Radiation Effects Computer Experiments

Preface

1 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

References

2 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

References

4 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)

References

5 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

References

6 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

References

7 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)

References

8 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)

References

9 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)

References

10 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)

References

11 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

References

12 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

References

13 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

References

14 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)

References

15 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 > 136K

16 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

References

Glossary

Index

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.