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Research Papers

# Sputtering of Graphite by Hydrogen Isotopes in the Fusion Environment: A Molecular Dynamics Simulation StudyPUBLIC ACCESS

[+] Author and Article Information
Qiang Zhao, Yang Li, Zheng Zhang

Beijing Key Laboratory of Passive Safety
Technology for Nuclear Energy,
North China Electric Power University,
Beijing 102206, China

Xiaoping Ouyang

Beijing Key Laboratory of Passive Safety
Technology for Nuclear Energy,
North China Electric Power University,
Beijing 102206, China;
Northwest Institute of Nuclear Technology,
Xi'an 710024, Shaanxi, China

Manuscript received October 31, 2017; final manuscript received May 25, 2018; published online September 10, 2018. Assoc. Editor: Dmitry Paramonov.

ASME J of Nuclear Rad Sci 4(4), 041022 (Sep 10, 2018) (4 pages) Paper No: NERS-17-1279; doi: 10.1115/1.4040495 History: Received October 31, 2017; Revised May 25, 2018

## Abstract

The sputtering of graphite due to the bombardment of hydrogen isotopes is crucial to successfully using graphite in the fusion environment. In this work, we use molecular dynamics to simulate the sputtering using the large-scale atomic/molecular massively parallel simulator (lammps). The calculation results show that the peak values of the sputtering yield are between 25 eV and 50 eV. When the incident energy is greater than the energy corresponding to the peak value, a lower carbon sputtering yield is obtained. The temperature that is most likely to sputter is approximately 800 K for hydrogen, deuterium, and tritium. Below the 800 K, the sputtering yields increase with temperature. By contrast, above the 800 K, the yields decrease with increasing temperature. Under the same temperature and incident energy, the sputtering rate of tritium is greater than that of deuterium, which in turn is greater than that of hydrogen. When the incident energy is 25 eV, the sputtering yield at 300 K increases below an incident angle at 30 deg and remains steady after that.

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## Introduction

The materials of fusion power reactors withstand complex and extreme working conditions that require high temperatures, radiation, hydrogen embrittlement, and so on [13]. During the process of nuclear fusion, the plasma facing materials (PFMs) are exposed to an environment that of incident particles and high neutron flux [4,5]. The surface of the PFMs is subjected to erosion by energetic ions and neutral atoms escaping from the plasma. The divertor plates as an important part of the PFMs are also exposed to hydrogen (H), deuterium (D), and tritium (T) [6].

Although tungsten has attracted considerable attention in recent years, graphite is a potential candidate material for divertor plates. It is widely used as divertor plate material because of its excellent thermal conductivity, superior mechanical properties, good resistance to high heat loads, and good fabrication flexibility [710]. For example, graphite is used in the first wall of the Korea Superconducting Tokamak Advanced Research and the divertor plates of the Large Helical Device at the National Institute in Japan [1113]. When graphite is irradiated with H, D, and T, the erosion of graphite can lead to many undesired effects on the divertor. A thorough understanding of graphite exposed to H, D, and T is essential to applications as a divertor.

Previous studies have reported the reaction process for the diffusion and absorption of hydrogen isotopes in graphite [14,15]. Many researchers have used molecular dynamics to study the erosion of hydrogen isotopes. Ito and Nakamura found that hydrogen isotopes are absorbed by the graphite surface at an incident energy of 5 eV, whereas almost all of them are reflected at an energy of 15 eV [16]. Experiments in many ion beam facilities have shown that ion bombardment of graphite can produce impurities and lead to corrosion [1719]. Moreover, the T inventory in the divertor plates that leads to a significant reduction of the lifetime has been studied [20]. In addition, graphite is easily sputtered. Sputtered atoms can contaminate the plasma environment of the fusion reactor [16]. Takeguchi et al. experimentally studied the dependence of the sputtering yield by low-energy hydrogen on the particles flux [21]. Liang et al. [22] and Hopf and Jacob [23] studied the sputtering of graphite only at a specific energy or temperature using the Monte Carlo method. However, the previous studies have not performed a systematic and comprehensive stimulation of sputtering in the fusion environment, which is required to design a more suitable divertor. In this work, we use classical molecular dynamics to simulate the sputtering of graphite under bombardment with H, D, and T.

## Calculation Model and Details

The classical molecular dynamics large-scale atomic/molecular massively parallel simulator (lammps) code was used in this simulation to study interactions between hydrogen isotopes and carbon. The application of appropriate potentials is essential in the simulation. In the past, many scientists used reactive empirical bond order (REBO) [24] potential to describe the chemical reaction between carbon and hydrogen isotopes. However, this potential is not good enough to be applied in our work, because the long-range dispersion forces of carbon are not contained in the REBO potential. The deficiency is remediated in the adaptive intermolecular reactive empirical bond order (AIREBO) potential by including the Lennard–Jones (LJ) potential [25,26]. Therefore, we will use the AIREBO potential to describe interatomic interaction. The AIREBO potential consists of three terms [27,28] Display Formula

(1)$E=12∑i∑j≠i[EijREBO+EijLJ+∑k≠i,j∑l≠i,j,kEkijltors]$

where $EijREBO$ is the sum of repulsive and attractive pairwise potentials that are determined by the atom types (carbon or hydrogen) of atoms i and j, $EijREBO$ depends not only on the distance rij between the two atoms but also the position and chemical identity of atoms close to the i − j bond; $EijLJ$ adds long-range interactions to $EijREBO; Ekijltors$ depends on dihedral angles that are determined by the atom type (carbon or hydrogen) of atoms i, j, k, and l.

The crystal structure of the carbon sample used in this simulation is hexagonal close-packed. We used a three-dimensional cell with a size of 16 × 16 × 7 lattices. A lattice parameter of 2.45 Å [29] was used to construct the carbon sample. There are 7168 carbon atoms in the simulation; the bottom layer of atoms is fixed to support the structure. The boundary conditions of the X- and Y-directions were periodic, whereas the Z-direction is nonperiodic. During the simulations, we had two procedures, the equilibrium process and bombardment process. In the equilibrium process, mobile carbon atoms were assigned an initial velocity with a Gaussian distribution according to the desired temperature. Then, the equilibrium process was performed for 1000 steps during 1 ps.

During the bombardment process, 1000 hydrogen or isotope atoms were injected at a regular time interval of 0.003 ps. The X- and Y-directions of the injecting point were set at random. The Z-direction of the injection point was 42 Å. The incident ions were set to the specific energy (velocity). The system was in a microcanonical ensemble, where the number of atoms, volume, and the total energy are conserved until the atoms leave in the Z-direction. The temperature of the system varied from 300 K to 1000 K. The energy of incident atoms varied from 10 eV to 200 eV. The incident angle is defined as the angle between the incident ions and the Z direction. The incident angle chosen in this paper were 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, and 75 deg.

## Results and Discussion

The effect of temperature on the sputtering was studied at 300 K, 400 K, 600 K, 800 K, and 1000 K. Figure 1 shows the carbon sputtering yield for graphite bombarded by D ions with incident energies of 10 eV to 200 eV. We defined the sputtering yield as the number of sputtered atoms divided by the total number of atoms. The data taken from Hopf and Jacob [23] were simulated using srim, and our results are simulated by lammps. We see that the three curves have the same trend, with peaks at approximately 25 eV. After 25 eV, the sputtering yields decrease. Because the simulation results we took from Hopf et al. do not give the exact temperature, some discrepancies are seen from it.

Figure 2 shows the carbon sputtering yield as a function of the target temperature for graphite bombarded by D ions with an incident energy of 50 eV, compared with the simulation results by TRIDYN [22] and the experimental results [30]. As shown, the values from 400 K to 900 K are very close to other results, and all maximum values are at approximately 800 K. However, a few discrepancies remain at both ends, which can be improved in future research. Overall, our simulation results agree well with previous results.

Next, we simulated the sputtering under different energies, setting the temperature from 300 K to 1000 K. Figure 3 shows the carbon sputtering yield as a function of the incident ion energy for D ions at target temperatures of 300 K to 1000 K. Figure 3 shows peak values of sputtering yields are between 25 eV and 50 eV. The sputtering rates of the peak value are nearly five times larger than those of the 200 eV bombardments. A higher incident energy causes a lower carbon sputtering yield.

To further understand the above results, we simulated the range of D ions in graphite with srim [31] software. Figure 4 shows the depth of the incident D ions as a function of incident energy. The range increases with the incident energy. Low energy of incident D ions only stays in the shallow layer. The D ions only need to collide a few times to transfer their energy to the surface of carbon atoms. The energy is transferred to the surface without much loss, so one incident D ion can cause many carbon atoms to sputter. For the high-energy incident ions, they mostly stop in one of the bottom three layers (approximately 13.4–20.1 Å) or penetrate the graphite. When the incident ions remain in the bottom layers, they undergo frequent of collisions to reach the surface. The ions lose much energy due to collisions, which causes some of them to stop, whereas the remaining ions reach the surface with low energy. Thus, the sputtering yield becomes lower than the number of incident ions with low incident energy.

Figure 3 also shows that the curve on the top is 800 K. This is the highest sputtering value during the simulated temperature. Below 800 K, the sputtering yields increase with temperature. We conclude that the temperature that is most likely to cause sputtering is approximately 800 K. In graphite, the layers interact through van der Waals forces [32,33], while carbon atoms in the same layer are coupled by covalent bonds. Compared with covalent bonds, the bond of the van der Waals interaction is much weaker. As the temperature increases, the vibration of atoms becomes increasingly sharp. The kinetic energy of the carbon atoms is sufficient to break the van der Waals bond along the Z-direction, so the sputtering value increases. However, when the temperature reaches 800 K, atomic vibrational amplitudes are sufficient to break the covalent bond. Thus, the carbon atoms can move not only in the Z-direction but also in the XY plane. In this case, when incident ions collide with the carbon atoms, the sputtering atoms travel not only in the Z direction but also in the X- and Y-directions, so the sputtering yields decrease.

Figure 5 shows the carbon sputtering yield as a function of incident energy due to T ions at target temperatures of 300 K to 1000 K. Compared with D ions, we find a smaller temperature effect on T ions. Sputtering under different temperatures has a small discrepancy. Sputtering peaks all locate at approximately 25 eV.

Figure 6 shows the carbon sputtering yield as a function of incident ion energy due to H, D, and T ions at target temperatures of 800 K. It is clear that the sputtering values of T ions are the largest and those of H are the smallest. The sputtering values of T ions are approximately three to five times larger than that of D ions, and the sputtering values of D ions are approximately three to ten times larger than those of H ions. These results are due to the weight of the incident particles. Of the isotopes of hydrogen, the mass of H is smallest, so for the same incident energy, the H ions have the fastest speed compared to that of D and T ions. Therefore, H ions have the largest incident depth. Before the hydrogen atoms transfer their energy to the target atoms on the surface, they lose the most energy among hydrogen isotopes; therefore, the sputtering values of H ions are the smallest. In the same way, we can explain why the sputtering values of T ions are the largest. According to above results, the peak values of the sputtering yield locate between 25 eV and 50 eV. Furthermore, we choose to bombard graphite with 25 eV H, D, and T ions at 300 K to examine sputtering yield variations with the angle of the incident ions. Figure 7 shows the carbon sputtering yield as a function of incident angle for graphite bombarded by 25 eV H, D, and T ions at 300 K. The figure shows the sputtering yields increase gradually with the incident angle below 30 deg. When the incident angle is greater than 30 deg, the sputtering yield remains steady. As the incident angle increases, the velocity in the Z-direction decreases and the velocity in the X- and Y-directions increases, so there are more collisions between the surface carbon atoms and incident ions; thus, the sputtering yield increases below the 30 deg and remains steady after that.

## Conclusions

This study has developed a comprehensive model to simulate the sputtering of graphite bombarded by hydrogen isotopes under a fusion environment. We reached the following conclusions: (1) the peak values of the sputtering yield are from 25 eV to 50 eV. When the incident energy exceeds the energy corresponding to the peak value, a lower carbon sputtering yield is obtained; (2) the temperature that is most likely to cause sputtering is approximately 800 K for hydrogen, deuterium, and tritium ions; (3) for the same temperature and incident energy, the sputtering rate of tritium is greater than that of deuterium, and the sputtering rate of deuterium is greater than that of hydrogen; and (4) when the incident energy is 25 eV, the sputtering yield at 300 K increases below an incident angle of 30 deg and remains steady after that.

## Funding Data

• The Fundamental Research Funds for North China Electric Power University (Grant No. 2017MS079)

## Nomenclature

• E =

AIREBO potential energy, eV

• $EijLJ$ =

Lennard–Jones potential energy, eV

• $EijREBO$ =

REBO potential energy, eV

• $Ekijltors$ =

torsion potential energy, eV

Subscripts or Superscripts
• AIREBO =

AIREBO potential

• i =

precursor group index

• j =

precursor group index

• k =

precursor group index

• l =

precursor group index

• LJ =

Lennard–Jones potential

• REBO =

REBO potential

• tors =

torsion potential

Acronyms
• AIREBO =

adaptive intermolecular reactive empirical bond order

• LAMMPS =

Large-scale atomic/molecular massively parallel simulator

• LJ =

Lennard–Jones

• PFMs =

plasma facing materials

• REBO =

reactive empirical bond order

• SRIM =

stopping and range of ions in matter

• tors =

torsion

• TRIDYN =

transport of ions in matter simulation code including dynamic composition changes

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## References

Miyahara, A. , and Tanabe, T. , 1988, “ Graphite as Plasma Facing Material,” J. Nucl. Mater., 155, pp. 49–57.
Pimenta, M. , Dresselhaus, G. , Dresselhaus, M. S. , Cancado, L. , Jorio, A. , and Saito, R. , 2007, “ Studying Disorder in Graphite-Based Systems by Raman Spectroscopy,” Phys. Chem. Chem. Phys., 9(11), pp. 1276–1290. [PubMed]
Linke, J. , Escourbiac, F. , Mazul, I. , Nygren, R. , Rödig, M. , Schlosser, J. , and Suzuki, S. , 2007, “ High Heat Flux Testing of Plasma Facing Materials and Components–Status and Perspectives for ITER Related Activities,” J. Nucl. Mater., 367, pp. 1422–1431.
Küppers, J. , 1995, “ The Hydrogen Surface Chemistry of Carbon as a Plasma Facing Material,” Surf. Sci. Rep., 22(7–8), pp. 249–321.
Kim, H. , Noh, S. , Kweon, J. , and Lee, C. E. , 2013, “ Influence of Irradiation With Low-Energy Helium Ions on Graphite and Tungsten for Fusion Applications,” J. Korean Phys. Soc., 63(7), pp. 1422–1426.
Ferro, Y. , Jelea, A. , Marinelli, F. , Brosset, C. , and Allouche, A. , 2005, “ Density Functional Theory and Molecular Dynamic Studies of Hydrogen Interaction With Plasma-Facing Graphite Surfaces and the Impact of Boron Doping,” J. Nucl. Mater., 337, pp. 897–901.
Kim, H. , Lee, S. , Ohn, Y. , Noh, S. , Kweon, J. , Park, J. , Lee, C. E. , Woo, H.-J. , Park, S.-J. , and Chung, K.-S. , 2012, “ Damage in Graphite Tiles Irradiated With Helium Plasmas,” J. Korean Phys. Soc., 61(5), pp. 832–834.
Wright, P. , Davis, J. , Macaulay-Newcombe, R. , Hamilton, C. , and Haasz, A. , 2003, “ Chemical Erosion of DIII-D Divertor Tile Specimens,” J. Nucl. Mater., 313, pp. 158–162.
Yang, S. J. , Choe, J.-M. , Jin, Y.-G. , Lim, S.-T. , Lee, K. , Kim, Y. S. , Choi, S. , Park, S.-J. , Hwang, Y. , Kim, G.-H. , and Park, C. R. , 2012, “ Influence of H+ Ion Irradiation on the Surface and Microstructural Changes of a Nuclear Graphite,” Fusion Eng. Des., 87(4), pp. 344–351.
Shimada, M. , Costley, A. , Federici, G. , Ioki, K. , Kukushkin, A. , Mukhovatov, V. , Polevoi, A. , and Sugihara, M. , 2005, “ Overview of Goals and Performance of ITER and Strategy for Plasma-Wall Interaction Investigation,” J. Nucl. Mater., 337, pp. 808–815.
Yoshida, M. , Tanabe, T. , Ohno, N. , Yoshimi, M. , and Takamura, S. , 2009, “ High Temperature Irradiation Damage of Carbon Materials Studies by Laser Raman Spectroscopy,” J. Nucl. Mater., 386, pp. 841–843.
Hino, T. , and Yamashina, T. , 1993, “ Review on Plasma Facing Materials and Suitable Divertor Configuration of a Fusion Experimental Reactor,” Mater. Trans., JIM, 34(11), pp. 1106–1110.
Patil, Y. , Khirwadkar, S. , Belsare, S. , Swamy, R. , Khan, M. , Tripathi, S. , and Bhope, K. , 2015, “ R&D on Divertor Plasma Facing Components at the Institute for Plasma Research,” Nukleonika, 60(2), pp. 285–288.
Vietzke, E. , Wada, M. , and Hennes, M. , 1999, “ Reflection and Adsorption of Deuterium Atoms and Molecules on Graphite,” J. Nucl. Mater., 266, pp. 324–329.
Atsumi, H. , 2002, “ Hydrogen Bulk Retention in Graphite and Kinetics of Diffusion,” J. Nucl. Mater., 307, pp. 1466–1470.
Ito, A. , and Nakamura, H. , 2007, 2008, “ Hydrogen Isotope Sputtering of Graphite by Molecular Dynamics Simulation,” Thin Solid Films, 516(19), pp. 6553–6559.
Andersen, H. H. , and Bay, H. L. , 1981, “ Sputtering Yield Measurements,” Sputtering by Particle Bombardment I, Springer, Berlin, pp. 145–218.
Roth, J. , Vietzke, E. , and Haasz, A. , 1991, “ Erosion of Graphite Due to Particle Impact,” Atomic and Plasma-Material Interaction Data for Fusion, Vol. 1, International Atomic Energy Agency, Vienna, Austria, p. 63.
Goebel, D. , Bohdansky, J. , Conn, R. , Hirooka, Y. , LaBombard, B. , Leung, W. , Nygren, R. , Roth, J. , and Tynan, G. , 1988, “ Erosion of Graphite by High Flux Hydrogen Plasma Bombardment,” Nucl. Fusion, 28(6), p. 1041.
Baskes, M. , Brice, D. , Heifetz, D. , Dylla, H. , Wilson, K. , Doyle, B. , Wampler, W. , and Cecchi, J. , 1984, “ Tritium Inventory and Permeation in TFTR,” J. Nucl. Mater., 128, pp. 629–635.
Takeguchi, Y. , Kyo, M. , Uesugi, Y. , Tanaka, Y. , and Masuzaki, S. , 2009, “ Erosion and Dust Formation of Graphite Materials Under Low-Energy and High-Flux Atomic Hydrogen Irradiation,” Phys. Scr., 2009(T138), p. 014056.
Liang, J. , Mayer, M. , Roth, J. , Balden, M. , and Eckstein, W. , 2007, “ Hydrogen Isotopic Effects on the Chemical Erosion of Graphite Induced by Ion Irradiation,” J. Nucl. Mater., 363, pp. 184–189.
Hopf, C. , and Jacob, W. , 2005, “ Bombardment of Graphite With Hydrogen Isotopes: A Model for the Energy Dependence of the Chemical Sputtering Yield,” J. Nucl. Mater., 342(1–3), pp. 141–147.
Brenner, D. W. , Shenderova, O. A. , Harrison, J. A. , Stuart, S. J. , Ni, B. , and Sinnott, S. B. , 2002, “ A Second-Generation Reactive Empirical Bond Order (REBO) Potential Energy Expression for Hydrocarbons,” J. Phys.: Condens. Matter, 14(4), p. 783.
Ito, A. , Wang, Y. , Irle, S. , Morokuma, K. , and Nakamura, H. , 2009, “ Molecular Dynamics Simulation of Hydrogen Atom Sputtering on the Surface of Graphite With Defect and Edge,” J. Nucl. Mater., 390, pp. 183–187.
Petucci, J. , LeBlond, C. , Karimi, M. , and Vidali, G. , 2013, “ Diffusion, Adsorption, and Desorption of Molecular Hydrogen on Graphene and in Graphite,” J. Chem. Phys., 139(4), p. 044706. [PubMed]
Marian, J. , Zepeda-Ruiz, L. , Gilmer, G. H. , Bringa, E. M. , and Rognlien, T. , 2006, “ Simulations of Carbon Sputtering in Amorphous Hydrogenated Samples,” Phys. Scr., 2006(T124), p. 65.
Stuart, S. J. , Tutein, A. B. , and Harrison, J. A. , 2000, “ A Reactive Potential for Hydrocarbons With Intermolecular Interactions,” J. Chem. Phys., 112(14), pp. 6472–6486.
Crowell, A. , 1954, “ Approximate Method of Evaluating Lattice Sums of r−n for Graphite,” J. Chem. Phys., 22(8), pp. 1397–1399.
Balden, M. , and Roth, J. , 2000, “ New Weight-Loss Measurements of the Chemical Erosion Yields of Carbon Materials Under Hydrogen Ion Bombardment,” J. Nucl. Mater., 280(1), pp. 39–44.
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## Figures

Fig. 1

The carbon sputtering yield for graphite bombarded by D ions with an incident energy of 10 eV to 200 eV. The dot curve is taken from Ref. [23] using srim. The curves with circle and square symbols are our simulation results using lammps.

Fig. 2

The carbon sputtering yield as a function of target temperature for graphite bombarded by D of 50 eV incident energy

Fig. 3

The carbon sputtering yield for graphite bombarded by 10 eV to 200 eV D ions at different temperatures

Fig. 4

The depth of incident D ions as a function of incident energy

Fig. 5

The carbon sputtering yield as a function of incident energy for graphite bombarded by T ions at target temperatures of 300 K to 1000 K

Fig. 6

The carbon sputtering yield as a function of incident energy for graphite bombarded by H, D, and T ions at 800 K

Fig. 7

The carbon sputtering yield as a function of incident angle for graphite bombarded by 25 eV H, D, and T ions at 300 K

## Errata

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