Louisette Priester. Grain Boundaries. From Theory to Engineering. ^ Springer. sciences

Transcription

1 Louisette Priester Grain Boundaries From Theory to Engineering sciences ^ Springer

2 Contents Part I From Grain Boundary Order to Disorder 1 Geometrical Order of Grain Boundaries Grain Boundary Geometry Crystallographical Parameters Equivalent Rotations: Disorientation Pvodrigues Vector and Quaternions Bicrystallography General Methodology: From the Dichromatic Complex to the Grain Boundary Dichromatic Pattern: Coincidence Site Lattice (CSL) Translation Lattice of the Bicrystal (DSC Lattice) Extension of the Coincidence Notion Generalization of the Coincidence: O-Lattice and 02-Lattice Interest and Limit of the Bollmann Approach Different Types of Grain Boundaries: Terminology Terminology Based on the Macroscopic Parameters Terminology Based on the Microscopic Parameters Practical Distinction Between Grain Boundaries 25 References 27 2 Mechanical Stress Order of Grain Boundaries Continuous Approach: The Frank-Bilby Equation Discrete Approach: The Read and Shockley Model Bollmann's Discrete Approach: Intrinsic Dislocations Primary Intrinsic Dislocations Secondary Intrinsic Dislocation 37 xi

3 xii Contents Interest and Limit of the Intrinsic Dislocation Model Partial Intergranular Dislocations Stress Fields Associated to Intrinsic Dislocations 45 References 47 3 Atomic Order of Grain Boundaries Hard Sphere Model: Geometrical Construction Structural Unit Model Principle Hierarchy of the Descriptions Multiplicity of the Descriptions Geometrical Construction of the Grain Boundary Structure, Algorithm for the Determination of the Grain Boundary Structure Determination of the Grain Boundary Structure by the Strip Method Interests and Limits of the Structural Unit Model: Any Model has its Exceptions Three-Dimensional Tilt Grain Boundaries in Metals Asymmetrical Tilt Grain Boundaries in Metals Twist Grain Boundaries in Metals Grain Boundaries in Covalent Materials Grain Boundaries in Ionic Materials Structural Unit Model/Intrinsic Grain Boundary Dislocations Principle of the SU/GBD Model Characterization of the Dislocations Associated to Structural Units Application of the SU/GBD Model to Tilt Grain Boundaries Limits of the SU/GBD Model for the Twist Grain Boundaries Structural Unit/Disclination Model 91 References 92 4 Grain Boundary Order/Disorder and Energy Grain Boundary Order or Disorder at... High Temperature? Solid/Solid Phase Transformations at Grain Boundaries Grain Boundary Pre-melting? 95

4 Contents xiii 4.2 Interfacial Energy: Thermodynamic Aspects and Energy Factors Macroscopic Degrees of Freedom and Interfacial Energy Variation of the Interfacial Energy with the Misorientation Angle Variation of the Interfacial Energy with the Grain Boundary Plane Inclination Microscopic Degrees of Freedom and Interfacial Energy Variation of the Interfacial Energy with the in Plane Rigid Body Translation Variation of the Interfacial Energy with the Expansion Normal to the Grain Boundary Plane Variation of the Interfacial Energy with Local Individual Atomic Relaxations Are There any Geometrical Criteria of Minimum Energy? Low Sigma Value Criterion High Gamma Value Criterion High d Value Criterion High Gamma Value with Constant d Criterion Energy and Classification of Grain Boundaries: The Limits Classification Directly Based on the Grain Boundary Energy Classification Based on the Grain Boundary Interplanar Spacing Grain Boundary Order or Disorder: What Conclusion? 127 References 132 Part II From Ideal to Real Grain Boundary 5 Defects in the Grain Boundary Structure Point Defects Linear Defects: Extrinsic Dislocations Definition of an Extrinsic Dislocation Geometrical Characteristics of an Extrinsic Dislocation Origin of an Extrinsic Dislocation Extrinsic Dislocation Core 142 References Grain Boundary Segregation Driving Forces Equilibrium Segregation Elastic Interactions Electronic Effects 151

5 xiv Contents 6.2 Thermodynamic Approaches of Equilibrium Segregation Gibbs Adsorption Isotherm Segregation in Regular Solid Solution Without Interaction Segregation in Regular Solid Solution with Interactions Segregation Models Based on the Statistical Mechanics Model of Regular Solid Solution with the Bragg-Williams Approximation Mean Field Approximation (MFA) Models Average Segregation at Grain Boundaries Dependence of the Average Grain Boundary Segregation on the Temperature and the Solute Concentration Influence of the Interaction Term on the Average Segregation Relation Between Segregation and Grain Boundary Structure Segregation and Grain Boundary Geometrical Parameters Grain Boundary Segregation and Intrinsic Dislocations Grain Boundary Segregation and Grain Boundary Atomic Structure Grain Boundary Segregation and Grain Boundary Electronic Structure Prewetting Transition Upon Segregation at Grain Boundaries Concept of Complexions Role of Extrinsic Dislocations in Grain Boundary Equilibrium Segregation Non-equilibrium Segregation at Grain Boundaries Concluding Remarks 213 References Precipitation at Grain Boundaries Energetic Aspect Different Types of Interfaces and Precipitates Coherent Interface Semicoherent Interface Incoherent Interface Different Types of Precipitates 223

6 Contents xv 7.3 Generalised Wulff Construction for Nucleus Eqmlibrium at Grain Boundary Equilibrium Condition for a Nucleus at a Grain Boundary Principle of the Generalised Wulff Construction Equilibrium Shape of Two-Dimensional Nuclei at Grain Boundaries Influence on the Grain Boundary Plane on the Nucleus Shape Equilibrium Shape of Three-Dimensional Nuclei at Grain Boundaries Grain Boundary Puckering Phenomenon Grain Boundary Precipitate Growth Migration of a Curved Incoherent Interface Migration of a Planar Interface (Coherent or Semicoherent) Localisation of Grain Boundary Precipitates on Extrinsic Dislocations 237 References Interactions Between Dislocations and Grain Boundaries Long-Range Elastic Interaction: Image Force Dislocation Configurations in the Vicinity of a Grain Boundary Short-Range Interactions Between Linear and Planar Defects Combination Processes Decomposition Processes Transmission Processes Entrance of a Dissociated Dislocation in a Grain Boundary Simulation of the Interaction of a Lattice Dislocation with a Grain Boundary 261 References Intergranular Stress Relaxation Extrinsic Dislocation Accommodation Models Extrinsic Dislocation Core Delocalisation Extrinsic Dislocation Decomposition and Product Reorganisation Extrinsic Dislocation Incorporation Within the Intrinsic Structure 274

7 xvi Contents 9.2 Evolution of Extrinsic Dislocation Stress Fields Random Disordered Dislocation Wall Model Quasi-Equidistant Grain Boundary Model Evolution of Extrinsic Dislocation Stress Fields with Time Experimental Studies of Extrinsic Dislocation Accommodation Accommodation in Symmetrical Tilt Grain Boundaries in Semiconductors Accommodation in Singular, Vicinal and General Grain Boundaries in Metals Accommodation Kinetics Conclusion on the Extrinsic Dislocation Relaxation Phenomena 300 References 300 Part HI From the Free to the Constrained Grain Boundary 10 The Triple Junction Triple Junction Geometry Geometrical Parameters and Triple Junction Classification Tricrystallography Triple Junction Equilibrium Thermodynamic Approach: Limits Equilibrium in Terms of Intrinsic Dislocations Equilibrium in Terms of Structural Units Triple Junction Energy Calculation of the Triple Junction Energy Experimental Determination of the Triple Junction Energy Triple Junction Defects Intrinsic Defects of a Triple Junction: Geometrical Approach Extrinsic Defects of a Triple Junction: Mechanical Approach From Tricrystal to Polycrystal 333 References Grain Boundary Network: Grain Boundary Texture Criteria for Grain Boundary Distribution Misorientation Criterion Grain Boundary Plane Criterion Non Geometrical Criteria Calculation of the Misorientation Distribution 344

8 Contents xvii Crystal Orientation and Grain Boundary Misorientation Distribution Functions Theoretical Misorientation Distributions Experimental Grain Boundary Misorientation Distributions Different Types of Experimental Misorientation Distributions Effects of the Structure and of the Stacking Fault Energy of the Material Effects of the Material Purity Effects of Thermo-Mechanical Treatments: Relation with Crystal Texture Grain Boundary Plane Distributions Five Grain Boundary Macroscopic Parameters Distributions Theoretical Approach Experimental Approach Grain Boundary Property Distributions Grain Boundary Diffusivity Distribution Grain Boundary Energy Distribution Triple Junction Distributions Limit for Application of the Coincidence Index Combination Rule Theoretical Approach of the Triple Junction Distribution Experimental Triple Junction Distributions Grain Boundary Energy Distribution Starting from the Dihedral Angle Distribution at Triple Junctions Local Grain Boundary Texture Different Types of Clusters Observed Cluster Configurations Simulated Cluster Configurations Percolation Concept Applied to Grain Boundary Networks Infinite Grain Boundary Network Finite Grain Boundary Network Correlated Percolation 429 References 433 Epilogue 435 Recommended Reading 437 Index 439