Self-interstitial Atoms Research Articles

Pronounced inhibitory mechanism of Cr on vacancy-like defects in Fe9Cr alloy irradiation with helium ions

• First-principles calculations combined with positron annihilation spectroscopy. • The He atoms aggregate among (1 1 0) planes in the perfect Fe and Fe9Cr models. • Fe atoms around the He clusters are inclined to emit spontaneously. • The doping of Cr repels the He atoms and weakens the growth of He clusters. First-principles calculations and positron annihilation spectroscopy were used to investigate the effect of Cr atoms on He-induced vacancy-like defects in pure Fe and Fe9Cr alloys. The He atom is not energetically favorable at both the surface and the subsurface, but it becomes stable under the third atomic layer from the surface. The diffusion of He atoms to the vacuum and aggregation of He atoms into clusters coexist. We observed that the interstitial He n clusters prefer to stay along the (1 1 0) plane. Moreover, the small He n clusters induce strong lattice distortions, and the emission of a self-interstitial Fe atom located at the adjacent He n cluster is energetically favorable for n > 2 and vacancy formation energies of Fe9Cr are higher than that of Fe. This suggests that Cr atoms could effectively enhance the stability of Fe atoms around He n clusters but that the Fe atoms would still like to shift from the vicinity of He n to the surfaces of the models. In the experiment, Fe and Fe9Cr alloys were irradiated with He ions to a dose of 1 × 10 16 cm 2 and the positron annihilation results showed that the Fe9Cr alloy has a smaller relative S (ΔS) parameter value than pure Fe. The experimental results matched well with the theoretical analysis. These results would help provide additional insights into the behavior of He in irradiated Fe and Fe9Cr surfaces, necessary for the interpretation of the growth of the He bubble.

Basic study of the relaxation volume of crystalline defects in bcc iron

The relaxation volume (Ωrel), here determined per extra-atom or vacant site, of common crystalline defects in bcc iron (Fe) was calculated from molecular dynamics (MD) simulation cells containing defects of varying size and/or density. To this end, we used both real and reciprocal space data: for the former, the change in the MD cell volume was calculated, while for the latter, we computed X-ray diffraction reciprocal space maps to evaluate the change in the lattice parameter. We show that 〈110〉 dumbbell self-interstitial atoms have the largest Ωrel, ∼1.5atomic volume (∼1.5 Ω0). C15 clusters of size 12 and 48 atoms show Ωrel of ∼ 0.91 Ω0 and ∼ 0.98 Ω0, respectively, and similar values are found for ½〈111〉 and 〈100〉 interstitial dislocation loops, with Ωrel ∼ 0.905 Ω0 and Ωrel ∼ 0.873 Ω0, respectively. Single vacancies are characterized by a negative Ωrel, ∼−0.11 Ω0. For cavities, Ωrel rapidly increases to approach zero as the clusters grow. Using these values, we managed to predict (with an accuracy better than 2 %) the lattice strain in MD cells containing several types of defects, which indicates that the relaxation volumes can be summed up to estimate the microscopic (i.e., lattice) volume change.

Contribution of dislocation loop to radiation-hardening of RPV steels studied by STEM/EDS with surveillance test pieces

Microstructure and radiation-hardening of surveillance test pieces of reactor pressure vessel steels have been studied by STEM/EDS and Vickers micro-hardness measurements. In a low-Cu steel (0.06 wt%), the microstructures irradiated with fluence of 5.62 × 1023 n/m2 were found to include nano-size Ni–Si-rich solute clusters (SCs) and dislocation loops (DLs). Most of the DLs were sustained after post-irradiation annealing at 500 °C for 0.5 h, while the number density of SCs decreased. The stability of the DLs is suggestive of entanglement with solute atoms. On the other hand, Cu-rich SCs were observed in high-Cu steels (0.17 wt%) irradiated with fluence of 1.01 × 1023 n/m2 and 6.11 × 1023 n/m2, however, no DLs observed. The Cu content in the matrix seems to be crucial for the nucleation of the DLs, which suggests that the mobility of the vacancy coupled with Cu atom dominates the nucleation/annihilation of self-interstitial atom. The contribution of DLs and SCs are discussed on the basis of the Russell-Brown and Orowan models, respectively.

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]

A phase-field model for void and gas bubble superlattice formation in irradiated solids

A phase-field model to simulate the formation of both void and gas bubble superlattices is derived from a grand potential functional, assuming 1D diffusion of self-interstitial atoms. The model is capable of accounting for superlattice formation by either a nucleation and growth or spinodal decomposition mechanism; in this work, we focus on the nucleation and growth mechanism, using a discrete nucleation approach in the phase-field model. In simulations of void formation, short aligned rows of voids were initially formed, followed by growth in the size of the aligned rows, and finally leading to superlattice formation, consistent with experimental observations. Void superlattice spacing as a function of model parameters was quantified. Increased nucleation rates led to smaller superlattice spacing, while increased vacancy diffusivity led to larger superlattice spacing. In simulations of gas bubble superlattice formation, superlattice spacing decreased with increasing gas atom flux, consistent with experimental observations. Simulations with increasing ratio of gas atom flux to vacancy–interstitial pair production led to increased superlattice spacing, which is inconsistent with experimental observations at high gas atom flux rates; this discrepancy is attributed to the fact that the model does not account for bound gas atom–vacancy pairs that may dominate at high gas flux rates.

Geometrically necessary dislocation fingerprints of dislocation loop absorption at grain boundaries

We present a numerical methodology to compute the Nye-tensor fingerprints of dislocation loop absorption at grain boundaries (GBs) for comparison with TEM observations of irradiated polycrystals. Our approach links atomistic simulations of self-interstitial atom (SIA) prismatic loops gliding toward and interacting with GBs in body-centered cubic iron with experimentally extracted geometrically necessary dislocation (GND) maps to facilitate the interpretation of damage processes. The Nye-tensor analysis is strongly mesh-size dependent---corresponding to resolution-dependent TEM observations. The method computes GND fingerprints from discretized dislocation line segments extracted from molecular dynamics simulations of dislocation loops being absorbed at a GB. Specifically, we perform MD simulation of prismatic loops of two diameters and monitor the three stages of the absorption process: loop glide, the partial, and full absorption of the loops at a [1 0 0] symmetric tilt GB. These methods provide a framework for future investigations of the nature of defect absorption by grain boundaries under irradiation conditions.

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.

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.

Ab initio study of the effects of Cr on helium behaviors in Fe–YCr (Y = 9.38, 12.50 at%) austenitic binary alloys

The effects of Cr on helium diffusion, capture ability, and the stability of HenVm (V means vacancy) complexes (n = 0–6, m = 0–4) in Fe–YCr (Y = 9.38, 12.50 at%) binary alloys are evaluated using density functional theory (DFT). We found that Cr played a significant dual role in helium migration. The diffusion of helium between octahedral or tetrahedral interstitials cannot pass through tetrahedral or octahedral gaps. The presence of Cr or the increase of Cr contents both prevents the trapping of helium atoms by vacancies. We have confirmed that Cr content has no obvious effect on the radiation expansion resistance of the alloy models. At a higher or lower n/m ratio, the spontaneous emission of He or SIAs (self-interstitial atoms), or vacancies are predicted. Our work provides necessary information and additional knowledge for the interpretation of complex experimental data, such as micropore formation, void swelling, etc.

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.

On the relative contributions of point defect clusters to macroscopic swelling of metals

Swelling of metals under irradiation is commonly assessed by calculating the volume fraction of voids, which appear at temperatures where vacancies are mobile. However, other clusters are formed, which may also have an impact on swelling. In particular, interstitial loops have recently been considered to give a significant contribution to swelling owing to their large relaxation volume. In this work, we perform calculations in nickel, based on interatomic potentials, to estimate the contributions of the various point defect clusters. We show that voids produce much more swelling than loops and stacking fault tetrahedra, whose contribution is essentially due to the dislocation core field, inducing a dilatation per unit length of around 1b2, where b is the Burgers vector. Evaluation of swelling should indeed be done by summing formation volumes, not relaxation volumes, the latter being related to lattice parameter change as measured by x-ray diffraction. We also discuss the case of “lattice swelling” occurring when vacancies are immobile. When self-interstitial atoms cluster as dislocation loops, this swelling mode turns out to be nothing but “void” swelling in a regime where vacancy mobility is so low that vacancies do not cluster appreciably, leaving only interstitial loops visible in transmission electron microscopy.

The behaviors of dislocation loops punched by helium interstitials accumulation under the temperature gradient field in tungsten

ABSTRACT Enormous amounts of investigations have been made to understand the helium interstitials accumulation processes in tungsten, which is a promising candidate of plasma-facing materials in fusion reactors. However, the temperature gradient, which almost certainly exists in plasma-facing materials, was often neglected in previous studies. In view of this, the molecular dynamics method is employed to simulate the helium interstitials accumulation processes in tungsten at temperature gradient field in this study. The results show that in the temperature gradient field, the helium bubble formed by helium interstitials accumulation processes also grows via punching out 1/2<111> dislocation loops, which is similar to that at constant temperature. However, under the temperature gradient field, 1/2<111> dislocation loops always were emitted to the higher-temperature region. Combined with the first principle calculation, the formation energy of self-interstitial atom at high temperature should be responsible for this phenomenon.

Shear strain alters the structure and migration mechanism of self-interstitial atoms in copper

We use atomistic modeling to show that externally applied shear strain causes the lowest energy self-interstitial atom (SIA) structure in copper (Cu) to change from a ⟨100⟩-type dumbbell to a ⟨110⟩-type dumbbell. Concurrently, SIA migration switches from the three-dimensional (3D) random walk characteristic of ⟨100⟩-type dumbbells to a 1D mechanism analogous to that of crowdion SIAs. Furthermore, the relative energies of these two dumbbell structures as a function of strain are well predicted using elastic dipole tensors computed at zero strain, indicating that examination of these tensors may be used to assess the likelihood of strain-induced SIA structure transitions in other materials. Changes in lowest energy SIA structures and associated migration mechanisms stand to impact predictions of SIA behavior in irradiated solids.

The trapping effects of silicon and phosphorus on point defects in γ-Fe

The addition of silicon (Si) and phosphorus (P) to austenitic stainless steel is observed to reduce swelling, but the inhibition mechanism has not been well understood. In this work, the solute properties of Si and P, their interaction with point defect, vacancy-mediated migration energies were obtained through first-principles calculations, and the diffusion behavior of solutes and vacancies are evaluated by both methods by solving the Onsager matrix. The solution energies of Si and P in the antiferromagnetic (001) double-layer with face-centered tetragonal structure (fct_afmD) Fe imply their relative high solubility. Vacancies can be attracted by Si and P at 1NN sites with the binding energies of 0.12 ∼ 0.19 eV, and 0.30 ∼ 0.42 eV, respectively. The vacancy wind and the ratio of tracer diffusion coefficient demonstrate that Si and P will be dragged by vacancy, diffuse faster than that of Fe, and strongly promote vacancy diffusion at low temperature while they have weak inhibition at high temperature. Simultaneously, as a function of temperature, compared to the phenomenological Manning method, the results of the Green-function method generally exhibit a left shift. Furthermore, Si and P are also found to attract the self-interstitial atoms (SIAs). Our results indicate that solutes Si and P can both welcome vacancies and SIAs, promote vacancy diffusion at low temperature, in which the effect of P is much stronger than that of Si. Therefore, their addition to austenitic steels may be beneficial to enhance recombination rates of vacancy and SIAs, drop of net defect concentrations and result in a reduction of the rates of void growth under irradiation.

Determining the diffusion behavior of point defects in zirconium by a multiscale modelling approach

Zr alloys are commonly used materials for in-core components of pressurized water reactors. The evolution of defects in Zr under irradiation conditions will directly contribute to the degradation of reactor components. For a better understanding of the evolution process of defects in Zr, a multiscale simulation was performed to study the diffusion behavior of radiation-induced point defects. Because the existing potentials cannot accurately describe the energy differences of stable states self-interstitial atoms (SIAs) in Zr, an embedded atom method potential that can exactly reproduce the energy difference between metastable states and ground states, and the binding energy of divacancy of Zr, was first developed by fitting a potential to point defect properties calculated by density functional theory and other basic crystal properties. Based on the constructed potential, molecular dynamics (MD) and kinetic Monte Carlo simulations were conducted to investigate the migration of point defects. We determined several frequent migration paths of SIAs by kinetic study, which is rarely reported in previous MD studies. The SIA exhibits obvious anisotropic diffusion characteristics at low temperatures (<600 K). The most frequent migration path for SIAs is the jump between the two nearest basal octahedral (BO) sites in the basal plane, which means that SIAs diffuse faster along the basal plane than along the c axis. It is found that diffusion within the basal plane tends to be two-dimensional (2D) diffusion rather than 1D diffusion, and there is a significant correlation effect for diffusion of SIAs along the basal plane. Additionally, the existence of trivacancy-SIA complex was found in the process of divacancy migration, which can inhibit divacancy migration. Monovacancies and divacancies exhibit anisotropic diffusion characteristics in the considered temperature range Divacancies have a much faster diffusion rate than monovacancies in the present MD simulation and can easily dissociate at high temperatures (>900 K). The rapid migration of the divacancies may contribute to the formation of vacancy dislocation loops. These results are meaningful to understand the evolution process of radiation-induced defects.

Relative population of 1/2 and interstitial loops in alpha-Fe under irradiation: Effects of C15 cluster stability and loop one-dimensional movement

The relative stability of 1/2<111> and <100> dislocation loops, originating from anisotropic elasticity of alpha-Fe, was extensively exploited to explain experimentally observed variation in the relative population of the two loop types under varying irradiation temperatures. In this study, using cluster dynamics simulations taking into account the coevolution of C15 Laves phase structure (cluster) and loop reaction caused by defect one-dimensional (1-d) movement, we reveal new mechanisms that may underpin the variations in loop population of different Burgers vectors. We identify that C15 clusters have twofold roles in mediating loop evolution: (1) acting as buffers of self-interstitial atoms, (2) initiating loop nuclei via their collapses. The latter plays a critical role in nucleation of <100> loops and subsequently affects loop evolution of both types. We show that the loop relative population undergoes further re-arrangement via a transfer reaction driven by loop long-range diffusion. Our findings essentially demonstrate that, apart from the loop stability, the relative population of two loop types is governed by at least two other factors: C15 cluster stability and loop 1-d movement.

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.

Molecular dynamics study of radiation effects on tritium diffusion in zirconium tritides (δ-ZrT2-x)

Tritium diffusivity in zirconium tritides is key to tritium storage in tritium-producing burnable absorber rods. Experiments struggle with assessing tritium diffusivity in reactor environments because irradiated defects alter diffusion. Here molecular dynamics simulations are used to investigate the irradiation effects on tritium diffusion in δ-ZrT2-x. We found that for defect-free δ-ZrT2-x, diffusivity can be described by a single Arrhenius equation for composition range x = 0.01–0.07. The irradiated vacancies slightly increase diffusivity although have no effects on diffusion energy barriers. Interestingly, irradiated self-interstitial atoms substantially increase diffusivity and reduce the energy barriers due to a lattice expansion effect.

A Molecular Dynamics Study of Tungsten’s Interstitial Dislocation Loops Formation Induced by Irradiation under Local Strain

A molecular dynamics simulation was used to investigate the effect of applied strain on the formation of primary defects and the probability of interstitial dislocation loops (IDLs) formation of tungsten (W) during a collision cascade event. The research investigated primary knock-on atom energies of 1, 6, 10, and 14 keV, applied on a deformed W structure (form −1.4~1.6%). The peak and surviving number of Frenkel pairs (FPs) increased with increasing tension; however, these increases were more pronounced under higher strain due to the formation of IDLs. For 10 self-interstitial atoms (SIA) lengths, the strain effect reduces the clustering energy of the IDLs by about 7 eV. In general, the current findings suggest that strain effects should be carefully considered in radiation-damaged environments, particularly in low-temperature, high-radiation-energy environments. The compressed condition may advantage materials used in high-radiation-damage devices and power systems.

Modeling irradiation-induced intragranular gas bubble in tungsten under external tensile loading

Microstructure damage created by high-energy particle irradiation has an inevitable effect on the performance of material. Helium (He) as the transmutation element in irradiated solid prefers to occupy the vacancy (V) center to form HeV complex, which in turn induces the formation of He bubble. Herein, the external applied stress driven irradiation-induced He bubble formation and evolution in single-crystalline tungsten (W) has been investigated using the phase-field method. Importantly, the trapping and resolution kinetic behavior between He atom and He bubble is described by the diffusion coefficient in terms of rate theory continuum model, and the effect of external stress on the movements of vacancy, self-interstitial and He atom has been implemented into their diffusivities as well. We first concentrate on the intrinsic lattice distortion (stress) patterns of void and bubble to validate the developed model by comparing the reported numerical results. Then, the accelerated growth velocity of bubble along the loading direction is predicted, which agrees well with the previously observed stress pattern around the void/bubble. The evolution behaviors of the stress-assisted single, bi-dispersed and multiple bubbles vary with the direction and magnitude of external loading, indicating a strong correlation between the size and density of bubble and the loading level. It is found that with the contribution of increasing external stress, more bubbles can be generated at the formation stage and visible bubbles tend to reduce at the coarsening stage due to bubble coalescence.