Single Self-interstitial Atoms Research Articles

Atomic study of the trapped and migration patterns of point defects around screw dislocation in tungsten

The interaction of 1/2 〈1 1 1〉 screw dislocation and point defects, including vacancy and self-interstitial atom (SIA), was investigated by molecular dynamics (MD) simulations. Molecular statics (MS) are used to analyze the factors affecting the binding energy of point defects around the dislocation. The results show that the point defects around the dislocation core have the highest binding energy. In addition, we use elasticity theory to find that the point defects binding is interrelated to strain distribution of dislocation and the residual stress of point defects. Furthermore, nudged elastic band (NEB) calculations have been applied to find that vacancy and SIA tend to migrate along the dislocation line around the core region. The results can clearly show the interaction behavior of point defects and screw dislocation, and provide a reasonable explanation for the diffusion mechanism of mono-vacancy and a single SIA around the dislocation line.

Atomic modeling assessment of the interaction distance and effective bias for small defect clusters absorption at a void in BCC Fe

Cavity swelling plays a vital role in the microstructural evolution of ferritic-martensitic alloys under irradiation. Recent research reported that the classic thermal criterion of the critical size in cavity growth loses its explanatory power outside the intermediate temperature regimes. In contrast, the newly proposed bias-driven criterion performs nearly equivalently at the entire temperature range by introducing the concept of cavity bias. Molecular statics calculations were performed to determine the interaction energy landscape of single self-interstitial atom (SIA), single vacancy, di-SIA, di-vacancy, 7-SIA cluster, and 7-vacancy cluster interaction with a 59-vacancy void in BCC Fe. Additionally, molecular dynamics simulations were conducted to investigate the rotation and migration behavior of varying size SIA clusters in close proximity to the void. A homogenization method was established to describe the capture volume and mimic the one-dimensional diffusion behavior for large SIA clusters. The interaction distance between the void and defects was determined, and the effective bias was calculated as a function of the void size at 25 ℃, 300 ℃, and 500 ℃. The results provide important atomistic inputs for mesoscale modeling of defect evolution and microstructural changes, such as cluster dynamics simulation.

Coexistence of a self-interstitial atom with light impurities in a tungsten grain boundary

In this paper, we report on ab initio simulations results focused on completing a thorough energetic, structural, charge and mobility analysis of the synergistic behaviour of diverse defects, namely self-interstitial atoms (SIA) and light impurity atoms (LIA), i.e., He and H, that would appear in W when simultaneously irradiated with the latter. In particular, the influence of a W〈110〉/W〈112〉 grain boundary (GB) in the behaviour of coexisting defects is studied and compared with the results obtained in the bulk. Four possible scenarios are analysed concerning the occupation of the GBs with: (i) a single SIA (ii) the simultaneous presence of two different defects, that is, He-H or SIA-LIA pairs, and (iii) the three types of defects together. The most stable configuration in each of these scenarios is detailed. Results show that GBs act as trapping sites for SIAs and LIAs and that the interaction between He and H is weak in all the analysed arrangements. They also indicate that the introduction of a SIA in a GB preloaded with He and H affects each of the atoms differently, as the former tends to stay close to the extra W atom, while the latter finds more comfortable accommodations away from the other two defects. In bulk W, the qualitative behaviour of He and H is quite similar and the presence of a LIA strongly affects the preferred orientation of the SIA dumbbell. Additionally, defect mobilities along the GB have been assessed concluding that the SIAs tend to move along the interfacial grooves, so to recombine with the vacancies present there.

Modeling refractory high-entropy alloys with efficient machine-learned interatomic potentials: Defects and segregation

We develop a fast and accurate machine-learned interatomic potential for the Mo-Nb-Ta-V-W quinary system and use it to study segregation and defects in the body-centred cubic refractory high-entropy alloy MoNbTaVW. In the bulk alloy, we observe clear ordering of mainly Mo-Ta and V-W binaries at low temperatures. In damaged crystals, our simulations reveal clear segregation of vanadium, the smallest atom in the alloy, to compressed interstitial-rich regions like radiation-induced dislocation loops. Vanadium also dominates the population of single self-interstitial atoms. In contrast, due to its larger size and low surface energy, niobium segregates to spacious regions like the inner surfaces of voids. When annealing samples with supersaturated concentrations of defects, we find that in complete contrast to W, interstitial atoms in MoNbTaVW cluster to create only small ($\sim 1$ nm) experimentally invisible dislocation loops enriched by vanadium. By comparison to W, we explain this by the reduced but three-dimensional migration of interstitials, the immobility of dislocation loops, and the increased mobility of vacancies in the high-entropy alloy, which together promote defect recombination over clustering.

Interactions of solute atoms with self-interstitial atoms/clusters in vanadium: A first-principles study

The interactions of solute atoms with self-interstitial atoms (SIA)/clusters and their effect on stability of single SIAs and small SIA clusters in vanadium (V) were investigated using first-principles calculations. We calculated the binding energies of 16 substitutional solute elements (Cr, Ti, Al, Fe, Mo, Y, Nb, Cu, Mn, Ni, Ta, Zr, W, Si, S and P) with SIAs and found that the solute Cr/Fe/Mn/P/S prefers to form solute-V<111> mixed interstitial dumbbell. The interaction between solute Ti/Si/Y/Nb/Ta and <111> SIA dumbbell is attractive, while most of other solutes repel with the <111> SIA. The stable Cr- < 111> mixed interstitials and the Ti- < 111> SIA can attract five metal solutes (Ti, Y, Zr, Nb, and Ta), further stabilizing the SIA. The stability of small SIA clusters are determined and the parallel <111> SIA dumbbell clusters are the most stable configurations, followed by the parallel <110> SIA configurations. The small SIA clusters can attract three metallic solutes (Ti, Y and Zr) and two impurities (P and S), but will repel most solute atoms. The presence of solute atoms does not change the relative stability order among SIA clusters. The present calculations provide the basic data for understanding the influence solutes on the stability of SIAs/SIA clusters in V alloys under irradiation.

The effect of rhenium on the diffusion of small interstitial clusters in tungsten

In this work, we use atomistic simulations to investigate the mobility and stability of self-interstitial atom (SIA) clusters of size 1–5 in W-Re alloys. We apply molecular statics and molecular dynamics (MD) simulations to determine the dimensionality of diffusion of the clusters, the activation energy of translation and rotation, and the energy of dissociation. The results show a strong effect of Re on the diffusion properties of SIA clusters, but not on its stability. The diffusion mechanism of the single SIA changes from 1-D migration with on-site rotations to full 3-D diffusion on the MD time and length scale due to the addition of Re. Further, the mobility of the SIA clusters is greatly reduced by the addition of Re. The obtained results can be readily used to parameterize coarse grain models such as object kinetic Monte Carlo and rate theory models.

Strain rate effect on dislocation climb mechanism via self-interstitials

The climb mechanism of an edge-dislocation is investigated by combining Transition State Theory and potential energy surface searching technique (an atomistic modeling framework named as ABC-T). As common point defects, self-interstitial-atoms (SIAs) and their agglomeration around dislocations in ‘clouds’ have complex and significant impact on the onset of metal plasticity. Reproducing atomic details of the interactions between SIAs and dislocations in a dynamic scenario is crucial for understanding the dynamic strain aging, and also the irradiation hardening. In order to describe the kinetics of SIA clouds in the vicinity of an edge dislocation, we choose a single SIA bi-dumbbell in body-centered-cubic (BCC) Fe in this study. The bi-dumbbell is absorbed completely to form a jog pair in our simulations at realistic laboratory strain rate. While at higher strain rate dislocation pinning with a stop-and-go manner is induced by incomplete absorption. As a transition state before the jog pair, a defect attaches to dislocation line and requires much higher activation energy than the thermal energy at room temperature to further evolve. Although more realistic picture of this interaction needs free energy calculation and dynamics trajectory to confirm different evolution pathways, our results offer a direct qualitative comparison between strain rates revealing the intrinsic difficulty of dislocation climb.

Evolution pattern of collision cascades in bcc V with different grain boundary structures: an atomic scale study

In this paper, by means of atomic-scale simulations, we investigate modifications of the evolution pattern of collision cascades in bcc vanadium (V) with different grain boundary (GB) structures on picosecond (ps) timescale. In primary damage state, in agreement with previous results of bcc and fcc bi-crystals, we find that the GBs in V are biased towards interstitials. The biased absorption of interstitials over vacancies reduces the in-cascade annihilation of vacancy-interstitial pairs and leads to aggregation of more number of vacancies in the grains interiors. The sessile vacancies accumulate in the bulk and form immobile vacancy clusters; in contrast, the glissile interstitials disperse in the damage zone and mostly diffuse in the form of single self-interstitial atoms (SIAs)/di-interstitials towards the GB region. Moreover, meanwhile, as we discuss the mechanisms that reduce (or increase) the concentration of defects in bi-crystal structures on picosecond timescale, we study the energetics of defects in close vicinity of pristine GBs, as an alternative driving force that facilitates formation and accumulation of defects in the GB regions. Finally, in a prolonged irradiation, we examine stability and sink properties of the damaged GBs. The results reveal that, irrespective of GB structure, the presence of grain boundaries leads to aggregation of more number of vacancies in the grain interiors in continuous bombardment. Overall, based on the results obtained in the primary damage event and the prolonged irradiation, we conclude that the GBs in bcc V act as efficient defect sinks on the simulated time frame.

Kinetics of interstitial defects in α-Fe: The effect from uniaxial stress

Understanding defect kinetics in a stress field is important for multiscale modeling of materials degradation of nuclear materials. By means of molecular dynamics and molecular statics simulations, we calculate formation and migration energies of self-interstitial atoms (SIA) and SIA clusters (up to size of 5 interstitials) in alpha Fe and identify their stable configurations under uniaxial tensile strains. By applying uniaxial stress along [111], <111> oriented single SIA defects become more stable than <110> oriented SIA, which is opposite to stress-free condition. Diffusion of single SIA defects under [111] tensile stress is facilitated along [111] direction and the diffusion becomes one dimensional (1D). For SIA clusters, their diffusion under zero stress has gradual transition from three dimensional (3D) for small clusters to one dimensional (1D) for large clusters. Under the tensile stress along [111], the 3D to 1D transition is accelerated. For large SIA clusters, the stress effect is quickly saturated with less diffusivity enhancement in comparison with small SIA clusters.

Detection of one-dimensional migration of single self-interstitial atoms in tungsten using high-voltage electron microscopy.

The dynamic behaviour of atomic-size disarrangements of atoms—point defects (self-interstitial atoms (SIAs) and vacancies)—often governs the macroscopic properties of crystalline materials. However, the dynamics of SIAs have not been fully uncovered because of their rapid migration. Using a combination of high-voltage transmission electron microscopy and exhaustive kinetic Monte Carlo simulations, we determine the dynamics of the rapidly migrating SIAs from the formation process of the nanoscale SIA clusters in tungsten as a typical body-centred cubic (BCC) structure metal under the constant-rate production of both types of point defects with high-energy electron irradiation, which must reflect the dynamics of individual SIAs. We reveal that the migration dimension of SIAs is not three-dimensional (3D) but one-dimensional (1D). This result overturns the long-standing and well-accepted view of SIAs in BCC metals and supports recent results obtained by ab-initio simulations. The SIA dynamics clarified here will be one of the key factors to accurately predict the lifetimes of nuclear fission and fusion materials.

Application of hyper-molecular dynamics to self-interstitial diffusion in α-iron

The diffusion process of a single self-interstitial atom (SIA) in α-iron was studied by a hyper-molecular dynamics (hyper-MD) method that has been demonstrated to efficiently accelerate slow diffusive conformational transitions that occur in various materials. By adding a local bias potential, the acceleration of the dynamics becomes significantly higher at lower temperatures, e.g., on the order of 5 at 300K, without changing the dynamics of the diffusion process as calculated using a conventional MD simulation. The validity of the results demonstrates that the hyper-MD method with an appropriate local bias potential can be applicable for determination of the diffusion process of SIAs in bulk materials.

Dynamical behaviors of self-interstitial atoms in tungsten

The motion mechanisms and jump rate of single self-interstitial atoms (SIAs) are studied by molecular dynamics simulations and vibration analysis. The migration of SIAs is a sequent transformation between the 〈111〉 crowdion and dumbbell with a 0.027eV energy barrier. A soft mode contributes to this transformation, whose eigenvector shows that the atoms compressed by the SIAs have the largest amplitude. The jump rate of SIAs migration reaches 1Hz at 12K, which suggests that the thermal migration of SIAs dominates the nucleation of SIAs loops below 50K. SIAs rotate between the [111] and its equivalent directions with a 0.668eV energy barrier, which is controlled by a linear combination of libration and stretching mode. Our results show that the long wave phonon induced by the stress field of SIAs plays an important role in the 1D motion of SIAs.

Self-interstitial configurations in hcp Zr: a first principles analysis

The alignment of vacancy loops and voids along basal planes observed in irradiated Zr and Zr alloys requires anisotropic point-defect transport with a dominant contribution along the basal plane. For neutron irradiation, this can be explained by one-dimensional mobility of self-interstitial atom (SIA) clusters, but experiments with electron irradiation indicate unambiguously that even single SIA should exhibit anisotropic diffusion. No experimental information is available on SIA properties in Zr and the previous ab initio calculations did not provide any evidence of anisotropic diffusion mechanisms. An extensive investigation of SIAs in Zr has been performed from first principles using two different codes. It was demonstrated that the simulation cell size, type of pseudopotential, exchange-correlation functional and the c/a ratio are crucially important for determining the properties of interstitials in hcp Zr. The most stable SIA configurations lie in the basal plane, which should lead to SIA diffusion mainly along basal planes.

On the structure and mobility of point defect clusters in alpha-zirconium: a comparison for two interatomic potential models

A recent interatomic potential for alpha-zirconium (Zr) is used to investigate the atomic configuration and motion of point defect clusters. The structure of the single self-interstitial atom (SIA) has a strong influence on the properties of small clusters containing up to six interstitials. For a given number of defects in this size range, several configurations exist with similar formation energy but different dynamic properties, i.e. they may be sessile or glissile. The movement of small clusters is three-dimensional and involves combinations of the different configurations. As cluster size increases, the influence of the configuration of the stable single SIA vanishes and the interstitials orientate to achieve near-perfect crystal structure inside the cluster and a dislocation-core arrangement at the periphery. Movement of clusters larger than 12 SIAs is one-dimensional along the direction of the Burgers vector. The stable configurations of vacancy clusters are also studied. The results are compared with those predicted with a model based on an earlier interatomic potential.

Energy calculation of point defects in plutonium by embedded atom method

Plutonium is vulnerable to aging due to α radioactive decay. The properties and behaviors of point defects in plutonium are the basis for understanding plutonium aging. We have employed a molecular dynamics technique to calculate the formation energy and binding energy of point defects and small helium-vacancy clusters in plutonium, using embedded atom method, Morse pair potential and the Lennard-Jones pair potential for describing the interactions of Pu-Pu, Pu-He and He-He, respectively. A single self-interstitial atom’s steady configuration is 〈100〉 dumb-bell. An interstitial helium atom at octahedral site is more stable than that at tetrahedral site. As a result of high binding energy of an interstitial helium atom to a vacancy, helium atoms can combine with vacancies to form helium-vacancy cluster during the process of self-radiation. The formation energy of helium-vacancy cluster increases with the increasing number of helium atoms. When the number of helium atoms equals to the number of vacancy, the helium-vacancy cluster is rather stable. Both substitutional and interstitial helium atoms are trapped at the grain boundary (GB). The binding energy of the self-interstitial atom at GB core is higher than that of helium atom and vacancy.

Computer simulation of cascade damage in α-iron with carbon in solution

Molecular dynamics simulation method is used to investigate defect production by displacement cascades in iron with carbon (C) in solution. This is the first study of cascade damage in a metal containing interstitial solute. Iron is of particular interest because of the use of ferritic steels in plant for nuclear power generation. Cascades are simulated with energy in the range 5–20 keV in iron at either 100 or 600 K containing carbon with concentration in the range 0–1 at.%. C in solution has no discernible effect on the number of defects produced in cascades under any of the conditions simulated, nor on the clustered fraction of either self-interstitial atoms (SIAs) or vacancies. However, significant fractions of single SIAs and vacancies are trapped by C in the cascade process, irrespective of cascade energy. The fraction is independent of temperature for vacancies, but increases strongly with temperature for SIAs: this is a consequence of the higher mobility of the SIA.

On the migration and trapping of single self-interstitial atoms in dilute and concentrated Fe–Cr alloys: Atomistic study and comparison with resistivity recovery experiments

Atomistic simulations have been used to characterize the mobility of single self interstitial atoms (SIAs) in Fe–Cr alloys of different compositions. Density functional theory (DFT) results concerning the interaction energies between an SIA and Cr atoms in different configurations and relative positions have been extended to concentrated alloys by using an empirical potential (EP). This EP, fitted to a set of DFT data so as to provide a correct heat of mixing and point defect features, has been further validated. Static calculations using the EP allowed the existence of configuration traps for SIAs to be identified and their strength and concentration to be assessed. Dynamic simulations were used to estimate the diffusion coefficient of the SIA, as well as to characterize the primary damage state after low-temperature electron irradiation (1–5MeV), in Fe–Cr alloys of different Cr content. The results correlate with available experimental data and provide a qualitative and partially also quantitative explanation for the observed differences in the resistivity recovery stages in diluted and concentrated Fe–Cr alloys of different composition.

One-Dimensional Fast Migration of Vacancy Clusters in Metals

The migration of point defects, for example, crystal lattice vacancies and self-interstitial atoms (SIAs), typically occurs through three-dimensional random walk in crystalline solids. However, when vacancies and SIAs agglomerate to form planar clusters, the migration mode may change. We observed nanometer-sized clusters of vacancies exhibiting one-dimensional (1D) fast migration. The 1D migration transported a vacancy cluster containing several hundred vacancies with a mobility higher than that of a single vacancy random walk and a mobility comparable to a single SIA random walk. Moreover, we found that the 1D migration may be a key physical mechanism for self-organization of nanometer-sized sessile vacancy cluster (stacking fault tetrahedron) arrays. Harnessing this 1D migration mode may enable new control of defect microstructures such as effective defect removal and introduction of ordered nanostructures in materials, including semiconductors.

Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals

We investigate the structure and mobility of single self-interstitial atom and vacancy defects in body-centered-cubic transition metals forming groups 5B (vanadium, niobium, and tantalum) and 6B (chromium, molybdenum, and tungsten) of the Periodic Table. Density-functional calculations show that in all these metals the axially symmetric ⟨111⟩ self-interstitial atom configuration has the lowest formation energy. In chromium, the difference between the energies of the ⟨111⟩ and the ⟨110⟩ self-interstitial configurations is very small, making the two structures almost degenerate. Local densities of states for the atoms forming the core of crowdion configurations exhibit systematic widening of the ``local'' $d$ band and an upward shift of the antibonding peak. Using the information provided by electronic structure calculations, we derive a family of Finnis-Sinclair-type interatomic potentials for vanadium, niobium, tantalum, molybdenum, and tungsten. Using these potentials, we investigate the thermally activated migration of self-interstitial atom defects in tungsten. We rationalize the results of simulations using analytical solutions of the multistring Frenkel-Kontorova model describing nonlinear elastic interactions between a defect and phonon excitations. We find that the discreteness of the crystal lattice plays a dominant part in the picture of mobility of defects. We are also able to explain the origin of the non-Arrhenius diffusion of crowdions and to show that at elevated temperatures the diffusion coefficient varies linearly as a function of absolute temperature.

Dimensionality of interstitial cluster motion in bcc-Fe

We study self-interstitial cluster migration properties, such as dimensionality of the motion and activation energy barrier, as functions of the cluster size, by means of molecular-dynamics simulations in bcc-Fe. The atomic interactions are described using a recently proposed potential, fitted to reproduce self-interstitial atom (SIA) configuration energies in close agreement with the results of ab initio calculations. We show that this potential provides a dynamic migration energy for the single SIA in agreement with the experimental value. We also show that, in the case of clusters formed by up to five SIAs, the migration energy decreases with increasing cluster size, but remains higher than previously believed. This is the consequence of the change of the migration mechanism of these small clusters from purely three dimensional (3D) to preferentially one dimensional (1D) and of the fact that these clusters take different configurations during migration, including anomalous ones. While the concept of fast 1D diffusion of large SIA clusters remains valid, the obtained results suggest a revision of both the rapidity and the dimensionality of the motion of small interstitial clusters.