1. Specific Heat of Metals at High Temperatures 313 8.7.2. Specific Heat Anomalies at Phase Transitions 314 8.7.3. Specific Heat at Low Temperatures 315 8.7.4. Specific Heat of Organic Substances 316 8.7.5. Microcalorimetry 316

8.8. Conclusion 316 8.9. References 317

Chapter 9. Pulse Calorimetry 323

9.1. Introduction 323 9.2. Description of Methods 324

9.2.1. General Description 324

CONTENTS

9.2.2. Classification of Methods 324 9.2.3. Formulation of Equations 326 9.2.4. Measurement of Experimental Quantities 327

9.2.4.1. Measurement of Power 327 9.2.4.2. Measurement of Temperature 328 9.2.4.3. Recording of Quantities 328

9.3. Chronology of Developments 329

9.3.1. Developments Prior to 1970 329

9.3.1.1. Category la 329 9.3.1.2. Category lb 330

9.3.1.3. Category II 331

9.3.2. Developments Since 1970 332

9.3.2.1. Millisecond-Resolution Techniques 332

9.3.2.2. Microsecond-Resolution Techniques 336

9.4. A Millisecond-Resolution Technique 337

9.4.1. Pulse Circuit 337 9.4.2. Measurement of Power 338 9.4.3. Measurement of Temperature 339 9.4.4. Data Acquisition System 340 9.4.5. General Comments 340

9.5. A Microsecond-Resolution Technique 342 9.5.1. Pulse Circuit 342 9.5.2. Measurement of Power 344 9.5.3. Measurement of Temperature 345 9.5.4. Data Acquisition System 345 9.5.5. General Comments 346

9.6. Experimental Difficulties and Sources of Error 346

9.6.1. Errors in Directly-Measured Quantities 346

9.6.1.1. Errors in Electrical Measurements 346 9.6.1.2. Errors in Temperature Measurements 347 9.6.1.3. Errors in Data Acquisition 348

9.6.2. Errors Due to Departure from Assumed Conditions 349 9.6.3. Errors in Specific Heat 349

9.7. Summary and Conclusions 350 9.8. References 351

Chapter 10. Calorimetry at Very High Pressures 355

10.1. Introduction 355 10.2. Adiabatic Calorimetry 355

10.2.1. Principle 355 10.2.2. Measurements at Low Temperatures 356 10.2.3. Measurements Near Room Temperature 359

10.3. Steady-State, a.c.-Temperature Calorimetry 361

10.3.1. Principle of the Method 361 10.3.2. a. c.-Temperature Method Applied to Metals 362 10.3.3. a.c.-Temperature Method Applied to Thermal

Insulators 370

CONTENTS

10.4. Method Using a Steady-State Alternating Heat Flow 371

10.4.1. Principle 371

10.4.2. The Method Developed by Andersson and Bäckström 372

10.5. Methods Using a Heat Pulse 375

10.5.1. General Principle 375 10.5.2. Measurements on Conductors 375 10.5.3. Measurements on Insulators 382

10.5.3.1. Methods Where the Transient Temperature is Measured with a Thermocouple 384

10.5.3.2. The Probe Method 387

10.6. Discussion and Conclusions 391 10.7. References 392

Chapter 11. Differential Scanning Calorimetry 395

11.1. Introduction 395 11.2. D.S.C. Versus D.T.A.—History, Nomenclature, and Applications 396

11.2.1. Developments Leading to Current D.S.C. Techniques 396 11.2.2. Applications of D.T. A. and D.S.C. 398

11.3. Simple Theory of Heat Flow in D.T.A. and D.S.C. 399

11.3.1. Introduction 399 11.3.2. General Equations 399 11.3.3. Classical D.T.A. 401 11.3.4. Power-Compensated D.S.C. 402 11.3.5. Boersma-Type D.T.A. or Heat-Flux D.S.C. 403 11.3.6. Summary Comparison of Similarities and Differences

Among the Instruments 404 11.3.7 Further Literature on Mathematical Treatments 405

11.4. Types of Differential Scanning Calorimeter—Custom Versus Commercial 406

11.4.1. Custom-Built Scanning Calorimeters 406 11.4.2. Commercially-Available Differential Scanning

Calorimeters 406 11.4.3. Literature Reports Regarding Commercial

Instruments 408

11.5. Advantages and Disadvantages of D.S.C. for Heat-Capacity Measurement 409

11.5.1. Advantages 409 11.5.2. Disadvantages 409

11.6. Experimental Procedure for Measuring Accurate Heat Capacity by D.S.C. 410

11.6.1. Introduction 410 11.6.2. Instrument Calibration 410 11.6.3. Sample Encapsulation 413 11.6.4. Measurement of Heat Capacity 414

11.6.4.1. General Considerations 414 11.6.4.2. Heat Capacity by the 'Scanning Method' 416

CONTENTS

11.6.4.3. Heat Capacity by the 'Enthalpy Method' 419 11.6.4.4. Comparison of Scanning Versus Enthalpy

Methods 421 11.6.4.5. Heat Capacity Measurements on Cooling 423

11.7. Measurement of Enthalpy and Temperature of Transition by D.S.C. 423

11.7.1. Introduction 423 11.7.2. Individual Scans for the Transition 424 11.7.3. Transition Scans During Continuous Heat Capacity

Measurements 425

11.8. Sources of Error in Determination of Heat Capacity by D.S.C. 427

11.8.1. Introduction 427 11.8.2. Errors Not Actually Due to the Instrument 427 11.8.3. Sources of Error in the Instrument Itself 428

11.8.3.1. Errors in Temperature Measurement 428 11.8.3.2. Errors in Baseline Interpolation 429 11.8.3.3. 'Multiplicative' Errors 430 11.8.3.4. Conclusion on Errors Due to the

Instrument 430

11.9. Examples of Accurate Heat Capacity Investigations by D.S.C. 431 11.10. Analysis of Heat Capacity Data by D.S.C. 432 11.11. Conclusions 432 11.12. Thermal Analysis Societies and Journals 433 11.13. Acknowledgment 433 11.14. References 433

Chapter 12. Special Problems in Calorimetry of Radioactive Materials 437

12.1. 12.2.

12.3.

Introduction Calorimetric Implications of Radioactive Materials

12.2.1. Materials for Study

12.2.1.1.

12.2.1.2.

Naturally-Occurring Radioactive Materials Fission Products and Other Artificially-Produced Radioactive Isotypes Transuranic Materials

12.2.2.

12.2.1.3.

Experimental Safety Considerations

12.2.2.1. Radiation Safety

12.2.2.2. Criticality Hazards

Specific-Heat Determinations

12.3.1. Decay-Heat Considerations 12.3.2. Remote Operation of Calorimeters

12.3.2.1. Glove Boxes 12.3.2.2. Hoods 12.3.2.3. Caves

437 437

437

437

438 438

438

438 439

439

439 440

440 443 443

12.3.3. Safeguards 446

CONTENTS

12.3.4. Instrument Standardization and Radiation Damage 446 12.3.5. Decontamination of Equipment and Facilities 446

12.4. References 447 12.5. Appendix: A Bibliography of Calorimetry Using Radioactive

Materials 448

Appendix A. Materials of Construction in High-Temperature Calorimetry 453

1. Introduction 453 2. Mechanical Properties 454 3. Thermal Expansion 459 4. Heat Transfer Properties 460 5. Electrical Resistivity 463 6. Electron Emission 467 7. Thermal and Chemical Stability 468 8. Fabricability 471 9. References 472

Appendix B. Reference Materials for Calorimetry 473

1. Introduction 473 2. Materials Available from the United States 473 3. Materials Available from Other Sources 475 4. References 476

Appendix С Presentation of Thermophysical Data in the Scientific and Technological Literature 477

1. Introduction 477 2. The Guide for Data Presentation 477 3. The Guide for Thermodynamic Data 478 4. Repositories for Thermophysical Data 478 5. References 479

Subject Index 481