Computed Electron Micrographs And Defect Identification

Preface 1. Introduction2. Introduction to the Basic Theory 2.1. Introduction 2.2. The diffraction of electrons by a crystal 2.3. The two-beam dynamical equations 2.4. The absorption parameters 2.4.1. The normal absorption coefficient n 2.4.2. The anomalous absorption coefficient A 2.5. The deviation of the crystal from the Bragg reflecting position 2.5.1. The deviation vector sg 2.6. The extinction distance 2.6.1. The theoretical two-beam extinction distance ℰg 2.6.2. The apparent extinction distance ℰga 2.7. The displacement vector R 2.7.1. The displacement due to a stacking fault 2.7.2. The displacement vector R for a dislocation 2.8. The foil normal F 3. Experimental Techniques 3.1. Introduction 3.2. Image-diffraction pattern rotation 3.3. Crystal tilting technique 3.4. Specific indexing of the orientation map and diffracting vectors 3.4.1. Experimental examples 3.5. Determination of beam direction Β 3.6. Determination of defect line direction u 3.7. Determination of foil normal F 3.8. Extinction distance 3.9. Determination of w 3.10. Determination of foil thickness 3.11. Anomalous absorption coefficient 4. Principles of Onedis 4.1. Introduction 4.2. The two basic principles 4.2.1. The generalised cross-section 4.2.2. Linear combinations 4.3. Modifications to the generalised cross-section to accomodate experimental situations 4.3.1. Tilted foils 4.3.2. Changes in the magnification and in the framing of computed micrographs 4.3.3. Variable foil thickness 4.4. Program geometry 4.5. The grey scale and printing the micrograph 5. Matching with Onedis 5.1. Introduction 5.2. Aluminium 5.3. β -brass 6. Principles of Twodis 6.1. Introduction 6.2. The two basic principles 6.2.1. The generalised cross-section 6.2.2. Linear combinations 6.3. The operation of the program 6.3.1. Examples of the cases which may be computed with TWODIS 6.3.2. Check sums and conventions 6.4. Program geometry and arrangement of the calculation 6.5. Extension of the program to more complex configurations 7. Matching with Twodis 7.1. Introduction 7.2. Example 1, defect A 7.3. Example 2, defect Β 8. Applications of the Technique 8.1. Introduction 8.2. Influence of elastic anisotropy on the invisibility of dislocations 8.3. Effective invisibility of images due to large values of w 8.4. Diffraction contrast from lines of dilation 8.5. Apparent anomalous absorption 8.6. Nature of stacking faults 8.7. Identification of bent dislocations 8.8. A dissociation reaction in β-brass 8.9. Contrast from partial dislocations 8.9.1. Partial dislocations bordering a single stacking fault 8.9.2. Partial dislocations separating intrinsic and extrinsic faults 8.10. Dissociated Frank dislocations 8.11. Growth of Frank loops by fault climb 8.12. Dislocation dipoles in nickel 8.13. Contrast from overlapping faults 8.14. Analysis of partial dislocations and stacking faults on closely spaced planes 9. Discussion of the Applications and Limitations of the Technique 9.1. Introduction 9.2. Uniqueness and the amount of information necessary to identify defects 9.3. Optimisation of the technique 9.4. Limitations in the theory 9.5. Restrictions inherent in the programs 10. Computer Programs 10.1. Introduction 10.1.1. Computer environment 10.1.2. Program speed 10.1.3. Program size 10.1.4. Program options 10.1.5. General conventions 10.2. Program ONEDIS for one dislocation and cubic crystals 10.2.1. General description 10.2.2. Data 10.2.3. Geometry 10.2.4. Error messages 10.2.5. Anisotropic elasticity 10.2.6. Picture output 10.2.7. Howie- Whelan differential equations 10.2.8. Picture legend 10.2.9. Listing of program ONEDIS 10.3. Subroutines 10.3.1. Subroutine ANCALC for cubic crystals 10.3.2. Subroutine NEWTON 10.3.3. Subroutine RKM 10.3.4. Subroutine DERIV for one dislocation 10.4. Special test version of program ONEDIS 10.5. Subroutine HALFTN 10.6. Programs for other crystal systems 10.6.1. Introduction 10.6.2. Program modification - general discussion 10.6.3. The tetragonal system - modification TETDIS 10.6.4. The hexagonal system - modification HEXDIS 10.6.5. The testing of programs developed for non-cubic crystal systems 10.6.6. Modification of other programs for non-cubic systems 10.7. Isotropic elasticity 10.8. Modification DELUGE 10.9. Program 'TWODIS for cubic crystals 10.9.1. Introduction 10.9.2. Program TWODIS 10.9.3. Listing of program TWODIS 10.9.4. Subroutine DERIV for two dislocations 10.10. Dark field pictures Appendix A.l. Introduction A.2. Single dislocations A.3. Single stacking faults A.4. Relations between dislocation-stacking fault images A.5. The symmetry of dislocation dipole images A.6. The effect of elastic symmetry on dislocation images References Subject Index