Vol.:(0123456789)1 3

Tungsten (2020) 2:15–33 https://doi.org/10.1007/s42864-020-00039-5

REVIEW PAPER

Interaction of radiation‑induced defects with tungsten grain boundaries at across scales: a short review

Xiang‑Yan Li1 · Yan‑Ge Zhang1 · Yi‑Chun Xu1 · Xue‑Bang Wu1 · Xiang‑Shan Kong1,2 · Xian‑Ping Wang1 · Qian‑Feng Fang1 · Chang‑Song Liu1

Received: 15 January 2020 / Revised: 14 February 2020 / Accepted: 2 March 2020 / Published online: 22 April 2020 © The Nonferrous Metals Society of China 2020

AbstractAs promising candidates for plasma-facing materials, tungsten-based materials suffer the irradiation of high-energy neutrons in addition to the hydrogen isotopes and helium irradiation and the high-thermal flux. Radiation-produced defects, e.g. self-interstitial atoms (SIAs) and vacancies (Vs), can induce the hardening and embrittlement of tungsten, meanwhile enhancing the retention of hydrogen isotopes and helium in tungsten. Reducing the grain size of materials to introduce a high density of defect sinks, e.g., grain boundaries (GBs) prevalent in nano-/ultrafine-crystalline materials, was demonstrated to be an effective approach for mitigating irradiation damage in tungsten. In this paper, we reviewed the theoretical advances in exploring radiation-resistance of nano-structured tungsten at across scales. It was concentrated on the results of molecular dynamics, molecular statics, and the object kinetic Monte Carlo simulations on the fundamental interaction of the radiation-created Vs and SIAs with the GB. These mechanisms include GB-promoted V/SIA migration and SIA-V recombination, interstitial-emission induced annihilation, coupling of the V migration close to the GB with the SIA motion within the GB, and interstitial reflection by the locally dense GB structure. We proposed the remaining scientific issues on the defect-GB interactions at across scales and their relation to experimental observations. We prospected the possible trends for simulat-ing the radiation damage accumulation and healing processes in nano-structured tungsten in terms of the development of the across-scale computational techniques and efficiency of the GB-enhanced tolerance of tungsten to irradiation under complex in-service conditions.

Keywords Nano-crystalline · Grain boundary · Radiation-resistance · Self-healing · Radiation damage · Tungsten

1 Introduction

As a promising candidate for plasma-facing materials (PFMs) in the future fusion reactors such as the first wall of a blanket and a diverter plate, tungsten (W) suffers the irra-diation of 14 MeV-neutrons, in addition to the bombardment

of low-energy hydrogen isotopes and helium ions at the typical operation temperature of 500–800 ºC at the first wall and 600–1300 ºC at the diverter [1]. These energetic neutrons introduce large quantities of self-interstitial atoms (SIAs), vacancies (Vs), and their clusters (SIAn, Vn) into W as well as substantial gaseous (hydrogen and helium) and solid transmutation products [1]. These defects evolve and agglomerate over long time scale, inducing the increase in yield strength of materials and bringing about radiation hardening. By acting as the trapping sites, the SIAn/Vn also promotes the retention of hydrogen isotopes and helium in W [2, 3]. Under the harsh condition of the radiation, tem-perature, and mechanical stress, W may not be able to retain its structural integrity in the future fusion reactors.

Over the past 50 years, distinct strategies for suppressing radiation damage have been proposed to achieve high irradia-tion resistance, e.g. minimizing the initial production amount of the defects and regulating defect diffusion and annihilation

Tungstenwww.springer.com/42864

Xiang-Yan Li and Yan-Ge Zhang contributed equally to this work.

* Xue-Bang Wu xbwu@issp.ac.cn

* Chang-Song Liu csliu@issp.ac.cn

1 Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China

2 Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China

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behavior near sinks [1]. Among the methods, engineering the material with a high density of defects sinks, e.g. grain bound-aries (GBs) in nano-crystalline (NC) metals, was demonstrated to be one of the effective options to suppress the accumulation of radiation-defects and thus mitigate the radiation damage in W [4–11] and in other metals [12–16]. For instance, neutron irradiation experiments at 873 K suggest that the density of voids in NC W (equiaxed grain sizes of 50–200 nm) is much smaller than that in pure commercial W (an average grain size of 20 μm) [5]. Quite recently, such enhanced radiation per-formance is also obtained in Kr2+ ion irradiated NC W (grain sizes of 35 and 85 nm) at 1073 K compared to W prepared through a severe plastic deformation (SPD) method (grain sizes of 80–400 nm) and coarse-grained (CG) W (grain sizes of 1–3 μm) [11]. However, irradiation experiments at room temperature suggest that the relation of the defect density to the grain size is not clear for the ultrafine and NC region with grain sizes of 60–500 nm; from the ultrafine region with the grain size of 200 nm to the fine region with the grain width of few micrometers, a decreasing trend in the defect density with the grain size increasing is observed [11]. At a low dose rate of 1.7 × 10–4 displacement per atom (dpa)·s−1, the swelling resist-ance of NC W is better than that of CG W [9], while at a high dose rate of 1.7 × 10–2 dpa·s−1, no difference in the swelling behavior is observed in the two systems exposed to the irradia-tion of 0.25 dpa [9]. Neutron irradiation at 563 K demonstrates that irradiation-induced hardening is significantly reduced for fine-grained W-0.3wt%TiC (a grain size of 0.9 μm) compared with pure W (an average particle size of 4.0 μm) [4].

Extensive theoretical efforts were made to understand the radiation performance of NC W in terms of the defect production [14, 17–21] and energetic and kinetic interac-tions with GBs of the defects [14, 17, 20, 22–29]. In this paper, the theoretical advances in the across-scale self-healing mechanisms for the radiation damage in NC W are reviewed. It is concentrated on the fundamental defect-GB interaction mechanisms mainly involving the segregation, diffusion, and recombination of defects near the GB. The working conditions for the processes at atomic and macro-scopic scales are analyzed. The effects of hydrogen/helium and transmutation alloying elements on the healing process are briefly discussed. The remaining scientific issues as well as the simulation techniques needed for modeling radiation damage accumulation are proposed.

2 Theoretical results on the interactions of radiation with GBs in W

Figure 1 illustrates the possible three interaction types of radiation with GBs in W (types I, II, III). Although a com-plete interplay picture involves the defect behavior not only near the GB [14, 17–29] but also in the bulk [30–34] or near

the surface [35–38], the focus in the present paper is on the former one. Type I is relevant to defect production near the GB [14, 17–21]. High-energy particles, such as neutrons, ions and electrons can displace the atoms from their normal lattice sites. Depending on the type of the incident energetic particles, the primary radiation structure differs, which may affect the initial defect distribution and further defect-GB interactions. A high-energy electron only produces isolated SIA-V pairs. As a high-energy neutron/ion passes through the material, it creates the primary knock-on atom (PKA). This atom further transfers its energy to the surrounding atoms, and consequently induces the displacement of some of them, which in turn causes a displacement cascade. Due to the existence of GBs, the morphology and development of the cascade are different to those in the bulk [30–33, 35]. The cascade could also directly affect the GB’s structure, energy and mobility. Type II is related to the defect behav-ior near the GB [14, 20, 22–28]. The stable defects formed after the annealing of the cascade interact with the GB via complex processes of segregation, annihilation, clustering, diffusion, dissociation, and emission from the GB. Research-ers proposed several self-healing mechanisms involving individual or multiple parts of these processes in W [14, 20, 22–28]. These mechanisms include GB-accelerated V/SIA migration and SIA-V recombination [14, 20, 22–28], interstitial-emission (IE) induced annihilation [24, 27, 28], coupling of the V approaching to the GB with the interstitial motion within the GB (CVI) [27], and interstitial reflection (IR) by the locally dense GB region [27]. In addition, the defects trapped at the GB also modify the GB’s kinetics (type III), leading to other self-healing mechanisms, such as the GB-motion induced trapping of bulk V-clusters [29].

2.1 Defect production near the GB in W at the time scale of nano‑seconds

Generally, molecular dynamics (MD) simulations are per-formed to explore the primary radiation damage in NC W. Although the simulation results may depend on the intera-tomic potential used, the accurate first-principles method could not be adopted considering the small size of the calcu-lation cell with one hundred of atoms. The simulation model is either a poly-crystalline structure containing several GBs or a bi-crystal GB. Depending on the PKA energy, the num-ber of atoms in the model varies from several thousands to millions. One atom in the calculation cell was chosen as a PKA and given of a certain kinetic energy with the velocity along a specific direction. Then, the system was relaxed at a certain ensemble for typical hundreds of picoseconds (ps). Several researchers performed MD simulations of the cas-cade near W GBs [18–21]. The potential used, PKA energy, temperature, PKA distance to the GB, and the GB type are varied. Park et al. [18] performed the cascade simulation in

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a W poly-crystalline structure at 1000 K. The potential for W they used is the many-body Finnis-Sinclair (FS)-type intera-tomic potential splined to the universal short-range Ziegler-Biersack-Littmark (ZBL) potential. Therefore, the potential is suitable for cascades simulation. The PKA of 100 keV was imposed along the ⟨1 3 5⟩ direction. They found that the SIA number in the single-crystalline W decays much faster than that in the NC W. The number of residual SIAs surviving in NC W is twice that in the single-crystal W after cooling down of the cascade. They observed the movement of the SIAs towards the GB. It was concluded that the attraction of the SIAs by the GB hinders the migration of the SIAs towards the GB, consequently reducing the SIA-V annihila-tion rate in the inner part of the cascade. Zhang et al. [19] constructed several bi-crystal structures including three tilt symmetric GBs of Σ5(3 1 0)/[0 0 1] (1/Σ represents the den-sity of the coincidence sites), Σ21(1 4 2)/[2 1 1], Σ85(9 2 0)/[0 0 1] and two twist GBs of Σ5[0 0 1] and Σ85[0 0 1]. They conducted MD simulations of cascades in the five bi-crystal

structures as well as the single crystal in W. The potential they employed is the FS type Derlet-Nguyen-Manh-Dudarev (DNMD) W potential, which was modified to smoothly con-nect the short-range ZBL potential. The potential not only reproduces the experimentally measured W defect thresh-old energies but also gives correct point defect configura-tions. The PKA imposed along the direction normal to the GB plane were given the kinetic energy of 10 and 20 keV respectively, with different distances from the GB plane. The simulation temperature was set at 4.2, 300 and 900 K. The number of residual SIAs in the NC W is much higher than that in the single-crystal W (Fig. 2a). The biased absorption of SIAs by the GB compared to the Vs was observed, finding the sensitivity of the defect production to the PKA distance from the GB (Fig. 2b, c). The small overlap of the cascade with the GB leads to the small size of the V-clusters. Mean-while, the mean SIAn size is smaller. It was also found that temperature affected the number of SIAs produced, whereas the number of Vs weakly depended on temperature. Such

Fig. 1 Schematic illustration of the possible interplay mechanisms of the radiation with the GB. Here, T denotes temperature, τ represents dose rate, rd is for radiation dose, and L is for grain size. The SIAn is indicated by the red sphere and the light green square denotes the Vn. The processes are mainly divided into three categories based on the involved defects’ objects. In category I, the atomic process 0 is the cascade, which initiates the production of defects (SIAn1, Vm1). In category II, the atomic processes include annihilation of the SIA-cluster (SIAm3) with a V-cluster (Vm3) in the bulk (process 1), near the GB (SIAn4-Vm3 in process 2 and SIAn3-Vm4 in process 2′), within the GB (SIAn4-Vm4 in process 3), the segregation of a SIAn3 (process 4) and Vm4 (process 5), clustering of the V/SIA in the bulk (SIAn2-SIAn3 in process 6 and Vm2-Vm3 in process 7), within the GB

(SIAn4-SIAn5 in process 8 and Vm4-Vm5 in process 9), the migration of a SIAn4/Vm4 out of the GB (processes 4′/5′), the dissociation of a bulk SIAn3/Vm3 (processes 6′/7′), the dissociation of a GB-trapped SIAn4/Vm4 (processes 8′/9′), the reflection of a SIAn3 by the locally dense GB region (process 10). In category III, process 11 denotes the defect-GB interaction process relevant to GB motion. EGB is the GB energy and MGB is the GB’s migration mobility. The curved black arrow illustrates possible coupling between the two processes, e.g. processes 3 and 5. The energetic and kinetic parameters charactering these atomic processes include binding energy (Eb), migration energy barrier (Em), and annihilation energy barrier (Eann). R denotes the interaction range of two defects

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temperature effect could be attributed to the intrinsic dif-ference in the mobility of the SIA and V in W: the SIA has an exceptional low migration energy barrier. Using the bond-order potential (BOP), Li et al. [20] performed similar simulations of the displacement cascades in the vicinity of a W symmetric tilt GB of Ʃ5(3 1 0)/[0 0 1] at 600 K. Note that, the potential was designed to simulate high-energy col-lisions. The PKA was located at a site of 3.5 nm normal to the GB initiated with 6 keV of kinetic energy and its veloc-ity was perpendicular to the GB. It was observed the SIA moved towards the GB during the simulation, while the V remained static during the subsequent simulations at 600 K (Fig. 3). Consequently, on the MD timescale, SIAs were collected at the GB, while the Vs became enriched near the GB. Also the extension of the GB region due to the trapping of the SIAs at the GB was observed. Li et al. [21] used the second nearest-neighbor modified embedded atom method (2NN-MEAM) potential coupled with the ZBL potential at

short-range conducted MD simulations of the interaction of irradiation-induced point defects with six symmetric tilt GBs of Ʃ5(2 1 0)/[0 0 1], Ʃ5(3 1 0)/[0 0 1], Ʃ5(5 1 0)/[0 0 1], Ʃ13(3 2 0)/[0 0 1], Ʃ17(4 1 0)/[0 0 1] and Ʃ17(5 3 0)/[0 0 1]. The PKA energy was assigned to be 3 and 5 keV respec-tively, and the simulated temperature was set at 300 K. The direction of the PKA is also normal to the GB. In addition to the biased absorption of the SIA over V and the extension of the GB possibly by the segregated SIAs at the GB, they proposed that the recombination of the V with SIA and the SIA migration towards the GB accounted for the reduction in the number of point defects near the GB in the primary radiation damage. The number of residual defects is related to the overlap degree of the peak defect zone of the cascade with the GB. The distribution of SIAs is relatively uniform nearby the GB, and the PKA energy mainly affects the V distribution near the GB.

Fig. 2 a Variation of the number of defects with time in the sin-gle crystal system (I-Total-si) and near the GB of Σ5(3 1 0)/[0 0 1] (I-Total-bi). For comparison, the results of a bulk PKA far away from the GB are also shown. Here, bulk V/SIA number is denoted

by V-Bulk-bi/ I-Bulk-bi. The PKA-GB distance is ~ 4.0 nm. The num-ber of vacancies of b Vs and c SIAs near the GB after annealing for 80 ps. In a–c, the PKA energy is 10 keV and temperature is 300 K. Reproduced with permission from Ref. [19]. Copyright 2015 Elsevier

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2.2 Energetics and kinetics of the V and SIA near a pristine W GB

The MD simulation results on the primary radiation dam-age in the neighboring region of the GB reveal the defects structure on a time scale of nano-seconds. To show whether the defects near the GB have a thermodynamic tendency to segregate to the GB (processes 4/4′ and 5/5′ in Fig. 1), researchers conducted molecular statics (MS) calculations of energetic properties of the V/SIA in a certain range of the GB at 0 K [20, 22–28]. To do this, one removes or inserts an atom near the GB, and then relaxes the GB structure using an energy-minimization method, e.g. descent steepest method. Comparing the total energy of the system with and without a V/SIA, one could obtain the formation energy of defects, segregation energy or V/SIA-GB binding energy (bulk defect formation energy minus that for the defect at the GB), defect-GB interaction length scale and meanwhile the stable configuration at the GB. Using the BOP, Li et al. [20] investigated the V/SIA energetic feature near the symmetric tilt GB of Σ5(3 1 0)/[0 0 1] in W (Fig. 4a, b). The potential gives correct stable SIA/V configurations, formation ener-gies and migration energy barriers in bulk W. They found that it was always an endothermic process for the formation of both the V and SIA near the GB. The formation energy of defects shows a reduced trend as the defects move from

the grain interior to the GB, which suggests an energetic condition for a V/SIA to reside at the GB core from the grain interior. There is also an obvious difference in the defect-GB interaction range and binding strength for the SIA and V relevant to the GB character. After the V/SIA residing at the GB core, the V formation energy decreases by only 0.86 eV, whereas the SIA formation energy reduces by as much as 7.5 eV. The V/SIA-GB interaction range is ~ 0.94/2.65 nm in the GB of Σ5(3 1 0)/[0 0 1]. In the other GBs of Σ13(3 2 0)/[0 0 1] and Σ25(4 3 0)/[0 0 1], the GB interaction range for Vs (SIAs) is 0.95, 1.44 nm (1.96, 1.85 nm), and the segrega-tion energy is 1.75 and 2.00 eV (7.8 and 7.9 eV). Using the embedded atom method (EAM) potential, Li et al. [20] also performed the MS calculations of SIA energetics in a total of 46 symmetric tilt GBs with the tilt axis of [0 0 1] give the SIA segregation energy of 7–9.5 eV. Results calculated using a first-principles method (Fig. 4c, d) in Σ5(3 1 0)/[0 0 1] by Chai et al. [23] suggest that the V formation energy reduces by only 1.53 eV, compared to the larger reduction of 6.6 eV for the SIA formation energy. The interaction range for the V/SIA is 0.84/1.24 nm. Despite the difference in the absolute values of the segregation energy and interaction range calculated by the MS and first-principles methods, the two approaches both give much larger segregation energy and interaction range for the SIA with the GB than that for the V. MS calculations of the interaction of the V/SIA with a low-angle GB of Ʃ85(7 6 0)/[0 0 1] with a misorienta-tion angle of 8.8° performed by Niu et al. [24] arrive at a similar conclusion, although the V/SIA-GB interaction range (2.4/5.8 nm) is much larger in the low-angle GB than that in high-angle GBs; the V/SIA segregation energy is 1.94/7.7 eV. By employing an improved many-body semi-empirical W potential, Chen et al. [25] systematically inves-tigated the V segregation energetics to a series of [1 0 0] symmetric tilt GBs in W. The potential well reproduces the bulk V formation energies comparable to the values given by first-principles calculations. It was found that the low-angle GBs have wider interaction range values compared to high-angle GBs (Fig. 5). The V-GB interaction range varying from 1 to 3 nm is associated with the GB character. For the low-angle GBs, the minimal V segregation energy is inde-pendent of the GB energy, while the V-GB binding energy varies from 0.76 to 2.61 eV for the high-angle GBs (Fig. 5a). Both the mean segregation energy and the interaction range length scale exhibit a negative correlation to the GB energy (Fig. 5b). These results suggest that the GB with high energy may have a strong capacity for absorbing defects. The radi-ation-damaged GB could act as a more efficient sink for defects than pure GB. He et al. [26] performed first-prin-ciples calculations of the V/SIA energetics near eight sym-metric tilt GBs in W, finding that the ability of a pure GB to absorb Vs increases with the GB energy increasing, and the capability of trapping SIAs (defined as the SIA segregation

Fig. 3 Several typical snapshots of MD simulation of the cascade near W GB of Σ5(3 1 0)/[0 0 1] at 600 K. Axes X and Y are along [3 1 0] and [1 3 0], respectively. Reproduced with permission from Ref. [20]. Copyright 2013 International Atomic Energy Agency (IAEA)

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energy) linearly increases with the excess volume of GB. The twin boundary has a limited capacity for absorbing the V. These energetic calculations of the V/SIA near the GB evidence the preferential absorption of the SIA over the V by the GB. These results contribute to the construction of the fundamental defect-GB interaction picture, such as the for-mation of a low defect formation energy region near the GB.

In addition to the thermodynamic driving force revealed by the MS calculations, researchers calculated the V/SIA migration kinetics near the GB (processes 4/4′ and 5/5′ in Fig. 1) [22, 24, 27, 28]. The initial migration path was con-structed by a linear interpolation method, producing the intermediate states between the initial and final states. The path was then relaxed using the nudged elastic band (NEB) method [39]. After the procedure, one could obtain the mini-mal energy path for the V/SIA migration near the GB. Mean-while, the migration energy barrier was also obtained. By analyzing the atom displacements along the migration path,

one could also gain the dynamics of the defects’ motion. Li et al. [20] calculated the V/SIA migration energy barriers near Σ5(3 1 0)/[0 0 1] (Fig. 6a, b). Their results suggest that the V migration energy barrier near the GB is reduced compared to that in the bulk, indicating the GB-accelerated diffusion of the V. The average barrier of V migration near the GB is (0.98 eV) much lower than the bulk value (1.8 eV). Particularly, the SIA is trapped by the GB spontaneously within a certain range of the GB. Calculations of the V dif-fusion near Σ85(7 6 0)/[0 0 1] by Niu et al. [24] also suggest that both the V formation energy and migration energy bar-rier are reduced as the V comes close to the dislocation core at the GB. Therefore, it becomes kinetically easier for Vs and SIAs to migrate towards the GB from the grain interior with the smaller defect migration barrier near the GB as the kinetic driving force. These kinetic calculations reveal the formation of a low energy barrier region for defects migra-tion near the GB.

Fig. 4 Variation of the V/SIA formation energy with the initial V/SIA distance from the GB of Σ5(3 1 0)/[0 0 1] in W for a Vs and b SIAs, respectively. Reproduced with permission from Ref. [20] . Copyright

2013 IAEA. c and d Corresponding results calculated using a first-principles method. Reproduced with permission from Ref. [23]. Cop-yright 2017 Elsevier

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2.3 Static interaction of the V with GB‑trapped SIAs near the W GB

Considering the typical primary damage state of the GB featured by the SIA localized at the GB and V enriched near the GB (Fig. 3), researchers investigated the energetics and kinetics of the V near the SIAs enriched at the GB (process 2 in Fig. 1) [20, 22, 24, 27, 28], as shown in Fig. 6c–f. Com-pared with the V properties near a pure GB (Figs. 4, 6a, b), the GB absorbing SIAs exhibits noticeable features as the further reduced formation energy, extended interaction range and reduced migration energy barrier for the V in the vicinity of the GB. Comparing results in Fig. 6c, d with those in Fig. 4a and c for the V near a pure GB, one could see that the V formation energy is substantially reduced. Meanwhile, the V-GB interaction range also extends. For instance, the range is only 0.94 nm in the pristine GB, while it is as large as 1.92 nm after the GB is artificially loaded with eight SIAs. Another striking feature is that the V for-mation energy at certain sites surrounding the SIA trapped at the GB becomes negative. It suggests the release of the system energy as a V is created at one of these sites. Such feature was originally observed near the Cu GB [40] and

also observed in a low-angle W GB of Σ85(7 6 0)/[0 0 1] [24]. Li et al. [20] examined the atom displacements before and after the relaxation of the GB with such a SIA-V pair, finding that the V actually spontaneously recombined with a SIA after the relaxation (in some cases, the delocalization of the V also leads to the negative value of V formation energy [24]). Therefore, a spontaneous annihilation region (SAR) is formed surrounding the SIAs stored at the GB. Such region also exists around the SIA-cluster residing within the GB [27] (Fig. 7a) or around a bulk SIA [20, 24, 34].

The MS calculations of the V migration kinetics near the SAR suggest that, after the SIAs are collected at the GB, the V migration energy barrier near the GB is further reduced (Fig. 6e, f) compared to that near a pure GB (Fig. 6a, b). For example, calculations by Li et al. [20] suggest that a V over-comes a series of low-energy barriers of 1.8, 1.1, 0.74 and 0.34 eV to recombine with a SIA trapped at the GB (Fig. 6f), while the V overcomes 1.8, 1.6, 1.6 and 0.42 eV sequentially to arrive at the GB and get trapped therein (Fig. 6b). The MS calculations show that the annihilation energy barriers for the V located at the first and second neighbors of the SAR are also reduced (Fig. 7b). These calculations reveal the atomic picture that an annihilation region with a low energy barrier forms near the GB collecting SIAs.

2.4 Interstitial emission induced annihilation near the GB

The IE mechanism was originally proposed in Cu GBs to explain the SIA-V annihilation near the GB [40, 41]. Other researchers examined the applicability of the mechanism to the recombination of defects in W [20, 22, 27, 28] and Fe NCs [42–44]. It was demonstrated that the SIA-V annihila-tion near GBs could proceed via a low energy barrier pro-cess (Figs. 6, 7); however, whether the IE works universally and the associated kinetic condition and the atomic detail of the IE are not clear. MS calculations suggest that a SIA at W GB is over 7.5 eV lower than the energy for the SIA in bulk W [20]. It is expected that the SIA, once bound to the GB, is impossible to re-migrate out of the W GB, apart from the direct interaction of the SIA with a nearby V. By connecting the initial position to the final location of each atom involved in the recombination, Li et al. [20] found that the SIA trapped at the W GB recombined with the V nearby via a ⟨1 1 1⟩ replacement process (Fig. 8a). In the cases of the SIA-V recombination induced by the V movement to its second nearest neighbor, the atomic sequence is mixed with ones along ⟨1 0 0⟩ direction. They also monitored the atom displacements during the annihilation, finding the collective motion of multiple atoms with a low energy barrier involved in the SIA-V recombination process (Fig. 8b–d). The con-certed nature of the annihilation is well manifested by the correlated atom displacements curves (Fig. 8c).

Fig. 5 Correlation of the a minimum V segregation energy and b mean V segregation energy on GB energy for a series of W [1 0 0] symmetric tilt GBs. Note that, in b the V length scale is defined as the half of the V-GB interaction range. Here the segregation energy is defined as the V formation energy at the GB minus that for a bulk V. Reproduced with permission from Ref. [25]. Copyright 2016 Springer-Nature

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To explore the kinetic condition of the IE in nano-struc-tured metals with distinct levels of the SIA-sink binding energies, Li et al. [28] proposed a MS method for calcu-lating the SIA-V annihilation energy barriers near a defect sink (process 2) in nano-structured metals (Fig. 9). They took advantage of the SIA segregation path near the GB/sur-face. The reversed path was constructed to be the initial SIA emission path, followed by the relaxation of the path with a V nearby using the NEB method. During the construction of the SIA-V recombination path, the picture of the SIA emission was embedded in the method (the emission degree could be adjusted by the emission degree parameter α in Fig. 9); thus the obtained annihilation is naturally to be via the SIA emission if the NEB relaxation does not change the annihilation mechanism. Their calculations in several GB/surface systems reveal the existence of multiple annihila-tion paths with low energy barriers (Fig. 10). Nevertheless, depending on the sites of the V located, the real annihilation mechanism could be the direct IE or the coupled V-hop with the IE. In some cases, the GB migration accompanied the annihilation.

The cumulative distribution of the number of annihilation sites was further calculated as a function of α (Fig. 9). It was found that the size of the annihilation region increased with

the increasing of the α (Fig. 11a, b), and therefore proposed the annihilation picture as the partial emission of the SIA from the sink induced the propagation or extension of the annihilation region around a SIA at the sink. Such picture was found to work in several other investigated GB/surface systems and exhibited the possibility of the universal fea-ture. The calculations of the frequency distribution of the annihilation energy barrier indicate that, as parameter α increases, the annihilation energy barrier shifts to a high value. It implies that the favorable kinetic condition for the annihilation is sacrificed to a certain extend to promote the increasing in the annihilation region.

To qualitatively understand the IE behavior near the GB/surface, Li et al. [28] further approximated the SIA poten-tial well near a sink as a triangle potential well (Fig. 11c, d), and recognized that the real SIA potential well near a sink has two dimensions. One is the depth of the potential well defined as the SIA-sink binding energy; the other is the well width as the SIA-sink interaction range. Different to the normal consideration of the binding energy as an indica-tor of the difficulty of the SIA emission from the sink, the restraining force for the IE from a sink was defined as the ratio of the SIA-sink binding energy to the potential well half-width. By definition, the ratio is actually the slope of

Fig. 6 a and b Kinetics of the V and SIA near the pristine W GB of Σ5(3 1 0)/[0 0 1]. a V and SIA migration energy barrier profiles near the GB; b one representative path for V migration into the GB from the grain interior. c and d Variation of the V formation energy near the SIA-loaded GB. c Profiles of V migration and annihilation energy barriers near a SIA-loaded GB; d one typical SIA-V annihilation

path near the GB. Axes X and Y are along [3 1 0] and [1 3 0], respec-tively. e Migration and annihilation energy barriers as a function of the V-GB distance. f Energy and structure variation during the V-SIA annihilation along a typical path. Reproduced with permission from Ref. [20]. Copyright 2013 IAEA

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the triangle potential well. It is also the average energy bar-rier that a SIA overcomes as migrating over a unit length of the distance away from the GB/surface. The emission-annihilation energy barrier is much lower than the SIA-sink binding energy.

2.5 SIA‑V annihilation induced by the coupled motion of the SIA movement along the GB with the V migration towards the GB

The above IE process is a static picture that does not involve the SIA motion along the GB. Such picture applies to the annihilation near the GB within which the SIA migration energy barrier is higher than that for the bulk V migration, e.g. in GBs of Σ25 and Σ85 (Fig. 12a). As stated above, the GB preferentially absorbs SIAs over Vs. Besides, the SIA migration energy barrier along the GB is smaller than that for the bulk V migration except in GBs of Σ25 and Σ85 (Fig. 12a). It implies that the SIA could move along the GB after segregation. Meanwhile, an annihila-tion region with a low energy barrier is formed around the SIAs collected at the GB. Therefore, as the SIA quickly migrates within the GB, the annihilation region around the

SIA extending to the bulk region nearby the GB simultane-ously scans along the GB. The V that enters the region via slow migration towards the GB would be recombined with the SIA via the IE. The dynamic picture includes three elements including the low-energy barrier annihilation region, the quick SIA motion along the GB and the slow motion of the V to approach the GB. Such dynamic anni-hilation picture was originally proposed near α-iron GBs by Li et al. [43] based on the results of MS, MD and object kinetic Monte Carlo (OKMC) simulations on the V/SIA diffusion and annihilation behavior. Via the concerted pro-cess of the SIA diffusion along the GB and the V migra-tion towards the GB (processes 3 and 5), the SIA trapped at the GB does not have to be directly re-emitted from the GB to recombine the V nearby. The mechanism was recently extended to the SIA-V annihilation near W GBs [27]. The picture was confirmed by MD simulations of the SIA-V pair behavior at 1000 K (Fig. 12b) and OKMC simulations of the SIA trajectories in a W GB (Fig. 12c). As for the GB with a high SIA migration energy barrier along the GB, the SIA is actually immobile within the GB plane after its segregation. Its annihilation with the V near the GB is via the direct encountering of the V with the SIA

Fig. 7 a Formation energy and migration energy barriers of the V near a GB with a SIAn (n = 1, 2, 6) trapped at the GB of Σ5(3 1 0)/[0 0 1]. The sites with a negative V formation energy ( Ef

V ) are enclosed

by the dashed red line. b Distribution of the migration and annihi-lation energy barriers (Ea) of a V near the SIAn trapped at the GB

of Σ5(3 1 0)/[0 0 1]. The symbols FNSAR, SNSAR, SIE and AIE are short for the first-nearest neighbor of the region, second-nearest neighbor of the region, spontaneous interstitial emission and activated interstitial emission, respectively. Reproduced with permission from Ref. [27]. Copyright 2017 IAEA

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(IE in Fig. 12d) or via the V motion within the GB after the V segregation at the GB.

Li et al. [27] also found that in some GBs, e.g. Σ5(2 1 0)/[0 0 1] and Σ5(3 1 0)/[0 0 1], the SIA migration energy is significantly lower than the migration barrier of bulk V, while the barrier for the SIA2 is reduced and comparable to that for bulk V migration. Meanwhile, the SIA has large positive SIA-SIA binding energy at the GB. Therefore, in these GBs, the SIA firstly diffuses within the GB plane after segregation and then gets clustered. As the clustered SIAs have a comparable mobility to that for the V nearby the GB, the annihilation is via their coupled motion (Fig. 12d).

2.6 Interstitial reflection‑induced annihilation near the GB

By combining the MD, MS and OKMC methods, Li et al. [27] investigated the SIAn behavior near W GBs of Σ5(2 1 0), Σ5(3 1 0), Σ13(3 2 0), Σ25(4 3 0), Σ85(7 6 0), and Σ113(8 7 0) with a common axis of [0 0 1]. They revealed the dependence of the SIAn behavior on the local structural feature of the GB. The MD simulations suggest that the local GB region with a low atomic density always traps the single SIA and SIA-cluster via a replacement process (Fig. 13a, c). The segregation details depend on the cluster size n. The

Fig. 8 a V annihilation process with a SIA in the SIAn (n = 1, 2, 6) at the GB Σ5(3 1 0)/[0 0 1]. Reproduced with permission from Ref. [27]. Copyright 2017 IAEA. b Energy variation during the annihila-tion; c normalized atomic displacements (d) for the atoms involved in

the recombination; d schematic illustration of the SIA-V recombina-tion process. Axes X and Y are along [3 1 0] and [1 3 0], respectively. Reproduced with permission from Ref. [20]. Copyright 2013 IAEA

Fig. 9 Schematic illustration of the SIA-V recombination near the GB/surface induced by the mechanisms of the V-hop or SIA emis-sion. The black curves represent the migration energy barrier curves for an isolated V/SIA. The dash blue curve denotes the potential well of an SIA-V pair. The V and SIA is represented by a red cubic and green sphere, respectively. Here, symbols Em1 and Em2 denotes the SIA-V recombination energy barriers via the processes of the IE and V-hop, respectively. S1 and S2 mark the system states as the SIA is located at the sink and in the vicinity of the sink, respectively. S3 and S4 represent the intermediate state lying between S1 and S2 and the system state after SIA-V recombination, respectively. The low-energy barrier annihilation region formed around a static SIA and partially emitted SIA from the sink is correspondingly represented by the red and pink spheres. Parameters α and ß characterize the emission degree of the SIA and V from potential well correspondingly. Repro-duced with permission from Ref. [28]. Copyright 2018 Elsevier

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single SIA approaches to the GB along ⟨1 1 1⟩ direction, while the SIA-cluster moves through the relative sliding of the SIA within the cluster before getting trapped by the GB. In some cases, the SIA-cluster is dissociated into the GB, while the remaining parts segregate into the vacant structural units nearby in most cases. In certain cases, it’s observed that the remaining SIAs of the SIA-cluster occasionally move away from the GB along the original ⟨1 1 1⟩ direc-tion after parts of the vacant sites at the loose GB region are occupied by the SIAs (Fig. 13b–d). Such motion of the SIAn was termed as the interstitial reflection (IR). They fur-ther demonstrated that the locally loose region has a limited capacity for absorbing the SIA, and consequently could not

accommodate excess SIAs, as evidenced by the frequently observed reflection of the newly created SIAn near the GB by the GB that is artificially loaded with the SIAn. Particu-larly, near the locally dense GB region, e.g. the region lying between the dislocation core of a small-angle GB, the SIAn was always observed to be reflected by the GB (Fig. 13e).

Li et al. [27] built the correlation of the SIAn segrega-tion/reflection behavior with the local GB structure feature by calculating the kinetics of the SIA near several local GB structures. They divided the SIA-GB interactions into three groups of I, II and III, based on the SIA configuration and kinetics near the GB (Fig. 14). The SIA of each type has a unique energy landscape. The SIA of type I resides at

Fig. 10 a Several typical paths for the SIA-V recombination induced by the IE near W GB of Σ5(2 1 0)/[0 0 1]. The SIA at the GB is shown by a large light green sphere. b Energy variation curves along

the annihilation reaction coordinate. c–j Several snapshots for SIA-V recombination near the GB. Reproduced with permission from Ref. [28]. Copyright 2018 Elsevier

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the locally vacant space; the SIA of type II is located at an interstitial site at the GB, while the SIA of type III cannot come close to the GB core with a locally dense region. Near this region, the SIA energy landscape first increases and then decreases, different to the decreasing trend for the SIA energy landscape near the region with a low atomic density. The OKMC evaluation of the annihilation efficiency sug-gests that the SIAn reflection by the GB enhances the bulk annihilation of the bulk (Fig. 15). OKMC simulations of the SIA trajectories near the GB reveal the dynamic picture for the SIA-V recombination near the different GB regions with distinct structural features at a macroscopic time-scale. By constructing two types of the SIA energy landscapes (one exhibits an increasing-decreasing trend with the SIA approaching to the GB; the other one just increases), they repeatedly observed the approaching-reflection of the SIA. Consequently, the SIA has a large probability to recombine with a bulk V before segregating to the sink.

2.7 Absorption of V‑clusters induced by the migrating of GB

With the radiation-defects segregating to the GB, the GB’s mobility is changed [29, 45]. Consequently, the GB motion

may occur during the defect-GB interaction. Wang et al. [45] found that the critical shear stress required for activating the GB’s migration was significantly reduced by either dis-placement cascade nearby or absorption of defect clusters in iron. Using an EAM potential for W, Borovikov et al. [29] investigated the interaction mechanism of the vacancy-type defects, e.g. void with the GB under the fusion condition of high mechanical stress in W. They constructed twelve symmetric-tilt W GBs of Σ5(0 1 2)/[1 0 0], Σ5(0 1 3)/[1 0 0], Σ13(0 1 5)/[1 0 0], Σ17(0 1 4)/[1 0 0], Σ9(2 2 1)/[1 1 0], Σ9(1 1 4)/[1 1 0], Σ13(0 2 3)/[1 0 0], Σ29(0 2 5)/[1 0 0], Σ11(1 1 3)/[1 1 0], Σ37(0 1 6)/[1 0 0], Σ25(0 1 7)/[1 0 0], and Σ65(0 1 8)/[1 0 0], along with six asymmetric general GBs of ( 2 0 4)[2 3 1]/(4 0 4)[3 2 3], ( 3 1 0)[1 3 2]/(5 1 1)[0 6 6], (3 1 0)[1 3 2]/(5 2 1)/[0 3 6], (4 2 0)[2 4 2]/(5 0 1)[1 4 5], (4 2 0)[1 2 5]/(6 3 0)[1 2 1], and (5 5 0)[1 1 7]/(2 2 1)[1 2 2]. After loading a fraction of SIAs into the GB, the system was aged at 1000 K for 0.1 ns. Then, the system was driven by applying a velocity to the atoms in the uppermost region, while the other atoms were set to be free. It was observed three distinct effects of the SIA loading on the GBs, includ-ing reduction of the sliding-friction force, activation of the GB coupled motion and the switch of the direction of the coupled motion. Furthermore, the general asymmetric GBs

Fig. 11 a Schematic illustration for the partial SIA emission induced propagation/extension of the low-energy barrier recombination region surrounding a SIA at Cu (1 0 0) surface. Here, Em1 and Em2 are the same as that in Fig.  9. b Frequency distribution of the annihilation

path number on the energy barrier; c restraining force for the IE in several GB/surface systems of W, Fe and Cu; d schematic illustration of the triangle SIA potential well at the sink. Reproduced with per-mission from Ref. [28]. Copyright 2018 Elsevier

27Interaction of radiation-induced defects with tungsten grain boundaries at across scales:…

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have low stress thresholds for coupled motion. It was fur-ther observed that as the GB passed through the material, it could sweep up the defects, such as voids and Vs on its way (Fig. 16). They therefore proposed that the stress-induced coupled motion of the GBs (process 11 in Fig. 1) in W acted as the possible radiation-damage healing mechanism.

2.8 Effects of the H/He and alloying elements on the healing process for radiation damage

In the above sections, the interaction of the displacement defects with the W GBs was mainly reviewed (Fig. 1). Nev-ertheless, in addition to these defects (SIAn and Vn), high concentrations of H/He as well as alloying elements, e.g. rhenium (Re) and osmium (Os) are all produced under the real irradiation conditions. These elements can significantly affect the microstructure evolution of defects and complicate

the defect-GB interaction processes/mechanisms described here [46–55].

First-principles calculations by Zhou et al. [46] suggest that it is energetically and kinetically favorable for the W GB of Σ5(3 1 0)/[0 0 1] to trap H coming from the bulk. The H-GB binding energy is as much as 1.11 eV, while the migration barrier of 0.13–0.16 eV is very low near the GB. In addition, H could also bind with the bulk SIAn prior to its segregation to the GB with the SIA-H binding energy (~ 0.43  eV [47]) as the energetic driving force. Conse-quently, the segregation of the SIAn may be suppressed to a certain extent by H, which may enhance the annihilation of bulk SIAn–V. H/He also prefers to bind with the V and small Vn to form stable complexes [48], which may hinder the segregation of the V. Furthermore, the interplay among the SIAn and H/He as well as the V within the GB can inevitably affect the healing efficiency of the mechanism reviewed in the present paper. Panizo-Laiz et al. [51] studied the effect

Fig. 12 a Energy barriers (Ea) for the single SIA and SIA2 migration along the GBs and SIA-SIA binding energy (Eb) at different GBs; b SIA-V recombination process near the GB via the SIA migration within the GB and the IE revealed by the MD simulations at 1000 K. Here, the SIA and V are respectively denoted by the green sphere and red filled square. The spontaneous recombination region surrounding the SIA is enclosed by the dashed pink circle. c Typical SIA trajec-

tories near the GB at 10,563 and 850 K drawn from OKMC simula-tions; d schematic illustration of the SIA-V annihilation picture near the GB. The red cubic is for a V, while the green sphere denotes a SIA. The red sphere around a SIA represents the low energy barrier annihilation region. Here processes 2, 3 and 5 are identical to that in Fig. 1. Reproduced with permission from Ref. [27]. Copyright 2017 IAEA

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of the GBs on the V and H behavior in W with different grain sizes by performing experiments and OKMC simula-tions. Their results suggest that the number of Vs in NC W is larger than that in single crystalline W in the studied range of 300–573 K, while only when the temperature is high enough, e.g. over 573 K, the number of Vs is reduced in samples with a large density of GBs. Their results also suggest that H migrates more effectively along vacancy free GBs than along the bulk.

First principles calculations by Suzudo et al. [49] sug-gested that the stable configuration of alloying elements Re and Os solutes in W was a mixed dumbbell with a W atom that migrates three-dimensionally. The intrinsic SIA in W is a crowdion migrating one-dimensionally. The change in the SIA configuration and migration style may suppress radiation-induced swelling. Calculations by Kong et al. [50] revealed the strong binding between Re and Os with V/SIA in W. The diffusion of the radiation-created point defects especially for the SIA could be impeded by the Re/Os, enhancing the annihilation of bulk SIA-V. Meanwhile, these alloying elements would also segregate to the GB,

consequently modifying the local GB environment [55]. Using a first-principles method, Zhang et al. [55] investi-gated the segregation of Re and its effect on the mechanical properties of a W GB of Ʃ5(3 1 0)/[0 0 1]. It was found that the energy of the single Re atom in the bulk is 0.57 eV higher than at the GB. It is therefore energetically favorable for Re atoms to segregate to the GB coming from the grain interior. Multiple Re atoms at the GB form distinct planar structures. One could speculate that the GB decorated by the alloying elements has different V/SIA properties from that near a pure GB.

2.9 Effect of radiation‑defects on the GB structure

Under cumulative radiation, amounts of defects segregate to the GBs where defects have low formation energy. Research-ers investigated the effect of the radiation defects at the GB on the GB structure [56–59]. In face-centered cubic metals of poly-crystallines Cu, Ag, Au and Ni, it is shown that the absorption of point Vs/SIAs can strongly modify the GB structure, inducing structural transformations of the GB.

Fig. 13 Typical snapshots of the SIA-cluster segregation and reflec-tion near the GBs of Σ5(3 1 0)/[0 0 1] and Σ113(8 7 0)/[0 0 1] loaded with a certain number of SIAs from MD simulations at 300 K within one nano-second. In a and b, axes X and Y are along [1 3 0] and [3

1 0] directions, respectively for Ʃ5(3 1 0)/[0 0 1], while for Ʃ113(8 7 0)/[0 0 1] in c–e, they are respectively along [7 8 0] and [8 7 0] direc-tions. Reproduced with permission from Ref. [27]. Copyright 2017 IAEA

29Interaction of radiation-induced defects with tungsten grain boundaries at across scales:…

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The presence of multiple metastable GB phases greatly enhances the capacity of the GB for absorbing radiation defects. Quite recently, Frolov et al. [56] investigated the phase transitions of W [1 0 0] and [1 1 0] symmetric tilt GBs using the Universal Structure Predictor Evolutionary Xtal-lography (USPEX) structure prediction code and atomistic simulations, and observed the similar first-order GB phase

transitions to that in Cu. The effect of the GB structural mul-tiplicity on the mechanisms of V/SIA absorption was further investigated. They revealed a two-step nucleation process: the point defects were absorbed through the formation of a meta-stable GB structure, followed by the transformation of this structure to a GB interstitial loop or a different GB phase.

Fig. 14 a–d SIA energy landscapes near several symmetric tilt GBs of Σ5(2 1 0), Σ13(3 2 0), Σ25(4 3 0), Σ85(7 6 0) and Σ113(8 7 0), respectively; e–i SIA migration trajectories near these W GBs. In e–i, axis X is along [1 2 0], [2 3 0], [3 4 0], [6 7 0] and [7 8 0] directions

for Σ5(2 1 0), Σ13(3 2 0), Σ25(4 3 0), Σ85(7 6 0) and Σ113(8 7 0), respectively. Correspondingly, axis Y is along [2 1 0], [3 2 0], [4 3 0], [7 6 0] and [8 7 0] directions, respectively. Reproduced with permis-sion from Ref. [27]. Copyright 2017 IAEA

Fig. 15 a and b Typical SIA trajectories near the GB with SIA energy landscapes of type I and II at 10,563 and 850 K; c SIA-V recombination fraction at 10,563 and 850 K in W for different SIA energy landscapes. Reproduced with permission from Ref. [27]. Copyright 2017 IAEA

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2.10 Theoretical results of cumulative displacement damage in NC W

To establish a quantitative relation of the simulation results to experimental observations, one has to simulate the cumu-lative radiation damage under a given experimental condi-tion using OKMC or cluster dynamics (CD). Compared to the extensive simulation work on the basic interactions of the radiation with the GB at the atomic scale, the work in this aspect is limited. Dunn et al. [60] applied spatially resolved stochastic cluster dynamics (SRSCD) to study the radiation damage (Frenkel pair implantation) accumulation in NC α-Fe near GBs at room temperature and at a dose rate of 10–7 dpa·s−1. They calculated the V accumulation in GBs, sink efficiency of GBs, and V-cluster profiles inside GBs, finding that the V/SIA-GB binding energies, V/SIA and small V-cluster diffusion along the GB affected the accu-mulation of defects greatly. However, their calculation mode only incorporated basic processes of V/SIA migration and binding in the bulk and near the GB. Furthermore, due to the lack of various defect energetics inside GBs, many of their model input parameters were treated as variables, e.g. the migration energy barriers of the single V/SIA inside GBs. Li et al. [43] built a detailed OKMC model to study the V/SIA behavior near iron GBs at long timescale and evalu-ate the contribution of the several segregation/annihilation processes to the healing radiation damage. In their model, the transitions are only considered from one stable site to another, while the transitions between two metal-stable states were neglected. The real energy landscape for the V/SIA was approximated by a squared potential well. The dif-fusion of the V/SIA inside the GB was set to be two-dimen-sional. Recently, Li et al. [27] extended the OKMC model to W GBs to study the recombination/accumulation of defects in NC W. El-Atwani et al. [9] performed KMC simulations of the damage evolution at room temperature and 1050 K to study the profile of the V at steady state near W GBs. The dose rate and grain size were set to be 1 × 10–4 dpa·s−1 and 50.6 nm, respectively. Note that, their model only contains several defect-GB interaction parameters. They found that,

at room temperature, the V concentration is slightly larger than that near the GB, while at 1050 K, the concentration decreases close to the GB. Nevertheless, the profiles in the two cases both are remarkably flat. They speculated that the SIA-V annihilation in the bulk is the dominant process, which seems to contract our intuition. OKMC simulations by El-Atwani et al. [11] suggest that the average V/SIA con-centration in the bulk decreases with the decreasing of the grain size at 1050 K, while the Cu3+ irradiation experiments at room temperature give a reverse trend [7].

3 Conclusion and outlook

In this paper, we reviewed the production of defects near the GB and interactions of the radiation-created defects with the W GB, which act as the basic elements of the self-healing mechanisms for radiation damage in W. MD simulations of the primary radiation damage near W GBs reveal the biased absorption of the SIA over V. GBs also affect the SIA and V distribution nearby themselves. However, the PKA energy is mainly restricted to several low energy values, and GB types explored are mainly some special symmetric tilt GBs. Given the recoil energy spectrum of the PKA (PKA energy is up to 100 keV), extensive studies should be conducted on the cascade for a broad PKA energy range in other general GBs. The interaction of the cascade induced by the high energy PKA with the GB should be investigated. The energetic and kinetic calculations near the GB suggest that it forms a low defect formation energy region and also a low energy bar-rier region for defects’ migration near the GB. Furthermore, the GB provides larger energetic driving force and wider interaction range for the SIA than that of the V, which could give rise to the GB’s preferential absorption of the SIA com-pared to the V. Yet, the SIA-cluster and V-cluster behaviors near the GB are rarely explored, e.g. their configurations, energetics and kinetics, and also the V/SIA energy levels near the clusters. The atomic and coarse-grained simulations of the V/SIA behaviors near the GB reveal several SIA-V annihilation mechanisms. The MS calculations suggest that

Fig. 16 Representative snap-shots of a MD simulation of the void-GB interaction under the applied stress. Reproduced with permission from Ref. [29]. Copyright 2013 IAEA

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a region for the SIA-V annihilation is formed with a low energy barrier at the GB. The partial emission of the SIA from the GB induces the propagation or extension of the annihilation region. The coupled SIA movement along the GB with the V migration near the GB could promote the SIA-V annihilation. The bulk V could recombine with the SIA reflected by the locally dense GB region. Under high mechanical stress, the coupled GB motion could lead to the absorbing of the long-lasting V-clusters and voids. These basic processes reviewed in the current paper help to under-stand the radiation-tolerance of NC W. Note that, most of the simulation results are obtained based on the empirical poten-tials, which are not developed specifically for the W GB and may only give the correct qualitative defect-GB interaction picture. As passing the interaction parameters to high level simulation techniques, one has to be careful. In the future, the energetics and kinetics of defects have to be checked by first-principles calculations.

Despite these theoretical advances, a large gap exists between the simulation results and experimental observa-tions. Until now, lots of theoretical efforts were made to explore the defect-GB interaction mechanisms. In the future, simulation works at long and large scales should be con-ducted to well explain the experimental results. The diffi-culty or challenge faced is listed as following. First, radiation conditions are complex, including the radiation temperature, radiation dose rate, radiation dose and grain size that often vary in a wide range in different experiments. Consequently, some certain of the mechanisms/processes could play a dom-inate role in accounting for the experimental observation in a specific parameter regime. The efficiency of the described relevant healing mechanisms under severe cumulative radia-tion conditions deserves further investigation. Second, there exists multiple interaction processes including defect gen-eration, diffusion, segregation and annihilation, clustering near the GBs, and also the processes associated with the structure, energetics and kinetics of the GB. Furthermore, the parameters characterizing the defect-GB interaction may depend on the types of GBs in NCs. The effect of the GB character on the defect-GB interaction is explored very lim-itedly. Particularly, it should be extended on the work of the interplay mechanisms of the radiation with the general asymmetric GBs given the large fraction of such GBs in real poly-crystalline materials. The defects at different GBs could have a distinct energy level, implying that the defects segregated at the GB from the grain interior could migrate from one GB with high energy level to another GB with low energy level. As a result, the boundary condition for the defects’ behavior within the GB is hard to deal with. Thus, how the radiation defects transport through the complex GB network remains to be explored. Third, experimental obser-vation is performed after a certain radiation dose. In other words, the accumulation radiation effects are observed. The

real radiation damage in materials is an inherently multi-scale phenomenon, spanning multiple time and space scales. Such multi-scale cumulative nature of the radiation damage renders the difficulty to explain theoretically directly based on the basic atomic processes. Besides, with the accumula-tion of radiation damage, the new atomic processes could emerge. Meanwhile, the interaction parameters would also change with the radiation dose. How the defects interact with the damaged GB far from the equilibrium state should be investigated in the next step. To accurately predict the radiation response of NCs on different scales, it requires the development of new simulation techniques, which have the feature to not only capture the basic defect-GB interac-tion mechanism but also correct the model prediction of the microstructure evolution as incorporating new processes/mechanisms into the model. The authors are developing a framework for studying the cumulative displacement dam-age in nanostructured metals based on parameter passing and structural feedback between atomic and coarse-grained techniques. Finally, the real self-healing mechanism could be complicated due to the synergistic effects of the hydro-gen retention, helium embrittlement and radiation-induced precipitates of solute elements together with the displace-ment damage outlined in the present review. In addition, the possible coupling effects between cascades with the thermal-diffusion processes also complicate the radiation-GB interaction pictures.

Acknowledgements This work was financially supported by the National Key Research and Development Program of China (Grant Nos. 2017YFE0302400, 2017YFA0402800, and 2018YFE0308102), the National Natural Science Foundation of China (Grant Nos. 11735015, 51871207, 51671185, U1832206, 51771181, U1967211 and 51971212), and by the Center for Computation Science, Hefei Institutes of Physical Sciences.

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Dr. Chang‑Song Liu (C. S. Liu) is a full professor of materials science and the selected person of "Hundred Talents Program" of Chinese Academy of Sciences (CAS). He finished his university life in Anhui Normal University, and then received his MS degree and Ph. D in the field of physics of condensed matter from ISSP, CAS. He held the faculty posi-tions of an associate (2001) and full professor (2003) in ISSP. During 2001–2003, he worked at the computational materials theory center at California State

University Northridge as a post doctor. Dr. Liu has published over 200 SCI papers in international journals including Nature Mater., PNAS, Phys. Rev. Lett., Phys. Rev. B, Acta Mater., Nucl. Fusion. His main research interests are those in materials sciences, granular materials, and liquid physics: 1) The microstructure, mechanical properties and radiation resistance of high-Z plasma facing materials (W- and Mo-based alloys) and nano-structural materials; 2) The microstructure properties of liquid/amorphous metals and alloys; 3) The dynamic properties of granular materials.