Radiation Effects Computer Experiments

Defects in Solids, Volume 13: Radiation Effects Computer Experiments provides guidance to persons interested in learning how to develop and use computer experiment programs to simulate defect production and annealing in solids. The book first elaborates on computer experiment methods and outline of defect properties computations. Topics include metal models used in defect property example calculations; configuration energy computation procedure; migration energy computation procedure; dynamical method; and Monte Carlo method. The publication also examines vacancies and divacancies and self interstitials. The manuscript takes a look at impurity atoms, defect migration, and vacancy clusters. Discussions focus on heterogeneous nucleation of vacancy clusters and voids, vacancy and divacancy migration, substitutional metallic large impurity atom, and vacancy clusters in face-centered cubic metals. The publication also tackles binary collision approximation cascade program construction and collision cascades and displacement spikes. The text is a valuable source of information for readers wanting to develop and use computer experiment programs to copy defect production and annealing in solids.

Preface1 Introduction 1.1 The Computer Experiment Concept 1.2 Defect Production Computer Experiments 1.3 Defect Annealing Computer Experiments 1.4 Defect Property Computer Experiments 1.5 Defect Interaction Computer Experiments 1.6 Nature of the Book 1.7 Plan of the Book Appendix A1 Computer Experiment Utility References2 Computer Experiment Methods 2.1 Introduction 2.2 Dynamical Method 2.2.1 Introduction 2.2.2 Central Difference Approximation 2.2.3 A Simple Dynamical Method Program 2.2.4 Static Equilibrium Atom Position Calculations 2.2.5 Critical Damping 2.2.6 Inelastic Atomic Collisions 2.3 Monte Carlo Method 2.3.1 Introduction 2.3.2 Probabilistic Selection 2.3.3 Mean Square Migration Distance 2.3.4 Defect Encounter Probability Calculations 2.3.5 Concurrent Migration of Many Defects 2.3.6 Primary Radiation Particle (PRP) Collision Chains 2.3.7 Frequently Used Probability Functions 2.4 Variational Method References (ch. 2) Appendix A2.1 Computational Cell Construction A2.1.1 Introduction A2.1.2 Simple Cubic Crystal A2.1.3 Body-Centered Cubic Crystal A2.1.4 Face-Centered Cubic Crystal A2.1.5 Hexagonal Close-Packed Crystal Appendix A2.2 Periodic Boundary Conditions Appendix A2.3 Elastic Continuum Boundary Conditions Appendix A2.4 Thermal Crystal Initial Conditions A2.4.1 Procedure (1) A2.4.2 Procedure (2) A2.4.3 Procedure (3) A2.4.4 Procedure (4) Appendix A2.5 Dynamical Method Integration Schemes A2.5.1 Central Difference Scheme A2.5.2 Euler-Cauchy Scheme A2.5.3 Simple Predictor-Corrector Scheme A2.5.4 Nordsieck Method for Newton's Equations A2.5.5 Comparison of the Four Schemes Appendix A2.6 Time Step Change in a Dynamical Method Program Appendix A2.7 Force Calculations Appendix A2.8 Atom Velocity Damping at the Computational Cell Boundary Appendix A2.9 Firsov Inelastic Collision Model for Dynamical Method Programs Appendix A2.10 Statistical Sampling A2.10.1 Discrete Sampling Space A2.10.2 Continuous Sample Space A2.10.3 Statistical Sampling Using a CDF A2.10.4 Statistical Sampling Using PDF (Rejection Technique) Appendix A2.11 Multiply Occupied Atom Sites References (Appendix A2)3 Outline of Defect Properties Computations 3.1 Introduction 3.1.1 Defect Types 3.1.2 Elemental and Compound Defects 3.1.3 Defect Property 3.2 Defect Energies 3.2.1 Configuration and Formation Energies 3.2.2 Migration Energy 3.2.3 Binding Energy 3.2.4 Dissociation Energy 3.3 Configuration Energy Computation Procedure 3.4 Migration Energy Computation Procedure 3.5 Entropy Calculations 3.6 Metal Models Used in Defect Property Example Calculations 3.7 Neighbor Shells in BCC, FCC and HCP Crystals 3.7.1 Introduction 3.7.2 Neighbor Shells in a BCC Crystal 3.7.3 Neighbor Shells in a FCC Crystal 3.7.4 Neighbor Shells in a HCP Crystal Appendix A3.1 BCC Computational Cell Site Maps Appendix A3.2 FCC Computational Cell Site Maps Appendix A3.3 HCP Computational Cell Site Maps References4 Vacancies and Divacancies 4.1 Introduction 4.2 Configuration and Binding Energies 4.3 Vacancy GE1% Displacement Field 4.3.1 Introduction 4.3.2 Vacancy Displacement Field in BCC Iron(m) 4.3.3 Vacancy Displacement Field in Nickel(m) 4.3.4 Vacancy Displacement Field in FCC Iron(m) 4.3.5 Vacancy Displacement Field in the HCP Metal(m) 4.4 Divacancy GE1% Displacement Field 4.4.1 Introduction 4.4.2 Divacancy Displacement Field in BCC Iron(m) 4.4.3 Divacancy Displacement Field in Nickel(m) 4.4.4 Divacancy Displacement Field in FCC Iron(m) 4.4.5 Divacancy Displacement Field in the HCP Metal(m) References5 Self Interstitials 5.1 Introduction 5.2 Self Interstitials in BCC Iron(m) 5.3 Self Interstitials in a FCC Metal 5.3.1 Introduction 5.3.2 Octahedral Self Interstitial in FCC Iron(m) 5.3.3 Octahedral Self Interstitial in Nickel(m) 5.3.4 Tetrahedral Self Interstitial in FCC Iron(m) 5.3.5 Tetrahedral Self Interstitial in Nickel(m) 5.3.6 [100] Split Self Interstitial in FCC Iron(m) 5.3.7 [100] Split Self Interstitial in Nickel(m) 5.3.8 [110] Axis Self Interstitial in FCC Iron(m) 5.3.9 [110] Axis Interstitial in Nickel(m) 5.3.10 [111] Split Interstitial in FCC Iron(m) 5.3.11 [111] Split Interstitial in Nickel(m) 5.3.12 (111)p Interstitial in FCC Iron(m) 5.4 Self Interstitials in the HCP Metal(m) 5.4.1 Introduction 5.4.2 Point A Split Self Interstitial 5.4.3 Octahedral Self Interstitial (Point B) 5.4.4 C-Axis Split Interstitial (Point C) 5.4.5 Point D Split Self Interstitial 5.4.6 Symmetrical Point Ε Interstitial 5.4.7 Asymmetrical Point Ε Interstitial References6 Impurity Atoms 6.1 Introduction 6.2 Substitutional Metallic Large Impurity Atom (LIA) 6.2.1 LIA(m) in BCC Iron(m) 6.2.2 LIA(m) in Nickel(m) 6.2.3 LIA(m) in FCC Iron(m) 6.2.4 LIA(m) in the HCP Metal(m) 6.3 Substitutional Metallic Small Impurity Atom (SIA) 6.3.1 SIA(m) in BCC Iron(m) 6.3.2 SIA(m) in Nickel(m) 6.3.3 SIA(m) in FCC Iron(m) 6.3.4 SIA(m) in the HCP Metal(m) 6.4 Helium 6.4.1 Introduction 6.4.2 Helium(m) in BCC Iron(m) 6.4.3 Helium(m) in Nickel(m) 6.4.4 Helium(m) in FCC Iron(m) 6.4.5 Helium(m) in the HCP Metal(m) 6.5 Carbon 6.5.1 Introduction 6.5.2 Interstitial Carbon(m) in BCC Iron(m) 6.5.3 Interstitial Carbon(m) in Nickel(m) 6.5.4 Interstitial Carbon(m) in FCC Iron(m) 6.5.5 Carbon(m) in the HCP Metal(m) 6.6 Carbon(m)-Vacancy and Carbon(m)-Interstitial Complexes 6.6.1 Carbon(m)-Vacancy Complexes in BCC Iron(m) 6.6.2 Carbon(m)-Interstitial Complexes in BCC Iron(m) 6.6.3 Carbon(m)-Vacancy Complexes in Nickel(m) 6.6.4 Carbon(m)-Self Interstitial Complexes in Nickel(m) 6.6.5 Effect of Carbon(m) on Frenkel Pair Production in Nickel(m) 6.6.6 Carbon(m)-Vacancy Complexes in FCC Iron(m) 6.6.7 Carbon(m)-Interstitial Complexes in FCC Iron(m) 6.6.8 Carbon Complexes in a HCP Metal 6.7 Helium Complexes 6.7.1 Introduction 6.7.2 Helium-Vacancy Complexes in Tungsten(m1) 6.7.3 Helium-Vacancy Complexes in Molybdenum 6.7.4 Helium Interactions with an Edge Dislocation 6.7.5 Helium(m)-Vacancy Complexes in BCC Iron(m) 6.7.6 Helium(m)-Interstitial Complexes in BCC Iron(m) 6.7.7 Helium(m)-Vacancy Complexes in Nickel(m) 6.7.8 Helium-Vacancy Complexes in Copper References7 Defect Migration 7.1 Introduction 7.2 Vacancy Migration 7.2.1 Vacancy Migration in Nickel(m) 7.2.2 Vacancy Migration in FCC Iron(m) 7.2.3 Vacancy Migration in BCC Iron(m) 7.2.4 Vacancy Migration in the HCP Metal(m) 7.3 Divacancy Migration 7.3.1 Divacancy Migration in BCC Iron(m) 7.3.2 Divacancy Migration in FCC Iron 7.4 Self-Interstitial Migration 7.4.1 Self-Interstitial Migration in a FCC Metal 7.4.2 Interstitial Migration in BCC Iron(m) 7.4.3 Interstitial Migration in a HCP Metal 7.5 Carbon(m) Migration 7.5.1 Carbon(m) Migration in Cubic Metals 7.5.2 Carbon(m) Migration in a HCP Metal 7.5.3 Migration of a Vacancy-Carbon(m) Complex in Nickel 7.6 Helium(m) Migration 7.6.1 Helium(m) Migration in Cubic Metals 7.6.2 Helium(m) Migration in the HCP Metal(m) 7.6.3 HE(m1)-V Complex Migration in Copper(m1) 7.6.4 HE(m1)-V Complex Migration in Tungsten(m1) 7.7 Dynamical Method Simulation of Defect Migration 7.7.1 Dynamical Method Simulation of Helium(m) Migration in BCC Iron(m) 7.7.2 Dynamical Method Simulation of Self Interstitial Diffusion in Tungsten(m3) References8 Vacancy Clusters 8.1 Introduction 8.2 Vacancy Clusters in BCC Iron(m) 8.2.1 Trivacancies 8.2.2 Trivacancy Configuration Change 8.2.3 Trivacancy Migration 8.2.4 Tetravacancies 8.2.5 Vacancy Clusters Larger than V4 8.3 Vacancy Clusters in FCC Metals 8.3.1 Trivacancies 8.3.2 Tetravacancies 8.3.3 Clusters Larger than V4 8.3.4 Dislocation Loop Formation 8.3.5 Vacancy Cluster Migration 8.4 Vacancy Clusters in the HCP Metal(m) 8.5 Heterogeneous Nucleation of Vacancy Clusters and Voids 8.5.1 Introduction 8.5.2 Carbon(m) Stabilization of V2(2) in BCC Iron(m) 8.5.3 Carbon Stabilization of Void Nuclei in BCC Iron(m) 8.5.4 Carbon(m) Stabilization of V2(1) in Nickel(m) 8.5.5 Helium(m1) Stabilization of Vacancy Clusters in Copper(m1) 8.5.6 Helium(m1) Stabilization of Vacancy Clusters in Tungsten(m1) References9 Interstitial Clusters 9.1 Introduction 9.2 Interstitial Clusters in FCC Iron(m) 9.3 Interstitial Loops in FCC Iron(m) 9.3.1 Introduction 9.3.2 Faulted (111) Interstitial Loops in FCC Iron(m) 9.3.3 Perfect (110) Interstitial Dislocation Loops in FCC Iron(m) 9.4 Interstitial Clusters in BCC Iron(m) References10 Isolated Frenkel Pair Production 10.1 Introduction 10.1.1 Frenkel Pair 10.1.2 Annihilation Region 10.1.3 Replacement Collision Chains 10.1.4 Displacement Energy Threshold 10.1.5 Frenkel Pair Production Time 10.1.6 Summary 10.2 Frenkel Pair Production Computational Procedure 10.2.1 Introduction 10.2.2 Computational Procedure 10.3 Case History: A 25 eV [010] Replacement Collision Chain in BCC Iron(m2) 10.4 Case History: A 25 eV [110] Replacement Collision Chain in FCC Iron(m2) 10.5 Frenkel Pair Production in Copper(m) 10.5.1 Introduction 10.5.2 Focussed Collision Chains in Copper(m) 10.5.3 Interstitial Local Modes 10.6 Isolated Frenkel Pair Production in BCC Iron(m1) 10.6.1 Introduction 10.6.2 Displacement Energy Threshold Directional Dependence 10.6.3 (111) Replacement Chains in BCC Iron(m1) 10.6.4 (100) Replacement Chains in BCC Iron(m1) 10.6.5 (110) Replacement Chains in BCC Iron(m1) 10.6.6 Off-Axis Shots 10.7 Frenkel Pair Production in Tungsten(m3) 10.8 Collision Chains in FCC Iron(m2) 10.9 Frenkel Pair Production in the HCP Metal(m) 10.9.1 Introduction 10.9.2 [1210] Replacement Collision Chain 10.9.3 [0001] Replacement Collision Chain 10.9.4 [1100] Replacement Collision Chain 10.10 Transition from One to Two Displacements 10.11 Effect of Thermal Vibrations on Frenkel Pair Production 10.11.1 Introduction 10.11.2 Effect of Thermal Vibrations of Frenkel Pair Production in FCC Iron(m2) 10.11.3 Effect of Thermal Vibrations on Frenkel Pair Production in Tungsten(m3) References11 Binary Collision Approximation Cascade Program Construction 11.1 Introduction 11.2 General Features of BCA Computer Program Construction 11.3 Box Method for Locating Defects and Atoms 11.3.1 Introduction 11.3.2 Indices of the Nearest Mesh Point 11.3.3 Box Indices from Mesh Point Indices 11.3.4 Box Number (NBOX) 11.3.5 Relative Mesh Point Indices (IR, JR, KR) 11.3.6 Mesh Point Position Number (NPOS) 11.3.7 Utility of NBOX and NPOS 11.3.8 Normal Atom Site Mesh Points 11.3.9 Rectangular Boxes 11.4 Target Atom Selection 11.4.1 Cell Method 11.4.2 Target Selection: Neighbor Method 11.5 Collision Geometry 11.6 Collision Time and Angle 11.7 Energy Transfer 11.8 Collision Asymmetry Due to Inelastic Loss 11.9 Multiple Targets 11.10 QUEUE Table 11.11 Vacancy and Interstitial Production Criteria Appendix A11.1 Hashing Technique Appendix A11.2 Heap Table Technique References12 Collision Cascades and Displacement Spikes 12.1 Introduction 12.2 Definitions 12.2.1 Collision Cascade 12.2.2 Displacement Event 12.2.3 Fresh Displacement Spike 12.2.4 Displacement Spike Annealing Regimes 12.3 Cascade Structure 12.3.1 Introduction 12.3.2 Low Energy Cascades in Iron(m1): Ε < 2.5keV 12.3.3 2.5keV Cascade in Iron(m1) 12.3.4 2.5keV Cascades in Tungsten(m4) 12.3.5 Secondary Cascades and Subcascades in FCC Iron(m1) 12.4 Cascade Collided Atom Volume 12.5 Displacement Efficiency References13 Defect Annealing Program Construction: The RINGO Program 13.1 Introduction 13.2 Flow Diagram for RINGO 13.3 Defect Tables and the MOVE Table 13.4 Defect Interaction Criteria 13.5 Time Step Change 13.6 RINGO Subprogrammes 13.7 Simulation of Impurity Atom and Defect Dissociation Effects on Defect Annealing References14 Defect Annealing Simulation 14.1 Introduction 14.2 Migration of a Point Defect to Fixed Point Sinks 14.3 Defect Encounter Probability 14.4 Long-Term Annealing Models 14.4.1 Introduction 14.4.2 Two-Jumps Model: FCC Crystal 14.4.3 Three-Jumps Model: FCC Crystal 14.4.4 Four-Jumps Model: FCC Crystal 14.4.5 Site Selection for the Two-, Three- and Four- Jumps Models 14.4.6 Ten-or-More Jumps Model: FCC Crystal 14.5 Saturated Defect State Annealing 14.5.1 Introduction 14.5.2 Infinite Volume Annealing Simulation 14.5.3 Finite Volume Annealing Simulation 14.6 Displacement Spike Annealing in Niobium(m) 14.6.1 Introduction 14.6.2 Displacement Spike Annealing Results 14.6.3 Saturated Defect State and 20keV Displacement Spike Annealing Compared 14.7 Displacement Spike Annealing in Iron(m1) 14.7.1 Introduction 14.7.2 Displacement Spike Annealing in BCC Iron(m) 14.7.3 20keV Displacement Spike Annealing in FCC Iron(m1) 14.7.4 100keV Displacement Spike Annealing in FCC Iron(m1) References15 Electron Irradiation Simulation 15.1 Introduction 15.2 HVEM Electron Irradiation at 0k 15.3 HVEM Electron Irradiation at 136K 15.4 HVEM Electron Irradiation at Τ > 136K16 Self-Ion Irradiation 16.1 Introduction 16.2 Spatial Distribution of PKA Ejection Sites 16.3 Vacancy Extent 16.4 PKA Energy Spectrum: MeV Energy Range Self-Atom Irradiation 16.5 Damage Energy Fraction 16.6 Damage Energy Transport 16.7 Comparison with LSS Theory 16.8 Short-Term Annealing of 4MeV Self-Atom Displacement Spike Ensembles in FCC Iron(FEV) 16.8.1 Average-Range Primary Atom Cascades 16.8.2 Short- and Long-Range Primary Atom Cascades ReferencesGlossaryIndex

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