Crystal Defects and Crystalline Interfaces

It is nonnal for the preface to explain the motivation behind the writing of the book. Since many good books dealing with the general theory of crystal defects already exist, a new book has to be especially justified, and here its main justification lies in its treatment of crystal­ line interfaces. About 1961, the work of the author, essentially based on the fundamental work of Professor F. C. Frank, started to branch away from the main flow of thought in this field and eventually led to a general geometrical theory which is presented as a whole for the first time in this book. Although nearly all that is presented has already been published in different journals and symposia, it might be difficult for the reader to follow that literature, as a new terminology and new methods of analysis had to be developed. Special emphasis is given to discussion and many diagrams are included in order that a clear view of the basic concepts be obtained. Intennediate summaries try to bring out the main points of the chapters. Instead of specific exercises, general suggestions for them are given. The part up to chapter 9 is considered more or less as introductory, so that the book can be studied without specific knowledge of crystals and crystal defects. The presentation of that part developed out of lectures given by the author at the Swiss Federal Institute of Technology (ETH) in Zurich.

1. Introduction.- 1.1. The Significance of Crystal Defects.- 1.2. The Nature of Crystal Defects.- 2. General Aspects of the Structure of Crystals.- 2.1. Outline.- 2.2. Mathematical Description of the Crystal.- 2.3. Classification of Crystal Structures.- 3. Some Special Crystal Structures.- 3.1. Outline.- 3.2. Close-Packed Structures.- 3.3. The Face-Centred Cubic Structure.- 3.4. The NaCl-Structure.- 3.5. The Diamond Structure.- 3.6. The Body-Centred Cubic Structure.- 3.7. The Close-Packed Hexagonal Structure.- 3.8. The Graphite Structure.- 3.9. Irregularities in the Stacking Sequence.- 3.10. Energy of Stacking Faults.- 3.11. Fibrous Structures.- Chapters 2–3. Summary and Discussion.- 4. Point Defects.- 4.1. General Considerations of the Field of Point Defects.- 5. The Individual Dislocation: Geometrical Basis.- 5.1. Outline.- 5.2. Definition of the Dislocation Line and the Burgers Vector.- 5.3. Relative Orientation of b and l.- 5.4. Motion of Dislocations.- 5.5. Dislocations and Moiré-Figures.- 6. Interaction Between a Dislocation and its Surroundings.- 6.1. Outline.- 6.2. Representation of the Stress Field.- 6.3. Forces Acting on a Dislocation.- 6.4. Energy of a Dislocation.- 6.5. The Line Tension.- 6.6. The Strain Field of a Dislocation.- 6.7. The Stress Field of a Dislocation.- Chapters 5–6. Summary and Discussion.- 7. The Interaction of Dislocations.- 7.1. Outline.- 7.2. Interaction Between two Parallel Screw Dislocations.- 7.3. Interaction Between two Parallel Edge Dislocations.- 7.4. Dislocation Reactions.- 7.5. Dislocation Reactions in Special Crystal Structures.- 8. Partial Dislocations.- 8.1. Outline.- 8.2. Partial Dislocations in the Face-Centred Cubic Structure.- 8.3. The Sequence of Partial Dislocations.- 8.4. Transformation of the Face-Centred Cubic ― into the Close-Packed Hexagonal Structure.- 9. Dualistic Representation of Dislocation Reactions.- 9.1. Introduction.- 9.2. The Significance of the b-Net.- 9.3. The Prediction of Dislocation Reactions.- 9.4. Dislocation Reactions Involving Partial Dislocations.- 9.5. Thompson’s Notation of the Burgers Vectors.- Chapters 7–9. Summary and Discussion.- 10. Short Description of the Relations Between Dislocations and Point Defects, and Dislocation Dynamics.- 10.1. Dislocations and Point Defects.- 10.2. Dislocation Dynamics.- 11. Dislocation Networks ― Subgrain Boundaries.- 11.1. Introduction.- 11.2. Frank’s Formula.- 11.3. Classification of Subgrain Boundaries.- 11.4. “Special” Subgrain Boundaries.- 11.5. Foreign Dislocations.- 11.6. “General” Subgrain Boundaries.- 11.7. The Energy of a Subgrain Boundary.- 11.8. Some Considerations of Recrystallization.- 11 9 Limiting Cases.- 11.10. Dualistic Representation in Three Dimensions.- 11. Summary and Discussion.- 12. General Geometrical Theory of Crystalline Interfaces.- 12.1. Introduction.- 12.2. The Coincidence-Site Lattice.- 12.3. The O-Lattice.- 12.4. The O-Lattice and Frank’s Formula.- 12.5. The b-Lattice.- 12.6. Various Aspects of the 0-Points.- 12.7. The Actual Formulation of the Transformation A.- 12.8. Choice Between Various Possible Transformations A.- 12.9. Solutions of the Basic Equation.- 12.10. The Behaviour of the O-Lattice upon Translation of Lattice 2.- 12.11. Translation of the O-Lattice for the Case of Rank (T) < 3.- 12.12. Subdivision of the Crystal Space into Cells.- 12. Summary and Discussion.- 13. Applications of the O-Lattice Theory.- 13.1. Outline.- 13.2. Example of an Optimum Phase Boundary.- 13.3. The Periodicity of the Pattern of Lattice Points.- 13.4. Displacement of the Pattern.- 13.5. Dislocation Networks in General Crystalline Interfaces.- 14. Completion of the Linear O-Lattice Theory and Extension to Non-Linear Problems.- 14.1. Outline.- 14.2. Dislocations and Burgers Vectors in Crystalline Interfaces.- 14.3. Non-Linear Problems.- Chapters 13–14. Summary and Discussion.- A 1 Matrix Calculation Procedures.- A 2 Moiré-Models.- A 3 The Direct Observation of Crystal Defects.- References.- Sources of the Illustrations.