Master equation and Fokker–Planck methods for void nucleation and growth in irradiation swelling

Surh, Michael P.; Sturgeon, J.B.; Wolfer, W.G.

doi:10.1016/j.jnucmat.2003.10.013

Cited by 44 publications

(46 citation statements)

References 20 publications

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“…2 includes that two vacancies are consumed by the reaction, that there is a factor of 1/2 to prevent double-counting of unique pairs of vacancies from the population ρ v , and that the relative diffusivity is twice D v . The net rate is identical to that used in a previous study [5]. Similar considerations also apply to pairs of substitutional helium and to thermal dissociation of vacancy dimers.…”

Section: Rate Theory Modelmentioning

confidence: 72%

“…Within the mean field continuum approximation, the collision rate is proportional to their relative diffusivity, D m,n , and effective collision cross-section, A m,n . As before [5,8], a bias factor Z m,n includes the effect of long-range interactions [32,33] on the binary reaction rates, K(m, n)ρ m ρ n , where ρ are densities of reactant species m = n and the rate coefficients are:…”

Section: Rate Theory Modelmentioning

confidence: 99%

“…Both the densities and the compositions of the MC elements evolve with time. Such split distribution functions have been used before in a Fokker-Planck treatment of void growth [5], and in non-equilibrium chemistry [23,29], and plasma physics applications [47]. In essence, the elements of P M C also constitute so-called "macroparticles", already in wide use for non-equilibrium plasma physics problems [48].…”

Section: Overviewmentioning

confidence: 99%

“…Transient and steady-state swelling behavior due to these processes have been studied recently [5,6,7,8]. However, only void reactions with vacancy or interstitial monomers are included in these studies.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Void nucleation, growth, and coalescence in irradiated metals

Surh

Sturgeon

Wolfer

2008

Journal of Nuclear Materials

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A novel computational treatment of dense, stiff, coupled reaction rate equations is introduced to study the nucleation, growth, and possible coalescence of cavities during neutron irradiation of metals. Radiation damage is modeled by the creation of Frenkel pair defects and helium impurity atoms. A multi-dimensional cluster size distribution function allows independent evolution of the vacancy and helium content of cavities, distinguishing voids and bubbles. A model with sessile cavities and no cluster-cluster coalescence can result in a bimodal final cavity size distribution with coexistence of small, high-pressure bubbles and large, low-pressure voids. A model that includes unhindered cavity diffusion and coalescence ultimately removes the small helium bubbles from the system, leaving only large voids. The terminal void density is also reduced and the incubation period and terminal swelling rate can be greatly altered by cavity coalescence. Temperature-dependent trapping of voids/bubbles by precipitates and alterations in void surface diffusion from adsorbed impurities and internal gas pressure may give rise to intermediate swelling behavior through their effects on cavity mobility and coalescence. IntroductionIrradiation of metals has long been known to culminate in macroscopic property changes including void swelling [1]. Characteristic stable voids and steady volumetric swelling develop for a range of temperatures and fluxes, independent of whether radiation bombardment damage occurs as disseminated Frenkel pairs or as small defect clusters. This can occur whether or not helium is generated along with atomic displacements. In either case, small, unstable voids, loops, and other defect clusters will develop almost immediately within the irradiated material. Their subsequent evolution determines the fluence required to create stable voids and achieve 1 arXiv:0803.3829v1 [cond-mat.mtrl-sci]

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Section: Rate Theory Modelmentioning

confidence: 72%

Section: Rate Theory Modelmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Void nucleation, growth, and coalescence in irradiated metals

Surh

Sturgeon

Wolfer

2008

Journal of Nuclear Materials

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“…Furthermore, to reach the typical size of dislocation loops or voids, which are observed experimentally, for instance, by transmission electron microscopy, the number of differential equations is very large. Grouping procedures or other approximate numerical schemes such as the Fokker-Planck formalism, which allows replacement of the N equations with a continuous variable x for large values of N, [296][297][298][299][300][301] thus have to be used. This becomes necessary when one wishes to take into account explicitly the chemistry of the materials, as is, for instance, the case for Cu atoms in ferritic steels, or if one wants to introduce a gas atom such as He for fusion or gamma heating modeling.…”

Section: Kmc and Mfrt: Evolution Of The Primary Damagementioning

confidence: 99%

Modeling Microstructure and Irradiation Effects

Becquart

Domain

2010

Metall Mater Trans A

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This article gives an overview of the strategy followed nowadays to model the evolution of metallic alloy microstructures under irradiation. For this purpose, multiscale approaches are very often used, which rely on modeling techniques appropriate to each time and space scale. The main methods used are ab-initio calculations, classical molecular dynamics (MD), kinetic Monte Carlo (KMC), mean field rate theory (MFRT), and dislocation dynamics (DD). These methods are briefly presented along with some of their typical uses and main drawbacks. Some examples are provided of the typical information obtained with each of the techniques.

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