SPECIFIC HEAT OF SOLIDS

Transcription

1 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

2 Contents Foreword to the Series, David R. Lide, Jr. Preface to the Series, Y. S. Touloukian Introduction xix xxi xxiii Chapter 1. Theory of Specific Heat of Solids 1 : J 1.1. Introduction , Definition of Specific Heat Relation of Specific Heat to Other Thermodynamic Quantities Historical Background Lattice Specific Heat The Einstein Model The Debye Model Theory of Harmonic Lattice Dynamics Dynamics of a One-Dimensional Diatomic Lattice Dynamics of a Three-Dimensional Lattice Determination of Phonon Dispersion Relations Calculation of Vibrational Frequency Spectra Thermodynamic Properties in the Harmonic Approximation Thermodynamic Properties of Lattice Vibrations in Anharmonic Crystals Quasiharmonic and Explicitly Anharmonic Contributions Total (Harmonic Plus Anharmonic) Contribution Contribution of Lattice Vacancies Electronic Specific Heat Statistics of an Electron Fermi Gas Specific Heat of Electrons in Normal Metals The Free Electron Model Experimental Specific Heat at Low Temperatures The Effect of Electron Band Structure and Many-Body Enhancement 40 vii

3 The Rigid-Band Model Specific Heat of Superconductors Specific Heat According to Classical Thermodynamics Thermodynamic Properties According to BCS Theory Specific Heat of Type II Superconductors Magnetic Specific Heat Spin-Wave Specific Heat Ferromagnetic and Ferrimagnetic Systems Antiferromagnetic Systems Specific Heat in the Critical Temperature Region Approximate Methods: The Weiss Molecular Field Model Statistical Methods: The Heisenberg and Ising Models The Schottky Anomaly Schottky Specific Heat in Paramagnetic Systems Nuclear Specific Heat Other Magnetic Contributions to Specific Heat Spin Fluctuations The Kondo or Single-Impurity Effect The Spin-Glass Effect Summary Appendix: Estimation and Correlation of Specific Heat Specific Heat at Low Temperatures Specific Heat at Moderate Temperatures Specific Heat at High Temperatures References 82 Chapter 2. Calorimetry Below 1 К Introduction Problems Encountered in the Temperature Range К Refrigeration Temperature Scale and Standards Thermometry Thermal Isolation Thermal Contact Application of Heat Sample Characteristics Calorimetric Technique Adiabatic Calorimetry Continuous-Heating Calorimetry Transient Calorimetry a.c. Calorimetry 106

4 Miscellaneous Examples of Low-Temperature Calorimetry Summary Acknowledgement References 110 Chapter 3. Calorimetry in the Range К Introduction Cryostats Location of Cryostat Minimization of Vibrational Heating Minimization of Radio-Frequency Heating Refrigerants Used in Cryostat Cryostat Design Cryostat Construction Thermometry Review of Temperature Scales in the Range К Conversion Between Temperature Scales Secondary Thermometers Thermometer Calibration Points Vapor Pressure Thermometry Superconducting Transition Points Thermometer Calibration Measuring Thermometer Resistance Checking or Extrapolating a Thermometer Calibration Using Specific Heat Measurements Note on Thermocouples Calorimeter Design Thermal Contact Between the Sample and Calorimeter The 'Tray' Technique The 'Copper Stud' Technique The 'Differential Contraction' Technique The 'Differential Expansion' Technique The 'Clamp' Technique The 'Spring Loaded Foot' Technique The'Plug'Technique The 'Loose Powder' Technique Compressed Powder Techniques The Heat Exchange Medium Technique Calorimeter Thermometer Calorimeter Heater Thermal Isolation of the Calorimeter Radiation High Vacuum Conduction Cooling the Calorimeter. Thermal Switches 126

5 To Rely on Thermal Conduction Through Leads To Use a Vapor Pressure 'Pot' on the Calorimeter Mechanical Heat Switch Superconducting Heat Switch Checking the Thermometer Calibration 'In Situ' Checking the Calorimeter Operation. Standard Sample Note on Differential Calorimeters Note on Measuring Condensed Gases Note on Measurements at High Pressure Note on Measurements in Magnetic Field Heat Capacity of Materials Used in Calorimeter Construction Isoperibol Calorimeters Adiabatic Calorimeters Continuous Heating Calorimeters Novel Techniques 'Traditional' Methods Adapted for Small Sample Steady-State a.c. Temperature Calorimetry Temperature Wave Method Diffuse Temperature Pulse Method (sometimes called Heat Pulse Technique) Temperature Relaxation Methods Resistive SQUID Calorimetry Differential Calorimetry with Small Samples Novel Techniques with Larger Samples Large Sample Weakly Coupled to Heat Sink Cooling Curve Method Special Situations Short Time-Scale Experiments Annealing Experiments Thin Film Experiments Small Particle Experiments Experiments on Radioactive Materials Automated Calorimetry in the К Temperature Range The Development of Automation Self-Balancing Instruments Some General Considerations Some Typical Systems 'Off-Line' Systems 'On-Line' Systems 'On-Line' Systems for 'Novel' Techniques Analysis of Data. Accuracy Reduction of Observations to Molar Specific Heat The Various Contributions to Specific Heat Lattice Specific Heat Electronic Specific Heat Nuclear Specific Heat 143

6 Magnetic Specific Heat Superconducting Transition Impurities Analysis and Presentation of Results Accuracy References Chapter 4. Calorimetry in the Range К Introduction Cryostat Design Immersion or Not? Immersion in a Refrigerant Bath Aneroid-Type Cryostat Cooling and/or Quenching Adiabatic Technique Aneroid-Type Adiabatic Cryostat Immersion-Type Adiabatic Cryostat Combination Immersion-Aneroid-Type Adiabatic Cryostat Filling-Tube-Type Cryostat Control of Heat Exchange with the Calorimeter Isoperibol Technique Typical Isoperibol Cryostats Calorimeter Design General Considerations Calorimeter with Internal Thermometer and Heater Calorimeter with Thermometer-Heater on Outer Surface Calorimeter for Liquids and Condensable Gases Special Calorimeters Calculations Involved in Calorimetric Operation Thermometry and Temperature Scales Thermometric Sensors Thermometer Calibration and Thermometric Scales Temperature Calibration and Thermometric Scales Special Thermometers Thermocouples and Thermels The Trend Toward Automation in Data Acquisition The Trend Toward Smaller Samples Measurement Techniques and Adjuvant Circuitry Energy Circuitry A.1.2. Resistance Thermometry Circuitry Adiabatic Jacket Control Circuitry Special Techniques Inverse Temperature Drop-Calorimetry Calorimetry at High Pressures

7 Calorimetry in Magnetic Fields Calorimetry by the Thermal Relaxation Method Laser-Flash Calorimetry High-Resolution Heat Capacity Calorimeter Flow Calorimetry Transitions Phase and Otherwise Reference Standards for Thermophysical Calorimetry Procedures for Data Handling and Presentation Calculation of C p and Other Thermophysical Properties General Principles Derived Quantities The Extrapolation to Zero Kelvin Conduction Electron and Debye Contributions The Zero Point Entropy Other Matters of Calculational Relevance Routine Details Errors Associated with Thermophysical Data The Lattice Heat Capacity Comparison of DSC and Adiabatic Approaches Concluding Remarks Acknowledgement References 185 Chapter 5. Adiabatic Calorimetry Above 300 К Introduction 191 The Principle of Adiabatic Calorimetry Continuous Heating Discontinuous Heating Nonadiabatic Conditions 194 General Design and Operation Design Operation Continuous Heating Operation Discontinuous Heating 197 Adiabatic Shield and Calorimeter Cell and Sample Design Radiation Shields Conduction Shields Sample and Cell Heater Design 206 Temperature Measurements in High-Temperature Calorimetry Resistance Thermometry Thermocouple Thermometry Thermocouple Errors Factors Governing the Use of Thermocouples in High-Temperature Adiabatic Calorimetry 220 Corrections to the Measured Specific Heat 221

8 XIII Correction for the Sample Heater Correction for Heat Leakage from the Sample Continuous Heating Corrections for Heat Leakage from the Sample Discontinuous Heating Corrections Using a Cell 229 Errors and Accuracy of Specific Heat Measurements Systematic Errors Random Errors Accuracy of Specific Heat Measurements Computer Operation of Calorimeters Survey of Adiabatic Calorimeters Closure Acknowledgements Bibliography References Chapter 6. Drop Calorimetry Above 300 К Introduction Fundamental Concepts and Relationships in Drop Calorimetry Ideal Drop-Calorimetric Experiment Real Drop-Calorimetric Experiment; Some Error Sources Sample Sample Temperature Sample Heat Loss; Encapsulation Classification and Description of Drop-Calorimetric Apparatus Furnaces Calorimeters Liquid-Bath Type Metal-Block Type Adiabatic-Receiving Type Phase-Change (Isothermal) Type Analysis and Presentation of Drop-Calorimetric Data References Chapter 7. Levitation Calorimetry Introduction Levitation Methods Electromagnetic Levitation Laboratory Levitation Systems Design of Levitation Coils Calorimeter Designs The Rice University Levitation Calorimeter The Levitation Chamber The Radiation Gate Calorimeter Block and Jacket Assembly 278

9 XFV CONTENTS Isothermal Bath and Controls Flow Gas Purification The Quartz Thermometer Optical Pyrometry Data Reduction Enthalpy Determination Temperature Determination Radiation Loss Correction Conduction Loss Correction The Enthalpy Function Enthalpies and Heat Capacities of Liquid Metals Acknowledgements References Appendix: Nomenclature 297 Chapter 8. Modulation Calorimetry Introduction Theory of Modulation Calorimetry Modulation of Heating Power Direct Heating Electron-Bombardment Heating Use of Electrical Heaters Modulated-Light Heating Induction Heating Measurement of Temperature Oscillations Methods Based on the Temperature Dependence of Sample Resistance Supplementary-Current Method Third-Harmonic Method Equivalent-Impedance Method Photoelectric Detectors Thermocouples and Resistance Thermometers Use of Phase-Locked Detectors Measurements at High Modulation Frequencies Accuracy of Modulation Measurements Applications of Modulation Calorimetry Specific Heat of Metals at High Temperatures Specific Heat Anomalies at Phase Transitions Specific Heat at Low Temperatures Specific Heat of Organic Substances Microcalorimetry Conclusion References 317 Chapter 9. Pulse Calorimetry Introduction Description of Methods General Description 324

10 Classification of Methods Formulation of Equations Measurement of Experimental Quantities Measurement of Power Measurement of Temperature Recording of Quantities Chronology of Developments Developments Prior to Category la Category lb Category II Developments Since Millisecond-Resolution Techniques Microsecond-Resolution Techniques A Millisecond-Resolution Technique Pulse Circuit Measurement of Power Measurement of Temperature Data Acquisition System General Comments A Microsecond-Resolution Technique Pulse Circuit Measurement of Power Measurement of Temperature Data Acquisition System General Comments Experimental Difficulties and Sources of Error Errors in Directly-Measured Quantities Errors in Electrical Measurements Errors in Temperature Measurements Errors in Data Acquisition Errors Due to Departure from Assumed Conditions Errors in Specific Heat Summary and Conclusions References 351 Chapter 10. Calorimetry at Very High Pressures Introduction Adiabatic Calorimetry Principle Measurements at Low Temperatures Measurements Near Room Temperature Steady-State, a.c.-temperature Calorimetry Principle of the Method a. c.-temperature Method Applied to Metals a.c.-temperature Method Applied to Thermal Insulators 370

11 10.4. Method Using a Steady-State Alternating Heat Flow Principle The Method Developed by Andersson and Bäckström Methods Using a Heat Pulse General Principle Measurements on Conductors Measurements on Insulators Methods Where the Transient Temperature is Measured with a Thermocouple The Probe Method Discussion and Conclusions References 392 Chapter 11. Differential Scanning Calorimetry Introduction D.S.C. Versus D.T.A. History, Nomenclature, and Applications Developments Leading to Current D.S.C. Techniques Applications of D.T. A. and D.S.C Simple Theory of Heat Flow in D.T.A. and D.S.C Introduction General Equations Classical D.T.A Power-Compensated D.S.C Boersma-Type D.T.A. or Heat-Flux D.S.C Summary Comparison of Similarities and Differences Among the Instruments Further Literature on Mathematical Treatments Types of Differential Scanning Calorimeter Custom Versus Commercial Custom-Built Scanning Calorimeters Commercially-Available Differential Scanning Calorimeters Literature Reports Regarding Commercial Instruments Advantages and Disadvantages of D.S.C. for Heat-Capacity Measurement Advantages Disadvantages Experimental Procedure for Measuring Accurate Heat Capacity by D.S.C Introduction Instrument Calibration Sample Encapsulation Measurement of Heat Capacity General Considerations Heat Capacity by the 'Scanning Method' 416

12 Heat Capacity by the 'Enthalpy Method' Comparison of Scanning Versus Enthalpy Methods Heat Capacity Measurements on Cooling Measurement of Enthalpy and Temperature of Transition by D.S.C Introduction Individual Scans for the Transition Transition Scans During Continuous Heat Capacity Measurements Sources of Error in Determination of Heat Capacity by D.S.C Introduction Errors Not Actually Due to the Instrument Sources of Error in the Instrument Itself Errors in Temperature Measurement Errors in Baseline Interpolation 'Multiplicative' Errors Conclusion on Errors Due to the Instrument Examples of Accurate Heat Capacity Investigations by D.S.C Analysis of Heat Capacity Data by D.S.C Conclusions Thermal Analysis Societies and Journals Acknowledgment References 433 Chapter 12. Special Problems in Calorimetry of Radioactive Materials Introduction Calorimetric Implications of Radioactive Materials Materials for Study Naturally-Occurring Radioactive Materials Fission Products and Other Artificially-Produced Radioactive Isotypes Transuranic Materials Experimental Safety Considerations Radiation Safety Criticality Hazards Specific-Heat Determinations Decay-Heat Considerations Remote Operation of Calorimeters Glove Boxes Hoods Caves Safeguards 446

13 Instrument Standardization and Radiation Damage Decontamination of Equipment and Facilities References Appendix: A Bibliography of Calorimetry Using Radioactive Materials 448 Appendix A. Materials of Construction in High-Temperature Calorimetry Introduction Mechanical Properties Thermal Expansion Heat Transfer Properties Electrical Resistivity Electron Emission Thermal and Chemical Stability Fabricability References 472 Appendix B. Reference Materials for Calorimetry Introduction Materials Available from the United States Materials Available from Other Sources References 476 Appendix С Presentation of Thermophysical Data in the Scientific and Technological Literature Introduction The Guide for Data Presentation The Guide for Thermodynamic Data Repositories for Thermophysical Data References 479 Subject Index 481