Point Defect Fluxes Research Articles

Coupled surface and bulk diffusion in crystals

We analyze point defect bulk and surface diffusion near the crystal–vacuum interface and show that bulk diffusion is coupled with surface diffusion via the atomic processes in the intermediate subsurface layer. A set of self-contained differential equations describing the interaction of self-interstitials and bulk vacancies with the surface of crystal is proposed. The results show the existence of the fundamental relation between the equilibrium concentrations of the point defects in bulk and at the surface of the crystal. For the case of silicon, the energy barrier differences that restrict the point defect fluxes between the bulk and surface of the crystal are estimated.

Effect of neutron irradiation on ductility of tungsten foils developed for tungsten-copper laminates

Severe plastic deformation of tungsten (W) is known to be an efficient way to reduce its inherently high ductile-to-brittle transition temperature (DBTT), what is essential for its use in components of a fusion reactor. Thin rolled W foils possess superior mechanical behaviour at room temperature (RT), as demonstrated in previous works. It was then proposed to expand the beneficial mechanical properties of the foil to bulk by fabricating tungsten-copper (W-Cu) laminate composites, which can be used for structural applications. Neutron irradiation in HFIR resulted in embrittlement of the laminate already after 0.016dpa, with the W foil determining the composite behaviour.In this work, for the first time, we investigate the effect of neutron irradiation on individual W foil, and determine the resulting DBTT shift with the help of cantilever bend tests, using bulk W and the W-Cu composite as reference. The W foil and the bulk samples were irradiated to 0.15dpa at 400 °C in the BR-2 reactor in Mol (Belgium). We also hypothesise that diffusion of Cu atoms into W could modify the response to irradiation in these materials. We substantiate it with complementary density functional theory (DFT) ab initio calculations to analyse the Cu-vacancy and Cu-self-interstitial interaction, which helps to elucidate co-alignment of the fluxes of point defects and Cu solutes in W matrix.Irradiated foil was found to retain its ductility at RT. No significant irradiation hardening or DBTT shift were detected in the irradiated W foil compared to the bulk W. The different irradiation effect on embrittlement in individual foils and in the laminate may be attributed to the irradiation-assisted diffusion of Cu solutes in W foil, which could form intermetallic phases and affect the accumulation of lattice defects.

Radiation-resistant binary solid solutions via vacancy trapping on solute clusters

Additions of solute that trap vacancies slow down vacancy diffusion and promote point-defect recombination in alloys subjected to irradiation. Such selective alloying can thus help to minimize the detrimental consequences resulting from point defect fluxes. The current work investigates the effect of solute additions on the recombination rate using kinetic Monte Carlo simulations for a model alloy system, which was parametrized to Cu-Ag in the dilute limit, but with an increased solubility limit, ≈ 0.86 at.% at 300 K. As the solute concentration was increased above 0.1 at.%, solute clustering was observed and led to a strong increase in recombination rate. The beneficial effects of solute clustering on reducing vacancy mobility, and reducing solute drag, were analyzed by calculating relevant transport coefficients using the KineCluE code (Schuler et al., Computational Materials Science (2020) 172,109,191). Moreover, it was observed in the KMC simulations that large recombination rates resulted in a shift of steady-state distributions of solute cluster sizes to smaller clusters compared to equilibrium distributions in the solid solution. This shift is rationalized as resulting from the irreversible character of the interstitial-vacancy recombination reaction. These results suggest a novel irradiation effect on phase stability where a high recombination rate increases the solubility limit of a solute at steady state over its equilibrium value.

Multiscale modeling of the effects of temperature, radiation flux, and sink strength on point-defect and solute redistribution in dilute Fe-based alloys

In this work, we investigate the radiation-induced segregation (RIS) resulting from the coupling between the atomic and point defect (PD) fluxes towards the structural defects of the microstructure. This flux coupling depends on the migration mechanisms of PDs and atoms, including thermal diffusion mechanisms and forced atomic relocations (FAR) occurring in displacement cascades. We derive an analytic model of the PD and solute RIS profiles accounting for PD production and mutual recombination, the FAR mechanism, and the overall sink strength of the microstructure controlling the elimination of PDs at structural defects. From this model, we present a parametric investigation of diffusion and RIS properties in dilute Fe-$B$ ($B$ = P, Mn, Cr, Si, Ni, and Cu) binary alloys, in the form of quantitative temperature/radiation flux/sink strength maps. As in previous works, we distinguish three kinetic domains for the diffusion and RIS properties: the recombination domain, the sink domain, and the thermal domain. Both our analytical approach and numerical applications demonstrate that the diffusion and RIS behaviors of PDs and solute atoms largely differ from one kinetic domain to another. Moreover, at high radiation flux, low temperature, and large sink strength, FARs tend to destroy the solute RIS profiles and therefore reduce the overall amount of RIS by forcing the mixing of solute and host atoms, especially close to PD sinks. Finally, we provide quantitative criteria to emulate in-reactor RIS behaviors by ion irradiation.

Attempts on representing sink strengths with machine learning formulations and the long-term role of crystalline interfaces in the development of irradiation-induced bubbles

The present article addresses an early-stage attempt on replacing the analyticity-based sink strength terms in rate equations by means of a surrogate representation. Here we emphasise, in the context of multiscale modelling, a combinative use of machine learning with scale analysis, through which a set of fine-resolution problems of partial differential equations describing the local sink behaviour, can be asymptotically sorted out from the mean-field kinetics. Hence the training of machine learning formulation is restrictively oriented, that is, to express the local and already identified, but analytically unavailable nonlinear functional relationships between the sink strengths and other local continuum field quantities. Besides, the normally faster diffusion mechanisms on crystalline interfaces are particularly modelled by locally planar rate equations, and their linkages with rate equations for bulk diffusion are formulated by imposing an irregular boundary condition where point defect fluxes are discontinuous across the interfaces. Thus the distinctive role of crystalline interfaces as partial sinks and quick diffusion channels can be investigated. Methodologicalwise, the present treatment is also applicable for studying more complicated situation of long-term sink behaviour observed in irradiated materials.

Effect of temperature history on swelling behavior of V-Fe binary alloy irradiated in a fast reactor Joyo

Abstract An on-line instrumented material irradiation rig (MARICO-II) was used for investigating temperature history effect for void swelling behavior in V-Fe binary alloys irradiated at a fast rector, Joyo. Neutron irradiation were performed at 477C with 7.5 dpa in the temperature control capsule (TC capsule) and at 482C maximum temperature with 20.4 dpa in the conventional capsule with monitoring temperature. In the TC capsule, voids was formed and distributed homogeneously, on the other hand a lot of tiny void formation or bimodal void distribution were observed in the conventional capsule, The void swelling rate of V-Fe alloys irradiated in the TC capsule was larger than that in the conventional capsule and it is caused by the imbalance of point defect flux to sink due to void nucleation at the low temperature transient regime in start-up and shutdown period of each cycle in neutron irradiation, that is temperature history effect for swelling behavior of V-Fe binary alloys during neutron irradiation.

Unusual irradiation-induced disordering in Cu3Au near the critical temperature: An in situ study using electron diffraction

Abstract

Defect-interface interactions in irradiated Cu/Ag nanocomposites

In this work, we employ transmission electron microscopy and helium ion irradiation to study the response of biphase interfaces to radiation induced point defect fluxes from the two adjoining phases. Analysis of interface-affected defect accumulation was carried out over a wide range of radiation damage levels from near zero displacement per atom (dpa) to 16 dpa and helium concentrations of 0 at.% to 8 at.%. Results show a strong interface density dependence in which Cu/Ag interfaces in the nanolayered regions spaced <500 nm were remarkably microstructural stable over the entire range without accumulating micro-scale defects, while those spaced >1 μm apart were destroyed. We report the concomitant development of a bubble-free zone in Cu that was independent of defect levels and interface-contacting bubbles zone in Ag. This finding is explained by bias segregation to the interface of interstitials from Ag and vacancies to misfit dislocation nodes in the interface from Cu. The point defect transfer across the interface can be explained by the spatial variation in interface pressure within the interface and gradient in pressure across the interface, both originating from the lattice mismatch and surface energy difference between the two crystals.

Modeling the long-term evolution of dilute solid solutions in the presence of vacancy fluxes

This work investigates the long-term evolution of dilute solute atoms in face-centered-cubic (fcc) alloys driven by sustained vacancy fluxes, as for instance in the case of materials subjected to energetic particle irradiation. Employing the five-jump frequency framework, we provide compact analytic expressions of the Onsager matrix for dilute vacancy-solute systems in form of a ratio of polynomial functions of jump frequencies. The drag ratio is found to be a function of only two independent variables, which enables a systematic study of both the flux coupling and trapping behavior between solutes and point defects. Using an existing diffusivity database for a total of 182 solutes in 5 fcc solvents, we show that, while most vacancy-binding solutes have indeed a positive drag ratio, there are some solutes with positive, but small, or even negative drag ratio. This previously unnoticed feature is interesting as it would ensure that the trapping solute remains in the matrix despite the accumulation of irradiation dose. In the case where the drag ratio is positive, we propose a kinetic model of solute depletion over time due to flux coupling with vacancies and apply it to a Cu-1 at. % Sb alloy. This study reveals that solutes are not simply dragged to sinks by point defects, but affect the flux of point defects to sinks by modifying the transport coefficients and the driving force for point-defect elimination.

Formation of deformation substructures in FCC crystals under the influence of point defect fluxes

The article deals with sub-structural transformations in FCC crystals under the influence of point defect fluxes. Different relationships between accumulation of point defects in crystal and substructure transformations, in particular during the process of fragmented dislocation structure formation have been received.

Anti-radiation mechanisms in nanoporous gold studied via molecular dynamics simulations

The radiation resistance performance of nanoporous (NP) gold is investigated by cascade simulations of a gold nanowire using molecular dynamics. The role of the surface on primary defect production was clarified: the mean size of the vacancy clusters (VCs) near the surface in the nanowire becomes larger compared to that of a single crystal. In the surface region, the reduction of the formation and migration energies of point defects leads to a continuous flux of point defects towards the free surface, which retards the formation and growth of defect clusters, resulting in a good anti-radiation performance. In the cascade region, however, the retained vacancies tend to form larger sessile VCs due to their low migration energies and large attractive forces, resulting in radiation damage. The competition between these two factors determines the anti-radiation behavior of NP gold.

Defect sink characteristics of specific grain boundary types in 304 stainless steels under high dose neutron environments

Radiation induced segregation (RIS) is a well-studied phenomena which occurs in many structurally relevant nuclear materials including austenitic stainless steels. RIS occurs due to solute atoms preferentially coupling with mobile point defect fluxes that migrate and interact with defect sinks. Here, a 304 stainless steel was neutron irradiated up to 47.1dpa at 320°C. Investigations into the RIS response at specific grain boundary types were used to determine the sink characteristics of different boundary types as a function of irradiation dose. A rate theory model built on the foundation of the modified inverse Kirkendall (MIK) model is proposed and benchmarked to the experimental results. This model, termed the GiMIK model, includes alterations in the boundary conditions based on grain boundary structure and expressions for interstitial binding. This investigation, through experiment and modeling, found specific grain boundary structures exhibiting unique defect sink characteristics depending on their local structure. Such interactions were found to be consistent across all doses investigated and to have larger global implications, including precipitation of Ni–Si clusters near different grain boundary types.

A sharp interface model for void growth in irradiated materials

A thermodynamic formalism for the interaction of point defects with free surfaces in single-component solids has been developed and applied to the problem of void growth by absorption of point defects in irradiated metals. This formalism consists of two parts, a detailed description of the dynamics of defects within the non-equilibrium thermodynamic frame, and the application of the second law of thermodynamics to provide closure relations for all kinetic equations. Enforcing the principle of non-negative entropy production showed that the description of the problem of void evolution under irradiation must include a relationship between the normal fluxes of defects into the void surface and the driving thermodynamic forces for the void surface motion; these thermodynamic forces are identified for both vacancies and interstitials and the relationships between these forces and the normal point defect fluxes are established using the concepts of transition state theory. The latter theory implies that the defect accommodation into the surface is a thermally activated process. Numerical examples are given to illustrate void growth dynamics in this new formalism and to investigate the effect of the surface energy barriers on void growth. Consequences for phase field models of void growth are discussed.

Modeling plastic deformation of post-irradiated copper micro-pillars

We present here an application of a fundamentally new theoretical framework for description of the simultaneous evolution of radiation damage and plasticity that can describe both in situ and ex situ deformation of structural materials [1]. The theory is based on the variational principle of maximum entropy production rate; with constraints on dislocation climb motion that are imposed by point defect fluxes as a result of irradiation. The developed theory is implemented in a new computational code that facilitates the simulation of irradiated and unirradiated materials alike in a consistent fashion [2]. Discrete Dislocation Dynamics (DDD) computer simulations are presented here for irradiated fcc metals that address the phenomenon of dislocation channel formation in post-irradiated copper. The focus of the simulations is on the role of micro-pillar boundaries and the statistics of dislocation pinning by stacking-fault tetrahedra (SFTs) on the onset of dislocation channel and incipient surface crack formation. The simulations show that the spatial heterogeneity in the distribution of SFTs naturally leads to localized plastic deformation and incipient surface fracture of micro-pillars.

Relationship between lath boundary structure and radiation induced segregation in a neutron irradiated 9 wt.% Cr model ferritic/martensitic steel

Ferritic/Martensitic (F/M) steels with high Cr content posses the high temperature strength and low swelling rates required for advanced nuclear reactor designs. Radiation induced segregation (RIS) occurs in F/M steels due to solute atoms preferentially coupling to point defect fluxes which migrate to defect sinks, such as grain boundaries (GBs). The RIS response of F/M steels and austenitic steels has been shown to be dependent on the local structure of GBs where low energy structures have suppressed RIS responses. This relationship between local GB structure and RIS has been demonstrated primarily in ion-irradiated specimens. A 9wt.% Cr model alloy steel was irradiated to 3dpa using neutrons at the Advanced Test Reactor (ATR) to determine the effect of a neutron radiation environment on the RIS response at different GB structures. This investigation found the relationship between GB structure and RIS is also active for F/M steels irradiated using neutrons. The data generated from the neutron irradiation is also compared to RIS data generated using proton irradiations on the same heat of model alloy.

The role of niobium carbide in radiation induced segregation behaviour of type 347 austenitic stainless steel

The effect of niobium carbide precipitates on radiation induced segregation (RIS) behaviour in type 347 stainless steel was investigated. The material in the as-received condition was irradiated using double-loop 4.8 MeV protons at 300 °C for 0.43 dpa (displacement per atom). The RIS in the proton irradiated specimen was characterized using double-loop electrochemical potentiokinetic reactivation (DL-EPR) test followed by atomic force microscopic examination. The nature of variation of DL-EPR values with the depth matched with the variation of the calculated irradiation damage (dpa) with the depth. The attack on grain boundaries during EPR tests was negligible indicating absence of chromium depletion zones. The interface between niobium carbide and the matrix acts as a sink for point defects generated during irradiation and this had reduced point defect flux toward grain boundaries. The attack was noticed at a few large cluster of niobium carbide after the DL-EPR test at the depth of maximum attack for the irradiated specimen. Pit-like features were not observed within the matrix indicating the absence of chromium depletion regions within the matrix.

Structural transformations, distribution of nonequilibrium vacancies, and anomalous diffusion in plastically deformed metals and alloys upon mechanical alloying

Processes of structural transformations leading to the generation of fluxes of nonequilibrium point defects and anomalously high rates of diffusion of substitutional impurities in nanostructured metallic systems upon mechanical alloying have been investigated. The basic contribution to the anomalous acceleration of diffusional mass transfer was shown to come from the nonequilibrium vacancies generated by processes of the deformation-induced migration of intercrystallite boundaries. The influence of interstitial atoms on the diffusion and processes of recrystallization was found to be negligible. The specific features of the formation of strongly supersaturated substitutional solid solutions upon severe plastic deformation of metals and alloys have been examined.

A continuum based microstructure model of inhomogeneous hardening and recovery as a pre-stage of recrystallization nucleation

AbstractStarting from the fundamental relation between the diffusion flux of point defects (vacancies, interstitials) and the gradient of the diffusion potential the diffusion equation is set up and applied to the calculation of the concentrations of both types of point defects. Thereby, all possible sources and sinks and their mutual effects are taken into consideration. These equations are coupled with the equations for the temporal derivatives of dislocation density, porosity, pore size and temperature. For the close-up region of spherical inhomogeneities (pores, hard inclusions) and a grain boundary this system of six partial differential equations is solved numerically. For simplicity a one dimensional model in space is used and uniaxial tension or pure shear load is assumed. Hardening and the simultaneous recovery are characterized by the local and temporal development of the point defect concentrations and especially of the dislocation density, which is proportional to the intrinsic strain energy. The gradients of both strain energy and lattice rotation determine the formation and growth of recrystallization nuclei. It is the aim of this work to present a new mathematical model and also to give a perceptual general view on the concerted action of the fundamental physical processes, which necessarily lead to hardening, recovery (softening) and recrystallization nucleation. Moreover it seems to be a basis of a future general theory of microstructure changes.

Response of nanocrystalline3Csilicon carbide to heavy-ion irradiation

Nanostructured materials are generally believed to be more radiation resistant. This study reports on Au-ion-induced amorphization in nanocrystalline $3C\text{-SiC}$, characterized using x-ray diffraction, transmission electron microscopy and Raman spectroscopy. Full amorphization at room temperature occurs at a comparable dose to that for bulk SiC single crystals. The behavior is primarily attributed to a high ion flux and sluggish migration of point defects produced during irradiation. The results may have a significant implication of using nanophased SiC in extremely high radiation environments.

Atomistic Simulations of Copper Precipitation and Radiation Induced Segregation in α-Iron

We present Monte Carlo simulations of the first stages of the coherent precipitation of Cu in α-Fe during thermal ageing and under irradiation. The simulations are based on a diffusion model by vacancy and self-interstitial jumps, the parameters of which are fitted on ab initio calculations. The simulations of precipitation kinetics during thermal ageing are compared with experimental ones. They reveal that precipitates containing up to several tens of atoms can be much more mobile than individual copper atoms, due to the trapping of vacancies in Cu. Monte Carlo simulations are also used to analyze the coupling between fluxes of point defects and Cu which occurs under irradiation and the possible resulting radiation induced segregation phenomena.