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Alloy Physics
A Comprehensive Reference
Edited by
Wolfgang Pfeiler
Innodata9783527614202.jpg
Alloy Physics
Edited by
Wolfgang Pfeiler
Alloy Physics
A Comprehensive Reference
Edited by
Wolfgang Pfeiler
The Editor
Professor Wolfgang Pfeiler
Universität Wien
Fakultät für Physik
Dynamik Kondensierter Systeme
Strudlhofgasse 4
1090 Wien
Österreich
Cover
Domain structure in an L12-ordered single
crystal as obtained by Monte-Carlo
simulation. Colours show the four possible
variants of ordered domains.
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Contents
Preface XIX
Foreword XXIby Robert W. Cahn
Motto XXIII
List of Contributors XXV
1 Introduction 1Wolfgang Pfeiler
1.1 The Importance of Alloys at the Beginning of the Third
Millennium 11.2 Historical Development 51.2.1 Historical Perspective 51.2.2 The Development of Modern Alloy Science 91.3 Atom Kinetics 121.4 The Structure of this Book 13
References 18
2 Crystal Structure and Chemical Bonding 19Yuri Grin, Ulrich Schwarz, and Walter Steurer
2.1 Introduction 192.2 Factors Governing Formation, Composition and Crystal Structure of
Intermetallic Phases 202.2.1 Mappings of Crystal Structure Types 212.3 Models of Chemical Bonding in Intermetallic Phases 252.3.1 Models Based on the Valence (or Total) Electron Numbers 252.3.2 Quantum Mechanical Models for Metallic Structures 292.3.3 Electronic Closed-Shell Configurations and Two-Center Two-Electron
Bonds in Intermetallic Compounds 312.3.3.1 Zintl–Klemm Approach 32
V
2.3.3.2 Extended 8�N Rule 332.3.3.3 Bonding Models in Direct Space 342.4 Structure Types of Intermetallic Compounds 362.4.1 Classification of the Crystal Structures of Intermetallic
Compounds 372.4.2 Crystal Structures Derived from the Closest Packings of Equal
Spheres 372.4.3 Crystal Structures Derived from the Close Packings of Equal
Spheres 402.4.4 Crystal Structures Derived from the Packings of the Spheres of
Different Sizes 432.4.5 Selected Crystal Structures with Complex Structural Patterns 442.5 Quasicrystals 482.5.1 Introduction 482.5.2 Quasiperiodic Structures in Direct and Reciprocal Space 502.5.3 Formation and Stability 522.5.4 Structures of Decagonal Quasicrystals (DQCs) 532.5.5 Structures of Icosahedral Quasicrystals 552.6 Outlook 59
References 60
3 Solidification and Grown-in Defects 63Thierry Duffar
3.1 Introduction: the Solid–Liquid Interface 633.1.1 Structure of the Solid–Liquid Interface 633.1.2 Kinetics of the Solid–Liquid Interface 653.1.3 Chemistry of the Solid–Liquid Interface: the Segregation
Problem 673.1.4 Temperature of the Solid–Liquid Interface 693.2 Solidification Structures 703.2.1 The Interface Stability and Cell Periodicity 713.2.2 Dendrites 743.2.2.1 Different Types of Dendrites 753.2.2.2 Kinetics of Columnar Dendrites 783.2.2.3 Kinetics of Equiaxed Dendrites 813.2.2.4 Characteristic Dimensions of the Dendrite 833.2.2.5 Microsegregation 853.2.3 Rapid Solidification 863.2.3.1 Absolute Stability and Diffusionless Solidification 863.2.3.2 Nonequilibrium Phase Diagrams 873.2.3.3 Structure of the Rapidly Solidified Phase 873.2.4 Eutectic Structures 903.2.4.1 Size of the Eutectic Structure 903.3 Defects in Single and Polycrystals 933.3.1 Defects in Single Crystals 94
VI Contents
3.3.1.1 Point Defects 943.3.1.2 Twins 973.3.1.3 Grains 983.3.2 Grain Structure of an Alloy 1013.3.2.1 Equiaxed Growth in Presence of Refining Particles 1033.3.2.2 Columnar to Equiaxed Transition 1073.3.3 Macro- and Mesosegregation 1103.4 Outlook 114
References 117
4 Lattice Statics and Lattice Dynamics 119Véronique Pierron-Bohnes and Tarik Mehaddene
4.1 Introduction: The Binding and Atomic Interaction Energies 1194.2 Elasticity of Crystalline Lattices 1244.2.1 Linear Elasticity 1254.2.2 Elastic Constants 1254.2.3 Cases of Cubic and Tetragonal Lattices 1274.2.4 Usual Elastic Moduli 1284.2.5 Link with Sound Propagation 1304.3 Lattice Dynamics and Thermal Properties of Alloys 1324.3.1 Normal Modes of Vibration in the Harmonic Approximation 1334.3.1.1 Classical Theory 1334.3.1.2 Diatomic Linear Chain 1364.3.1.3 Quantum Theory 1384.3.1.4 Phonon Density of States 1414.3.1.5 Lattice Specific Heat 1434.3.1.6 Debye’s Model 1444.3.1.7 Elastic Waves in Cubic Crystals 1464.3.1.8 Vibrational Entropy 1474.4 Beyond the Harmonic Approximation 1494.4.1 Thermal Expansion 1504.4.2 Thermal Conductivity 1514.4.3 Soft Phonon Modes and Structural Phase Transition 1534.5 Experimental Investigation of the Normal Modes of Vibration 1564.5.1 Raman Spectroscopy 1564.5.2 Inelastic Neutron Scattering 1574.6 Phonon Spectra and Migration Energy 1604.7 Outlook 165
References 168
5 Point Defects, Atom Jumps, and Diffusion 173Wolfgang Püschl, Hiroshi Numakura, and Wolfgang Pfeiler
5.1 Point Defects 1735.1.1 A Brief Overview 1735.1.1.1 Types of Point Defects 173
Contents VII
5.1.1.2 Formation of Equilibrium and Nonequilibrium Defects 1755.1.1.3 Mobility 1785.1.1.4 Experimental Techniques 1795.1.2 Point Defects in Pure Metals and Dilute Alloys 1875.1.2.1 Vacancies 1875.1.2.2 Self-Interstitial Atoms 1935.1.2.3 Solute Atoms 1955.1.3 Point Defects in Ordered Alloys 1975.1.3.1 Point Defects and Properties of the Material 1975.1.3.2 Statistical Thermodynamics 1995.1.3.3 Equilibrium Concentrations – Examples 2085.1.3.4 Abundant Vacancies in some Intermetallic Compounds 2135.2 Defect Migration: Microscopic Diffusion 2175.2.1 The Single Atom Jump 2175.2.1.1 Transition State Theory 2175.2.1.2 Alternative Methods 2215.2.2 Solid Solutions 2225.2.2.1 Random Walk 2225.2.2.2 Correlated Walk – the Interaction of Defect and Atom 2285.2.2.3 Diffusion Walk with Chemical Driving Force 2345.2.2.4 Diffusion Walk in an Inhomogeneous Crystal 2375.2.3 Atom Migration in Ordered Alloys 2385.2.3.1 Experimental Approach to Atom Kinetics in Ordered Alloys 2385.2.3.2 Jumps Within and Between Sublattices 2395.2.3.3 Jump Cycles and Cooperative Atom Jumps 2465.3 Statistical Methods: from Single Jump to Configuration
Changes 2525.3.1 Master Equation Method 2535.3.2 Continuum Approaches to Microscopic Diffusion and their
Interrelationship with Atom Jump Statistics 2535.3.3 Path Probability Method 2555.3.4 Monte Carlo Simulation Method 2555.4 Macroscopic Diffusion 2565.4.1 Formal Description 2565.4.1.1 Fick’s Laws 2565.4.1.2 Nonreciprocal Diffusion, the Kirkendall Effect 2595.4.1.3 Nonideal Solutions 2615.4.2 Phase Transformations as Diffusion Phenomena 2635.4.2.1 Spinodal Decomposition 2635.4.2.2 Nucleation, Growth, Coarsening 2645.4.3 Enhanced Diffusion Paths 2655.4.3.1 Dislocation-Core Diffusion 2665.4.3.2 Grain-Boundary Diffusion 2685.4.3.3 Diffusion along Interfaces and Surfaces 2705.5 Outlook 272
References 274
VIII Contents
6 Dislocations and Mechanical Properties 281Daniel Caillard
6.1 Introduction 2816.2 Thermally Activated Mechanisms 2836.2.1 Introduction to Thermal Activation 2836.2.2 Interactions with Solute Atoms 2856.2.2.1 General Aspects 2856.2.2.2 Low Temperatures (Domain 2, Interaction with Fixed Solute
Atoms) 2866.2.2.3 Intermediate Temperatures (Domain 3, Stress Instabilities) 2896.2.2.4 High Temperatures (Domain 4, Diffusion-Controlled Glide) 2916.2.3 Forest Mechanism 2926.2.4 Peierls-Type Friction Forces 2936.2.4.1 The Kink-Pair Mechanism 2936.2.4.2 Locking–Unlocking Mechanism 2956.2.4.3 Transition between Kink-Pair and Locking–Unlocking
Mechanisms 2976.2.4.4 Observations of Peierls-Type Mechanisms 2986.2.5 Cross-Slip in fcc Metals and Alloys 3056.2.5.1 Elastic Calculations 3056.2.5.2 Atomistic Calculations 3076.2.5.3 Experimental Results 3076.2.6 Dislocation Climb 3096.2.6.1 Emission of Vacancies at Jogs 3096.2.6.2 Diffusion of Vacancies from Jogs 3106.2.6.3 Jog Density and Jog-Pair Mechanism 3116.2.6.4 Effect of Over- (Under-) Saturations of Vacancies: Chemical
Force 3136.2.6.5 Stress Dependence of the Dislocation Climb Velocity 3146.2.6.6 Experimental Results 3146.2.7 Conclusions on Thermally Activated Mechanisms 3166.3 Hardening and Recovery 3166.3.1 Dislocation Multiplication versus Exhaustion 3176.3.1.1 Dislocation Sources 3186.3.1.2 Dislocation Exhaustion and Annihilation 3206.3.2 Dislocation–Dislocation Interaction and Internal Stress: the Taylor
Law 3216.3.3 Hardening Stages in fcc Metals and Alloys 3236.3.3.1 Stage II (Linear Hardening) 3246.3.3.2 Stage III 3296.3.3.3 Stage IV 3306.3.3.4 Strain-Hardening in Intermetallic Alloys 3306.4 Complex Behavior 3306.4.1 Yield Stress Anomalies 3306.4.1.1 Dynamic Strain Aging 331
Contents IX
6.4.1.2 Cross-Slip Locking 3326.4.2 Fatigue 3336.4.2.1 Microstructure of Fatigued Metals and Alloys 3346.4.2.2 Comparison with Stages II and III of Monotonic Strain
Hardening 3356.4.2.3 Intrusions, Extrusions and Fracture 3356.4.2.4 Conclusions 3366.4.3 Strength of Nanocrystalline Alloys and Thin Layers 3366.4.3.1 The Hall–Petch Law (Grain Size Db 20 nm) 3376.4.3.2 Hall–Petch Law Breakdown (Grain Size Da 20 nm) 3376.4.4 Fracture 3386.4.5 Quasicrystals 3396.5 Outlook 342
References 342
7 Phase Equilibria and Phase Transformations 347Brent Fultz and Jeffrey J. Hoyt
7.1 Alloy Phase Diagrams 3477.1.1 Solid Solutions 3477.1.2 Free Energy and the Lever Rule 3517.1.3 Common Tangent Construction 3537.1.4 Unmixing and Continuous Solid Solubility Phase Diagrams 3547.1.5 Eutectic and Peritectic Phase Diagrams 3567.1.6 More Complex Phase Diagrams 3577.1.7 Atomic Ordering 3597.1.8 Beyond Simple Models 3627.1.9 Entropy of Configurations 3637.1.10 Principles of Phonon Entropy 3657.1.11 Trends of Phonon Entropy 3677.1.12 Phonon Entropy at Elevated Temperatures 3697.2 Kinetics and the Approach to Equilibrium 3717.2.1 Suppressed Diffusion in the Solid (Nonequilibrium
Compositions) 3717.2.2 Nucleation Kinetics 3737.2.3 Suppressed Diffusion in the Liquid (Glasses) 3747.2.4 Suppressed Diffusion in a Solid Phase (Solid-State
Amorphization) 3757.2.5 Combined Reactions 3767.2.6 Statistical Kinetics of Phase Transformations 3777.2.7 Kinetic Pair Approximation 3787.2.8 Equilibrium State of Order 3807.2.9 Kinetic Paths 3807.3 Nucleation and Growth Transformations 3827.3.1 Definitions 382
X Contents
7.3.2 Fluctuations and the Critical Nucleus 3847.3.3 The Nucleation Rate 3877.3.4 Time-Dependent Nucleation 3917.3.5 Effect of Elastic Strain 3937.3.6 Heterogeneous Nucleation 3957.3.7 The Kolmogorov–Johnson–Mehl–Avrami Growth Equation 3977.4 Spinodal Decomposition 3997.4.1 Concentration Fluctuations and the Free Energy of Solution 4007.4.2 The Diffusion Equation 4027.4.3 Effects of Elastic Strain Energy 4047.5 Martensitic Transformations 4067.5.1 Characteristics of Martensite 4067.5.2 Massive and Displacive Transformations 4117.5.3 Bain Strain Mid-Lattice Invariant Shear 4127.5.4 Martensite Crystallography 4137.5.5 Nucleation and Dislocation Models of Martensite 4157.5.6 Soft Mode Transitions, the Clapp Lattice Instability Model 4177.6 Outlook 418
References 420
8 Kinetics in Nonequilibrium Alloys 423Pascal Bellon and Georges Martin
8.1 Relaxation of Nonequilibrium Alloys 4248.1.1 Coherent Precipitation: Nothing but Solid-State Diffusion 4258.1.2 Cluster Dynamics, Nucleation Theory, Diffusion Equations: Three
Tools for Describing Kinetic Pathways 4268.1.3 Cluster Dynamics 4278.1.3.1 Dilute Alloy at Equilibrium 4278.1.3.2 Fluctuations in the Gas of Clusters at Equilibrium 4298.1.3.3 Relaxation of a Nonequilibrium Cluster Gas 4298.1.4 Classical Nucleation Theory 4328.1.4.1 Summary of CNT 4328.1.4.2 Source of Fluctuations Consistent with CNT 4338.1.4.3 A First Application 4358.1.5 Kinetics of Concentration Fields 4368.1.6 Conclusion 4388.2 Driven Alloys 4388.2.1 Examples of Driven Alloys 4398.2.1.1 Alloys Subjected to Sustained Irradiation 4398.2.1.2 Alloys Subjected to Sustained Plastic Deformation 4478.2.1.3 Alloys Subjected to Sustained Electrochemical Exchanges 4498.2.2 Identification of the Relevant Control Parameters: Toward a
Dynamical Equilibrium Phase Diagram 4508.2.3 Theoretical Approaches and Simulation Techniques 454
Contents XI
8.2.3.1 Molecular Dynamics Simulations 4558.2.3.2 Microscopic Master Equation 4568.2.3.3 Kinetic Monte Carlo Simulations 4588.2.3.4 Kinetics of Concentration Fields under Irradiation 4608.2.3.5 Nucleation Theory under Irradiation 4668.2.4 Self-Organization in Driven Alloys: Role of Length Scales of the
External Forcing 4688.2.4.1 Compositional Patterning under Irradiation 4698.2.4.2 Patterning of Chemical Order under Irradiation 4788.2.4.3 Compositional Patterning under Plastic Deformation 4808.2.5 Practical Applications and Extensions 4818.2.5.1 Tribochemical Reactions 4818.2.5.2 Pharmaceutical Compounds Synthesized by Mechanical
Activation 4838.3 Outlook 484
References 484
9 Change of Alloy Properties under Dimensional Restrictions 491Hirotaro Mori and Jung-Goo Lee
9.1 Introduction 4919.2 Instrumentation for in-situ Observation of Phase Transformation of
Nanometer-Sized Alloy Particles 4929.3 Depression of the Eutectic Temperature and its Relevant
Phenomena 4949.3.1 Atomic Diffusivity in Nanometer-Sized Particles 4949.3.2 Eutectic Temperature in Nanometer-Sized Alloy Particles 4969.3.3 Structural Instability 5009.3.4 Thermodynamic Discussion 5039.3.4.1 Gibbs Free Energy in Nanometer-Sized Alloy Systems 5039.3.4.2 Result of Calculations 5059.4 Solid/Liquid Two-Phase Microstructure 5089.4.1 Solid–Liquid Phase Transition 5089.4.2 Two-Phase Microstructure 5149.5 Solid Solubility in Nanometer-Sized Alloy Particles 5189.6 Summary and Future Perspectives 521
References 522
10 Statistical Thermodynamics and Model Calculations 525Tetsuo Mohri
10.1 Introduction 52510.2 Statistical Thermodynamics on a Discrete Lattice 52710.2.1 Description of Atomic Configuration 52710.2.2 Internal Energy 53410.2.3 Entropy and Cluster Variation Method 536
XII Contents
10.2.4 Free Energy 54210.2.5 Relative Stability and Intrinsic Stability 54410.2.6 Atomistic Kinetics by the Path Probability Method 54910.3 Statistical Thermodynamics on Continuous Media 55210.3.1 Ginzburg–Landau Free Energy 55210.3.2 Diffusion Equation and Time-Dependent Ginzburg–Landau
Equation 55410.3.3 Width of an Interface 55710.3.4 Interface Velocity 55910.4 Model Calculations 56010.4.1 Calculation of a Phase Diagram 56110.4.1.1 Ground-State Analysis 56110.4.1.2 Effective Cluster Interaction Energy 56410.4.1.3 Phase Diagram 56810.4.2 Microstructural Evolution Calculated by the Phase Field Method 57210.4.2.1 Hybrid Model 57210.4.2.2 Toward the First-Principles Phase Field Calculation 57610.5 Future Scope and Outlook 580
Appendix: CALPHAD Free Energy 582References 585
11 Ab-Initio Methods and Applications 589Stefan Müller, Walter Wolf, and Raimund Podloucky
11.1 Introduction 58911.2 Theoretical Background 59011.2.1 Density Functional Theory 59011.2.2 Computational Methods 59411.2.3 Elastic Properties 59811.2.4 Vibrational Properties 60111.3 Applications 60611.3.1 Structural and Phase Stability 60611.3.2 Point Defects 61211.3.3 Diffusion Processes 61611.3.4 Impurity Effects on Grain Boundary Cohesion 62211.3.5 Toward Multiscale Modeling: Cluster Expansion 62511.3.6 Search for Ground-State Structures 63911.3.7 Ordering and Decomposition Phenomena in Binary Alloys 64111.4 Outlook 648
References 649
12 Simulation Techniques 653Ferdinand Haider, Rafal Kozubski, and T.A. Abinandanan
12.1 Introduction 65312.2 Molecular Dynamics Simulations 654
Contents XIII
12.2.1 Basic Ideas 65412.2.2 Atomic Interaction, Potential Models 65612.2.2.1 Pairwise Interaction 65612.2.2.2 Many-Body Potentials, the EAM Method 65712.2.3 Practical Considerations 65912.2.4 Different Thermodynamic Ensembles: Thermostats, Barostats 65912.2.5 Implementation of MD Algorithms 66112.2.6 Practical Aspects: Time Steps 66212.2.7 Evaluation of Data: Use of Correlation Functions 66212.2.8 Applications to Alloys, Alloy Dynamics, and Alloy Kinetics 66412.3 Monte Carlo Simulations 66712.3.1 Foundations of Stochastic Processes – Markov Chains and the Master
Equation 66712.3.2 The Idea of Sampling 66812.3.3 Markov Chains as a Tool for Importance Sampling 67012.3.4 General Applicability 67112.3.4.1 Simulation and Characterization of System Properties in
Thermodynamic Equilibrium 67112.3.4.2 Simulation of Relaxation Processes Toward Equilibrium 67312.3.4.3 Simulation of Nonequilibrium Processes and Transport
Phenomena 67312.3.5 Limitations: Finite-Size Effects and Boundary Conditions 67412.3.6 Numerical Implementation of MC 67512.3.6.1 Classical Realization of Markov Chains 67512.3.6.2 ‘‘Residence Time’’ Algorithm 67612.3.6.3 The Problem of Time Scales 67712.3.7 Applications to Alloys 67812.3.7.1 General Assumptions 67812.3.7.2 Physical Model of an Alloy 67912.3.8 Practical Aspects 68112.3.9 Review of Current Applications in Studies of Alloys 68212.3.9.1 Computation of Phase Diagrams using Grandcanonical
Ensemble 68312.3.9.2 Reverse and Inverse Monte Carlo Methods: from Experimental SRO
Parameters to Atomic Interaction Energies 68312.3.10 Going beyond the Ising Model and Rigid-Lattice Simulations 68512.3.11 Monte Carlo Simulations in View of other Techniques of Alloy
Modeling 68612.4 Phase Field Models 68612.4.1 Introduction 68612.4.2 Cahn–Hilliard Model 68712.4.2.1 Energetics 68712.4.2.2 Interfacial Energy and Width 68912.4.2.3 Dynamics 69112.4.3 Numerical Implementation 691
XIV Contents
12.4.4 Application: Spinodal Decomposition 69312.4.5 Cahn–Allen Model 69412.4.5.1 Kinetics 69512.4.6 Generalized Phase Field Models 69612.4.6.1 Key Features of Phase Field Models 69612.4.6.2 Precipitation of an Ordered Phase 69712.4.6.3 Grain Growth in Polycrystals 69812.4.6.4 Solidification 70012.4.7 Other Topics 70012.4.7.1 Anisotropy in Interfacial Energy 70012.4.7.2 Elastic Strain Energy 70112.5 Outlook 702
Appendix 702References 703
13 High-Resolution Experimental Methods 707
13.1 High-Resolution Scattering Methods and Time-Resolved
Diffraction 707Bogdan Sepiol and Karl F. Ludwig
13.1.1 Introduction: Theoretical Concepts, X-Ray, and Neutron Scattering
Methods 70713.1.2 Magnetic Scattering 71013.1.2.1 Magnetic Neutron Scattering 71013.1.2.2 Magnetic X-Ray Scattering 71513.1.3 Spectroscopy 72113.1.3.1 Coherent Time-Resolved X-Ray Scattering 72213.1.3.1.1 Homodyne X-Ray Studies of Equilibrium Fluctuation Dynamics 72313.1.3.1.2 Heterodyne X-Ray Studies of Equilibrium Fluctuation Dynamics 72513.1.3.1.3 Studies of Critical Fluctuations with Microbeams 72613.1.3.1.4 Coherent X-Ray Studies of the Kinetics of Nonequilibrium
Systems 72613.1.3.1.5 Coherent X-Ray Studies of Microscopic Reversibility 72913.1.3.2 Phonon Excitations 72913.1.3.2.1 Inelastic X-Ray Scattering 73013.1.3.2.2 Nuclear Inelastic Scattering 73213.1.3.3 Quasielastic Scattering: Diffusion 73313.1.3.3.1 Quasielastic Methods: Mössbauer Spectroscopy and Neutron
Scattering 73813.1.3.3.2 Nuclear Resonant Scattering of Synchrotron Radiation 74113.1.3.3.3 Pure Metals and Dilute Alloys 74313.1.3.3.4 Ordered Alloys 74413.1.3.3.5 Amorphous Materials 74513.1.4 Time-Resolved Scattering 749
Contents XV
13.1.4.1 Technical Capabilities 75013.1.4.2 Time-Resolved Studies – Examples 75113.1.5 Diffuse Scattering from Disordered Alloys 75613.1.5.1 Metallic Glasses and Liquids 75713.1.5.2 Diffuse Scattering from Disordered Crystalline Alloys 75913.1.6 Surface Scattering – Atomic Segregation and Ordering near
Surfaces 76213.1.7 Scattering from Quasicrystals 76313.1.8 Outlook 764
References 765
13.2 High-Resolution Microscopy 774Guido Schmitz and James M. Howe
13.2.1 Surface Analysis by Scanning Probe Microscopy 77513.2.1.1 Functional Principle of Scanning Tunneling and Atomic Force
Microscopy 77613.2.1.2 Modes of Measurement in AFM 77913.2.1.3 Cantilever Design for the AFM 78113.2.1.4 Exemplary Studies by Scanning Probe Microscopy 78313.2.1.4.1 Chemical Contrast by STM and Surface Ordering 78313.2.1.4.2 Microstructure Characterization and Surface Topology by AFM 78513.2.1.4.3 Imaging of Nanomagnets by Magnetic Force Microscopy 78913.2.2 High-Resolution Transmission Electron Microscopy and Related
Techniques 79113.2.2.1 Principles of Image Formation in and Practical Aspects of High-
Resolution Transmission Electron Microscopy 79313.2.2.1.1 Principles of Image Formation 79313.2.2.1.2 Practical Aspects of HRTEM 79613.2.2.2 In-Situ Hot-Stage High-Resolution Transmission Electron
Microscopy 79713.2.2.3 Examples of HRTEM Studies of Dislocation and Interphase
Boundaries 79913.2.2.3.1 Disclinations in Mechanically Milled Fe Powder 79913.2.2.3.2 Interphase Boundaries in Metal Alloys 80213.2.2.3.3 Diffuse Interface in CuaAu 80213.2.2.3.4 Partly Coherent Interfaces in AlaCu 80713.2.2.3.5 Incoherent Interfaces in TiaAl 81113.2.3 Local Analysis by Atom Probe Tomography 81713.2.3.1 The Functional Principle of Atom Probe Tomography 81913.2.3.2 Two-Dimensional Single-Ion Detector Systems 82313.2.3.3 Ion Trajectories and Image Magnification 82713.2.3.4 Tomographic Reconstruction 83013.2.3.5 Accuracy of the Reconstruction 83313.2.3.6 Specimen Preparation 83613.2.3.7 Examples of Studies by Atom Probe Tomography 837
XVI Contents
13.2.3.7.1 Decomposition in Supersaturated Alloys 83713.2.3.7.2 Nucleation of the First Product Phase 84313.2.3.7.3 Diffusion in Nanocrystalline Thin Films 84713.2.3.7.4 Thermal Stability of GMR Sensor Layers 85013.2.4 Future Development and Outlook 853
References 857
14 Materials and Process Design 861
14.1 Soft and Hard Magnets 861Roland Grössinger
14.1.1 What do ‘‘Soft’’ and ‘‘Hard’’ Magnetic Mean? 86114.1.1.1 Intrinsic Properties Determining the Hysteresis Loop (Anisotropy,
Magnetostriction) 86314.1.1.2 Extrinsic Properties – Microstructure 86414.1.2 Soft Magnetic Materials 86514.1.2.1 Pure Fe and FexSi 86714.1.2.2 NiaFe Alloys 86814.1.2.3 Soft Magnetic Ferrites 86914.1.2.4 Amorphous Materials 87114.1.2.5 Nanocrystalline Materials 87214.1.3 Hard Magnetic Materials 87314.1.3.1 AlNiCo 87614.1.3.2 Ferrites 87714.1.3.3 SmaCo 87814.1.3.4 NdaFeaB 87914.1.3.5 Nanocrystalline Materials 88014.1.3.6 Industrial Nanocrystalline Hard Magnetic Materials 88214.1.4 Outlook 883
References 883
14.2 Invar Alloys 885Peter Mohn
14.2.1 Introduction and General Remarks 88514.2.2 Spontaneous Volume Magnetostriction 88814.2.3 The Modeling of Invar Properties 88914.2.4 A Microscopic Model 89314.2.5 Outlook 894
References 895
14.3 Magnetic Media 895Laurent Ranno
14.3.1 Data Storage 89514.3.1.1 Information Storage 895
Contents XVII
14.3.1.2 Competing Physical Effects 89614.3.1.3 Magnetic Storage 89714.3.2 Magnetic Recording Media 90514.3.2.1 Particulate Media 90514.3.2.2 Continuous Media – Film Media 90614.3.2.3 Perpendicular Recording 90714.3.3 Outlook 909
Further Reading 910
14.4 Spin Electronics (Spintronics) 911Laurent Ranno
14.4.1 Electrical Transport in Conductors 91114.4.1.1 Conventional Transport 91114.4.1.2 Role of Disorder 91314.4.1.3 Transport in Magnetic Conductors 91414.4.2 Magnetoresistance 91514.4.2.1 Cyclotron Magnetoresistance 91614.4.2.2 Anisotropic Magnetoresistance (AMR) 91614.4.2.3 Giant MR (GMR) and Tunnel MR (TMR) 91614.4.2.4 Magnetic Field Sensors 91814.4.2.5 Magnetic RAM 92014.4.3 Outlook 921
Further Reading 921
14.5 Phase-Change Media 921Takeo Ohta
14.5.1 Electrically and Optically Induced Writing and Erasing
Processes 92114.5.2 Phase-Change Dynamic Model 92514.5.3 Alternative Functions 93314.5.4 Outlook 938
References 938
14.6 Superconductors 939Harald W. Weber
14.6.1 Fundamentals 93914.6.2 Superconducting Materials 94414.6.3 Technical Superconductors 94614.6.4 Applications 952
Further Reading 953
Index 955
XVIII Contents
Preface
Just after Wiley-VCH’s consulting editor, Ed Immergut, invited me to edit a book
on ‘‘alloy physics’’, I hesitated greatly before agreeing, as I was a bit shocked by
the breadth of the topic to be covered in such a book. I therefore first suggested a
volume on Atom Jumps in Intermetallics to reduce the area correspondingly, butfinally agreed to Alloy Physics because it would appeal to a much broader audienceincluding physicists, materials scientists, physical chemists, and metallurgists in
academic as well as in industrial laboratories.
Writing ‘‘alloy physics’’ into an Internet search engine, I suddenly realized that
indeed there seems to be a need for such a reference book. I therefore started to
prepare a tentative outline, and found that this could be done in a straightforward
way and in a comparatively short time. Another surprise was the great number of
very positive referee reports on my outline – four of them arrived within just two
days after I sent out my outline!
The next step was to find and motivate chapter authors to take part in the proj-
ect. The resulting book now contains 14 chapters, written by an international
team of authors, some of whom have written their text by correspondence across
the Atlantic.
An essential point is that the book does not avoid overlaps between chapters: on
the contrary, I hope that looking at fundamental problems in alloy physics from
different aspects will make the book even more interesting and useful.
I am very grateful to my colleague Wolfgang Püschl for continual discussions,
comments, and suggestions, to our student David Reith for the use of one of his
simulation pictures for the cover, and last but not least to my dear wife Heidi for
her great patience and encouragement.
Vienna, May 2007 Wolfgang Pfeiler
XIX
Foreword*
The word ‘alloy’, from the old French, originally carried overtones of base metals
contaminating noble ones, and the word is still sometimes used in this sense
in literary metaphor. Today, however, we know that the true practical value of an
alloy derives from the knowledge and ingenuity that has gone into the choice of
constituents, proportions and heat-treatment, and an aristocratic alloy often
emerges from a mix of base metals. So, ‘nobility’ in alloys is a function of under-
standing, not of scarcity in the earth’s crust.
This important book sets out the sources of the modern understanding of
alloys, in great depth. The book represents the intimate mingling of physics
with metallurgy – whether that is called alloy physics or physical metallurgy is of
no consequence. It is some time since an overview of this whole field has been
published and the time is very ripe for this new venture. The book not only mixes
theory and experiment in a very helpful way but it also comprehensively covers
the world community of alloy physicists.
Sitting at the centre of the spider’s web is a notable Austrian physicist: Wolf-
gang Pfeiler’s office is in the Boltzmanngasse, named after the genial theorist
who first properly understood the entropy of mixtures. All of us in the profession
owe Wolfgang a great debt for his skill and persuasiveness in drawing together
such a distinguished array of contributors.
Cambridge, March 2007 Robert W. Cahn, FRS
* Robert Wolfgang Cahn (1924–2007) passed away on April 9th, 2007.
Professor Robert Cahn was one of the first promoters of ‘Materials Science’ (see
his recent book ‘The Coming of Materials Science’, Pergamon 2001) and soon
became an international leader in this field. Aside of his own intense scientific
research he was editor of many compendia and book series and founded four
journals. His memoirs have recently been published (‘The Art of Belonging’,
Book Guild Publishing 2005).
XXI
Motto
Georgii Agricolae, De re metallica libri XII, quibus Officia, Instrumenta, Machinae,ac omnia denique ad Metallicam spectantia, non modo luculentissime describuntur, sed& per effigies, suis locis insertas, adiunctis Latinis, Germanisque appellationibus ita oboculos ponuntur, ut clarius tradi non possint. Eiusdem de animantibus subterraneisLiber, ab Autore recognitus: cum Indicibus diversis, quicquid in opere tractatum est,pulchre demonstrantibus. Basileae MDLVI:Metallicus praeterea sit oportet multarum artium & disciplinarum non ignarus:
Primo Philosophiae, ut subterraneorum ortus & causas, naturasque noscat: Nam adfodiendas venas faciliore & commodiore uia perveniet, & ex effossis uberiores capietfructus. Secundo Medicinae, ut fossoribus & aliis operariis providere possit, ne in mor-bos, quibus prae caeteris urgentur, incidant: aut si inciderint, vel ipse eis curationes ad-hibere, vel ut medici adhibeant curare. Tertio Astronomiae, ut cognoscat coeli partes,atque ex eis venarum extensiones iudicet. Quarto Mensurarum disciplinae, ut & metiriqueat, quam alte fodiendus sit puteus, ut pertineat ad cuniculum usque qui eo agitur, &certos cuique fodinae, praesertim in profundo, constituere fines terminosque. Tum nu-merorum disciplinae sit intelligens, ut sumptus, qui in machinas & fossiones habendisunt, ad calculos revocare possit. Deinde Architecturae, ut diversas machinas substruc-tionesque ipse fabricari, vel magis fabricandi rationem aliis explicare queat. Postea Pic-turae, ut machinarum exempla deformare possit. Postremo Iuris, maxime metallici sitperitus, ut & alteri nihil surripiat, & sibi petat non iniquum, munusque aliis de iurerespondendi sustineat. Itaque necesse est ut is, cui placent certae rationes & praeceptarei metallicae hos aliosque nostros libros studiose diligenterque legat, aut de quaque reconsulat experientes metallicos, sed paucos inveniet gnaros totius artis.‘‘Furthermore, there are many arts and sciences of which a miner should not
be ignorant. First there is Philosophy, that he may discern the origin, cause, and
nature of subterranean things; for then he will be able to dig out the veins easily
and advantageously, and to obtain more abundant results from his mining. Sec-
ondly, there is Medicine, that he may be able to look after his diggers and other
workmen, that they do not meet with those diseases to which they are more liable
than workmen in other occupations, or if they do meet with them, that he him-
self may be able to heal them or may see that the doctors do so. Thirdly follows
Astronomy, that he may know the divisions of the heavens and from them judge
the direction of the veins. Fourthly, there is the science of Surveying that he may
XXIII
be able to estimate how deep a shaft should be sunk to reach the tunnel which is
being driven to it, and to determine the limits and boundaries in these workings,
especially in depth. Fifthly, his knowledge in Arithmetical Science should be such
that he may calculate the cost to be incurred in the machinery and the working of
the mine. Sixthly, his learning must comprise Architecture, that he himself may
construct various machines and timber work required underground, or that he
may be able to explain the method of the construction to others. Next, he must
have knowledge of Drawing, that he can draw plans of his machinery. Lastly,
there is the Law, especially that dealing with metals, that he may claim his own
rights, that he may undertake the duty of giving others his opinion on legal mat-
ters, that he may not take another man’s property and so make trouble for him-
self, and that he may fulfill his obligations according to the law.
It is therefore necessary that those who take interest in the methods and pre-
cepts of mining and metallurgy should read these and others of our books studi-
ously and diligently; or on every point they should consult expert mining people,
though they will discover few who are skilled in the whole art.’’
This translation follows Hoover and Hoover (1950).
Thus, here in the introduction to his famous work, Agricola gives us a plethora
of skills and arts which are indispensable for anyone extracting metal ores from
the bowels of the earth and processing them. This enumeration is more than
symbolic for the conditions the modern alloy physicist has to fulfill. Although
the development of science has carried his tasks to other levels of sophistication,
as a result they are no less numerous and diverse than those of the medieval met-
alworker. It is the intended spirit of this book to provide, by presenting solid
knowledge and different viewpoints, the wide horizon which favors significant
scientific progress.
Reference
Hoover, H.C. and Hoover, L.H. (1950)
Georgius Agricola: De Re Metallica,
Translation of the first Latin Edition of 1556,Dover Publications, Inc., New York, p. 3.
XXIV Motto
List of Contributors
T. A. Abinandanan
Indian Institute of Science
Department of Materials
Engineering
Bangalore 560 012
India
Pascal Bellon
University of Illinois at Urbana-
Champaign
Department of Materials Science
and Engineering
1304 W. Green St.
Urbana, IL 61801
USA
Daniel Caillard
CEMES-CNRS
29 rue Jeanne Marvig, BP4347
31055 Toulouse Cedex 4
France
Thierry Duffar
INPG Grenoble, SIMAP-EPM
ENSEEG – BP 75
38402 St. Martin d’Hères
France
Brent Fultz
California Institute of Technology,
mail 138-78
Pasadena, CA 91125
USA
Yuri Grin
Max-Planck-Institut für Chemische
Physik fester Stoffe
Nöthnitzer Straße 40
01187 Dresden
Germany
Roland Grössinger
Vienna University of Technology
Institut für Festkörperphysik
Wiedner Hptstr. 8-10/138
1040 Vienna
Austria
Ferdinand Haider
Universität Augsburg
Institut für Physik
Universitätsstr. 1
86135 Augsburg
Germany
James M. Howe
University of Virginia
School of Engineering and Applied
Science
Department of Materials Science and
Engineering
P.O. Box 400745
Charlottesville, VA 22904-4745
USA
XXV
Jeffrey J. Hoyt
Mc Master University and
Brockhouse
Institute for Materials Research
Department of Materials Science
and Engineering
1280 Main Street West
Hamilton, Ontario, L8S 4L7
Canada
Rafal Kozubski
Jagellonian University
M. Smoluchowski Institute of
Physics
ul. Reymonta 4
30-059 Cracow
Poland
Jung-Goo Lee
Korea Institute of Machinery &
Materials
Advanced Materials Research
Division
66 Sangnam-dong, Changwon-
City
Kyeongnam 641-831
Korea
Karl F. Ludwig, Jr.
Boston University
Physics Department,
590 Commonwealth Ave
Boston, MA 02215
USA
Georges Martin
CEA-Siège, Cab. H.C.
91191 Gif sur Yvette Cedex
France
Tarik Mehaddene
Technische Universität München
Physik Department E13/FRMII
James Franck Str. 1
85747 Garching
Germany
Peter Mohn
Vienna University of Technology
Center for Computational Materials
Science
Institut für Allgemeine Physik
Gumpendorferstraße 1a/134
1060 Vienna
Austria
Tetsuo Mohri
Hokkaido University
Graduate School of Engineering
Division of Materials Science and
Engineering
Sapporo 060-8628
Japan
Hirotaro Mori
Osaka University
Research Center for Ultra-High Voltage
Electron Microscopy
7-1 Mihogaoka, Ibaraki
Osaka 567-0047
Japan
Stefan Müller
Universität Erlangen-Nürnberg
Lehrstuhl für Festkörperphysik
Staudtstraße 7
91058 Erlangen
Germany
Hiroshi Numakura
Kyoto University
Department of Materials Science and
Engineering
Yoshida Hon-machi, Sakyo-ku
Kyoto 606-8501
Japan
now with:
Osaka Prefecture University
Department of Materials Science
Gakuen-cho 1-1, Naka-ku
Sakai 599-8531
Japan
XXVI List of Contributors
Takeo Ohta
Ovonic Phase Change Institute
Yamato Sogyo Incubation Center
102 Takabatake-cho, Nara-city,
Nara 630-8301
Japan
and
Energy Conversion Devices, Inc.
2956 Waterview Drive
Rochester Hills, MI 48309
USA
Wolfgang Pfeiler
University of Vienna
Faculty of Physics
Dynamics of Condensed Systems
Strudlhofgasse 4
1090 Vienna
Austria
Véronique Pierron-Bohnes
Institut de Physique et Chimie
des Matériaux de Strasbourg
UMR 7504 CNRS-ULP
23 rue du Loess, BP 43
67034 Strasbourg Cedex 2
France
Raimund Podloucky
University of Vienna
Faculty of Chemistry
Department of Physical
Chemistry
Sensengasse 8
1090 Vienna
Austria
Wolfgang Püschl
University of Vienna
Faculty of Physics
Dynamics of Condensed Systems
Strudlhofgasse 4
1090 Vienna
Austria
Laurent Ranno
Institut Néel, CNRS/UJF
25 avenue des Martyrs
BP 166
38042 Grenoble Cedex 9
France
Guido Schmitz
Westfälische Wilhelms-Universität
Münster
Institut für Materialphysik
Wilhelm-Klemm-Straße 10
48149 Münster
Germany
Ulrich Schwarz
Max-Planck-Institut für Chemische
Physik fester Stoffe
Nöthnitzer Straße 40
01187 Dresden
Germany
Bogdan Sepiol
University of Vienna
Faculty of Physics
Dynamics of Condensed Systems
Strudlhofgasse 4
1090 Vienna
Austria
Walter Steurer
ETH Zurich
Department of Materials
Laboratory of Crystallography
Wolfgang-Pauli-Str. 10
8093 Zurich
Switzerland
List of Contributors XXVII
Harald W. Weber
Vienna University of Technology
Atominstitut der Österreichischen
Universitäten
Stadionallee 2
1020 Vienna
Austria
Walter Wolf
Materials Design s.a.r.l.
44 avenue F.-A. Bartholdi
72000 Le Mans
France
XXVIII List of Contributors