One-dimensional atomic transport by clusters of self-interstitial atoms in iron and copper

Atomic-scale computer simulation has been used to study the thermally activated atomic transport of self-interstitial atoms (SIAs) in the form of planar clusters in pure Cu and f-Fe. There is strong evidence that such clusters are commonly formed in metals during irradiation with high-energy particles and play an important role in accumulation and spatial distribution of surviving defects. An extensive study of the mobility of SIA clusters containing two to 331 interstitials has been carried out using the molecular dynamics simulation technique for the temperature range from 180 to 1200 K. The results obtained show that clusters larger than three to four SIAs are one-dimensionally mobile in both Cu and Fe. Large clusters of more than 100 SIAs in Cu and 300 SIAs in Fe have significantly reduced mobility. The problem of describing one-dimensional (1D) motion in three-dimensional space is discussed. An attempt is made to describe the mobility of SIA clusters within the approximation of 1D diffusion. For clusters in both metals the effective migration energy of 1D diffusion as estimated via the jump frequency of the cluster centre of mass is found to be independent of the number of SIAs in the clusters, although the cluster jump frequency decreases with increasing cluster size. Mechanisms of 1D mobility of interstitial clusters are discussed.     

Unlimited damage accumulation in metallic materials under cascade-damage conditions

Most experiments on neutron or heavy-ion cascade-produced irradiation of pure metals and metallic alloys demonstrate unlimited void growth as well as development of the dislocation structure. In contrast, the theory of radiation damage predicts saturation of void size at sufficiently high irradiation doses and, accordingly, termination of accumulation of interstitial-type defects. It is shown in the present paper that, under conditions of steady production of one-dimensionally (1-D) mobile clusters of self-interstitial atoms (SIAs) in displacement cascades, any one of the following three conditions can result in indefinite damage accumulation. First, if the fraction of SIAs generated in the clustered form is smaller than some finite value of the order of the dislocation bias factor. Second, if solute, impurity or transmuted atoms form atmospheres around voids and repel the SIA clusters. Third, if spatial correlations between voids and other defects, such as second-phase precipitates or dislocations, exist that provide shadowing of voids from the SIA clusters. The driving force for the development of such correlations is the same as for void lattice formation and is argued to be always present under cascade-damage conditions. It is emphasised that the mean-free path of 1-D migrating SIA clusters is typically at least an order of magnitude longer than the average distance between microstructural defects; hence, spatial correlations on the same scale should be taken into consideration. A way of developing a predictive theory is discussed. An interpretation of the steady-state swelling rate of ～1%/displacement per atom (dpa) observed in austenitic steels is proposed.     

One-dimensional migration of interstitial clusters in SUS316L and its model alloys at elevated temperatures

For self-interstitial atom (SIA) clusters in various concentrated alloys, one-dimensional (1D) migration is induced by electron irradiation around 300 K. But at elevated temperatures, the 1D migration frequency decreases to less than one-tenth of that around 300 K in iron-based bcc alloys. In this study, we examined mechanisms of 1D migration at elevated temperatures using in situ observation of SUS316L and its model alloys with high-voltage electron microscopy. First, for elevated temperatures, we examined the effects of annealing and short-term electron irradiation of SIA clusters on their subsequent 1D migration. In annealed SUS316L, 1D migration was suppressed and then recovered by prolonged irradiation at 300 K. In high-purity model alloy Fe-18Cr-13Ni, annealing or irradiation had no effect. Addition of carbon or oxygen to the model alloy suppressed 1D migration after annealing. Manganese and silicon did not suppress 1D migration after annealing but after short-term electron irradiation. The suppression was attributable to the pinning of SIA clusters by segregated solute elements, and the recovery was to the dissolution of the segregation by interatomic mixing under electron irradiation. Next, we examined 1D migration of SIA clusters in SUS316L under continuous electron irradiation at elevated temperatures. The 1D migration frequency at 673 K was proportional to the irradiation intensity. It was as high as half of that at 300 K. We proposed that 1D migration is controlled by the competition of two effects: induction of 1D migration by interatomic mixing and suppression by solute segregation.     

Dislocation decoration and raft formation in irradiated materials

Experimental observations of dislocation decoration with self-interstitial atom (SIA) clusters and of SIA cluster rafts are analysed to establish the mechanisms controlling these phenomena in bcc metals. The elastic interaction between SIA clusters, and between clusters and dislocations is included in kinetic Monte Carlo (KMC) simulations of damage evolution in irradiated bcc metals. The results indicate that SIA clusters, which normally migrate by 1D glide, rotate due to their elastic interactions, and that this rotation is necessary to explain experimentally-observed dislocation decoration and raft formation in neutron-irradiated pure iron. The critical dose for raft formation in iron is shown to depend on the intrinsic glide/rotation characteristics of SIA clusters. The model is compared with experimental observations for the evolution of defect cluster densities (sessile SIA clusters and nano-voids), dislocation decoration characteristics and the conditions for raft formation.     

Vacancy effects on one-dimensional migration of interstitial clusters in iron under electron irradiation at low temperatures

We performed in situ observation of one-dimensional (1D) migration of self-interstitial atom (SIA) clusters in iron under electron irradiation at 110–300 K using high-voltage electron microscopy. Most 1D migration was stepwise positional changes of SIA clusters at irregular time intervals at all temperatures. The frequency of 1D migration did not depend on the irradiation temperature. It was directly proportional to the damage rate, suggesting that 1D migration was induced by electron irradiation. In contrast, the 1D migration distance depended on the temperature: distribution of the distance ranged over 100 nm above 250 K, decreased steeply between 250 and 150 K and was less than 20 nm below 150 K. The distance was independent of the damage rate at all temperatures. Next, we examined fluctuation in the interaction energy between an SIA cluster and vacancies of random distribution at concentrations 10^?4–10^?2, using molecular statics simulations. The fluctuation was found to trap SIA clusters of 4 nm diameter at vacancy concentrations higher than 10^?3. We proposed that 1D migration was interrupted by impurity atoms at temperatures higher than 250 K, and by vacancies accumulated at high concentration under electron irradiation at low temperatures where vacancies are not thermally mobile.     

Time delay matrix at the spectrum edge and the minimal chaotic cavities

Self-interstitial interactions causing volume expansion in bcc Fe are studied through an idealized microstructure evolution model in which only self-interstial atoms (SIAs) are inserted. Using a combination of non-equilibrium molecular dynamics simulations and a metadynamics algorithm, meta-stable SIA clusters are observed to nucleate and grow into dislocation loops or localized amorphous phases, both contributing to swelling behavior persisting well beyond the atomistic time scale. A non-monotonic local density variation with dose rate is found and attributed to competing evolutions of different defective structures.     

Stability and mobility of mono- and di-interstitials in alpha-Fe

We report a detailed ab initio study of the stability and migration of self-interstitial atoms (SIAs) and di-interstitials (di-SIAs) in alpha-Fe. The <110> dumbbell is confirmed to be the most stable SIA configuration, 0.7 eV below the <111> dumbbell. The lowest-energy migration path corresponds to a nearest-neighbor translation-rotation jump with a barrier of 0.34 eV. The most stable configuration for di-SIAs consists of <110> parallel dumbbells. Their migration mechanism is similar to that for SIAs, with an activation energy of 0.42 eV. These results are at variance with predictions from existing empirical potentials and allow one to reconcile theory with experiments.     

Anisotropic interaction between self-interstitial atoms and 1/2<111> dislocation loops in tungsten

We investigate the interaction between 111 self-interstitial atoms(SIAs) and 1/2111 self-interstitial dislocation loops in tungsten(W) via atomistic simulations. We explore the variation of the anisotropic distribution of binding energies with the shapes and sizes of the 1/2[111] loop and the nonequivalent configurations of 111 SIAs. For an arbitrarily shaped loop, SIA can be more easily trapped in the concave region of the loop than the convex region, which forms a loop whose curvature is closer to that of a circular loop. The direction of SIAs can largely affect the interaction behaviors with the loop. The capture distance of an SIA by the edge of a circular-shaped 1/2[111] loop is clearly elongated along the direction of the SIA; however, it weakly depends on the size of the loop. Then, we analyze the slanted ring-like capture volume of 111 SIAs formed by the circular loop based on their generated anisotropic stress fields. Furthermore, the binding energies obtained from the elastic theory and atomistic simulations are compared. The results provide a reasonable interpretation of the growth mechanism of the loop and the anisotropic interaction that induces irregular-shaped capture volume, affording an insight into the numerical and Object Kinetic Monte Carlo simulations to evaluate the long-term and large-scale microstructural evolution and mechanical properties of W.     

Effects of stacking fault energies on formation of irradiation-induced defects at various temperatures in face-centred cubic metals

ABSTRACT

By using the six sets of interatomic potentials for face-centred cubic metals that differ in the stacking fault energy (SFE) while most of the other material parameters are kept almost identical, we conducted molecular dynamics simulations to evaluate the effects of SFE on the defect formation process through collision cascades. The simulations were performed at 100, 300 and 600?K, with a primary knock-on atom energy of 50 keV. The number of residual defects is not dependent on the SFE at all the temperatures. For clusters of self-interstitial atoms (SIAs), their clustering behaviour does not depend on the SFE, either. However, the ratio of glissile SIA clusters tends to decrease with increasing SFE. This is because perfect loops, the edges of which split into two partial dislocations with stacking fault structures between them in most cases, prefer to form at lower SFEs. The enhanced formation of glissile SIA clusters at lower SFEs can also be observed even at increased temperature. Because most large vacancy clusters have stacking fault structures, they preferentially form at lower SFE; however, it is observed only at the lowest temperature, where the mean size increases with decreasing SFE. At higher temperatures, because of their extremely low number density, the vacancy clustering behaviour does not depend on the SFEs.     

Interactions between clusters of self-interstitial atoms via a conservative climb in BCC–Fe

We conduct kinetic Monte Carlo simulations for the conservative climb motion of a cluster of self-interstitial atoms (SIAs) towards another SIA cluster in BCC–Fe; the conservative climb velocity is inversely proportional to the fourth power of the distance between them, as per the prediction based on Einstein’s equation. The size of the climbing cluster significantly affects its conservative climb velocity, while the size of the cluster that originates the stress field does not. The activation energy for the conservative climb is considerably greater than that derived in previous studies and strongly dependent on the climbing cluster size. The results presented in this study are the atomistic evaluation of the behaviour of SIA clusters through three-dimensional motion, which cannot be achieved using molecular dynamics techniques alone.     

Interdiffusion in two-layer Pd/Ag films II. “Cold” homogenization mechanisms

Interdiffusion processes in thin epitaxial polycrystalline Pd/Ag films in the temperature range 20–500°C are studied by transmission electron microscopy, electron diffraction and electrical resistance methods. Homogenization is investigated both during condensation and under conditions of postcondensation annealing.The basic processes of homogenization associated with GB diffusion along migrating boundaries. It is found that in real polycrystal films with wide spectrum of grain sizes few mechanisms can occur simultaneously or subsequently: recrystallization induced diffusion, diffusion induced grain boundary migration, activation of bulk diffusion in fine grain clusters, bulk diffusion through interphase boundary. The conditions for prevailing one of them can be provided by changing condensation and postcondensation annealing temperatures or by choosing certain grain size.     

Rates of diffusion controlled reactions for one-dimensionally-moving species in 3D space

ABSTRACT

The asymmetry in diffusion dimensionality between self-interstitial atom (SIA) clusters and vacancies is a fundamental feature of irradiation damage in crystals, leading to a defect buildup imbalance that manifests itself as measurable dimensional and mechanical property changes. It is well known that, while vacancies and mobile vacancy clusters diffuse in a three-dimensional (3D) fashion, SIA clusters perform one-dimensional motion along mostly rectilinear trajectories. Despite this, a complete set of kinetic coefficients, including coagulation reaction rates and sink strengths, does not exist for 1D-moving objects. In this paper, we derive analytical expressions for these coefficients from continuum diffusion theory particularised to 1D motion. Moreover, we carry out kinetic Monte Carlo simulations of numerical replicas of the geometry of diffusing particles and sinks to validate the proposed solutions. Our simulations, which are conducted entirely independently from the analytical derivations, reveal excellent agreement with the proposed expressions, adding confidence to their validity. We compare the 1D and 3D cases and discuss their relevance for kinetic codes for damage accumulation calculations.     

Simulation of the interaction between an edge dislocation and ⟨111⟩ interstitial dislocation loops in α-iron

ABSTRACT

The dependence of the interactions of intermediate-size ½<111> self-interstitial atom (SIA) loops with an edge dislocation on strain rate and temperature was investigated by molecular dynamics (MD) simulations for the interatomic potential derived by Ackland et al. (A97). For low temperatures (T?=?1?K), the mechanisms of the interactions were in agreement with recent literature. It was shown that a second passing of the dislocation through the loop led to a different mechanism than the one that occurred upon first passing. Since these mechanisms are associated with different SIA loop sizes, and since the loop lost a number of SIAs upon first interaction, it was deduced that the dividing threshold between large and small loops (rendering them strong or weak obstacles, respectively) is at the vicinity of the loop size studied (169 SIAs). For higher temperatures (T?=?300?K), the strain rate dependence proved strong: for low strain rates, the dislocation absorbed the loop as a double super-jog almost immediately and continued its glide unimpeded. For a high strain rate, the dislocation was initially pinned due to the formation of an almost sessile segment leading to high critical stress.     

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors.The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.     

Lowest energy structures of self-interstitial atom clusters in α-iron from a combination of Langevin molecular dynamics and the basin-hopping technique

A combination of simulated annealing with Langevin molecular dynamics and the basin-hopping with occasional jumping (BHOJ) technique was used to systematically determine the most stable configurations of self-interstitial atom (SIA) clusters I _n (n = 1–38) in α-iron. In addition to the original BHOJ technique, we introduced an additional long jumping process in which a randomly selected less-bounded atom is moved to a neighbouring site of another SIA in the cluster to enhance the probability of locating the global minimum structure. With the obtained putative lowest energy structures, the binding energies as a function of cluster size were estimated. We also determined the sizes of particular stable clusters based on their geometrical symmetry. Furthermore, the values were extrapolated based on accurately determined formation energies, and are available for immediate use in kinetic Monte Carlo or rate theory models.     

Molecular dynamics simulations of point defects in plutonium grain boundaries

A modified analytic embedded atom method (MAEAM) potential is constructed for fcc updelta-Pu. Molecular dynamics (MD) simulations with the potential are performed to investigate the interactions between two symmetrical tilt grain boundaries (GBs) and point defects such as He atom, vacancy and self-interstitial atom (SIA) in Pu. The calculated results show that point defect formation energies are on average lower than those in the lattice but variations from site to site along the GBs are very remarkable. Both substitutional and interstitial He atoms are trapped at GBs. Interstitial He atom is more strongly bound at the GB core than the substitutional He atom. The binding energy of SIA at GB core is higher than those of He atom and vacancy. GB core can bind many He atoms and SIAs due mainly to the fact that it contains many vacancies. Compared with He atom and SIA, the vacancy far from GB core is difficult to diffuse into the core. The GBs can act as sinks and sources of He atoms and SIAs, which may be a reason for the swelling of Pu after a period of self-irradiation because of the higher concentration of vacancy in the bulk.     

Obstacles for one-dimensional migration of interstitial clusters in iron

Interstitial clusters are known to cause frequent one-dimensional (1D) jumps (stepwise positional changes) under electron irradiation around room temperature. The distance of 1D jumps in iron was examined in detail through in-situ observation using high-voltage electron microscopy. The 1D jump distance was found to be longer for smaller clusters in specimens of higher purity, although the distance did not depend on the irradiation beam intensity and electron energy. The distribution of the 1D jump distance was well described by the distribution of the free path of interstitial clusters migrating through randomly distributed impurity atoms. The 1D jump process is considered as fast 1D diffusion of interstitial clusters at low activation energy from the point where the cluster detrapped from an impurity atom to the point where the cluster was trapped again by another impurity. Electron irradiation provides a trigger for causing 1D migration by detrapping of clusters from impurity atoms.     

硅单粒子位移损伤多尺度模拟研究

本文结合分子动力学方法和动力学蒙特卡罗方法, 研究了单个粒子入射硅引起的位移损伤缺陷的产生和演化过程; 基于Shockley-Read-Hall理论计算了单个粒子入射引起的位移损伤缺陷导致的泄漏电流增加及其演化过程, 比较了缺陷退火因子与泄漏电流退火因子之间的差异, 并将计算结果与实验值进行了对比. 结果表明, 计算泄漏电流时, 仅考虑一种缺陷的情况下缺陷退火因子与泄漏电流退火因子相同, 考虑两种缺陷类型情况下二者在数值上有所区别, 但缺陷退火因子仍能在一定程度上反映泄漏电流的退火行为. 分子动力学模拟中采用Stillinger-Weber势函数和Tersoff势函数时缺陷退火因子和泄漏电流退火因子与实验结果一致, 基于Stillinger-Weber势函数的计算结果与实验值更为接近.     

Radiation-induced glide motion of interstitial clusters in concentrated alloys

We propose a mechanism for glide motion, i.e. one-dimensional (1D) migration, of interstitial clusters in concentrated alloys driven by high-energy particle irradiation. Interstitial clusters are fundamentally mobile on their respective 1D migration tracks, but in concentrated random alloys they are stationary at the position where the fluctuating formation energy achieves a local minimum. Irradiation changes the microscopic distribution of solute atoms through atomic displacement and recovery of the produced Frenkel pairs, which causes cluster 1D migration into a new stable position. In molecular dynamics simulations of interstitial clusters up to 217i in Fe–Cu alloys, stepwise 1D migration was observed under interatomic mixing or shrinkage of the cluster: a single 1D migration was induced by two exchanges per atom or cluster radius change by two interatomic distances. The 1D migration distance ranged up to several nanometers. We compared the frequency and distance of 1D migration with those for in situ observation using high-voltage electron microscopy, allowing for the extremely large rate of interatomic mixing and cluster shrinkage in the present simulation.