Diffusion Of Self-interstitial Atoms Research Articles

Migration mechanisms of mono-/di-interstitials in vanadium with alloying Ti/Cr

Self-interstitial atoms (SIAs) are the dominant self-defects at equilibrium in metals, but many questions such as their diffusion characteristics are still open, and studies of the Ti/Cr effect on the kinetics of SIAs are very scarce in vanadium alloy. In this work, we systemically investigated the migration mechanisms of mono/di-interstitials as well as the effect of alloying elements Ti/Cr on the kinetics of SIAs using first-principles calculations. The findings reveal that 〈111〉SIA exhibits three migration mechanisms, including one dimensional (1D) migration, translation-rotation and translation, corresponding energy barriers of 0.008, 0.19 and 0.44 eV. Different migration pathways are activated at high temperatures, which supports the experimental observation of 3D migration of SIAs under high temperatures. We determined the di-SIA (two parallel 〈111〉SIA) migration by both successive and simultaneous jumping paths, the lowest migration barrier is 0.009 eV via successive jumping path passing a translation state. Moreover, based on three migration mechanisms of SIA, SIA migrating to Ti region possesses the lower barrier than pure vanadium, in verse the barrier is relative high and then hinders the SIA diffusion. The alloying Ti has a pinning effect on SIAs. And we explored how SIA to form mixed V-Cr interstitial and its migration of 〈111〉V-Cr. Finally, we estimated the effect of Ti on SIA diffusivity by empirical formulas.

Molecular dynamics insights on the self-interstitial diffusion in α-Beryllium

Beryllium has some unique properties and plays a key role in many special applications. However, Beryllium (α-Be) is of close-packed hexagonal (HCP) crystal structure, which has a strong anisotropic feature and limits its applications. In this work, diffusion behaviors of the self-interstitial atom (SIA) in α-Be at the temperature of 300–1100 K are studied using molecular dynamics simulations. It is observed that the diffusion mechanisms are not only dominated by the SIA jumps among the BO and BS sites on the basal plane, but also by the jumps among the C and O sites along the c-axis, which strongly depend on temperature. Diffusion behaviors of SIA can be divided into two stages with the temperature of 300–800 K and 800–1100 K, respectively, in which diffusion coefficient component of the c-axis (D c) is higher than that of the basal plane (D b) at first and then becomes closer to the D b after 800 K, in consistent with diffusion mechanisms. When the temperature rises from 300 K to 1100 K, the total diffusion coefficient of SIA (D t) increases gradually from 0.34 × 10−4 cm2 s−1 to 1.13 × 10−4 cm2 s−1. With the temperature increasing from 300 K to 1100 K, the anisotropy factor (η = D c /D b) of SIA diffusion drastically decreases from 1.76 to 1.01 in α-Be, while the η increases from 0.21 to 0.70 in α-Zr with the temperature from 500 K to 1100 K.

Self-interstitial atom properties in Nb–Mo–Ta–W alloys

Self-interstitial atoms (SIA) are generated in collision cascades during high-energy particle irradiation of crystalline materials. In pure metals, SIA generally adopt split configurations and display fast mobilities along one-dimensional trajectories. This differentiates them from vacancies, which move in confined three-dimensional paths. This asymmetry is one of the pillars of irradiation damage theories that have been successful in explaining a number features of the irradiation response of pure metals and dilute alloys. However, in complex concentrated alloys consisting of several metallic elements in equal or near equal proportions, lattice distortions associated with compositional fluctuations change the potential energy landscape on atomic scales, leading to SIA structures not seen in their pure metal counterparts. In this paper, we use atomistic simulations to study the properties of self-interstitial atoms in the quaternary equiatomic Nb–Mo–Ta–W refractory alloy. Chemically, these SIA defects adopt a variety of structures involving all pairs of atoms. We find the 〈111〉 orientation to be the most common among all split configurations, but we also observe – surprisingly – a relatively high occurrence of octahedral SIA. In terms of their diffusivities, we find two clearly distinguished regimes below and above 600 K, where the SIA diffusion changes dimensionality from 1D to 3D. We calculate the migration energies and diffusion pre-factors in both regions, from which we extract the translational and rotational components of the defect migration. We find values of 0.25 eV and pre-factors of ∼10−11 m2 s−1 in the low temperature regime, and 0.57 eV and ∼10−8 m2 s−1 in the high temperature one. From this, we estimate a rotational energy barrier of 0.37 eV.

Unveiling the interaction of nanopatterned void superlattices with irradiation cascades

Nanopatterned microstructures in materials can have a profound impact on materials’ physical and chemical properties. While voids are typically considered as detrimental defects in irradiated materials, the patterning of nanoscale voids causes the formation of void superlattices and provides a highly efficient mechanism for gas storage. Despite the important applications of nanopatterned defect superlattices, how they degrade under irradiation remains unclear. Here we provide direct observation of the evolution of void superlattices under irradiation and elucidate the interaction of void superlattices with irradiation cascades. We reveal that the instability of void superlattices under irradiation is caused by heterogenous void shrinkage and demonstrate the imperative role of mixed 1D/3D diffusion of self-interstitial atoms and injected inert gas atoms on void shrinkage and void superlattice instability. Understanding the degradation mechanisms of nanopatterned microstructures is essential to designing damage-tolerant materials and broadening their applications in extreme environments.

Interstitialcy-based reordering kinetics of Ni[formula omitted]Al precipitates in irradiated Ni-based super alloys

Neutron irradiation tends to promote disorder in ordered alloys through the action of the thermal spikes that it generates, while simultaneously introducing point defects and defect clusters. As they migrate, these point defects will promote reordering of the alloys, acting against irradiation-induced disordering. In this study, classical molecular dynamics and a highly parallel accelerated sampling method are used to study the reordering kinetics of Ni3Al under the diffusion of self-interstitial atoms (SIA). By monitoring the order parameter and potential energy from atomistic simulations, we show that the SIA acts as a reordering agent in Ni3Al. A mean-field rate theory model of the interstitialcy-based reordering kinetics is introduced, which reproduces simulation data and predicts reordering at temperatures as low as 500 K.

The effect of impurity niobium on diffusion of self-interstitial atom and self-diffusion by interstitial mechanism in zirconium: an atomistic simulation

The effect of niobium on diffusion of self-interstitial atom and self-diffusion by interstitial mechanism has been simulated by the molecular dynamics method in zirconium at a temperature up to 1000 K. It has been shown that even a small amount of niobium impurity in the HCP Zr matrix entails significant qualitative and quantitative changes in the diffusion coefficient of a self-interstitial atom and self-diffusion by the interstitial mechanism.

Effect of confinement of SIA cluster diffusion by impurities on radiation defect accumulation due to 14 MeV neutrons in tungsten

Impurities acting as traps reduce the self-interstitial atom (SIA) cluster mobility, thereby increasing recombination and, in turn, enhancing radiation-resistance of polycrystalline materials. However, at elevated temperatures, depending on SIA-trap (impurity) binding energy, SIA clusters may trap and detrap (detach) numerous times. In tungsten, SIA clusters of all sizes glide one-dimensionally (1D) along their Burgers vector direction. This can result in detrapped SIA clusters to retrace their original 1D path, confining their 1D-glide between traps. However, SIA clusters can change the direction of their 1D-glide by overcoming a rotation barrier and impurities or solutes are known to reduce this barrier. A lower rotation barrier can result in detrapped SIA clusters to diffuse in a random 1D direction, effectively leading to 3D (net-3D) diffusion. Here we investigate the effect of two cases of SIA diffusion, namely the confined-1D diffusion and the net-3D diffusion, on the damage accumulation in polycrystalline tungsten under 14 MeV neutron irradiation using the object kinetic Monte Carlo method. Simulations were performed using cascade debris obtained from molecular dynamics simulations with primary knock-on atom (PKA) energies corresponding to 14 MeV neutrons. In the simulations with net-3D diffusion, SIA clusters of all sizes diffuse in a random 1D direction after the clusters detrap. While for the confined 1D diffusion case, clusters larger than size 5 retain their original direction of 1D glide. In both types of simulations, trapped vacancies are assumed to be permanently immobilized. Unexpectedly, the damage accumulation was lower with confined 1D diffusion than that with net-3D. We present a systematic comparison of the influence of the two cases of SIA diffusion on the radiation damage accumulation as a function of dose rate, detrapping barrier, and impurity concentration at 1025 K.

Symmetry breaking during defect self-organization under irradiation

One of the most intriguing phenomena under radiation is the self-organization of defects, such as the void superlattices, which have been observed in a list of bcc and fcc metals and alloys when the irradiation conditions fall into certain windows defined by temperature and dose rate. A superlattice features a lattice parameter and a crystal structure. Previously, it has been shown that the superlattice parameter is given by the wavelength of vacancy concentration waves that develop when the uniform concentration field becomes unstable. This instability is driven thermodynamically by vacancy concentration supersaturation and affected by the irradiation condition. However, a theory that predicts the superlattice symmetry, i.e., the selection of superlattice structure, has remained missing decades after the first report of superlattices. By analyzing the nonlinear recombination between vacancies and self-interstitial-atoms (SIAs) in the discrete lattice space, this work establishes the physical connection between symmetry breaking and anisotropic SIA diffusion, allowing for predictions of void ordering during defect self-organization. The results suggest that while the instability is driven thermodynamically by vacancy supersaturation, the symmetry development is kinetically rather than thermodynamically driven. The significance of SIA diffusion anisotropy in affecting superlattice formation under irradiation is also indicated. Various superlattice structures can be predicted based on different SIA diffusion modes, and the predictions are in good agreement with atomistic simulations and previous experimental observations.

Chemical effects on He bubble superlattice formation in high entropy alloys

The probable formation mechanism of He bubble superlattices relies on long range anisotropic diffusion of self-interstitial atoms (SIAs). Here we study He ion irradiation of pure Ni and two equiatomic concentrated solid-solution alloys (CSAs) of FeNi and FeCrNiCo. It is expected from the significantly reduced diffusion of SIAs in CSAs, including high entropy alloys (HEAs), that long range anisotropic SIA migration cannot be active. We report the formation of a He bubble lattice in pure Ni, and for the first time in FeNi and FeCrNiCo systems under 30 keV He ion irradiation at room temperature. The ion dose and flux required to form a bubble superlattice increase with chemical complexity. Comparing to Ni, SIA clusters change directions more frequently due to anisotropic elementally-biased diffusion from the higher degree of chemical non-homogeneity in CSAs. Nevertheless, anisotropic 1-D diffusion of interstitial defects is possible in these complex alloys over incrementally longer time scales and irradiation doses. The sluggish diffusion, characteristic in CSAs, leads to smaller superlattice parameters and smaller bubble diameters. The chemical biased SIA diffusion and its effects on He evolution revealed here have important implications on understanding and improving radiation tolerance over a wide range of extreme conditions.

Energetics and diffusion of point defects in Au/Ag metals: A molecular dynamics study**Project supported by the National Natural Science Foundation of China (Grant Nos. 51401237, 11474358, and 51271198), the Fund from Shaanxi Provincial Education Department, China (Grant No. 18JK1207), and the Defence Technology Foundation of China (Grant No. 2301003).

To reveal the potential aging mechanism for self-irradiation in Pu–Ga alloy, we choose Au–Ag alloy as its substitutional material in terms of its mass density and lattice structure. As a first step for understanding the microscopic behavior of point defects in Au–Ag alloy, we perform a molecular dynamics (MD) simulation on energetics and diffusion of point defects in Au and Ag metal. Our results indicate that the octahedral self-interstitial atom (SIA) is more stable than the tetrahedral SIA. The stability sequence of point defects for He atom in Au/Ag is: substitutional site octahedral interstitial site tetrahedral interstitial site. The He–V cluster (, V denotes vacancy) is the most stable at n = m. For the mono-vacancy diffusion, the MD calculation shows that the first nearest neighbour (1NN) site is the most favorable site on the basis of the nudged elastic band (NEB) calculation, which is in agreement with previous experimental data. There are two peaks for the second nearest neighbour (2NN) and the third nearest neighbour (3NN) diffusion curve in octahedral interstitial site for He atom, indicating that the 2NN and 3NN diffusion for octahedral SIA would undergo an intermediate defect structure similar to the 1NN site. The 3NN diffusion for the tetrahedral SIA and He atom would undergo an intermediate site in analogy to its initial structure. For diffusion of point defects, the vacancy, SIA, He atom and He–V cluster may have an analogous effect on the diffusion velocity in Ag.

Atomistic simulation of diffusion of the self-interstitial atom in HCP Zr

The paper is devoted to atomistic simulation of the self-interstitial migration in HCP Zr. The simulation has been carried out on the basis of three different interatomic potentials taken from the literature. The location of self-interstitial atoms (SIA), that is defined as a crystal lattice site, whose corresponding Wigner–Seitz cell contains two atoms, was traced. Combined method based on molecular dynamics (MD) and kinetic Monte Carlo (KMC) method was proposed for an atomistic simulation of the SIA migration in HCP zirconium. Calculations of SIA diffusion coefficient were performed for temperatures range from 300 to 1000 K by two methods: ‘pure’ MD simulation and a proposed MD-KMC method. Both methods provided close results. At that, proposed combined MD-KMC method required significantly shorter computational time. All three potentials provided SIA with anisotropic diffusion. At a temperature of 800–1000 K, the estimates of the diffusion coefficient values obtained at different potentials were close. At temperatures below 800 K, significant qualitative and quantitative differences were observed between the results obtained at different potentials. For one of the used potentials, the anomalous dependence of the SIA diffusion coefficient in the basal plane on the temperature was observed.

A modified W–W interatomic potential based on ab initio calculations

In this paper we have developed a Finnis–Sinclair-type interatomic potential for W–W interactions that is based on ab initio calculations. The modified potential is able to reproduce the correct formation energies of self-interstitial atom (SIA) defects in tungsten, offering a significant improvement over the Ackland–Thetford tungsten potential. Using the modified potential, the thermal expansion is calculated in a temperature range from 0 to 3500 K. The results are in reasonable agreement with the experimental data, thus overcoming the shortcomings of the negative thermal expansion using the Derlet–Nguyen–Manh–Dudarev tungsten potential. The W–W potential presented here is also applied to study in detail the diffusion of SIAs in tungsten. We reveal that the initial SIA initiates a sequence of tungsten atom displacements and replacements in the 〈1 1 1〉 direction. An Arrhenius fit to the diffusion data at temperatures below 550 K indicates a migration energy of 0.022 eV, which is in reasonable agreement with the experimental data.

Effect of anisotropy, SIA orientation, and one-dimensional migration mechanisms on dislocation bias calculations in metals

Swelling in metals exposed to neutron irradiation has long been known to be enhanced by the preferential absorption of interstitials rather than vacancies, by dislocations. A common measure of this preference is called the dislocation bias factor and is computed from the ratio of the capture efficiency of interstitials to that of vacancies, by dislocations. Bias factors calculated through analytical and numerical means have been known to be approximately an order of magnitude larger than those expected by empirical swelling data. While this discrepancy has been justified by some in the past, it has remained an issue of debate among many. A major issue that has not been explored, however, is the effect of the numerous assumptions and approximations in previous studies. In this study, we explore the effect of three major assumptions of past studies. First, anisotropy in the displacement fields of both point-defects and dislocations is accounted for in our calculations. This relieves the assumption that self-interstitial atoms (SIAs) are centers of dilatation in isotropic media. Secondly, since SIAs have energetically-preferred orientations in dislocation stress fields, we use a spatially dependent elastic dipole tensor that accounts for preferred orientations. Lastly, since SIAs are known to undergo fast one-dimensional (1-D) migration in the Burgers direction in the vicinity of dislocations, we specify a fraction of SIAs to migrate one-dimensionally using a modified SIA diffusion tensor. These attributes are implemented into a combined finite-element method (FEM) rate-theory (RT) approach to calculate dislocation bias factors in body-centered cubic iron and face-centered cubic copper. In copper, we observe a significant increase in the bias when anisotropy and preferred SIA orientations are considered. In iron, our results show a drastic decrease in the bias when anisotropy and 1-D SIA motion are implemented, but these effects are countered when preferred SIA orientations are considered.

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 radiation-induced segregation: Contribution of interstitial mechanism in Fe–Cr alloys

In this work, we perform molecular dynamics simulations to study the diffusion characteristics of a self-interstitial atom (SIA) in BCC Fe–Cr alloys and corresponding mass transport of Fe and Cr atoms via SIA migration mechanism. The calculations have been performed in the temperature range 600–1000K in the alloys with Cr content 5–25at.%, which is relevant for ferritic/martensitic steels. The results of atomistic simulations have been applied to evaluate the contribution of SIA diffusion mechanism to radiation-induced segregation (RIS) phenomenon. An original treatment is proposed in this work to account for the contribution from both vacancy and SIA mechanisms to RIS at sinks for point defects in multi-component system. By combining available experimental data on diffusion of Fe and Cr via vacancy mechanism with the results of MD simulations for SIAs, we demonstrate that enrichment of sinks by Cr atoms is possible in the Fe–Cr alloys containing less than 13% Cr. This result is discussed in the light of available experimental data on the RIS in Fe–Cr alloys and ferritic/martensitic steels. It is predicted that the degree of the Cr enrichment goes up with decreasing Cr content in the alloy and irradiation temperature.

Stability and diffusion properties of self-interstitial atoms in tungsten: a first-principles investigation

Employing a first-principles method based on the density function theory, we systematically investigate the structures, stability and diffusion of self-interstitial atoms (SIAs) in tungsten (W). The〈111〉 dumbbell is shown to be the most stable SIA defect configuration with the formation energy of ∼9.43 eV. The on-site rotation modes can be described by a quite soft floating mechanism and a down-hill “drift” diffusion process from 〈110〉 dumbbell to 〈111〉 dumbbell and from 〈001〉 dumbbell to 〈¹10〉 dumbbell, respectively. Among different SIA configurations jumping to near neighboring site, the 〈111〉 dumbbell is more preferable to migrate directly to first-nearest-neighboring site with a much lower energy barrier of 0.004 eV. These results provide a useful reference for W as a candidate plasma facing material in fusion Tokamak.

Derivation of kinetic coefficients by atomistic methods for studying defect behavior in Mo

A multiscale concept for irradiated materials simulation is formulated based on coupling molecular dynamics simulations (MD) where the potential was obtained from ab initio data of energies of the basic defect structures, with kinetic mesoscale models. The evolution of a system containing self-interstitial atoms (SIAs) and vacancies in crystalline molybdenum is investigated by means of MD. The kinetics of formation of di-SIA clusters and SIA–vacancy recombination is analyzed via approaches used in the kinetic theory of radiation ageing. The effects of 1D diffusion of SIAs, temperature, and defect concentrations on the reaction rates are also studied. This approach can validate both the kinetic mechanisms and the appropriate kinetic coefficients, offering the potential to significantly reduce the uncertainty of the kinetic methodology and providing a powerful predictive tool for simulating irradiation behavior of nuclear materials.

Formation and diffusion of self-interstitial atoms in silicon crystals under hydrostatic pressure: Quantum-chemical simulation

A theoretical modeling of the formation of Frenkel pairs and the diffusion of a self-interstitial atom in silicon crystals at normal and high (hydrostatic) pressures has been performed using molecular dynamics, semiempirical quantum-chemical (NDDO-PM5, PM6), and ab initio (SIESTA) methods. It is shown that, in a silicon crystal, the most stable configuration of a self-interstitial atom in the neutral charge state (I 0) is the split configuration 〈110〉. The shifted tetrahedral configuration (T 1) is stable in the singlet and triplet excited states, as well as in the charge state Z = +2. The split 〈110〉 interstitial configuration remains stable under hydrostatic pressure (P ≤ 80 kbar). The activation barriers for diffusion of self-interstitial atoms in silicon crystals are determined to be as follows: ΔE a (Si)(〈110〉 → T 1) = 0.59 eV, ΔE a (Si)(T 1 → T′1) = 0.1 eV, and ΔE a (Si)(T 1 → 〈110〉) = 0.23 eV. The hydrostatic pressure (P ≤ 80 kbar) increases the activation barrier for diffusion of self-interstitial atoms in silicon crystals. The energies of the formation of a separate Frenkel pair, a self-interstitial atom, and a vacancy are determined. It is demonstrated that the hydrostatic pressure decreases the energy of the formation of Frenkel pairs.

Cluster Dynamics modelling of irradiation growth of zirconium single crystals

This paper aims at modelling irradiation growth of zirconium single crystals as a function of neutron fluence. The Cluster Dynamics approach is used, which makes it possible to describe the variation of irradiation microstructure (dislocation loops) with neutron fluence. From the irradiation microstructure, the strain can be calculated along the axes of the lattice structure. The model is applied to the growth of annealed zirconium single crystals at 553 K measured by Carpenter and Rogerson in 1981 and 1987. The model is found to fit the experimentally measured growth of Zr single crystals very nicely, even at large neutron fluence where the ‘breakaway growth’ occurs. This was made possible by considering in the model the growth of vacancy loops in the basal planes. This growth of vacancy loops in the basal planes could be modelled by taking into account that diffusion of self-interstitial atoms (SIA) is anisotropic and that there exist in the basal planes some nucleation sites for vacancy loops (iron clusters), the density of which is considered constant over time.

Diffusion anisotropy and void development under cascade irradiation

Cascade irradiation of metals gives rise to swelling as a result of the creation of voids and the evolution of the void ensemble. Under suitable circumstances, the originally disordered void distribution transforms into to a void lattice. As demonstrated previously, the understanding of the evolution and the unique features of the void ensemble requires a difference in the anisotropy of the diffusion (DAD) of vacancies and self-interstitial atoms (SIAs), which is achieved by one-dimensional diffusion of the SIAs. On the other hand, void swelling has been successfully modeled in terms of three-dimensional diffusion of both vacancies and SIAs. In the present paper it is shown that these seemingly contradicting interpretations and all related observations can be quantitatively reconciled by a small DAD created by only ∼1% of SIAs diffusing one-dimensionally. It is also demonstrated that at the initial stage of void-lattice formation, ordering occurs mainly on close-packed crystal planes, which is in contrast to the naive expectation that one-dimensional diffusion of SIAs should result in a void ordering along close-packed directions. Finally it is found that, in the case of a small DAD, voids annihilate via stochastic shrinkage much faster than by coalescence. This falsifies the argument in the literature that one-dimensional diffusion of SIAs would necessarily lead to the coalescence of voids and destabilization of the void lattice.