Details
Phases of Matter and their Transitions
Concepts and Principles for Chemists, Physicists, Engineers, and Materials Scientists1. Aufl.
106,99 € |
|
Verlag: | Wiley-VCH (D) |
Format: | |
Veröffentl.: | 20.10.2023 |
ISBN/EAN: | 9783527836932 |
Sprache: | englisch |
Anzahl Seiten: | 704 |
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Beschreibungen
<b>Phases of Matter and their Transitions</b> <p><b>An all-in-one, comprehensive take on matter and its phase properties</b> <p>In <i>Phases of Matter and their Transitions,</i> accomplished materials scientist Dr. Gijsbertus de With delivers an accessible textbook for advanced students in the molecular sciences. It offers a balanced and self-contained treatment of the thermodynamic and structural aspects of phases and the transitions between them, covering solids, liquids, gases, and their interfaces. <p>The book lays the groundwork to describe particles and their interactions from the perspective of classical and quantum mechanics and compares phenomenological and statistical thermodynamics. It also examines materials with special properties, like glasses, liquid crystals, and ferroelectrics. The author has included an extensive appendix with a guide to the mathematics and theoretical models employed in this resource. <p>Readers will also find: <ul><li>Thorough introductions to classical and quantum mechanics, intermolecular interactions, and continuum mechanics</li> <li>Comprehensive explorations of thermodynamics, gases, liquids, and solids</li> <li>Practical discussions of surfaces, including their general aspects for solids and liquids</li> <li>Fulsome treatments of discontinuous and continuous transitions, including discussions of irreversibility and the return to equilibrium</li></ul> <p>Perfect for advanced students in chemistry and physics, <i>Phases of Matter and their Transitions</i> will also earn a place in the libraries of students of materials science.
<p>Preface xvi</p> <p>List of Frequently Used Symbols and Abbreviations xxi</p> <p>SI Units, Physical Constants, and Conversion Factors xxvii</p> <p>Summary of Notation xxxi</p> <p><b>1 Introduction 1</b></p> <p>1.1 Constituents of Matter 1</p> <p>1.2 Matter and Energy: Interaction and Change 3</p> <p>1.3 Mass and Charge 4</p> <p>1.4 Macroscopic and Microscopic Approaches 6</p> <p>1.5 Gases, Liquids, and Solids 7</p> <p>1.6 What to Expect? 11</p> <p>1.7 Units and Notation 12</p> <p>References 13</p> <p>Further Reading 14</p> <p><b>2 Classical Mechanics 15</b></p> <p>2.1 Frames, Particles, and Coordinates 15</p> <p>2.2 From Newton to Hamilton 17</p> <p>2.3 Hamilton’s Principle and Lagrange’s Equations 19</p> <p>2.4 Conservation Laws 21</p> <p>2.5 Hamilton’s Equations 24</p> <p>2.6 Hamilton’s Principle for Continuous Systems 26</p> <p>2.7 The Virial Theorem 27</p> <p>2.8 Final Remarks 28</p> <p>References 28</p> <p>Further Reading 29</p> <p><b>3 Quantum Mechanics 30</b></p> <p>3.1 Quantum Concepts 30</p> <p>3.1.1 Fundamental Quantum Kinematics 30</p> <p>3.1.2 Operators and their Representation 33</p> <p>3.1.3 Fundamental Quantum Kinetics 35</p> <p>3.2 Interpretation and Some Exact Solutions 37</p> <p>3.2.1 The Particle in a Box 39</p> <p>3.2.2 The Harmonic Oscillator 40</p> <p>3.2.3 The Rigid Rotator 41</p> <p>3.2.4 Many Particles 42</p> <p>3.3 Approximate Quantum Mechanics Solutions 43</p> <p>3.3.1 The Born–Oppenheimer Approximation 43</p> <p>3.3.2 The Variation Principle 44</p> <p>3.3.3 The Hartree–Fock Method 47</p> <p>3.3.4 Perturbation Theory 51</p> <p>3.3.5 The Density Operator 53</p> <p>3.4 Final Remarks 55</p> <p>References 55</p> <p>Further Reading 56</p> <p><b>4 Intermolecular Interactions 57</b></p> <p>4.1 The Semi-classical Approach 57</p> <p>4.1.1 Electrostatic Interaction 59</p> <p>4.1.2 Induction Interaction 62</p> <p>4.1.3 Dispersion Interaction 63</p> <p>4.1.4 The Total Interaction 64</p> <p>4.2 The Quantum Approach 66</p> <p>4.3 Model Interactions 69</p> <p>4.4 Refinements 72</p> <p>4.4.1 Hydrogen Bonding 72</p> <p>4.4.2 Three-Body Interactions 74</p> <p>4.4.3 Accurate Empirical Potentials 74</p> <p>4.5 Final Remarks 75</p> <p>References 76</p> <p>Further Reading 77</p> <p><b>5 Continuum Mechanics 78</b></p> <p>5.1 The Nature of the Continuum 78</p> <p>5.2 Kinematics 79</p> <p>5.2.1 Material and Spatial Coordinates 79</p> <p>5.2.2 General Deformations 80</p> <p>5.2.3 The Small Displacement Gradient Approximation 81</p> <p>5.3 Balance Equations 83</p> <p>5.4 Kinetics 85</p> <p>5.4.1 The Principle of Virtual Power 86</p> <p>5.4.2 Linear Momentum 86</p> <p>5.4.3 Angular Momentum 88</p> <p>5.4.4 Cauchy’s Equations of Motion 88</p> <p>5.5 The Stress Tensor 89</p> <p>5.6 Mechanical Energy 90</p> <p>5.7 Final Remarks 91</p> <p>References 92</p> <p>Further Reading 92</p> <p><b>6 Macroscopic Thermodynamics 93</b></p> <p>6.1 Classical Thermodynamics 93</p> <p>6.1.1 The Four Laws 93</p> <p>6.1.2 Quasi-Conservative and Dissipative Forces 99</p> <p>6.1.3 Equations of State 100</p> <p>6.1.4 Mechanical and Thermal Equilibrium 101</p> <p>6.1.5 Auxiliary Functions 101</p> <p>6.1.6 Some Derivatives and their Relationships 103</p> <p>6.1.7 Chemical Content 103</p> <p>6.1.8 Chemical Equilibrium 106</p> <p>6.2 The Local State and Internal Variables 110</p> <p>6.2.1 The Behavior of Internal Variables 111</p> <p>6.2.2 The Local State 113</p> <p>6.3 Field Formulation 115</p> <p>6.3.1 The First Law 115</p> <p>6.3.2 The Second Law 116</p> <p>6.4 The Linear Approximation in Non-equilibrium Thermodynamics 118</p> <p>6.5 Final Remarks 122</p> <p>References 122</p> <p>Further Reading 123</p> <p><b>7 Microscopic Thermodynamics 125</b></p> <p>7.1 Basics of Statistical Thermodynamics 125</p> <p>7.1.1 Preliminaries 125</p> <p>7.1.2 Entropy and Partition Functions 128</p> <p>7.1.3 Fluctuations 132</p> <p>7.2 Noninteracting Particles 134</p> <p>7.2.1 Single Particle 134</p> <p>7.2.2 Many Particles 134</p> <p>7.2.3 Pressure and Energy 135</p> <p>7.3 The Semi-classical Approximation 136</p> <p>7.4 Interacting Particles 141</p> <p>7.5 Internal Contributions 142</p> <p>7.5.1 Vibrations 142</p> <p>7.5.2 Rotations 145</p> <p>7.5.3 Electronic Transitions 147</p> <p>7.6 Some General Aspects 148</p> <p>7.6.1 Mode or Average? 148</p> <p>7.6.2 Fluctuations and Other Ensembles 149</p> <p>7.6.3 Equipartition of Energy 150</p> <p>7.6.4 The Gibbs–Bogoliubov Inequality 151</p> <p>References 152</p> <p>Further Reading 154</p> <p><b>8 Gases 155</b></p> <p>8.1 Basic Kinetic Theory of Gases 155</p> <p>8.2 The Virial Expansion 159</p> <p>8.2.1 Some Further Remarks 162</p> <p>8.3 Equations of State 164</p> <p>8.4 The Principle of Corresponding States 168</p> <p>8.4.1 The Extended Principle 171</p> <p>8.5 Transition State Theory 174</p> <p>8.5.1 Chemical Kinetics Basics 174</p> <p>8.5.2 The Equilibrium Constant 175</p> <p>8.5.3 Potential Energy Surfaces 176</p> <p>8.5.4 The Activated Complex 177</p> <p>8.5.5 The Link to Experiment 179</p> <p>8.6 Dielectric Behavior 180</p> <p>8.6.1 Basic Aspects 180</p> <p>8.6.2 The Debye–Langevin Equation 182</p> <p>8.6.3 Frequency Dependence 185</p> <p>8.6.4 Estimating μ and α 190</p> <p>References 193</p> <p>Further Reading 196</p> <p><b>9 Liquids 197</b></p> <p>9.1 Approaches to Liquids 197</p> <p>9.2 Distribution Functions, Structure, and Energetics 198</p> <p>9.2.1 Structure 200</p> <p>9.2.2 Energetics 203</p> <p>9.3 The Integral Equation Approach 206</p> <p>9.3.1 The Ornstein–Zernike Equation 206</p> <p>9.3.2 The Yvon–Born–Green Equation 209</p> <p>9.3.3 Other Integral Equations 210</p> <p>9.3.4 The Potential of Mean Force 212</p> <p>9.4 Comparison: Hard-Sphere and Lennard-Jones Results 214</p> <p>9.5 Scaled-Particle Theory 217</p> <p>9.6 Structural Models 218</p> <p>9.6.1 Cell Models 220</p> <p>9.6.2 Hole Models 226</p> <p>9.6.3 Some Other Implementations of Hole Theory 231</p> <p>9.7 The Generalized van der Waals Model 237</p> <p>9.8 Phonon Theory of Liquids 240</p> <p>9.9 The Quantum Cluster Equilibrium Model 244</p> <p>9.10 Some Continuum Aspects 245</p> <p>9.11 Dielectric Behavior 249</p> <p>References 255</p> <p>Further Reading 259</p> <p><b>10 Solids 260</b></p> <p>10.1 Inorganics and Metals 260</p> <p>10.2 Polymers 263</p> <p>10.3 Lattice Concepts 265</p> <p>10.4 Crystalline Structures 267</p> <p>10.5 Bonding: The Quantum-mechanical Approach 270</p> <p>10.5.1 The Nearly Free Electron Approximation 270</p> <p>10.5.2 The Tight Binding Approximation 275</p> <p>10.5.3 Density Functional Theory 278</p> <p>10.6 Bonding: The Empirical Approach 282</p> <p>10.6.1 Atoms, Ions, and Electronegativity 282</p> <p>10.6.2 Covalent and Molecular Crystals 286</p> <p>10.6.3 Ionic Crystals: The Classical Approach 287</p> <p>10.6.4 Ionic Crystals: Electronegativity Approaches 290</p> <p>10.6.5 Metallic Crystals 294</p> <p>10.7 Lattice Dynamics 296</p> <p>10.8 Two Simple Models 299</p> <p>10.9 Properties 300</p> <p>10.9.1 Heat Capacity 300</p> <p>10.9.2 Thermal Expansivity 302</p> <p>10.9.3 Bulk Modulus 303</p> <p>10.10 Defects 304</p> <p>10.10.1 Zero-dimensional Defects 305</p> <p>10.10.2 One-dimensional Defects 308</p> <p>10.10.3 Other Defects 310</p> <p>10.11 Thermo-elasticity 312</p> <p>10.11.1 Elastic Behavior 312</p> <p>10.11.2 Stress States and the Associated Elastic Constants 313</p> <p>10.11.3 Elastic Energy 314</p> <p>10.11.4 A Matter of Notation 315</p> <p>10.11.5 Anisotropic Materials 316</p> <p>10.11.6 The Effect of Temperature 319</p> <p>10.12 Final Remarks 320</p> <p>References 320</p> <p>Further Reading 325</p> <p><b>11 Interfaces 326</b></p> <p>11.1 Thermodynamics of Interfaces 326</p> <p>11.2 One-Component Surfaces: Semiempirical Considerations 331</p> <p>11.3 One-Component Surfaces: Theoretical Considerations 336</p> <p>11.3.1 Density Functional Theory 336</p> <p>11.3.2 Capillary Wave Theory 341</p> <p>11.4 Solid Surface Structure 343</p> <p>11.4.1 Surface Roughening 345</p> <p>11.5 Adsorption at Interfaces 349</p> <p>11.5.1 Solutions 349</p> <p>11.5.2 Thermodynamics of Adsorption 355</p> <p>11.5.3 Statistics of Adsorption 357</p> <p>11.5.4 Adsorption Isotherms 360</p> <p>11.6 Final Remarks 366</p> <p>References 366</p> <p>Further Reading 370</p> <p><b>12 Phase Transitions: General Aspects 371</b></p> <p>12.1 Some General Considerations 371</p> <p>12.2 The Clapeyron and Clapeyron–Clausius Equation 375</p> <p>12.3 The Mosselman Solution for the Clapeyron Equation 376</p> <p>12.4 The Ehrenfest–Prigogine–Defay Equations 378</p> <p>12.5 Landau and Landau-like Theory 380</p> <p>References 383</p> <p>Further Reading 384</p> <p><b>13 Discontinuous Phase Transitions: Liquids ↔ Gases 385</b></p> <p>13.1 Thermodynamics of Evaporation 385</p> <p>13.1.1 Evaporation in the Presence of an Inert Gas 387</p> <p>13.2 Kinetics of Evaporation 388</p> <p>13.2.1 Classical Kinetic Theory 388</p> <p>13.2.2 Secondary Effects 393</p> <p>13.2.3 Other Approaches 394</p> <p>13.3 The Reverse Transition: Condensation 395</p> <p>13.3.1 Drops and Bubbles 395</p> <p>13.3.2 Classical Nucleation Theory 397</p> <p>13.3.3 Nucleation Kinetics 399</p> <p>13.3.4 Modifications 401</p> <p>13.3.5 Molecular Aspects 404</p> <p>References 408</p> <p>Further Reading 410</p> <p><b>14 Discontinuous Phase Transitions: Solids ↔ Liquids 411</b></p> <p>14.1 Melting or Fusion 411</p> <p>14.2 Mechanical or Bulk Melting 414</p> <p>14.2.1 Vibrational Instability 414</p> <p>14.2.2 Lattice Instability 418</p> <p>14.2.3 Vacancies 418</p> <p>14.2.4 Interstitials 419</p> <p>14.2.5 Dislocations 422</p> <p>14.2.6 Interstitialcies 424</p> <p>14.2.7 Simulations 427</p> <p>14.3 Thermodynamic or Surface-Mediated Melting 428</p> <p>14.3.1 Melting of Nanoparticles 428</p> <p>14.3.2 Vacancies Revisited 430</p> <p>14.3.3 Dislocations Revisited 432</p> <p>14.4 Polymer Melting 434</p> <p>14.5 The Influence of Pressure 436</p> <p>14.6 Other Aspects 440</p> <p>14.7 Melting in Perspective 442</p> <p>14.8 The Reverse Transition: Freezing or Solidification 444</p> <p>14.8.1 Nucleation and Growth 444</p> <p>14.8.2 Some Further Remarks 446</p> <p>14.8.3 Polymers and Metals 448</p> <p>14.8.4 Water 451</p> <p>References 452</p> <p>Further Reading 457</p> <p><b>15 Continuous Phase Transitions: Liquids ↔ Gases 458</b></p> <p>15.1 Limiting Behavior 458</p> <p>15.2 Mean-Field Theory: Landau Theory 461</p> <p>15.2.1 Landau-Like Theory: Fluid Transitions 463</p> <p>15.3 Scaling 465</p> <p>15.3.1 Homogeneous Functions 465</p> <p>15.3.2 Scaling Potentials 466</p> <p>15.3.3 Scaling Lattices 467</p> <p>15.4 Renormalization 469</p> <p>15.5 Final Remarks 475</p> <p>References 476</p> <p>Further Reading 476</p> <p><b>16 The Liquid Crystal Transformation 478</b></p> <p>16.1 Nature and Types 478</p> <p>16.2 The Nematic–Isotropic Transformation 480</p> <p>16.2.1 The Orientation as Internal Variable 480</p> <p>16.2.2 The Discontinuous Transformation 481</p> <p>16.3 Alternative Approaches 482</p> <p>16.3.1 Maier–Saupe Theory 483</p> <p>16.3.2 The Coil–Helix Transformation 485</p> <p>16.3.3 Onsager Theory 486</p> <p>16.4 Some Extensions 489</p> <p>16.5 Elastic Energy and Defects 491</p> <p>16.6 The Fréedericksz Transformation 494</p> <p>References 496</p> <p>Further Reading 497</p> <p><b>17 Dielectric Behavior and the Ferroelectric Transformation 498</b></p> <p>17.1 Preliminaries and Dielectric Materials 498</p> <p>17.1.1 General Remarks 498</p> <p>17.1.2 Dielectric Materials 500</p> <p>17.2 Electronic Polarization 501</p> <p>17.3 Vibrational Polarization 503</p> <p>17.3.1 Three Models 507</p> <p>17.4 Orientational Polarization 510</p> <p>17.5 Space–Charge Polarization 511</p> <p>17.6 Ferroelectric Materials 512</p> <p>17.7 Ferroelectric Behavior 516</p> <p>17.7.1 The Thermodynamic Approach 516</p> <p>17.7.2 The Microscopic Approach 518</p> <p>References 521</p> <p>Further Reading 523</p> <p><b>18 The Glass Transition 525</b></p> <p>18.1 What Is a Glass? 525</p> <p>18.1.1 Glassy Materials 528</p> <p>18.1.2 Property Changes at T<sub>g</sub> 529</p> <p>18.2 The Thermodynamic Approach 530</p> <p>18.3 The Structural Approach 535</p> <p>18.3.1 Free Volume Theory 536</p> <p>18.3.2 Continuous Transition Theory 539</p> <p>18.4 The Lattice Gas Approach 541</p> <p>18.5 Phonon Theory for Glasses 543</p> <p>18.6 Mode-Coupling Theory 546</p> <p>18.7 Final Remarks 549</p> <p>References 550</p> <p>Further Reading 553</p> <p><b>19 Irreversibility and the Return to Equilibrium 555</b></p> <p>19.1 Some Considerations 555</p> <p>19.2 The Boltzmann Approach 557</p> <p>19.2.1 Time Invariance 558</p> <p>19.2.2 Recurrence 560</p> <p>19.3 The Gibbs Approach 561</p> <p>19.4 The Formal Approach 563</p> <p>19.5 The Physical Approach 567</p> <p>19.6 The Information Theory Approach 571</p> <p>19.6.1 A Brief Review 571</p> <p>19.6.2 High and Low Probability Manifolds 572</p> <p>19.7 Closure 578</p> <p>References 580</p> <p>Further Reading 583</p> <p><b>Appendix A Guide to Mathematics Used 584</b></p> <p>A. 1 Symbols and Conventions 584</p> <p>A. 2 Derivatives, Differentials, and Variations 584</p> <p>A. 3 Composite, Implicit, Homogeneous, Complex, and Analytic Functions 586</p> <p>A. 4 Extremes and Lagrange Multipliers 588</p> <p>A. 5 Legendre Transforms 588</p> <p>A. 6 Coordinate Axes Rotations 589</p> <p>A. 7 Change of Variables 590</p> <p>A. 8 Calculus of Variations 591</p> <p>A. 9 Matrices and Determinants 592</p> <p>A. 10 The Eigenvalue Problem 594</p> <p>A. 11 Matrix Decompositions 597</p> <p>A. 12 Scalars, Vectors, and Tensors 598</p> <p>A. 13 Tensor Analysis 601</p> <p>A. 14 Gamma, Dirac, and Heaviside Functions 603</p> <p>A. 15 Laplace and Fourier Transforms 604</p> <p>A. 16 Some Useful Expressions 606</p> <p>Further Reading 607</p> <p><b>Appendix B Elements of Special Relativity Theory 608</b></p> <p>B.1 Lorentz Transformations 608</p> <p>B.2 Velocities, Contraction, Dilatation, and Proper Quantities 610</p> <p>B.3 Relativistic Lagrange and Hamilton Functions 611</p> <p>References 612</p> <p>Further Reading 612</p> <p><b>Appendix C The Lattice Gas Model 613</b></p> <p>C. 1 The Lattice Gas Model 613</p> <p>C. 2 The Zeroth or Mean-Field Approximation 613</p> <p>C. 3 The First or Quasi-Chemical Approximation 615</p> <p>C. 4 Athermal Entropy for Chain-Like Molecules 619</p> <p>References 621</p> <p>Further Reading 621</p> <p><b>Appendix D Elements of Electrostatics 622</b></p> <p>D.1 Coulomb, Gauss, Poisson, and Laplace 622</p> <p>D.2 A Dielectric Sphere in a Dielectric Matrix 624</p> <p>D.3 A Dipole in a Spherical Cavity 626</p> <p>Further Reading 627</p> <p><b>Appendix E Elements of Probability and Statistics 629</b></p> <p>E.1 Probability 629</p> <p>E.2 Single Variable 631</p> <p>E.3 Multiple Variables 632</p> <p>E.4 The Normal Distribution and the Central-Limit Theorem 633</p> <p>References 635</p> <p>Further Reading 635</p> <p><b>Appendix F Selected Data 636</b></p> <p>References 650</p> <p><b>Appendix G Answers to Selected Problems 652</b></p> <p>Index 659</p>
<p><i><b>Gijsbertus de With, PhD,</b> is Professor Emeritus of Materials Science at Eindhoven University of Technology in the Netherlands. His research is focused on the structure and interfacial phenomena related to the chemical and thermomechanical behavior of multi-phase materials.</i>
<p><b>An all-in-one, comprehensive take on matter and its phase properties</b> <p>In <i>Phases of Matter and their Transitions,</i> accomplished materials scientist Dr. Gijsbertus de With delivers an accessible textbook for advanced students in the molecular sciences. It offers a balanced and self-contained treatment of the thermodynamic and structural aspects of phases and the transitions between them, covering solids, liquids, gases, and their interfaces. <p>The book lays the groundwork to describe particles and their interactions from the perspective of classical and quantum mechanics and compares phenomenological and statistical thermodynamics. It also examines materials with special properties, like glasses, liquid crystals, and ferroelectrics. The author has included an extensive appendix with a guide to the mathematics and theoretical models employed in this resource. <p>Readers will also find: <ul><li>Thorough introductions to classical and quantum mechanics, intermolecular interactions, and continuum mechanics</li> <li>Comprehensive explorations of thermodynamics, gases, liquids, and solids</li> <li>Practical discussions of surfaces, including their general aspects for solids and liquids</li> <li>Fulsome treatments of discontinuous and continuous transitions, including discussions of irreversibility and the return to equilibrium</li></ul> <p>Perfect for advanced students in chemistry and physics, <i>Phases of Matter and their Transitions</i> will also earn a place in the libraries of students of materials science.