Simulation of a Spatial Organization of Point Defects in Irradiated Systems

Abstract

In the framework of rate theory, a generalized statistical approach has been proposed to describe the spatial organization of point defects of the vacancy type into clusters and pores in irradiated systems. The approach makes allowance for the generation of point defects by elastic fields, as well as for defect interaction. The model is applied to study the defect pattern formation in pure nickel. The conditions required for the pattern formation at actual irradiation regimes in reactors have been analyzed. The peculiarities of microstructure changes at various temperatures and dose accumulation rates have been obtained both analytically and numerically. The defect pattern period and the change of a characteristic pattern size have been studied by applying the statistical methods to analyze the obtained numerical data. The results are in good correspondence with well-known experimental observations of the defect microstructure formation in irradiated materials under reactor conditions. K e y w o r d s: rate theory, spatial organization of point defects of the vacancy type, clusters, pores, irradiated systems, defect pattern formation, irradiation in reactors, numerical simulation.

Self-Organization of an Ensemble of Vacancies under the Spinodal Decomposition of Binary Systems at Continuous Irradiation

“…It was found experimentally and theoretically (numerical simulation) that the dynamics of an ensemble of defects and the properties of the created defect patterns depend on irradiation conditions (the dose rate and the temperature) [7,8]. This dependence is explained, first of all, by a reduction of the diffusion component contribution, when the defect distribution in the system is obtained by the irradiation on accelerators in comparison with the case of reactor irradiation conditions [9,10]. As a rule, the processes of defect generation in cascades, defect annealing, and defect cluster formation are simulated in theoretical researches by molecular dynamics methods.…”

Universality and self-similar behaviour of non-equilibrium systems with non-Fickian diffusion

“…Next, we drop the primes for convenience. This approach is widely used to study the pattern formation processes in chemical systems, at condensation under deterministic (see [10][11][12]) and stochastic conditions (see [13][14][15][16]), at epitaxial growth [20,21], at the formation of point defect clusters due to irradiation effect [24][25][26]41] and at other physical systems manifesting interactions between their elements. The obtained model cannot be used immediately to model the pyramidal islands formation because it does not take into account discrete steps (sharp interfaces) between terraces in pyramids.…”

“…In the process of pyramidal islands growth at molecular beam epitaxy, it was found that a structure of pyramids essentially depends on interactions of the elements forming the pattern described by a concentration dependent diffusion coefficient [18][19][20][21]. While studying the arrangement of point defects in solids at particle irradiation according to the swelling rate theory [22,23], it was found that vacancies can arrange into nanosize clusters due to their interactions described by a nonlinear diffusion flux [24][25][26][27]. This effect can lead to abnormal grain growth dynamics when vacancies segregate on the grain boundaries in a stochastic manner [28].…”

An Atomic Scale Study of Structural and Electronic Properties for $\alpha$-Zirconium with Single Vacancies and Vacancy Clusters

“…The obtained results regard to lattice and energy constants allowing one to construct interatomic interaction potential and explore restructuring processes of atomic structure at atomic displacement cascades realization in the framework of molecular dynamics methods [9][10][11]. Combined results of ab initio calculations and molecular dynamics simulations give the possibility to construct the evolution equations for point defects densities and their loops, in the framework of the continuum rate theory, and modelling the system evolution according to Monte Carlo methods [12][13][14][15][16]. A realization of such multiscale modelling procedure is very ambitious problem needing to its solution a huge database of structural element parameters, development of corresponding computation codes cross-linked with different hierarchical levels of description, and huge computational resources.…”