Diffusion in Crystalline Solids

Diffusion in Crystalline Solids addresses some of the most active areas of research on diffusion in crystalline solids. Topics covered include measurement of tracer diffusion coefficients in solids, diffusion in silicon and germanium, atom transport in oxides of the fluorite structure, tracer diffusion in concentrated alloys, diffusion in dislocations, grain boundary diffusion mechanisms in metals, and the use of the Monte Carlo Method to simulate diffusion kinetics. This book is made up of eight chapters and begins with an introduction to the measurement of diffusion coefficients with radioisotopes. The following three chapters consider diffusion in materials of substantial technological importance such as silicon and germanium. Atomic transport in oxides of the fluorite structure is described, and diffusion in concentrated alloys, including intermetallic compounds, is analyzed. The next two chapters delve into diffusion along short-circuiting paths, focusing on the effect of diffusion down dislocations on the form of the tracer concentration profile. The book also discusses the mechanisms of diffusion in grain boundaries in metals by invoking considerable work done on grain-boundary structure. The last two chapters are concerned with computer simulation, paying particular attention to machine calculations and the Monte Carlo method. The book concludes by exploring the fundamental atomic migration process and presenting some state-of-the-art calculations for defect energies and the topology of the saddle surface. Students and researchers of material science will find this book extremely useful.

List of Contributors

Foreword

Preface

1. The Measurement of Tracer Diffusion Coefficients in Solids

I. Introduction

II. Preparation of Diffusion Samples

III. Annealing of Diffusion Samples

IV. Sectioning and Microsectioning

V. Counting of Radioactive Sections

VI. Determination of D from a Penetration Plot

VII. Conclusions

References

2. Diffusion in Silicon and Germanium

I. Introduction

II. Basic Features of Bulk Diffusion in Crystalline Solids

III. Self-Diffusion and Related Phenomena

IV. Survey of Foreign-Atom Diffusion

V. Oxidation-Influenced Diffusion of Group III and Group V Elements in Silicon

VI. A Barrier against Vacancy-Interstitial Recombination

VII. Diffusion of Group III and Group V Elements and Its Dependence on Doping

VIII. Anomalous Diffusion Phenomena

IX. Substitutional-Interstitial Interchange Diffusion and Application to Gold and Nickel in Silicon and to Copper in Germanium

X. Concluding Remarks

References

3. Atom Transport in Oxides of the Fluorite Structure

I. Introduction

II. Diffusion Studies

III. Conductivity and Relaxation

IV. Comparison of Ionic Conductivity and Oxygen Diffusion

References

4. Tracer Diffusion in Concentrated Alloys

I. Introduction

II. Theoretical Background

III. Empirical Rules

IV. Theoretical Considerations of the Kinetics of Diffusion in Random Alloys

V. Tracer Diffusion Experiments in Primary (Terminal) Phases

VI. Theoretical Considerations of Diffusion in Ordered Structures

VII. Tracer Diffusion Experiments in Intermediate Phases

VIII. Conclusions

References

5. The Mathematical Analysis of Diffusion in Dislocations

I. Introduction

II. The Dislocation Model

III. Solutions of the Diffusion Equations

IV. Properties of the Solutions

Appendix A. Derivation of Eq. (39)

Appendix B. The Poles of Eq. (39) for the Case of the Dislocation Array

Appendix C. Numerical Considerations in the Calculation of Q{η, ε/α)

Appendix D. Numerical Considerations in the Calculation of Q(η)

Appendix E. An Order of Magnitude Estimate of Δ

References

6. Grain Boundary Diffusion Mechanisms in Metals

I. Introduction

II. The Diffusion Spectrum

III. Present Knowledge of the Structure of Grain Boundaries and Their Line and Point Defects

IV. Review of Experiments Relevant to the Atom Jumping Mechanism in Boundaries

V. Model for Atom Jumping in Boundaries

VI. Influence of Boundary Structure on Boundary Diffusion

VII. Diffusion along Migrating Boundaries

VIII. Model for Grain Boundaries as Point Defect Sources and Sinks and Comparison with Experimental Observations

IX. Conclusions

References 37

7. Simulation of Diffusion Kinetics with the Monte Carlo Method

I. Introduction

II. Tracer Diffusion

III. Ionic Conductivity

IV. Chemical Diffusion

V. Conclusions

References

8. Defect Calculations beyond the Harmonic Model

I. Introduction

II. Lattice Dynamics

III. Vacancy Formation in fee Lennard-Jones Crystals

IV. Vacancy Migration

V. Analytical Treatment of Anharmonic Jump Frequency

VI. Conclusions

References

Index