The Interaction between He Bubble and Migrating Grain Boundary Induced by Shear Loading

Abstract

This work reveals the interaction mechanism between He bubble and grain boundary (GB) in bicrystal copper under shear loading via molecular dynamics simulations. The influences of He/vacancy ratio R_He/V, temperature T₀, and bubble diameter D₀ on the interaction mechanism are clarified. Specifically, two interaction modes, i.e., the GB traverses or is pinned on He bubble, are observed by changing the initial R_He/V, T₀, and D₀. As R_He/V increases, the influence of He bubble on GB migration shows a decrease–increase trend. Different He bubble evolutions are demonstrated by comparing their shapes, pressure, and volume. In the cases of low R_He/V, the medium temperatures (10–300 K) are found to accelerate the GB migration, but higher temperatures (600–900 K) will lead to the change in interaction mode and deteriorate the interaction process. Furthermore, a more noticeable bubble-drag effect on GB migration is observed in the samples with larger He bubble.

1. Introduction

The structural materials in the core of fusion and fission reactors are subjected to intense fluxes of energetic neutrons, resulting in the formation of irradiation defects, such as He bubbles, voids, dislocation loops, and stacking fault tetrahedrons (SFTs) [1,2,3,4,5]. These defects may directly cause the deterioration of the material’s mechanical properties, such as local hardening, embrittlement, and swelling [6,7,8]. Hence, it is of great importance to study the behavior of the irradiation defects in the structural materials for the development of radiation-resistant materials.

Compared to the coarse-grained materials, nanocrystalline materials exhibit superior radiation resistance due to the large volume fraction of grain boundaries (GBs) [9,10,11,12,13]. It was found that GBs can serve as effective sinks for irradiation-induced defects [14,15] and the sink efficiency is closely related to the defect types and the GB characteristics, including misorientation and local GB structure [16,17]. For example, the GB sink efficiencies on voids increased with the GB misorientation angle [17]. It was observed that the void would separate from GB or attach to and migrate with GB after the interaction [18]. Additionally, the coherent twin boundary (TB) showed high sink efficiency to SFTs, but its sink ability to voids is relatively low due to its simple boundary structure [19,20]. By using Molecular dynamics (MD) simulations, the interaction mechanism between irradiation defects and GB has been explored extensively. For example, Zhang et al. [21] simulated the interaction between voids and migrating GB in Cu by considering the effect of GB misorientation, void size, and temperature. The result revealed that the higher misorientation angle and temperature improved the GB’s ability to absorb the voids. Three interaction modes between a migrating GB and interstitial Frank loops were observed as a function of misorientation angle, i.e., the GB partially or completely absorbs the Frank loops, or slows down accompanied by dislocation emission [22]. Moreover, the absorption of immobile vacancies [23] and SFT [24] by GB was also indicated via MD simulations.

Different from the traditional void structure, He bubbles exhibit more complex microstructure effects due to their internal pressure [25,26]. It was proved that He bubbles with different He/vacancy ratios (R_He/V) will induce heterogeneous stress fields in the materials [27,28], especially, the formation of stacking fault octahedron (SFO) due to the expansion of high-pressurized He bubbles was observed both in experiments [29] and simulations [30,31]. Previous studies have demonstrated He bubbles with different R_He/V show different resistance to dislocations [32]. Obviously, this will also affect the process of interaction with GBs [33,34,35,36]. Ono et al. [34] observed the migration and coalescence of He bubbles at moving GBs in Fe and Fe-9Cr ferritic alloy. It was indicated that vacancy generation and migration will enhance the trapping of He by GBs and higher temperatures promote this process [35]. Recently, Niu et al. [36] observed the incoherent TBs are pinned by the He bubbles in the in-situ micropillar compression tests of nanotwinned Ag. However, the evolution of He bubbles during the interaction and its influence on GB’s migration is still unclear. The corresponding physical mechanism needs to be further systematically investigated.

In this work, MD simulations are carried out to investigate the interaction process between He bubbles and GBs in bicrystal copper. The effects of He/vacancy ratios R_He/V (0–5), temperatures T₀ (10–900 K), and bubble diameter D₀ (2–5 nm) are discussed through a detailed analysis of microstructures and mechanical quantities.

2. Computational Details

The MD simulations are performed with the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [37]. Here, we adopt the embedded-atom-method (EAM) potential developed by Mishin et al. [38] to describe the atomic interactions between Cu as it can accurately reflect the structural transformation and mechanical behavior of Cu [39,40]. Both Cu–He and He–He interatomic interactions are described by the Lennard-Jones potentials, which is written as follows:

$$\mathsf{\varnothing }\left(r\right)=4\epsilon \left[{\left(\frac{\sigma }{r}\right)}^a-{\left(\frac{\sigma }{r}\right)}^b\right]$$

(1)

where a = 9, b = 6, ε = 0.000745 eV, σ = 3.546 Å for the Cu–He interaction [41], and a = 12, b = 6, ε = 0.000876 eV, σ = 2.280 Å for the He–He interaction [42]. Figure 1a shows the initial configuration of the simulation system. The system dimension is approximately 15.4 nm × 24.3 nm × 15.2 nm containing about 4.8 × 10⁵ atoms. The [001] crystallographic orientation (z-axis) is set as the tilt axis and the GB is constructed by rotating grain A and grain B along it. Here we construct a Σ5{210}[001] symmetrical tilt GB (${\mathsf{\gamma }}_{GB}=953 \mathrm{mJ}/{\mathrm{m}}^2$) as representative to study the interaction between He bubble and GB due to its obvious shear-coupled migration behavior under external stress [21], as shown in Figure 1c. The He bubble is placed at a distance of 4.5 nm above the GB plane initially.

The He bubble is introduced by removing Cu atoms in a spherical region and then adding He atoms into this region. To investigate the influence of different initial states on the GB–bubble interaction process, we construct He bubbles with different He/vacancy ratios R_He/V (0–5), different initial temperatures T₀ (10–900 K), and different bubble diameters D₀ (2–5 nm). A few representative He bubbles (equilibrium structures) for different R_He/V are shown in Figure 1b. It should be noted that the pressurized He bubble will induce intense lattice distortion in the surrounding metal matrix. In particular, the He bubble evolves into an imperfect spherical shape with sessile dislocations along the edges of octahedron at R_He/V = 5.0. Before loading, an energy minimization procedure with the standard conjugate gradient method is carried out to obtain the minimum energy configuration of the simulation system. During relaxation, periodic boundary conditions are applied in all directions. The system is first relaxed at a designed temperature and 0 bar pressure using the isothermal isobaric (NPT) ensemble for 100 ps, followed by further relaxation at the canonical (NVT) ensemble for 100 ps after introducing He atoms, to obtain a stable initial configuration.

The interaction between He bubble and GB is realized by moving the GB. As shown in Figure 1a, a slab of 1 nm thick atomic layer at the top of grain A and the bottom of grain B is selected as loading control region. The atoms in these two regions are set as rigid and maintain a perfect lattice structure. A constant shear velocity of $v_s=-2 \mathrm{m}/\mathrm{s}$ parallel to x-axis is applied to the top control region and the atoms in the bottom control region keep stationary. Under shear, the GB migrates upward at a normal velocity ($v_n$), which is supported by a series of periodic processes, i.e., when the stress reaches a critical value, the GB jumps upwards from one equilibrium position to another one, accompanied by the fluctuation of local stress [24,43]. During shear loading, the boundary condition along y orientation is changed to non-periodic. The loading process is carried out under the canonical (NVT) ensemble with a time step of 2 fs. All the results are visualized using the open-access software OVITO [44].

3. Results and Discussion

3.1. Effects of He/Vacancy Ratio

Two interaction modes are observed depending on the R_He/V of the He bubble, i.e., the GB traverses (mode 1) or is pinned on (mode 2) the He bubble. As shown in Figure 2a, the GB continues to migrate with a slightly slow-down after the interaction in mode 1 (R_He/V ≤ 3.0). However, in mode 2, the GB almost stops migrating after the interaction (R_He/V = 5.0). These two interaction modes are also reflected in the stress evolution (Figure 2b), in which a more significant increase in stress is observed in mode 2 during the interaction. The representative snapshots in R_He/V = 0.5 and R_He/V = 5.0 are plotted in Figure 2c,d to illustrate these two interaction modes intuitively. In mode 1 (Figure 2c), the GB traverses the He bubble with a deformed He bubble leaving behind after the interaction. The interaction process does not cause direct dislocation emission at the GB. Different from mode 1, dislocations are emitted from GB when interaction (Figure 2(d2)), then multiply and propagate rapidly into the grains (Figure 2(d3)) in mode 2. Although the GB keeps migrating in all cases in mode 1 after the interaction, the influence of He bubble on GB migration shows a decrease–increase trend as R_He/V increases. As indicated in Figure 2a, the GB migration show a slighter slow-down in R_He/V = 0.5 than R_He/V = 0 (void) or other cases in mode 1 after the interaction. Moreover, in Figure 2b, although the stress increase occurs during the interaction in all the 5 cases in mode 1, it recovers to its initial value and remains stable soon after the interaction in R_He/V = 0.5, different from the fluctuation of stress at a higher value in other cases. This suggests that the resistance of He bubble to GB migration is weakened in R_He/V = 0.5.

Take R_He/V = 0, 0.5, 2.0, and 5.0 as representatives; the atomistic slice images (viewed along the [001] tilt axis) about the dynamic interaction process at 300 K are shown in Figure 3. The shear deformation occurs in grain B with the GB migrating upward under shear, as the blue atomic lines indicate in Figure 3. For the cases in mode 1 (Figure 3a–c), the time when GB contacts with He bubble is slightly different (Figure 3(a1)–(c1)) due to the expansion of the pressurized He bubbles. During the interaction, the contacted segment of GB is pinned at the bubble, resulting in the curvature of GB (Figure 3(a3)–(c3)). Then, the GB gradually separates from He bubble (Figure 3(a4)–(c4)). The time of the separation is about 2.50 ns, 2.30 ns, and 2.65 ns for R_He/V = 0, R_He/V = 0.5, and R_He/V = 2.0, respectively, suggesting the weaker hindrance to GB in R_He/V = 0.5. It is also observed that the GB atoms in R_He/V = 0.5 are less disordered after the interaction compared to R_He/V = 0 and 2.0, as indicated in Figure 3e. These disordered regions provide the embryo for dislocation nucleation; thus, it is normal to observe dislocations emission at GB in R_He/V = 0 and 2.0 (Figure 4) but not in R_He/V = 0.5 (Figure 2(c3)) after a period of development. The special behavior exhibited in R_He/V = 0.5 can be attributed to the internal pressure of He bubble, which can neutralize the stress in the matrix around the He bubble caused by surface tension. The lower pressure in R_He/V = 0.5 reduces the resistance to GB migration and also the interaction time; thus, the disordered regions have less time to develop resulting in the easier self-healing of GB in the subsequent evolution. As the R_He/V increases, the He bubble becomes more irregular after the interaction, i.e., from an initial circle shape to the final ellipse (R_He/V = 0 and 0.5) and triangle (R_He/V = 2.0) shape. When R_He/V increases to 5.0, the lattice distortion around the He bubble becomes more obvious, and significantly affects the interaction process. As shown in Figure 3d, the GB interacts with the SFO around the high-pressurized bubble firstly (Figure 3(d1)), followed by the absorption of SFO by GB during the interaction (Figure 3(d2)). In this case, GB is strongly pinned by He bubble and will not separate from it in the subsequent evolution. As shown in Figure 3(d3), the GB plane becomes seriously uneven, accompanied by the emission of new dislocations. The changes in GB structure during interaction and the stress dissipation induced by dislocation emission directly lead to the difficulty in GB migration for R_He/V = 5. Meanwhile, He bubble is trapped and elongated by GB, turning into a platelet-shaped large bubble. In particular, some He atoms may even escape from the original He bubble to form a small He cluster, as the red dotted circle in Figure 3(d4) indicates. It was verified that the diffusivity of He atoms along GB is much larger than that in bulk [45,46], which explains the irregular deformation of the He bubble in GB. It should be mentioned that the large platelet-shaped bubble in GB was also observed in previous experiments [14].

As mentioned above, the He bubbles with different R_He/V will evolve into different shapes after the interaction. Here, we further analyze the corresponding evolution of the bubble pressure and volume (Figure 5). The internal pressure is calculated according to the virial theorem [47] and the volume is obtained by the Voronoi tessellation analysis technique [48]. The He bubble undergoes three stages during the whole process, i.e., keeping constant before the interaction, fluctuating during the interaction, and stabilizing after the interaction. In R_He/V = 0.5, the bubble pressure increases gradually during the interaction, and finally stabilizes at 1.3 GPa (about 0.65 GPa higher than its initial equilibrium pressure). However, in R_He/V = 2.0 and 5.0, violent fluctuation occurs during the interaction, i.e., the pressure drops rapidly at the time GB contacts with the bubble, followed by a slight increase and decrease. Consequently, the bubble pressure after the interaction is much lower than its initial value. The sudden drops in pressure in R_He/V = 2.0 and 5.0 can be verified by atomic displacement, as the insets in Figure 3 show. For example, it is observed in Figure 3(d1) that the atoms around the bubble move abruptly towards the GB once the SFO is destroyed. The evolution of bubble volume shows an opposite trend to its pressure, as indicated in Figure 5b. Different from the compact lattice atoms in the perfect FCC structure, the GB provides an efficient diffusion channel for the vacancies or interstitials dissociated from the He bubble. Once the GB interacts with the He bubble, the atoms in the contacted part are rearranged. In R_He/V = 0.5, the vacancies in the unsaturated bubble will diffuse to the GB due to the structural transformation of GB with the aid of thermal diffusion and GB migration, resulting in the shrinkage of the He bubble. This phenomenon is similar to the dissolution mechanism observed in void [21]. As for R_He/V = 2.0 and 5.0, the bubble pressure is released through the rearrangement of atoms in the He bubble and GB, and also the nucleation and propagation of dislocations from the bubble.

3.2. Effects of Temperature

The He bubbles and GB are both temperature sensitive, and their properties vary greatly with the temperature. In detail, as the temperature increases, the pressure of He bubble increases, and the GB structure becomes more and more disordered. These changes induced by temperatures directly affect the GB–He bubble interaction behavior.

The influence of temperature on the interaction process is investigated by changing the initial temperature T₀ from 10 K to 900 K at R_He/V = 0.5 and D₀ = 2 nm. As shown in Figure 6, the GB–He bubble interaction mode changes from mode 1 to mode 2 with T₀ increasing. The GB separates from the He bubble at 2.75 ns at 10 K (Figure 6(a4)), 0.45 ns later than that in 300 K (Figure 3(b4)). However, no separation is observed when T₀ increases to 600 K and 900 K. The atomic thermal motion is intensified with the temperature increasing, which promotes the GB migration, and reduces the formation of disordered regions and stress concentration at GB. Thus, we can observe faster GB migration at 300 K than 10 K after the interaction (Figure 6d). As T₀ increases to 600 K and 900 K, due to the increasing fraction of disordered atoms, the GB migration is slower even at the beginning and almost stops after the interaction (Figure 6d). The results indicate that the influence of He bubble on GB migration is first weakened then strengthened, as T₀ increases from 10 K to 900 K.

The shape and pressure evolutions of the He bubble are also indicated in Figure 6. Similar to T₀ = 300 K, the final bubble pressure after the interaction at T₀ = 10 K is higher than its initial pressure. However, at T₀ = 600 K and 900 K, the bubble pressure fluctuates greatly and is finally reduced to a very low value (Figure 6e). The He bubble undergoes greater deformation at higher temperatures compared to lower temperatures. For example, at T₀ = 600 K, the He bubble is elongated and trapped into GB at 2.50 ns (Figure 6(b3)). Then, the dislocations and stacking faults are emitted at GB and He bubble, accompanied by the expansion of the He bubble (Figure 6(b4)). This is consistent with the bubble pressure evolution observed at 600 K. It is worth mentioning that the expansion of He bubbles observed at the higher temperature is quite different from the case of voids in which increasing temperature promotes the annihilation of voids (see Figure 7). As shown in Figure 7, the void shrinkage, or even annihilation, can be clearly observed as the temperature increases. Such difference between the He bubble and void can be attributed to the increasing internal pressure of the He bubble with the increasing temperature (see Figure 6e). At higher temperatures, the He atoms will diffuse more rapidly along the GB under the dual action of the higher internal pressure and the intensified atomic thermal motion, causing the expansion of He bubbles. It should be mentioned this obvious expansion of the He bubble at 600 K and 900 K may cause serious deterioration of the material, such as direct cracking at GB.

3.3. Effects of Bubble Size

The influence of bubble size on the interaction process is investigated by changing the He bubble diameter D₀ from 2 nm to 5 nm at R_He/V = 0.5 and T₀ = 300 K. Similar to the effect of temperature, the GB–He bubble interaction mode changes from mode 1 to mode 2 with D₀ increasing. As shown in Figure 8a–c, the larger the He bubble, the earlier the GB contacts with it. This is due to the shorter distance between the GB and the down edge of the larger He bubble since we set the initial distance between GB and He bubble center to be same (4.5 nm) for different samples. As the He bubble size increases, the total GB-bubble interaction time increases and more severe GB deformation occurs during the interaction (see in Figure 8(a3)–(c3)). It is observed the GB separates from the He bubble at 3.35 ns for D₀ = 3 nm (Figure 8(a4)), 1.38 ns earlier than that for D₀ = 4 nm (Figure 8(b4)). However, no separation is observed when D₀ increases to 5 nm in our simulation time due to the greater resistance of larger He bubble to the GB migration. The GB migration process is reflected in Figure 8d. As the bubble diameter increases from 2 nm to 5 nm, the slowing down of GB migration after the interaction is observed, and the decrease in velocity is more evident for larger He bubble samples. The shape of the He bubble after interaction is similar (ellipse-shaped) for different bubble size samples. Figure 8e shows the pressure evolution of He bubbles. It should be noted that the initial internal pressure of the He bubble decreases with the increase in D₀. During interaction, the pressure of the He bubble fluctuates and the final bubble pressure after the interaction is higher than its initial pressure for all different size bubbles. However, the time when He bubble pressure reaches equilibrium is different for different samples, which is closely related to interaction process. In particular, the pressure of the 5 nm He bubble increases more gently and needs more time to reach equilibrium due to its longer interaction time (Figure 8e).

4. Conclusions

In summary, the current work reveals two interaction modes between GB and He bubble with different R_He/V, T₀ and D₀, i.e., the GB traverses the He bubble directly or is pinned on the He bubble with new dislocations emitted. As R_He/V increases, the resistance of the He bubble to GB migration is first weakened then strengthened which is influenced by the bubble pressure and the lattice distortion around the He bubble. Meanwhile, the shrinkage (at lower R_He/V) or expansion (at higher R_He/V) of the He bubble after the interaction is observed depending on the R_He/V. For low R_He/V, the temperature accelerates the GB migration in the range of 10–300 K, but it leads to the change in interaction mode and deteriorates the interaction process at higher temperatures (600 K and 900 K). The noticeable bubble-drag effect on GB migration is observed in the samples with larger He bubble.