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分享wiley图书一本：Diffusion-controlled Solid State Reactions
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这本书在alloy，thin films，nano systems这些方面讲的好。 Contents Editor’s Preface XVII List of Contributors XIX 1Introduction1 Andriy M. Gusak 2 Nonequilibrium Vacancies and Diffusion-Controlled Processes at Nanolevel 11 Andriy M. Gusak 2.1 Introduction 11 2.2 Beyond Darken’s Approximation 12 2.3 The Model for Regular Chains of Ideal Vacancies Sinks/Sources 17 2.4 Description of Interdiffusion in Alloys at Random Power of Distributed Vacancy Sinks 20 2.5 Linear Phase Growth and Nonequilibrium Vacancies 22 2.6 Intermetallic Layer Growth at Imposed Current and Nonequilibrium Vacancies Damping Effect 25 2.7 Possible Role of Nonequilibrium Vacancies in Spinodal Decomposition 26 2.8 Nanoshell Collapse 29 2.9 The Role of Nonequilibrium Vacancies in Diffusion Coarsening 32 2.10 Conclusions 34 References 34 3 Diffusive Phase Competition: Fundamentals 37 Andriy M. Gusak 3.1 Introduction 37 3.2 Standard Model and the Anomaly Problem 37 3.3 Criteria of Phase Growth and Suppression: Approximation of Unlimited Nucleation 45 3.4 Incubation Time 47 3.5 Should We Rely Upon the Ingenuity of Nature? Nucleation Problems and Meta-Quasi-Equilibrium Concept 49 3.6 Suppression of an Intermediate Phase by Solid Solutions 52 3.6.1 Unlimited Nucleation 53 3.6.2 Finite Rate of Nuclei Formation 54 3.7 Phase Competition in a Model of Divided Couple 55 References 59 4 Nucleation in a Concentration Gradient 61 Andriy M. Gusak 4.1 Introduction 61 4.2 Nucleation in Nonhomogeneous Systems: General Approach 63 4.3 Thermodynamics of the Polymorphic Mode of Nucleation in a Concentration Gradient 65 4.3.1 Homogeneous Nucleation: General Relations 65 4.3.2 Spherical Nuclei 66 4.3.3 Ellipsoidal Nuclei 68 4.3.4 MC Simulations of the Shape of the Nucleus 70 4.3.5 Stress Effects 71 4.4 Thermodynamics of the Transversal Mode of Nucleation in a Concentration Gradient 74 4.4.1 Homogeneous Nucleation: General Relations 74 4.5 Thermodynamics of the Longitudinal Mode of Nucleation in a Concentration Gradient 79 4.6 Nucleation in Systems with Limited Metastable Solubility 81 4.6.1 Nucleation of a Line Compound at the Interface During Interdiffusion 82 4.6.2 Nucleation in between Dilute Solutions 86 4.6.3 Nucleation in between Two Growing Intermediate Phase Layers 86 4.6.4 Nucleation in between a Growing Intermediate Phase and a Dilute Solution 88 4.6.5 Application to Particular Systems 91 4.7 Conclusions 95 References 97 5 Modeling of the Initial Stages of Reactive Diffusion 99 Mykola O. Pasichnyy and Andriy M. Gusak 5.1 Introduction 99 5.2 First Phase Nucleation Delay in Al–Co Thin Films 100 5.2.1 The Problem of Nucleation in a Concentration Gradient Field 101 5.2.2 Basic Model 102 5.2.3 Transversal Mode 105 5.2.4 Polymorphic Mode 107 5.2.4.1 Polymorphic Mode without Shape Optimization 108 5.2.4.2 Polymorphic Mode with Shape Optimization 109 5.2.5 Discussion and Conclusions 110 5.3 Kinetics of Lateral Growth of Intermediate Phase Islands at the Initial StageofReactiveDiffusion 112 5.3.1 Problem Formulation 112 5.3.2 Physical Model 114 5.3.3 Numerical Results 116 5.3.4 Analytical Solution for the Steady State 117 5.3.5 Asymptotic Thickness of an Island 118 5.3.6 Estimates 119 5.3.7 Conclusions 121 5.4 MC-Scheme of Reactive Diffusion 121 5.4.1 Formulation of the Problem 121 5.4.2 The Model 122 5.4.3 Nucleation of Phase A2B1at the Interface A–A1B2 124 5.4.4 Competitive Nucleation of Phases A1B2and A2B1at the Interface A–B 129 5.4.5 Lateral Competition 131 5.4.6 Conclusions 131 References 132 Further Reading 133 6 Flux-Driven Morphology Evolution 135 Andriy M. Gusak 6.1 Introduction 135 6.2 Grain Growth and Ripening: Fundamentals 136 6.2.1 Main Approximations of the LSW Approach 136 6.2.2 Traditional Approaches to the Description of Grain Growth 138 6.3 Alternative Derivation of the Asymptotic Solution of the LSW Theory 139 6.4 Flux-Driven Ripening at Reactive Diffusion 142 6.4.1 Experimental Results 143 6.4.2 Basic Approximations 144 6.4.3 Basic Equations 145 6.5 Flux-Driven Grain Growth in Thin Films during Deposition 148 6.5.1 ‘‘Mushroom Effect’’ on the Surface of a Pair of Grains: Deterministic Approach 150 6.5.2 Analysis of Flux-Driven Grain Growth 151 6.5.3 Stochastic Approach 154 6.5.4 Monte Carlo Simulation of Flux-Driven Grain Growth 155 6.5.5 Lateral Grain Growth in Aluminum Nanofilm during Deposition 156 6.5.5.1 Hillert’s Model 160 6.5.5.2 Models Leading to a Rayleigh Distribution 161 6.5.5.3 Pair Interaction Model (Di Nunzio) 161 6.6 Flux-Induced Instability and Bifurcations of Kirkendall Planes 163 6.6.1 Kirkendall Effect and Velocity Curve 164 6.6.2 Stable and Unstable K-Planes 165 6.6.3 Experimental Results 166 6.6.4 General Instability Criterion 168 6.6.5 Estimation of Markers’ Distributions Near the Virtual K-Plane 169 6.6.6 Spatial Distribution of Markers 170 6.6.7 Possible Alternative to the Multilayer Method 171 6.7 Electromigration-Induced Grain Rotation in Anisotropic Conducting Beta Tin 173 6.8 Thermomigration in Eutectic Two-Phase Structures 178 6.8.1 Thermomigration Induced Back Stress in Two-Phase Mixtures 183 6.8.2 Thermomigration-Driven Kirkendall Effect in Binary Mixtures 184 6.8.3 Stochastic Tendencies in Thermomigration 185 References 186 7 Nanovoid Evolution 189 Tatyana V. Zaporozhets and Andriy M. Gusak 7.1 Introduction 189 7.2 Kinetic Analysis of the Instability of Hollow Nanoparticles 191 7.2.1 Introduction 191 7.2.2 Mechanism of Nanoshell Shrinkage 192 7.2.3 Models of Nanovoid Shrinkage 194 7.2.3.1 Model 1: Shrinkage of Pure Element Nanoshells 195 7.2.3.2 Model 2: Shrinkage of a Binary Compound Nanoshell with Steady State Approximation for Both Vacancies and B Species 197 7.2.3.3 Model 3: Steady State and Non–Steady State Vacancies for Component B 200 7.2.3.4 Model 4: Non–Steady State Vacancies and Atoms 204 7.2.4 Segregation of Pure B at the Internal Surface 205 7.2.5 Kinetic Monte Carlo Simulation of Shrinkage of a Nanoshell 206 7.2.5.1 Model 1MC: Pure B-Shell in Vacuum 207 7.2.5.2 Model 2MC: Ordered IMC Nanoshell in Vacuum 208 7.2.6 Influence of Vacancy Segregation on Nanoshell Shrinkage 208 7.2.7 Summary 215 7.3 Formation of Compound Hollow Nanoshells 216 7.3.1 Introduction 216 7.3.2 Model of Nanoshell Formation 216 7.3.3 Simplified Analysis of the Competition Between ‘‘Kirkendall-Driven’’ and ‘‘Curvature-Driven’’ Effects 218 7.3.4 Rigorous Kinetic Analysis 220 7.3.5 Results and Discussion 225 7.3.6 Summary 228 7.4 Hollow Nanoshell Formation and Collapse in One Run: Model for a Solid Solution 229 7.4.1 Introduction 229 7.4.2 Shrinkage 229 7.4.3 Formation of a Hollow Nanoshell from Core–Shell Structure without the Influence of Ambient Atmosphere 233 7.4.4 Results of the Phenomenological Model 234 7.4.5 Monte Carlo Simulation of the Vacancy Subsystem Evolution in the Structure ‘‘Core–Shell’’ 238 7.4.5.1 Formation of a NanoShell in a MC simulation 239 7.4.5.2 Crossover from Formation to Collapse 239 7.4.5.3 Shrinkage and Segregation Kinetics in an MC Simulation 241 7.4.6 Summary 241 7.5 Void Migration in Metallic Interconnects 245 7.5.1 Hypotheses and Experiments 245 7.5.2 The Model 248 7.5.3 Results 249 7.5.3.1 Migration of Voids in Bulk Cu and Determination of the Calibration Factor between MCS and Real Time 249 7.5.3.2 Void Migration Along the Metal/Dielectric Interface 250 7.5.4 Simplified Analytical Models of Trapping at the GBs and at the GB Junctions 253 7.5.5 Summary 255 References 256 8 Phase Formation via Electromigration 259 Semen V. Kornienko and Andriy M. Gusak 8.1 Introduction 259 8.2 Theory of Phase Formation and Growth in the Diffusion Zone at interdiffusion in an External Electric Field 260 8.2.1 External Field Effects on Intermetallic Compounds Growth at Interdiffusion 260 8.2.2 Criteria for Phase Suppression and Growth in an External Field 267 8.2.3 Effect of an External Field on the Incubation Time of a Suppressed Phase 270 8.2.4 Conclusions 271 8.3 Effects of Electromigration on Compound Growth at the Interfaces 272 8.4 Reactive Diffusion in a Binary System at an Imposed Electric Current at Nonequilibrium Vacancies 275 8.4.1 Equation for the Growth of an Intermediate Phase taking into Account Nonequilibrium Vacancies 275 8.4.2 Analysis of the Equation for the Rate of Intermediate Phase Growth in Limiting Cases 279 8.4.3 Numerical Solution of the Equation for the Intermediate Phase Rate of Growth 281 8.4.4 Conclusion 286 References 286 9 Diffusion Phase Competition in Ternary Systems 289 Semen V. Kornienko, Yuriy A. Lyashenko, and Andriy M. Gusak 9.1 Introduction 289 9.2 Phase Competition in the Diffusion Zone of a Ternary System 289 9.2.1 Phase Competition in the Diffusion Zone of a Ternary System with Two Intermediate Phases 290 9.2.2 Influence of Pt on Phase Competition in the Diffusion Zone of the Ternary (NiPt)–Si System 295 9.2.2.1 Basic Considerations 295 9.2.2.2 Effect of Pt on Phase Competition in the Diffusion Zone of Ni–Si 297 9.2.2.3 Calculations and Discussion 300 9.3 Ambiguity and the Problem of Selection of the Diffusion Path 302 9.3.1 General Remarks 302 9.3.2 Analytical Solution of the Simplified Symmetric Model 304 9.3.3 Numerical Calculations for a Complex Model 309 9.3.4 Conclusions 320 9.4 Nucleation in the Diffusion Zone of a Ternary System 321 9.4.1 Model Description 321 9.4.2 Algorithm and Results for the Model System 325 9.4.3 Discussion 327 References 329 Further Reading 331 10 Interdiffusion with Formation and Growth of Two-Phase Zones 333 Yuriy A. Lyashenko and Andriy M. Gusak 10.1 Introduction 333 10.2 Peculiarities of the Diffusion Process in Ternary Systems 334 10.2.1 Notations 334 10.2.2 Thermodynamic Peculiarities 335 10.2.3 Diffusion Peculiarities 336 10.2.4 Types of Diffusion Zone Morphology in Three-Component Systems 337 10.3 Models of Diffusive Two-Phase Interaction 340 10.3.1 Model Systems 341 10.3.2 Phenomenological Approach to the Description of Interdiffusion in Two-Phase Zones 345 10.3.3 Choice of the Diffusion Interaction Mode 348 10.4 Results of Modeling and Discussion 350 10.4.1 One-Dimensional Model of Interdiffusion between Two-Phase Alloys 350 10.4.2 The Problem of Indefiniteness of the Final State 352 10.4.3 Diffusion Path Stochastization in the Two-Phase Region 353 10.4.4 Invariant Interdiffusion Coefficients in the Two-Phase Zone 354 10.4.5 Conclusions 356 References 356 Further Reading 358 11 The Problem of Choice of Reaction Path and Extremum Principles 359 Andriy M. Gusak and Yuriy A. Lyashenko 11.1 Introduction 359 11.2 Principle of Maximal Entropy Production at Choosing the Evolution Path of Diffusion-Interactive Systems 359 11.3 Nonequilibrium Thermodynamics: General Relations 361 11.3.1 Isolated Systems 361 11.3.2 System in a Thermostat 363 11.3.3 Inhomogeneous Systems: Postulate of Quasi-Equilibrium for Physically Small Volumes 364 11.3.4 Extremum Principles 366 11.4 Application of the Principles of Thermodynamics of Irreversible Processes: Examples 368 11.4.1 Criterion of First Phase Choice at Reaction–Diffusion Processes 368 11.5 Conclusions 378 References 379 12 Choice of Optimal Regimes in Cellular Decomposition, Diffusion-Induced Grain Boundary Migration, and the Inverse Diffusion Problem 381 Yuriy A. Lyashenko 12.1 Introduction 381 12.2 Model of Self-Consistent Calculation of Discontinuous Precipitation Parameters in the Pb–Sn System 382 12.2.1 General Description of the Model Systems 384 12.2.2 Model Based on the Balance and Maximum Production of Entropy 387 12.2.2.1 Phase Transformations and Law of Conservation of Matter 388 12.2.2.2 Calculation of the Driving Force 389 12.2.2.3 Calculation of Energy Dissipation in the Transformation Front along the Precipitation Lamella 389 12.2.2.4 Calculation of Energy Dissipation Close to the Transformation Front 393 12.2.3 Calculation of Entropy Production Taking into Account Grain Boundary Diffusion and Atomic Jumps through the Grain Boundary 400 12.2.3.1 Optimization Procedure and Calculation Results 401 12.3 Model of Diffusion-Induced Grain Boundary Migration (DIGM) Based on the Extremal Principle of Entropy Production by the Example of Cu–Ni Thin Films 405 12.3.1 Model Description 406 12.3.1.1 Mass Conservation and Thermodynamic Description 408 12.3.1.2 Calculation of the Entropy Production Rate due to Grain Boundary Diffusion 409 12.3.1.3 Calculation of the Driving Force 410 12.3.2 Results of Model Calculations for the Cu–Ni System 411 12.3.2.1 Determination of the Curvature of the Gibbs Potential 411 12.3.2.2 Diffusion Parameters of the System 412 12.3.2.3 Grain Boundary Mobility 412 12.3.2.4 Results of the Model Calculation for the Cu/Ni/Cu-Like System 412 12.4 Entropy Production as a Regularization Factor in Solving the Inverse Diffusion Problem 416 12.4.1 Description of the Procedure of the Inverse Diffusion Problem Solution for a Binary System 416 12.4.2 Results of Model Calculations 418 12.5 Conclusions 421 References 422 Further Reading 424 13 Nucleation and Phase Separation in Nanovolumes 425 Aram S. Shirinyan and Andriy M. Gusak 13.1 Introduction 425 13.2 Physics of Small Particles and Dispersed Systems 427 13.2.1 Nano-Thermodynamics 427 13.2.2 Production of Dispersed Systems 428 13.2.3 Anomalous Structures and Phases in DSs and Thermodynamic Estimates 428 13.2.4 Influence of DSs on the Temperature of the Phase Transformation 430 13.2.5 State Diagrams of DSs 431 13.2.6 Shift of the Solubility Limits in DSs 431 13.2.6.1 Depletion 432 13.2.7 Concluding Remarks 432 13.3 Phase Transformations in Nanosystems 433 13.3.1 Solid–Solid First-Order Phase Transitions 433 13.3.1.1 Geometry of a Nanoparticle and Nucleation Modes 433 13.3.1.2 Depletion Effect 435 13.3.1.3 Regular Solution 435 13.3.1.4 Change of Gibbs Free Energy 436 13.3.1.5 Minimization Procedure 437 13.3.1.6 Probability Factor of the Phase Transformation 439 13.3.2 Phase Diagram Separation 439 13.3.2.1 Variation of TemperatureT 439 13.3.2.2 Transition Criterion, Separation Criterion 440 13.3.2.3 VaryingR 441 13.3.2.4 VaryingC0 441 13.3.2.5 Phase Diagram 441 13.3.2.6 Size-Dependent Diagram and Solubilities in Multicomponent Nanomaterials 442 13.3.2.7 Critical Supersaturation 443 13.3.2.8 Concluding Remarks 444 13.4 Diagram Method of Phase Transition Analysis in Nanosystems 444 13.4.1 Gibbs’s Method of Geometrical Thermodynamics 445 13.4.2 Nucleation of an Intermediate Phase 446 13.4.2.1 Phase Transition Criterion 446 13.4.2.2 Model of Intermediate Phase 446 13.4.2.3 Separation in a Macroscopic Sample: Equilibrium State Diagram 447 13.4.2.4 Separation in DSs: Size-Dependent Phase Diagram 448 13.4.2.5 Influence of Size on Limiting Solubility 449 13.4.2.6 Influence of Size of an Isolated Particle on the Phase Transition Temperature 449 13.4.2.7 Concluding Remarks 450 13.5 Competitive Nucleation and Growth of Two Intermediate Phases: Binary Systems 451 Case 1 454 Case 2 454 Case 3 or Crossover Regime 455 13.5.1 Application to the Aluminum–Lithium system 456 13.5.2 Concluding Remarks 458 13.6 Phase Diagram Versus Diagram of Solubility: What is the Difference for Nanosystems? 458 13.6.1 Some General Definitions 461 13.6.1.1 What are the ‘‘solidus’’ and ‘‘liquidus’’? 461 13.6.1.2 What is the ‘‘Limit of Solubility’’? 461 13.6.2 Nanosized Solubility Diagram 462 13.6.2.1 Solubility Limit 462 13.6.2.2 Liquidus 462 13.6.2.3 Solidus 462 13.6.2.4 Nanosized Solubility Diagram 462 13.6.3 Nanosized Phase Diagram 463 13.6.3.1 Three Types of Diagrams 463 13.6.3.2 T–CDiagram at FixedR 464 13.6.3.3 VaryingR 465 13.6.3.4 Concluding Remarks 465 13.7 Some Further Developments 465 13.7.1 Solubility Diagram of the Cu–Ni Nanosystem 465 13.7.2 Size-Induced Hysteresis in the Process of Temperature Cycling of a Nanopowder 466 13.7.2.1 Concluding Remarks 468 13.A Appendix: The Rule of Parallel Tangent Construction for Optimal Points of Phase Transitions 469 13.A.1 Resume 470 References 471 Index 475 |
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