Papers by Keyword: Cluster Dynamics

Abstract: The Cluster Dynamics method is assessed for the investigation of fission gas behaviour in a krypton-implanted and annealed UO₂ sample. The simulation results are then compared to Thermal Desorption Spectroscopy (TDS) data. A release mechanism is proposed: the initial burst is related to krypton migration via an interstitial mechanism, while the second stage of the release process can be accounted for by the diffusion of krypton in a substitutional position. This latter mechanism is compatible with a diffusion coefficient of 4.10^-21 m²/s.

Abstract: We compare three models of 2D precipitation kinetics that give access to different time-space scales. Kinetic Monte Carlo simulations (KMC), cluster dynamics (CD) and nucleation-growth-coalescence model (NGCM), based on a same atomic model, lead to an excellent agreement as long as the interfacial free energy is evaluated accurately and the interaction between diffusion fields is taken into account in the CD. The NGCM model noticeably improves the previous approaches of the same kind by using a constrained-equilibrium hypothesis to describe the solid solution. Moreover, in the coalescence regime, we show that CD leads to cluster distributions that are wider and more symmetric than the LSW distribution due to the probabilistic feature of the growth law of a cluster, that makes it differ from the purely deterministic NGCM approach.

Abstract: Cluster dynamics (CD) is used to study the evolution of the size distributions of vacancy clusters (VC), self-interstitial atom (SIA) clusters (SIAC) and Cr precipitates in neutron irradiated Fe-12.5at%Cr alloys at T = 573 K with irradiation doses up to 12 dpa and a flux of 140 ndpa/s. Transmission electron microscopy (TEM) and small angle neutron scattering (SANS) data on the defect structure of this material irradiated at doses of 0.6 and 1.5 dpa are used to calibrate the model. A saturation behavior was found by CD for the free vacancy and free SIA concentrations as well as for the number density of the SIAC and the volume fraction of the Cr precipitates for neutron exposures above 0.006 dpa. The CD simulations also indicate the presence of VC with radii less than 0.5 nm and a strong SIAC peak with a mean diameter of about 0.5 nm, both invisible in SANS and TEM experiments. A specific surface tension of about 0.028 J/m² between the a matrix and the Cr-rich a' precipitate was found as best fit value for reproducing the long-term Cr evolution in the irradiated Fe-12.5%Cr alloys observed by SANS.

Abstract: The coupling between copper rich precipitates (CRP) and point defects in neutron irradiated iron alloys and VVER steels was investigated by means of cluster dynamics (CD) simulations. The consideration of the strain energy effect on CRP kinetics as well as the application of the regular solution model for the case of different fixed copper contents of CRP provides a good agreement between the simulation results and experimental data for complex iron based alloys with small (0.015 wt%) and high (0.42 wt%) copper content. It was found that the CD simulation is applicable to irradiated VVER steel with 0.07 wt% of copper.

Abstract: The aim of this paper is to give a short review on cluster dynamics modeling in the field of atoms and point defects clustering in materials. It is shown that this method, due to its low computer cost, can handle long term evolution that cannot, in many cases, be obtained by Lattice Kinetic Monte Carlo methods. Indeed, such a possibility is achieved thanks to an important drawback that is the loss of space correlations of the elements of the microstructures. Some examples, in the field of precipitation and irradiation of metallic materials are given. The limitations and difficulties of this method are also discussed. Unsurprisingly, it is shown that it goes in a very satisfactory way when the objects are distributed homogeneously. Conversely, the source term describing the primary damage under irradiation, by nature heterogeneous in space and time, is tricky to introduce especially when displacement cascades are produced.

Abstract: The precipitation kinetics path in multi-component alloys may involve a competition between atomic mobilities and precipitates thermodynamic stability. Cluster dynamics modelling (CDM) is a simulation method that allows to describe this competition without introducing any heuristic assumptions as, for example, in the classical theory of nucleation. CDM consists in solving numerically, for each time increment, the master equations expressing the balance of solute exchanges (absorption and emission) between clusters/precipitates. A key issue is the energetics of the nano-clusters in the nucleation range. The computation of the precipitate size distribution function allows the complete description of the precipitates kinetic evolution, in chemical composition and in size. The method is applied to the precipitation of the Al3(Zr,Sc) L12 phase in Al solid solutions. The model predicts fairly well in the precipitation path some observed coupling effects between the two solutes, particularly during the nucleation stage.

Abstract: We test the main approximations of the classical laws for nucleation, growth and coarsening by comparison with atomistic simulations of the kinetics of precipitation. We investigate the kinetics of phase separation in dilute A-B solid solutions by precipitation of B atoms in the Arich matrix. Classically, the kinetics is represented by the time evolution of the total number of particles and their mean radius. In this work, the kinetics is predicted by three types of models: (a) an Atomic-scale Kinetic Monte Carlo (AKMC) model based on a vacancy diffusion mechanism, (b) a Cluster Dynamics model, and (c) the MultiPreci model, based on the coupling of the classical laws of nucleation, growth and coarsening. Cluster Dynamics and the Multipreci model have been parameterized such that the thermodynamic and kinetic parameters (solubility, diffusion coefficient, interface energy) be identical to that of the AKMC. Under these conditions we find that the classical laws are in good agreement with the atomistic simulations as long as the thermodynamics of the solid solution remains strictly regular. As expected, Cluster Dynamics compares better with the atomistic simulations, especially if a precise description of the energetics of the smallest clusters is applied.