Development of advanced numerical algorithms for kinetic and dynamic simulations of irradiated systems : kinetic Monte Carmelo and dislocation dynamics

Abstract

Chapter 1
ABSTRACT
This thesis can be framed within the Computational Materials Sci¬ence field, and it has been devoted to the development of two new mod¬els concerning two of the most used methods in the Multiscale Modeling Approach, namely, kinetic Monte Carlo (kMC) and Dislocation Dynamics (DD). The first one aims to describe the diffusion and accumulation of de¬fects created in Radiation Damage, and the second follows the evolution of an ensemble of dislocations responding under some set of external loading conditions. Both methods are indispensable to the study of the change in the mechanical properties of materials exposed to irradiation.
The manuscript is divided in two main parts. The first one deals with the development of a new synchronous parallel kinetic Monte Carlo algorithm, and the second describes the formulation of a new algorithm to deal with partial dislocation within a DD methodology.
1.1 Part I: Synchronous Parallel Kinetic Monte Carlo
A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard n-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the al¬gorithm is not rigorous in the sense that boundary conflicts are ignored . We demonstrate, however, that, in the their absence, or if they were correctly accounted for, our algorithm solves the same master equation as the serial method. We test the validity and parallel performance of the method by
1.2. PART II: DISLOCATION DYNAMICS WITH PARTIAL DISLOCATIONS
solving several pure diffusion problems (i.e. with no particle interactions) with known analytical solution. We also study diffusion-reaction systems with known asymptotic behavior and find that, for large systems with in¬teraction radii smaller than the typical diffusion length, boundary conflicts are negligible and do not affect the global kinetic evolution, which is seen to agree with the expected analytical behavior. We have nevertheless quan¬tified the error incurred by ignoring boundary conflicts and discuss possible ways to make the method rigorous.
1.2 Part II: Dislocation Dynamics with Par¬tial Dislocations
We develop a nodal dislocation dynamics (DD) model to simulate plastic processes in crystals with low stacking fault energy where perfect dislocations split into partials, leaving a stacking fault between them. The algorithm has been applied to fcc systems. The model explicitly accounts for all slip systems and Burgers vectors observed in fcc systems, including stack¬ing faults and partial dislocations. We derive simple conservation rules that describe all partial dislocation interactions rigorously and allow us to model and quantify cross-slip processes, the structure and strength of dislocation junctions, and the formation of fcc-specific structures such as stacking fault tetrahedra. The DD framework is built upon isotropic non-singular linear elasticity, and supports itself on information transmitted from the atom¬istic scale. In this fashion, connection between the meso and micro scales is attained self-consistently with core parameters fitted to atomistic data. We perform a series of targeted simulations to demonstrate the capabilities of the model, including dislocation reactions and dissociations and dislo¬cation junction strength. Additionally we map the four-dimensional stress space relevant for cross-slip and relate our findings to the plastic behavior of monocrystalline fcc metals. Finally we study the interaction between a dislocation and a stacking fault tetrahedron (SFT) which is the most typical defect seen in fcc crystals under particle irradiation.