b. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China
Tungsten (W) is a desired plasma facing material (PFM) in the international thermonuclear experimental reactor (ITER), owing to its unique properties such as high melting point, high thermal conductivity, low sputtering yield, and low tritium retention [1-4]. Under the extreme working environment in ITER, the W-based PFM (W-PFM) is severely irradiated by many energetic particles from the plasma core, causing structural damage in W as well as releasing some W atoms from the W surfaces. Such released tungsten atoms or particles from the W-PFM may sputter into the fusion plasma, and damage the nuclear fusion seriously [5, 6]. So, investigating the sputtered W particles from W surfaces is of great importance.
Commonly, the energetic particles from the plasma core are the neutrons, hydrogen ions, helium ions and so on. Of these particles, a neutron has much high kinetic energy and is very small in size, and thus it most probably penetrates into the deep region in W-PFM. On the contrary, the larger-sized particles like hydrogen ions and helium ions have lower kinetic energy, and they bombard the atoms at surface region of W-PFM mostly. In addition, the W self-sputtering also leads to the erosion at W surfaces. So, it is reasonable to assume that the sputtered atoms from the W-PFM are predominately originated from the bombardment of hydrogen and helium as well as the W clusters. In experiment, Wu et al.  and Hechtl et al.  respectively measured the sputtering yield with varying energy and angle of the incident particle. They all found the sputtering yield increased with increasing the incident energy of the coming particle, whereas the sputtering yield increased and then decreased as the incident angle changes from 0° to 90°. Especially, the biggest sputtering yield occurred at the incident angle of around 60° if the incident energy was large enough. On the theoretical side, Niu et al.  and Salonen et al.  employed molecular-dynamic (MD) simulations to investigate the relation between the number of sputtered atoms and the energy of incident ions or W clusters, and their results were consistent with those in experiments. All of these efforts demonstrate that some of W atoms at surface of W-PFM can be sputtered under proper incident angles and incident kinetic energy of an energetic particle. In other words, the ejection of W atoms from W-PFM is dependent on both the incident energy and the incident angle of an energetic particle. However, the relationship above is uncovered on the atomic scale. In addition, there are intrinsic defects in the surface region. How do the intrinsic defects influence the sputtering yield at the W surface during the process of irradiation?
In the present work, we combine molecular dynamic simulations with an environment-dependent tight-binding (TB) potential model to study how an atom can be released from the W-PFM when the W-PFM is bombarded by energetic particles. Our calculations reveal that the sputtering induced by the irradiation depends on both the kinetic energy and the incident angle of a primary knock-on atom (PKA). Moreover, during irradiation, the intrinsic interstitials in the surface region favor creating sputtered W atoms, while the atomic vacancies in the surface region suppress sputtering of the W atoms. According to our simulations, we suggest that generating atomic vacancies in W surface region and controlling the incidence angles of PKAs to be 45°-65° are two effective ways to reduce the sputtering yield at W surfaces during irradiation in ITER.II. Computational details
As we know, of the various surfaces of W, the W(110) surface is the most stable in the various surfaces of W. Because of this, we focus on the sputtering events in the W(110) surface. In present work, a slab model is selected to mimic the W(110) surface. This slab with the size of 35.93 Å×34.93 Å×26.95 Å contains about 2000 W atoms. Here, the periodic conditions are adopted in x and y directions only. As shown in Fig. 1, the atom marked with red shown at the surface is chosen as the PKA, and θ is the incidence angle of PKA.
To trace the formation process of sputtered atoms, it is necessary to focus on the trajectory of the PKA as well as the status of atoms arising from the collision of the PKA. To do this, we perform molecular-dynamic simulations at the TB level. where the force acting on the ith particle in the system is described by:
Here, Eband is the energy contributed from the electronic band structure, and Erep is the repulsive energy. The details of Eband and Erep were presented in Ref.. We stress that the TB potential model we used here counts for the spirit of quantum theory and employs a smaller basis set [11, 12], which considerably reduces the computational demand with respect to the ab initio potentials [13, 14]. More importantly, it can more precisely and convincingly describe many properties including the bonding character between W atoms than the regular empirical potentials.
Since the temperature of W-PFM in the reactor is about 800 K, our slab is heated at 800 K via performing canonical ensemble MD simulations with about 20000 steps, where the interval of each time step is 1 fs. By checking the evolution of the kinetic energy of the system on the time, we ensure that the slab reaches the thermodynamic equilibrium at 800 K.
In addition, to examine some of our results, we carry out the density functional theory (DFT) calculations implemented in the Vienna ab initio simulation package (VASP) [15, 16]. In our DFT calculations, the exchange and correlation interactions between electrons are treated by Perdew-Burke-Ernzerhof , and the projector-augmented wave method with a plane-wave cutoff of 350 eV is adopted. For the electronic self-consistency loop a total energy convergence criterion of 1×10-4 eV is required. Both the lattice constants and the internal coordinates of each system are fully optimized until the residual Hellmann-Feynman forces are smaller than 0.01 eV/Å.III. RESULTS AND DISCUSSION A. Irradiation-induced sputtering in perfect surface
Firstly, we investigate whether or not the PKA can lead to sputtering in the perfect W(110) surface region. Generally speaking, if an atom is collided by other atoms so that it possesses the momentum towards the outside and gains enough kinetic energy to overcome the chemical binding between this atom and its neighboring atoms, this collided atom may escape from the surface, which is the so-called a sputtered atom. Basically, the sputtered atom at the W surface is relevant to a threshold of kinetic energy for this atom at finite temperatures. To evaluate the threshold of the kinetic energy, we set a W atom at the topmost atomic layer to have a certain kinetic energy and let it have a momentum towards the outside of the system at 800 K. It is found that when the given kinetic energy is smaller than the value of about 14.5 eV, the W atom can move towards the outside first and then is attracted back on the surface, not leaving away from the surface finally. In this case, no sputtering occurs actually. However, if the given kinetic energy of the surface atom is more than 14.5 eV, this atom can escape from the surface, forming a sputtered atom. So, the value of 14.5 eV is the minimum kinetic energy for the formation of sputtering at W surface at 800 K. Here, the value of 14.5 eV is actually the energy barrier for the W atom escaping from the surface. For a comparison, we calculated the energy barrier for a W atom leaving away from the surface at zero temperature by performing DFT calculations. The energy barrier calculated by VASP is 12.93 eV, less than 14.5 eV. Even so, both values are comparable each other. So, it is qualitatively reasonable to treat the sputtering of W atoms from W surface by using our TB calculations.
Basically, the kinetic energy of a sputtered atom is mainly obtained from the collision between atoms, which is originated from the energetic PKA. In other words, the creation of a sputtered atom at W surface is relevant to the initial kinetic energy and the incident angle of a PKA.
Now, we study how the incident angle of the PKA influences the formation of a sputtered atom at W surface. In our treatment, the kinetic energy of the PKA is selected to be 200 eV, and the incident angle varies from 15° to 81° as shown in Fig. 2(a). For each given incident angle of the PKA, we carefully simulate the structural evolution arising from the PKA in surface region, and record the sputtered atom if it occurs. As shown in Fig. 2(a), when the incident angle of the PKA is larger than 65°, sputtering appears. Otherwise, no sputtered atom is observed at all. In particular, the maximum number of sputtered atoms is found at θ=77°. These features strongly indicate that only the PKA with large incident angles can create sputtering at W surface, being in agreement with the literatures [18-21].
Secondly, for the case of θ=77°, the kinetic energy of PKA is changed from 100 eV to 300 eV at the step of 100 eV. As shown in Fig. 2(b), when the kinetic energy is as low as 100 eV, no sputtering occurs, when the kinetic energy is no less than 200 eV, sputtering atoms appear. So, even at the maximum sputtering incident angle of PKA, the PKA with a lower kinetic energy cannot drive other atoms to be sputtered.
To gain deep understandings of the observation above, Figure 3 shows some snapshots of the moving atoms in the surface region for the cases of 15° and 77°. In these snapshots, the blue balls stand for the atoms whose kinetic energy are less than 14.5 eV, and the red ones for those with energy being more than 14.5 eV. Meanwhile, each arrow shows the direction of the momentum vector of the attached atom. As seen in Fig. 3(a), when the PKA incident angle is small, the atoms with large kinetic energy locate at the deep region in the system. However, as seen in Fig. 3(b)-(d) , when the PKA incident angle becomes large, the atoms with large kinetic energy mostly appear in the top region of the surface.
Especially, for the case of the incident angle of 77°, the PKA having kinetic energy of 100 eV causes few energetic W atoms at the surface region, and these energetic W atoms collide with the other W atoms, losing part of kinetic energy. As a result, they do not have enough kinetic energy to eject from the surface; On contrast, when PKA energy increases to be 300 eV, more energetic atoms are caused (Fig. 3(d)) in a broad region. Among these energetic atoms, some of the atoms at surface not only have momentum towards outside, but also have enough kinetic energy, so that they can escape from the surface, forming the sputtered atoms.
To go further, we pay our attention to the detailed process of sputtering on the atomic scale. To do this, the case with incident angle of 77° and kinetic energy of 200 eV as mentioned above is selected as a representative. Based on our simulations, the snapshots of the structures in the surface region at 0, 20, 40, 60, 80, and 100 fs are shown in Fig. 4. The green atom represents the PKA and the red atoms represent the sputtered atoms. In Fig 4(b), we could see clearly at 20 fs that the atom labeled with 1 is collided by the PKA, and thus it gains kinetic energy from the PKA so as to displace from its initial position significantly. In this process of the motion, the atom 1 approaches and collides the atom 2, causing the atom 2 to move towards the deeper region, the moving atom 2 knocks the atom 3, leading to that the atom 3 runs towards the outside (Fig. 4(d)). It is noted that although PKA induces more atoms to gain momentum, most of these atoms are not at surface or do not have enough kinetic energy to overcome the binding from the neighboring atoms. Consequently, the PKA causes sputtering at surface only in this case.
Overall, in order to suppress the sputtering at W surface, the PKA incident angle should be smaller than 65° and the kinetic energy of the PKA should be small too. For the former case, our suggestion can be considered in experiments. As we know, the W-PFM in experiment is actually assembled with many pieces of W-tiles. According to the geometry of the reactor, the surface of each W-tile can be prepared, so that the optimal incident angle of the PKA in this W-tile can be satisfied.
We should emphasize that many W atoms at surfaces are the PKAs when the surfaces are irradiated by energetic particles. However, most of the PKAs are not closen to each other spatially, and thus it is suitable to consider one PKA in the larger-sized supercell in our simulations. For the cases in which the PKAs are quite close to each other, the damage of the surface arising from the irradiation is heavier highly. In this case, more W atoms will probably escape from the surfaces.B. Irradiation-induced damages in perfect surface
Besides the sputtering, many vacancies and interstitials may be generated by the irradiation of the energetic particles too. Physically, creating an atomic vacancy is accompanied by the occurrence of an interstitial atom in the system. Because of this, we only show the number of atomic vacancies arising from the collision of PKA. The variation of the number of generated vacancies over the PKA with different incident angels and kinetic energy is plotted in Fig. 5. As shown in Fig. 5(a), the number of the vacancies is small when incident angle of the PKA is between 45°-65°, at kinetic energy of 200 eV, and the number of the vacancies is the largest when the angle reaches 81°. Clearly, the number of vacancies introduced by the irradiation also correlated with the incidence angle of PKA.
Similarly, for the given incident angle 77°, the number of vacancies caused by the PKA with different kinetic energies (100, 200, or 300 eV) is also treated. As shown in Fig. 5(b), the higher the kinetic energy of the PKA is, the more the number of the generated vacancies is. Our calculations above indicate that when the kinetic energy of a PKA is large enough, atomic vacancies are created. More interestingly, when the incident angle of a PKA is within 45°-65°, the PKA damages the surface region weakly. According to this observation, the optimum incident angles of a PKA are suggested to reduce the irradiation damage of the W surface.C. Irradiation-induced sputtering in the defective surface
Since the surface region contains vacancies and the interstitials, we extend our attention to the effect of these defects on PKA-induced sputtering at surface. Figures 6 respectively shows the structural models containing vacancies and interstitials.
In our simulations, we consider the PKA locating at different positions in surface. For comparison, the considered PKA have the same incident angle of 70.6° and the same incident energy of 200 eV. All of our considered cases can be sorted into three typical ones: In case 1, the direction of starting motion of the PKA just points to a defect M (M is either a vacancy or an interstitial) nearby; In case 2, the direction of starting motion of the PKA points to an atom near the defect M; In case 3, the direction of starting motion of the PKA is far from any defect. The number of the sputtered atoms, Nsputtered atoms, for these three cases is summarized in Table I. As seen in Table I, when the PKA moves closely to an interstitial defect, more sputtered atoms are generated. However, this does not appear in the case with atomic vacancies. These observations can be understood as follows.
The interstitial atom strains the local structure around itself and thus enhances the repulsive interaction between atoms. In this situation, the migrating PKA aggravates the interior stress of the strained region. During the process of releasing such enhanced interior stress, parts of kinetic energy and the related momentum distribute to some atoms at topmost surface, making more atoms be sputtered out with respect to the case of the perfect surface.
Unlike the interstitial atom, the atomic vacancy in the surface region may locally release the stress arising from the PKA in part. This significantly reduces the magnitude of the distributed kinetic energy and the related momentum around the vacancy. As a result, when the weakened kinetic energy reaches the atoms at the topmost layer, it is difficult to drive more atoms to be released from the system.
When the PKA moves far away from the vacancies or interstitial atoms existing in the surface region, the stress caused from the PKA is not affected by the defects almost. So, the situation of the surface atoms arising from the PKA motion is almost the same as that of the PKA motion in the perfect surface.IV. Conclusion
An MD simulation at the TB level is used to simulate the damage caused by irradiation on W(110) surface. We find that to reduce the irradiation damage, the incident energy of PKA should be as small as possible and the incident angle of PKA should be controlled between 45° and 65°. Moreover, we find that the interstitials gets sputtering more easily and the intrinsic vacancies can reduce sputtering significantly.V. Acknowledgments
This work is supported by the National Magnetic Confinement Fusion Program (No.2013GB107004), the National Natural Science Foundation of China (No.11275191). The Computational Center of USTC is acknowledged for computational support.
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b. 中国科学院合肥物质研究院等离子物理研究所, 合肥 230026