Modeling self-organization of nano-size vacancy clusters in stochastic systems subjected to irradiation

Abstract

A study of the self-organization of vacancy clusters in irradiated materials is presented. Using a continuum stochastic model we take into account dynamics of point defects and their sinks with elastic interactions of vacancies. Dynamics of vacancy clusters formation is studied analytically and numerically under conditions related to irradiation in both reactors and accelerators. We have shown a difference in patterning dynamics and studied the external noise influence related to fluctuation in a defect production rate. Applying our approach to pure nickel irradiated under different conditions we have shown that vacancy clusters having a linear size ≃ 6 nm can arrange in statistical periodic structure with nano-meter range. We have found that linear size of vacancy clusters at accelerator conditions decreases down to 20%, whereas a period of vacancy clusters reduces to 6.5%.

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.…”

“…On the other hand, the effects of defect generation, migration to sinks, interaction, and diffusion can be studied at the mesoscopic level in the framework of the quasichemical reaction rate theory [8,[13][14][15][16][17]. In the framework of this approach, where the analyzed ensemble of defects is described by equations of the reactiondiffusion type for the concentration of point defects, it becomes possible to reveal specific features in the change of the defect pattern type [18], to study the dynamic and statistical properties of a defect redistribution and their dependence on irradiation conditions [9,10], and to reveal the influence of fluctuation components on the patterning [19]. In addition, according to works [20][21][22], this approach together with the nucleation theory were used to explain the abnormal dynamics of grain growth in irradiated systems, when the vacancies go beyond the grain boundaries [23].…”

“…Studying the redistribution of vacancies in the system that reached a certain concentration of radiationinduced damages remains rather a challenging problem at present. Its solution in the case of one-component system was discussed in works [9,10,18,19,23], where the supersaturation with vacancies was shown to result in their assembling into stable spatial patterns. The slow-down of the decomposition process in non-irradiated systems at its initial stage by non-equilibrium vacancies was studied in work [30].…”

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.…”

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

“…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].…”