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MSE+206+Introduction

MSE+206+Introduction - Imperfections in Crystalline Solids...

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1 Imperfections in Crystalline Solids William D. Nix Department of Materials Science and Engineering Stanford University An incomplete set of class notes for a graduate (undergraduate) class at Stanford University: Materials Science and Engineering 206 (196), Imperfections in Crystalline Solids March 2008 Prof. W.D. Nix Department of Materials Science and Engineering Stanford University Stanford CA 94305-2205 Phone: 650-725-2605 Fax: 650-725-4034 E-mail: [email protected]
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2 Table of Contents Introduction 4 Stress, Strain and Isotropic Elasticity 15 Stress 15 Strain 20 Elasticity 22 Elastic Strain Energy Density 27 Atomic Point Defects 29 Impurity Atom Defects 29 Substitutional and Interstitial Defects 29 Continuum Model of Displacements 30 Atomic Size Factors 35 Elastic Continuum Model of Point Defects 44 Equilibrium Concentration of Solute Atoms 60 Vacancies 71 Equilibrium Vacancy Concentration in Metals 71 Vacancies and Interstitials in Silicon 81 Point Defects in Strongly Ionic Solids 82 Kinetics and Mechanisms of Vacancies 86 Theoretical Foundations of Diffusional Creep 89 Vacancy Chemical Potential 98 Experimental Techniques for Vacancies 104 Enthalpy of Formation 105 Entropy of Formation 106 Constitutional Defects in Compounds 110 Divacancies and Other Vacancy Complexes 114 Motion of Vacancies 60 Point Defects in Ionic Crystals 67 Perfect MX Crystal 67 Imperfection Equilibria 68 Brouwer Approximation and Diagram 76 Dislocations 77 Slip by Dislocation Motion 77 Slip in Perfect Lattice 78 Slip by Dislocation Motion 80 Volterra Dislocations 83 Geometry of Dislocations 90 Edge, Screw and Mixed Dislocations 90 The Dislocation Loop 93 Cross-Slip and Climb 95 Dislocation Density 97 Frank’s Rule 99 Origin of Dislocations in Crystals 100 Dislocation Mechanics 106
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3 Elastic Properties of Isolated Dislocations 106 Screw Dislocations 106 Edge Dislocations 112 Forces on Dislocations 118 Elastic Interactions of Dislocations 124 Arrays of Dislocations 135 Dislocation Pile-Ups 135 Low Angle Boundaries 137 Polygonization 137 Energy of Low Angle Tilt Boundaries 145 Twist Boundaries 147 Dislocation Line Energy and Line Tension 154 Line Energy 154 Line Tension 156 Dislocation Reactions 161 Image Dislocations 163 Free Surface Effects 163 Multiple Images 165 Solution for an Interface 165 Application to Interface Problems 169 Structure of Dislocations 175 Peierls-Nabarro Model of Dislocation Core 177 Partial Dislocations 183 Close Packed Metals 183 Shockley Partials 184 Stacking Faults 187 Equilibrium Separation between Partials 191 Thompson Notation 195 Frank Partial 197 Slip Pyramids 199 Lomer-Cottrell Reaction 200 Extended Nodes 201 Misfit Dislocations in Thin Films 202 Dislocations in Diamond Cubic Structures 206 Crystal Structure 206 Glide and Shuffle Set 207 Partial Dislocations in BCC Metals 212 Partial Dislocations in CrCl 3 214 Superdislocations in Ordered Ni 3 Al 215 Faults in Ordered Ni 3 Al 220 Grain Boundary Structure 226 ± 5 Twist Boundary 226 Coincident Site Lattice (CSL) 226 Displacement Complete (DSC) Lattice 226
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4 Introduction We start with some remarks about why so much attention is focused on the study of crystal imperfections.
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