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

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Domain structure in an L12-ordered single

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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