Generalized rate theory for spatially inhomogeneous systems of point defect sinks

Diffusion coefficients and thermal stability of small helium–vacancy clusters in iron

“…In order to estimate the kinetic parameters of a cluster He n v m , n He atoms were simply distributed randomly over a compact cluster of m empty lattice sites (with m > n) and let the unoccupied vacancies perform diffusion jumps with probabilities determined by Boltzmann factors appropriate for each particular jump. As the employed Monte-Carlo code estimates the average 2 · 10 À6 7.5 · 10 4 2 · 10 À6 9.0 · 10 5 2.0 · 10 À6 8.61 · 10 5 v 3 4 · 10 À6 8.5 · 10 4 5 · 10 À7 2.6 ·10 7 5.1 · 10 À7 2.41 · 10 7 v 4 8 · 10 À5 8.5 · 10 3 1.5 · 10 À6 4.9 · 10 6 --v 5 --1.8 · 10 À6 1.7 · 10 6 --Hev 2 1.5 · 10 À2 7.8 · 10 3 7.9 · 10 À4 8.5 · 10 4 8.2 · 10 À4 1.00 · 10 5 Hev 3 >2.5 4.5 · 10 3 1.4 · 10 À2 1. time for each performed jump and evaluates a position of the cluster centre, the trajectory of each cluster can be traced jump by jump until a predefined limit of vacancy jumps (typically 50-100 millions) is reached or until the cluster dissociates. Having in mind that according to ab initio calculations helium atoms and vacancies are bound to each other up to the second nearest neighbour (NN) separations, a cluster dissociation is assumed to occur when at least one vacancy or He atom is found at a larger than 2NN separation from any other vacancy/He atom that belonged to the initial cluster.…”

“…At elevated temperatures this results in the formation of He gas bubbles (that is, clusters of vacancies (v) containing a certain amount of He atoms inside), which are known to cause swelling and the degradation of mechanical properties of irradiated steels, bearing a risk of material failure. In order to predict the kinetics of bubble growth in a broad range of time and length scales relevant for the operation of reactor structural components, one usually relies on analytical treatments in the framework on the chemical rate theory [1,2], or on appropriate simulation techniques, such as object kinetic Monte-Carlo (see e.g. [3,4]).…”

Self-organization kinetics in finite precipitate ensembles during coarsening

“…Continuation of this procedure results, generally, in a hierarchy of equations for the moments of q i . 18,22 However, in the case of a dilute precipitate system this hierarchy of equations can be truncated using different decoupling conventions. 22 Here we use the ''mean-field'' convention, assuming 22 that q i depends only on the parameters of the ith precipitate, q i ϭq i (r i ,R i ).…”

“…18,22 In particular, the average impurity concentration C at a spatial point r is obtained after the averaging over all positions and sizes of the precipitates and has the form 22…”

JERK, an event-based Kinetic Monte Carlo model to predict microstructure evolution of materials under irradiation

“…It is unfortunate that part of the delay distributions is badly known. Indeed they were evaluated in the frame of a binary collision approximation which becomes less and less accurate as time elapses, since, in the absence of any exact solution for the complex diffusion problem as a whole, we do not have at hand the proper distribution law for delays which take due account of the interference effects between reaction partners and of the shadowing effect between closely located sinks or nonlocal sinks like dislocations [5]. Up to now, only expensive and numerical treatments using the Laplace transform have been proposed, which cannot be included simply into the present procedure [6].…”