Trapping of gas atoms

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Table of contents

General Introduction 
1 Context and Literature review 
1.1 Introduction and Context
1.1.1 Pressurized Water reactor (PWR)
1.2 Description of the UO2 nuclear fuel
1.2.1 Chemical composition of Uranium dioxide
1.2.2 Fission and fission products
1.2.3 Fission gases
1.3 Defects in nuclear fuel
1.3.1 Point Defects
1.3.2 Extended Defects
1.4 Fission gas behaviour
1.5 Mechanisms of FGR
1.5.1 Recoil and Knock-out
1.5.2 Single gas atom transport
1.5.3 Trapping of gas atoms
1.5.4 Irradiation induced re-solution of gas atoms
1.5.5 Thermal re-solution of gas atoms
1.5.6 Diffusion in the temperature gradient
1.5.7 Grain boundary diffusion
1.5.8 Intra-granular bubble migration
1.5.9 Grain boundary sweeping
1.5.10 Inter-granular bubble interconnection
1.5.11 Burst release
1.6 Mechanisms associated with intra-granular gas release during PIA tests
1.7 Experimental observations during post-irradiation annealing (PIA)
1.7.1 Microstructure evolution during PIA tests
1.7.2 FGR during PIA tests
1.8 Modelling approaches for FGR
1.8.1 Booth Model
1.8.2 Improving the Booth Model
1.8.3 Speight’s Model for effective diffusion
1.8.4 Beyond Speight’s Model
1.8.5 FGR modules in Fuel performance codes
1.9 Detailed modelling of intra-granular bubbles
1.9.1 Different scales of modelling
1.9.2 Meso-scale modelling
1.9.3 Prominent meso-scale methods
Cluster Dynamics
Kinetic Monte Carlo (kMC)
Phase Field Model (PF)
1.9.4 Application of meso-scale modelling for intra-granular bubbles
Conclusions from the application of meso-scale models for intra-granular bubbles
1.10 In Closing
2 A new spatialized meso-scale model: BEEP Model 
2.1 BEEP Model: Introduction
2.1.1 Assumptions used in the model
2.2 Modelling methodology
2.2.1 Representation
2.2.2 Physical properties used in the model
2.3 Methodology adopted in the model
2.3.1 Initialization
2.3.2 Diffusion of point defects and crystal atoms
2.3.3 Space and Time Discretization
2.3.4 Bubble volume calculation
2.3.5 Determining the next center (« Target center ») of bubble
2.3.6 Re-drawing the bubble keeping the atom and volume balance
2.3.7 Random movement of the bubbles
2.4 Parallelizing the BEEP Model
2.4.1 Using OpenMP
2.4.2 Implementing sub-domains
2.4.3 Message Passing Interface (MPI)
2.5 Testing the Model
2.5.1 Crystal atom balance
2.5.2 Verification for calculation of solid ratio « RS »
2.5.3 Verification for diffusion calculation
2.5.4 Verification of particular functionalities of BEEP Model
Coalescence of two bubbles
Vanishing of a bubble in the presence of a large bubble
2.5.5 Verification for bubble movement
2.6 Technical note on the exterior region (« Flat bubble »)
2.7 In Closing
3 FGR due to bubble migration in a vacancy gradient 
3.1 Directed movement of intra-granular bubbles in a vacancy gradient
3.1.1 Evans’ model for directed movement of bubbles
3.1.2 Testing the movement and growth of bubbles in the BEEP Model
3.1.3 Grid size and Coalescence
3.2 Analysis of FGR via Directed Movement Mechanism
3.2.1 FGR values from experiments for comparison
3.2.2 Conditions for numerical analyses
3.2.3 FGR analysis
3.3 FGR analysis until vacancy gradient lasts
3.4 Uncertainty analysis of parameters
3.4.1 Uncertainty analysis of Dv
3.4.2 Uncertainty analysis of Ceq
3.5 In Closing
4 Brownian motion of bubbles and impact on FGR 
4.1 Random (Brownian) movement of bubbles
4.1.1 Bubble diffusion by volume diffusion mechanism
4.1.2 Bubble diffusion by surface diffusion mechanism
4.2 Influence of random bubble movement without vacancy diffusion
4.2.1 Random movement of bubbles due to volume diffusion mechanism
4.2.2 Random movement of bubbles due to surface diffusion mechanism
4.3 FGR due to combined random and directed bubble movement in a vacancy concentration gradient
4.4 Dependence of bubble diffusion coefficient via surface diffusion mechanism on the bubble radius
4.5 FGR due to combined movement until vacancy gradient lasts
4.6 Parametric investigation of Mikhlin’s suppression term
4.7 In Closing
5 Bubble movement via Dislocations 
5.1 Introduction to Dislocations
5.1.1 Mechanisms of Dislocation movement
Dislocation glide
Dislocation climb
5.2 Scenario of bubble movement with dislocation climb
5.3 Implementation of Dislocations in BEEP Model
5.3.1 Assumptions
5.3.2 Formulation
5.3.3 Methodology
Initialization
Visualization
Calculating the volume of pinned bubbles
Equilibrating bubbles on a dislocation
Center targets for bubbles pinned on dislocations
Updating dislocations
Calculating the new dislocation velocities
Choosing an acceptable Dt for dislocation evolution
5.4 First 3D Test Case for Dislocation and bubble movement
5.5 Scenario of FGR via bubble movement with Dislocations
5.5.1 Conditions for analysis
5.5.2 FGR analysis without any diffusion of vacancies from free surface
5.5.3 Factors influencing the velocity of dislocations
5.6 In Closing
General Conclusion