C. S. Becquart

Ecole Nationale Superieure de Chimie de Lille, Villeneuve d’Ascq, France; Laboratoire commun EDF-CNRS Etude et Modelisation des Microstructures pour le Vieillissement des Materiaux (EM2VM), France B. D. Wirth

University of Tennessee, Knoxville, TN, USA © 2012 Elsevier Ltd. All rights reserved.

1.14.1 Introduction 393

1.14.2 Modeling Challenges to Predict Irradiation Effects on Materials 394

1.14.3 KMC Modeling 395

1.14.4 KMC Modeling of Microstructure Evolution Under Radiation Conditions 396

1.14.4.1 Irradiation Rate 397

1.14.4.2 Transmutation Rate 397

1.14.4.3 Diffusion Rate 397

1.14.4.4 Emission/Dissociation Rate 398

1.14.5 Atomistic KMC Simulations of Microstructure Evolution in

Irradiated Fe-Cu Alloys 399

1.14.6 OKMC Example: Ag Fission Product Diffusion and Release in

TRISO Nuclear Fuel 404

1.14.7 Some Limits of KMC Approaches 406

1.14.8 Advanced KMC Methods 407

1.14.9 Summary and a Look at the Future of Nuclear Materials Modeling 408

References 408

1.14.1 Introduction

Many technologically important materials share a common characteristic, namely that their dynamic behavior is controlled by multiscale processes. For example, crystal growth, plasma processing of materi­als, ion-beam assisted growth and doping of electronic materials, precipitation in structural materials, grain boundary and dislocation evolution during mechanical deformation, and alloys driven by high-energy particle irradiation all experience cluster nucleation, growth, and coarsening that impact the evolution of the over­all microstructure and, correspondingly, property changes. These phenomena involve a wide range of length and time scales. While the specific details vary with each material and application, kinetic processes at the atomic to nanometer scale (especially related to nucleation phenomena) are largely responsible for materials evolution, and typically involve a wide range of characteristic times. The large temporal diversity of controlling processes at the atomic to nanoscale level makes experimental identification of the governing mechanisms all but impossible and clearly defines the need for computational modeling. In such systems, the potential benefits of modeling are at a maximum and are related to reduction in time and expense ofresearch and development and introduction of novel materials into the marketplace.

Systems in which the materials microstructure can be represented by multiple particles experiencing

Brownian motion and occasional collisions against one another and systems with other defects (dislocations, grain boundaries, surfaces, etc.) are in particular ame­nable to multiscale modeling. Within a multiscale approach, atomistic simulations (utilizing either elec­tronic structure calculations or semiempirical poten­tials) investigate controlling mechanisms and occurrence rates of diffusional and reactive interac­tions between the various particles and defects of interest, and inform larger length scale kinetic (Monte Carlo, phase field, or chemical reaction rate theory) models, which subsequently lead to the devel­opment of constitutive models for predictive contin­uum scale models. Simulating long-time materials dynamics with reliable physical fidelity, thereby providing a predictive capability applicable outside limited experimental parameter regimes is the prom­ise of such a computational multiscale approach.

A critical need is the development of advanced and highly efficient algorithms to accurately model nucleation, growth, and coarsening in irradiated alloys that are kinetically controlled by elementary (diffusive) processes involving characteristic time scales between
10~12 and ^10~3 s. The goal of this chapter is to describe the state of the art in kinetic Monte Carlo (KMC) simulation, as well as to identify a number of priority research areas, moving toward the goal of accelerating the development ofadvanced computational approaches to simulate nucleation, growth, and coarsening of radia­tion-induced precipitates and defect clusters (cavities and/or dislocation loops). It is anticipated that the approaches will span from atomistic molecular dynamics (MD) simulations to provide key kinetic input on governing mechanisms to fully three-dimensional (3D) phase field and KMC models to larger scale, but spatially homogeneous cluster dynamics models.