Self-interstitial Atom Clusters Research Articles

The temperature effect on the formation and growth of helium-vacancy clusters in bcc iron: a comprehensive molecular dynamics simulation

Bubble generation can significantly degrade the performance of fusion reactor structural materials. In this work, the temperature effects on the initial clustering of helium (He) atoms, the formation of helium-vacancy clusters (HenVm) and the subsequent growth of the clusters into bubbles in bcc iron under different conditions were simulated by molecular dynamics. The results show that He behaviors are primarily dominated by coalescence at temperature range from 400K to 500K, which leads to a preference for He to bind together. Conversely, when temperature is higher than 500K, dissociation become more prominent, causing large He clusters to be hard to form. Under the conditions of increasing He concentration and irradiation dose, the higher the temperature, the higher the density of HenVm clusters at He concentration around 100 appm. However, the temperature dependence reversed at high He concentration. The detailed analysis of formation cases revealed the percentage of nucleation sites for He bubbles at defects during He segregation. In addition, there is no significant difference among the He/V ratio of HenVm clusters formed at vacancies, interstitial dislocation loops (IDLs) and interstitial sites during the cluster growth. However, the He/V ratio of He bubbles growing on edge dislocation (ED) is overall lower than those growing at other formation sites, since the growth of HenVm clusters on ED requires a lower pressure to kick out self-interstitial atoms (SIAs) or SIA clusters. The average He/V ratio of He bubbles in bulk decreases as temperature rises from 400K to 800K, while the average ratio of HenVm clusters growing on ED is independent of temperature.

A hybrid rate theory model of radiation-induced growth

Differences in the diffusivity of radiation-produced defects along zirconium’s prismatic and basal planes result in radiation-induced growth (RIG) and creep. The difference in anisotropy of diffusion (DAD) model explains this behavior by assuming vacancies and self-interstitial atoms (SIAs) possess dissimilar ratios of in-basal-plane vs out-basal-plane diffusion coefficients. The self-interstitial cluster diffusion (SICD) model was proposed as an alternative to DAD, and relates growth to the formation of self-interstitial clusters which diffuse solely along the 〈a〉 direction. Here, we propose a hybrid model, in which the contribution of both effects are considered, which provides additional flexibility as compared to DAD or SICD taken individually. In this model, both anisotropic diffusing point defects and 1-dimensional (1-D) glissile SIA clusters are considered, which are removed in the internal and boundary sinks. Thirty-two DAD, SICD and hybrid models are fitted to a set of thirty-two RIG experiments. Good agreement between DAD and the experiments can be reached only by assuming unrealistically large SIA bias factors. In 9 of the 32 scenarios, good agreement between SICD and experiments could not be reached, indicating that the model lacks flexibility. Good agreement between the hybrid model and the experiments can be reached using realistic SIA bias factors; however, it requires assuming considerably lower vacancy bias factors than those found by ab initio calculations aimed at mono-vacancies, suggesting small vacancy clusters and loops play a more important role in RIG than previously thought.

Understanding the effect of phosphorous on the ion-irradiation behaviour of RPV model steels using atom probe tomography and nanoindentation

Understanding the formation of the embrittling Mn-Ni-Si (MNS)-rich clusters in reactor pressure vessel (RPV) steels is of economic, environmental, and safety importance. Hence we investigated the influence of phosphorous (P) on the formation of MNS-rich clusters in RPV model steels employing atom probe tomography and nanoindentation tests. The atom probe tomography results show that the average number density and volume fraction of clusters decrease slightly with an increase in the bulk P content; however, higher bulk P led to a slight increase in the average diameter of the clusters. A higher amount of bulk P led to higher Cu in the clusters; suggesting synergy between Cu and P. An increase in the irradiation hardening values was observed due to higher bulk P content. This is attributed to the stabilisation of the self-interstitial atoms (SIA) clusters by P. A higher recovery for the sample containing higher bulk P indicated that the SIA clusters dissolved after post-irradiation annealing.

Effect of grain boundaries and rigid inclusions on plasticity in nickel bicrystals containing helium bubbles and radiation-induced self-interstitial atom clusters

We use molecular dynamics to assess the effect of grain boundaries and rigid intergranular inclusions on plastic deformation in nickel (Ni) containing helium (He) bubbles and self-interstitial atom clusters. Our simulations show that plasticity in Ni bicrystals is relatively uniform, with no localized slip bands or nano-twins. We attribute this behavior to grain boundaries, which block dislocations and favor activation of new sources over persistent slip along a single plane. While there is no initiation of intergranular cracks, He bubbles at matrix/inclusion interfaces elongate along the tensile axis and migrate towards regions of high tension, potentially setting the conditions for formation of crack-like flaws via bubble coalescence. We discuss the implications of our work for understanding degradation of mechanical properties in Ni-base alloys in nuclear reactors.

Anisotropic diffusion of radiation-induced self-interstitial clusters in HCP zirconium: A molecular dynamics and rate-theory assessment

Under irradiation, Zr and Zr alloys undergo growth in the absence of applied stress. This phenomenon is thought to be associated with the anisotropy of diffusion of either or both radiation-induced point defects and defect clusters. In this work, molecular dynamic simulations are used to study the anisotropy of diffusion of self-interstitial atom clusters. Both near-equilibrium clusters generated by aggregation of self-interstitial atoms and cascade-induced clusters were considered. The cascade-induced clusters display more anisotropy than their counterparts produced by aggregation. In addition to 1-dimensional diffusing clusters, 2-dimensional diffusing clusters were observed. Using our molecular dynamic simulations, the input parameters for the “self-interstitial atom cluster bias” rate-theory model were estimated. The radiation-induced growth strains predicted using this model are largely consistent with experiments, but are highly sensitive to the choice of interatomic interaction potential.

Effect of free surfaces on localized plastic deformation in single-crystal nickel containing helium bubbles and radiation-induced self-interstitial atom clusters

This paper presents molecular dynamics (MD) simulations of plastic deformation in single-crystal Ni models containing internal distributions of helium (He) bubbles and self-interstitial atom (SIA) clusters corresponding to experimental characterization of ex-service Inconel X-750 components. We simulate single crystals with and without free surfaces at room temperature and 588K, the latter temperature corresponding to the Inconel X-750 service conditions. Both models are deformed under multiple slip to a maximum deviatoric strain of ∼10 %. A dislocation slip band forms in the model without free surfaces, but not in the model with free surfaces. However, the latter exhibits nano-twin nucleation from surfaces. Helium (He) bubbles that overlap with a slip band or a nano-twinned region deform more severely than other bubbles in the model. Nevertheless, the bubbles do not link up and do not form configurations that resemble incipient cracks.

MD Simulations of Collision Cascades in α-Ti. Statistics and Governing Mechanisms of Point Defect Cluster Formation

The outcomes of molecular dynamics simulations of primary damage formation in collision cascades initiated by primary knock-on atoms (PKA) with PKA energy 5 keV ≤Epka≤ 25 keV in α-titanium at 100 K ≤T≤ 900 K temperatures have been analysed. The fraction of vacancies, εv, and self-interstitial atoms (SIA), εi, in point defect clusters created in isolated collision cascades was evaluated. The corresponding averages ⟨εv⟩ and ⟨εi⟩ over cascade series with the same (Epka, T) parameters, the average size ⟨Nvac⟩ and ⟨Nsia⟩ of vacancy and SIA clusters, respectively, and the average vacancy ⟨Yvac ⟩ and SIA ⟨Ysia ⟩ cluster-per-cascade yield were found as well. Possible governing mechanisms have been suggested to explain ⟨εv⟩, ⟨εi⟩ , ⟨Nvac⟩, ⟨Nsia⟩, ⟨Yvac⟩ and ⟨Ysia⟩ dependence on (Epka,T).

Molecular dynamics study of primary damage in the near-surface region in nickel

We carried out a large-scale molecular dynamics (MD) simulation to study displacement cascades in the near-surface region in pure nickel. These MD simulations were performed both in the bulk and near-surface regions with primary knock-on atom (PKA) energies of EPKA=1,5, or 10keV and at temperatures T=300,425, or 525K. In our study, the primary knock-on atom was taken to be created by a neutron knocking off a lattice atom. Accordingly, cascades were initiated by giving a lattice atom the appropriate velocity corresponding to the PKA energy. Assuming isotropic neutron fluence, the PKA was initiated in random directions (including toward and parallel to the free surface) in both bulk and near-surface simulations. This contrasts with previous studies in which the cascades were initiated by the projectiles directed toward the free surface to mimic ion irradiation. Therefore, for every (T,EPKA), near-surface cascade simulations were performed also as a function of PKA's initiation depth. Present results provide quantitative information about defect production and clustering in the primary damage state for near-surface and bulk displacement cascades. The effect of EPKA and T on the defect production (averaged over all PKA directions) is similar for both the near-surface and bulk cascades. In both cases, the defect production increases with EPKA, but the temperature has minimal effect. However, the production and clustering of vacancies are higher for near-surface cascades. In contrast, the production and clustering of self-interstitial atoms are lower and increase monotonically with depth. The decrease in the average number of vacancies and average vacancy cluster size with increasing depth is not monotonic.

Diffusion Characteristics of Clusters of Self-Interstitial Atoms
 in Vanadium: Molecular Dynamics Data

The temperature dependences of diffusion characteristics of the irradiation-induced defects, namely, clusters of self-interstitial atoms (SIAs) containing up to five atoms, in bcc V (vanadium) have been studied by the method of molecular dynamics in the temperature range of 300–1000 K. The diffusion characteristics include the coefficient of diffusion, the tracer correlation factor, the average displacement before changing the direction of migration, and the frequency of changing the direction of migration. The values of the activation energy of diffusion and the activation energy of changing the direction of migration for the considered types of defects in different temperature ranges have been determined. The dependences of the mechanism of (1D vs 3D) diffusion of SIA clusters on the temperature and cluster size and their possible influence on the parameters of phenomenological models of changes in the microstructure of a material under irradiation (sink strengths of spherical absorbers) are discussed.

Diffusion Characteristics of Clusters of Self-Interstitial Atoms in Vanadium: Molecular Dynamics Data

Diffusion Characteristics of Clusters of Self-Interstitial Atoms in Vanadium: Molecular Dynamics Data

Investigating the Impact of Displacement Cascades on Tritium Diffusion in MgT2: A Molecular Dynamics Study.

Molecular dynamics methods were utilized to investigate displacement cascades and tritium diffusion in α-MgT2. It was observed from collision cascades results that the stable number of defects weakly depended on temperature, while the peak and stable number of defects linearly increased with increasing the primary knock-on atom energy. The results of the mean square displacement study revealed that defects had a significant impact on tritium diffusion. The clustering of magnesium self-interstitial atoms and diffusing tritium atoms results in an increased diffusion barrier, whereas the formation of clusters between tritium interstitial atoms is relatively difficult and has no significant impact on the diffusion barrier. The presence of magnesium and tritium vacancies has a minimal effect on the diffusion barrier due to the large number of diffusing tritium atoms that offset the adsorption of vacancies on diffusing atoms. Both magnesium and tritium interstitial atoms increase the collision probability of diffusing atoms, leading to an increased diffusion prefactor. Magnesium vacancies cause significant lattice distortion, increasing the diffusion barrier, while the impact of tritium vacancies on the diffusion barrier is small due to their minimal lattice distortion effect. The research uncovered significant disparities in the diffusion properties of hydrogen and tritium, indicating that the results of the study of hydrogen storage could not be applied to tritium.

Influence of carbon on the evolution of irradiation defects in tungsten

We have systematically investigated the influence of carbon (C) impurity on the aggregation, migration, and annihilation of neutron irradiation defects as well as the mechanical properties of tungsten (W), based on the object kinetic Monte Carlo (OKMC) calculations in combination with the theoretical models. Interestingly, although C has a strong attraction with both vacancy-type and interstitial-type irradiation defects, the C addition promotes the aggregation of former but inhibits latter in W. On the one hand, due to the weak repulsion of di-vacancy, it is difficult to form vacancy clusters spontaneously. However, the presence of C changes the interaction between vacancies from repulsion to attraction, thus promoting their clustering in W and leading to the increase of average size of vacancies cluster. On the other hand, because of the strong attraction, self-interstitial atoms (SIAs) tend to form clusters spontaneously. However, the C addition will slow down the diffusivity of SIAs due to the strong attraction between them, thereby blocking the aggregation of interstitial-type defects. Therefore, the number density of SIA clusters will increase with the increasing of C concentration, but the average size decreases significantly. Besides, the influence of C on the annihilation ratio of neutron irradiation defects is dependent on the temperature, which is mainly because the stability of C-SIA complexes and the migration of vacancies are strongly temperature dependent. Further, it is found that the increment of Vickers hardness in irradiated W at low temperature increases with the increasing of C concentration, which should be attributed to the enhanced effect of C on the retention of irradiation defects. When the C concentration is 2.5–5 appm, the model predictions are consistent with the experimental results. Consequently, although the concentration of impurity is extremely low in nuclear materials, it has significant effect on the defect evolution and mechanical properties under irradiation.

Long-timescale transformations of self-interstitial atom clusters of Cu using the SEAKMC method: The effect of setting an activation energy threshold for saddle point searches

On-the-fly kinetic Monte Carlo (kMC), a computational technique for atomistic simulations, has attracted attention because it increases the simulation timescale beyond that of molecular dynamics (MD) simulations while maintaining atomistic fidelity. However, for most kMC methods, when events with high and low activation energies coexist in the event list, trivial events with extremely low activation energies that do not essentially affect the phenomena of interest, so-called flicker events, are frequently selected, making it challenging to observe the key dynamics. In this study, we use Self-Evolving Atomistic kMC (SEAKMC), one of the on-the-fly kMC methods, to model the unstable-to-stable transformations of irregular three-dimensional self-interstitial-atom (SIA) clusters in Cu generated through collision cascade. By setting an activation energy threshold once every five steps, transformations into stable configurations are enhanced. The algorithm renders the simulation timescales one or two orders of magnitude longer than those possible with MD simulations. Further, the probability of transformations into stable configurations is increased by 40 times compared to that of the original SEAKMC method. In addition, we find that the stable configurations obtained by the transformation of the SIA clusters are mostly Frank loops. In summary, this new algorithm for the SEAKMC method helps to resolve the inefficiency of kMC methods resulting from the selection of flicker events and will aid the study of meso-timescale atomistic dynamics.

Insight into the loop-punching mechanism for He bubble growth: The plastic deformation modes and their competition

Loop-punching is the manner a helium (He) bubble enlarges itself through emitting a dislocation loop during its growth in metals. It has been demonstrated that there are two types of loop-punching: the two-stage loop-punching for small bubbles and the direct loop-punching for large bubbles. In this work, via the molecular dynamics (MD) simulations of helium bubble growth in tungsten (W), we revealed the crucial process from the bubble-attached self-interstitial atoms (SIAs) to the escapable dislocation loop in the two-stage loop-punching. Different from the conventional theory that the loop is merely the collection of the sequentially kicked-out SIAs, it is formed by the synergistic action of the atomic plane on the bubble surface being pushed into interstitial sites and the attached SIA cluster slipping. Building on this, two plastic deformation (PD) modes, the tangential PD and the normal PD, are extracted due to the generated SIAs’ directions tangent or normal to the bubble surface. The SIA-accumulation stage and the loop-emission stage of the two-stage loop-punching correspond to the tangential PD and the normal PD, respectively, while the direct loop-punching merely consists of the normal PDs. Therefore, the direct loop-punching is only a special form of the two-stage loop-punching that contains zero previous tangential PDs. Further, it is found the temperature plays an important role in the PD mode switch, suggesting the modes compete on the energy barriers, which accounts for the detachment of the attracted SIA cluster from the bubble.

Complete characterization of sink-strengths for 1D to 3D mobilities of defect clusters: Bridging between limiting cases with effective sink-strengths calculations.

In a companion paper, new analytical expressions of the cluster sink-strength (CSS) for two one-dimensional diffusers were proposed. These expressions are indispensable to any complete parameterisation of rate-equations cluster dynamics intending to model mobile interstitial clusters such as dislocation loops. Indeed, simulating the long-term microstructural evolution in systems with fast diffusing species such as self-interstitial atom (SIA) clusters relies on establishing the CSS for rate-equation cluster dynamics which critically depends on the complex mobilities of clusters. In this second paper, we will estimate effective CSSs by object kinetic Monte-Carlo (OKMC) on wide ranges of radii, rotation energies, diffusion coefficients, and concentrations of both reaction partners. The symmetric roles of some parameters are used to infer a generic form of a semi-analytical expression of the CSS depending on all these interaction parameters. It is composed of, on one hand, the various analytical expressions established as limiting cases and, on the other hand, of fitted transition functions that allow a gradual switching between them. The analysis of the residuals shows that the overall agreement is reasonably good: it is only in the transition zones that some significant discrepancies are located. This semi-analytical expression answers our practical need for CSSs evaluation in our typical range of conditions, but further extending this range to much smaller diffusion coefficients ratios, it is quite striking to see that the domain for 1D-1D mobility is very extended. It is only when approaching a ratio of 10−6 that the 1D-0 CSSs start becoming more relevant than the adapted 1D-1D CSSs which have completely different orders of magnitude and kinetic orders. Finally, the semi-analytical CSS expression is validated by comparing its implementation in rate-equation cluster dynamics to OKMC simulations of interstitial clusters aggregation. Companion paper: [1]

Complete characterization of sink-strengths for mutually 1D-mobile defect clusters: Extension to diffusion anisotropy analog cases

Simulating the long-term microstructural evolution in systems involving very fast diffusing species such as self-interstitial atom (SIA) clusters currently relies on mean-field or coarse-graining techniques. Rate-equation cluster dynamics (RECD) is one of the most popular of those when dealing with irradiated microstructure or second phase precipitation by thermal aging. Some of the most important input parameters of RECD are the absorption rates, also called cluster sink-strengths (CSS). These quantities crucially depend on the way clusters interact and diffuse and notably on the dimensionality of the involved random diffusion processes. As expected theoretically and experimentally confirmed, SIA clusters migrate in a one-dimensional fashion (possibly with random orientation changes, i.e. rotations of their Burgers vector). This complicates the calculation of the related CSS. When involving a 1D-mobile specie and an immobile reaction partner (a “1D-0” reaction) the expressions are quite well-known as well as the extension including random rotations (a “1DR-0” reaction). Expressions of CSS for absorptions between identical 1D-mobile species were proposed in the literature, but the general case of 1D-1D absorptions between different cluster classes is unknown. Here we propose a heuristic approach to such general expressions which turn out to depend on the respective capture radii of interacting clusters classes, concentrations and notably on the ratio of their respective diffusion coefficients through a power-law. In the companion paper [1], the same power-law formulation is found for 1D-3D absorptions but with different exponents, which thus appear as signatures of the dimensionality of the involved random motions. These limiting cases of CSS being established, they are finally implemented in an RECD calculation. The comparison with time-consuming kinetic Monte Carlo simulations completely validates their expression.

Helium interaction with solutes and impurities in neutron-irradiated nanostructured ferritic alloys: A first principles study

Density functional theory (DFT) calculations are performed to explore the binding between He and alloying solutes, impurities, and transmutation products expected in neutron irradiated nanostructured ferritic alloys (NFAs), here 14YWT is taken as an example. Elements that exhibit significant binding (attraction) with an interstitial He are: Y (binding energy = 0.46 eV), Mg (0.32), O (0.33), Ti (0.16), and C (0.15). Those that provide significant binding to a substitutional He are: O (1.44), Y (1.24), N (0.73), H (0.56), Mg (0.52), Ti (0.34), Si (0.34), C (0.33), Al (0.32), Ni (0.26), Ta (0.23), and Mn (0.16). The presence of these elements in Fe matrix could reduce the transport of He towards oxide particles, dislocations, and internal boundaries, and could promote He bubble nucleation in the matrix. For convenience, we compile existing binding energy data of He with Hen and HenV (He-vacancy) clusters. Dissociation pathway analysis reveals that, in general, the most likely dissociation of a HenV cluster is by a sequential emission of individual He atoms. Furthermore, larger bubbles are more prone to dissociation than smaller ones. In addition, we estimate the binding energy (segregation energy) of He in bulk Y2Ti2O7 (YTO) single crystal, YTO/Fe interface, and YTO particle embedded in Fe, with respect to interstitial He in Fe, from existing formation energies of He in these structures. We also compile available data of He binding with Fe self-interstitial atom (SIA), SIA clusters, and edge and screw dislocations. Note that given the absence of DFT data, the binding with SIA clusters and dislocations are gathered from simulations with empirical potentials. The data presented in this paper is important to inform multiscale simulations of He bubble accumulation.

Variation in formation and migration of self-interstitial atom clusters in electron irradiated copper with material purity and specimen preparation method

ABSTRACT In situ observation with high-voltage electron microscopy was used to survey effects of impurity atoms on the formation and one-dimensional (1D) migration of self-interstitial atom (SIA) clusters in copper under electron irradiation at 300 K. Specimens were prepared from copper materials of five nominal purities (9N, 6N, 5N, 4N, and 3N) using three methods with different annealing conditions. In standard (STD) specimens prepared through cold rolling and annealing in vacuum, SIA cluster formation and 1D migration depended little on the nominal purity. In non-annealed (NA) specimens prepared from high-purity materials (9N and 6N) using mechanical processing and electropolishing, the defect structure was found to be coarser than in STD specimens. In fact, SIA clusters in NA specimens had number density of more than an order of magnitude lower and an average size more than four times greater. Furthermore, 1D migration had the frequency of about an order of magnitude higher and distance extending more than twice longer. Results of bulk annealing (BA) specimens showed that annealing of as-received block material had minor effects. Distributions of 1D migration distance for all specimens were described using an earlier proposed trap model. These results were discussed assuming that SIA clusters are trapped by impurity atoms existing in as-received materials and those induced by annealing.

Vacancy migration in α-iron investigated using in situ high-voltage electron microscopy

ABSTRACT Modeling the microstructural evolution of irradiated materials requires knowledge of the migration energies of point defects, which results from energetic particle radiation. Herein, we measured the growth rate of self-interstitial atom (SIA) clusters in electron-irradiated α-iron at 275–320 K using in situ high-voltage electron microscopy. To improve the statistical accuracy of the measurement, we used photographic films and video data. This enabled analysis of a considerable amount of data by extracting several SIA clusters and tracking their size growth using image processing techniques. By fitting the temperature-dependent cluster growth rate to the Arrhenius relations derived using rate theory analysis, we obtained vacancy migration energy of  eV. The validity of the estimation method was confirmed from the consistency of the dependence of the damage rate on the cluster growth rate using the applied rate theory analysis. We also investigated the possible roles of faster motion of tri-vacancies compared to those of mono- and di-vacancies, as demonstrated by first-principles calculations, on the obtained migration energy using a kinetic analysis model. In addition, the effects of impurities leading to decrease in the cluster growth rate were briefly discussed.

A study of primary damage formation in collision cascades in titanium

Molecular dynamics (MD) simulations were applied to study radiation damage formation in collision cascades initiated by primary knock-on atoms (PKA) with energy EРКА = 5, 10, 15 and 20 keV in α-Ti at T = 100, 300, 600 and 900 K ambient temperatures. A series of 24 collision cascades was simulated for each (EРКА, Т) pair. The necessary sampling set size was justified by a simple a posteriori procedure. The number of Frenkel pairs and the fraction of vacancies, εv, and self-interstitial atoms (SIAs), εi in point defect clusters were evaluated as functions of (EРКА, Т). It was established that collision cascades in α-Ti are extended along PKA trajectories and tend to split into subcascades. In contrast to other elemental metals with close-packed crystal structure, εv≥ εi  in collision cascades in α-Ti. Moreover, both εv and εi ௜demonstrate weak temperature dependence. This is anindirect indication that both vacancy and SIA clusters created in collision cascades in α-Ti are stable in the considered temperature range