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Chemical sputtering of deuterated carbon surfaces at various surface temperatures
Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Chemical sputtering of deuterated carbon surfaces at various surface temperatures Jonny Dadras a,⇑, Predrag S. Krstic a,b a b
Department of Physics & Astronomy, University of Tennessee, Knoxville, TN 37996, United States Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
a r t i c l e
i n f o
Article history: Received 11 November 2010 Received in revised form 27 December 2010 Available online 5 January 2011 Keywords: Molecular dynamics Chemical sputtering Temperature dependence Amorphous carbon Erosion Deuterated surface
a b s t r a c t The chemical sputtering of deuterated amorphous carbon (a-C:D) surfaces irradiated by 1–50 eV deuterium atoms at surface temperatures between 300 and 1000 K was studied using classical molecular dynamics. A quasi-stationary state was reached by cumulative bombardment for each energy and temperature. Results were compared with available experimental data and previous modeling results and the applicability of molecular dynamics for thermally generated processes was discussed. An attempt is made to correct the absence of the thermally stimulated desorption/degassing of hydrogen from the MD simulations, which evolve at the longer time scales. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Many current and future fusion reactors (e.g. ITER, DEMO) rely on carbon based plasma-facing materials, either for divertor plates (ITER) or as a possible substrate for deposited metal layers [1]. Sputtering of hydrocarbons, besides eroding the plasma-facing walls and components, pollutes the plasma, degrading reactor performance. Tritium retention in carbon walls or in deposited carbon layers of a D–T reactor creates an issue of fusion radioactive waste. While the surfaces of the near-future pulsed experimental fusion machine (ITER) are kept cold, close to room temperature, the temperatures of the plasma-exposed surfaces in reactors that would be capable of energy conversion (DEMO) have to be elevated, possibly to 1000 K [2–4]. This motivates our study of the sputtering yield as function of surface temperature, for surfaces bombarded by hydrogen particles in the least described chemical sputtering energy range (i.e. below 50 eV). There are few theoretical/simulation studies of sputtering yields in this energy region. Salonen et al. [5] obtained results for a virgin (i.e. not cumulatively bombarded) a-C:T surface (tritiated to T/ C = 0.4) irradiated by tritium atoms following a Maxwell–Boltzmann distribution of impact energies with Erms = 10 eV, and for a range of incident angles. The authors of [5] found a noticeable peak in the sputtering yield around 900 K, claiming that this peak persists also for other surfaces composed of different hydrogen
⇑ Corresponding author. Tel.: +1 865 385 3949. E-mail address: [email protected] (J. Dadras). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.12.082
isotopes. We were unable to reproduce their results with a ‘‘virgin’’ surface at the single impact energy of 10 eV (see Fig. 1). The temperature dependence of the chemical sputtering yield of graphite bombarded by D (or H) has been studied experimentally by Mech et al. [6] and Balden et al. [7]. The authors of [6] used a beam of Dþ 2 and employed a quadrupole mass spectrometer to find the yield of carbon atoms, Ychem, from the yield of a collection of ejected stable hydrocarbons Ychem = ((CH4 + 2(C2H2 + C2H4 + C2H6) + 3(C3H6 + C3H8))/H. In [7] a beam of Dþ 3 ions was used, and the total chemical erosion was determined from a weight loss measurement. As can be seen in Fig. 2, the results of [7] are about five times larger than those of [6]. Both the difference in impacting molecular ions and of the method of erosion measurements could cause a discrepancy in these experiments [8]. The measurements show a noticeable peak in the sputtering yield at around 600– 700 K. We note that our calculation of the total carbon erosion yields in Fig. 2 include all ejected hydrocarbons CxDy which satisfy x 6 4, and are in a better agreement with measurements of Balden et al. [7]. Further details on the various experimental and theoretical aspects of the chemical sputtering, including its dependence on the surface temperature can be found in [9] and references therein. Our previous work [10–14] has demonstrated that classical molecular dynamic (MD) simulations using the Brenner–Tersoff reactive empirical bond-order (REBO) potential [15] could produce results in agreement with experimental data on specific hydrocarbon (methane and acetylene) chemical sputtering yields for a range of incident atom energies for surfaces at room temperature. The key element of that success has been mimicking as much as
J. Dadras, P.S. Krstic / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
Fig. 1. Comparison of carbon sputtering yields from simulations [5] for a plasma bombarding an a-C:T surface (triangles) with results of this work for a virgin a-C:D surface bombarded by 10 eV deuterium (squares). Error bars of the current results show the standard error obtained from one surface, the data from reference [5] show the standard error from six different surfaces.
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gies, in the range Ei = 1–50 eV. For each T and Ei, six surfaces which underwent between 1000 and 2000 impacts (where they reached the quasi-steady state) were selected for the sputtering simulations. The motion of atoms in the bottom 2 Å of the simulation cell was frozen in the direction of impact (Z), to prevent motion of the whole cell. Finally, each of the chosen cumulatively bombarded surfaces was relaxed for 100 ps. A surface, prepared by cumulative bombardment, is used for the sputtering simulation by a D atom of appropriate energy, impacting normally to the surface, at a random location in the plane (X,Y) of the simulation cell interface. The simulation is allowed to run for at least 30 ps, to collect all sputtered particles, and during that time no thermostat is applied. The surface is then reset and this process is repeated for 4800 random impact trajectories. Total number of trajectories used in this work, for all considered impact energies and surface temperatures exceeds seven million. Sputtering yields are calculated and averaged over all trajectories, followed by averaging over the six different surfaces at a given T and Ei. The reported error bars in this paper in most cases reflect the standard error of dispersion of the results across these six surfaces. It is noted that the results from the surfaces which turned out not to be in the steady state (total hydrogen yield differed from unity by more than 20%) are not taken into account. Our total sputtering yield, reported in this paper is a sum over all hydrocarbon CnDm (and carbon, Cn) sputtering yields for n 6 4, supported by most of the experiments on the chemical sputtering of carbon. As shown in our previous work [10–13], and in particular in [14], the MD simulations using the REBO potential seem to significantly overestimate contributions of heavier hydrocarbons. In Section 2 we present and analyze our results, comparing them with available experimental data, followed by our conclusions.
2. Results
Fig. 2. Comparison of sputtering yields for surfaces bombarded by 15 eV deuterium as a function of surface temperature. Experimental data [6] (hollow squares) and [7] (stars); present simulations (filled circles) with error bars representing standard error obtained from six different surfaces.
possible the conditions in ion-surface experiments. This was achieved by cumulatively bombarding the surface until a quasisteady-state is reached, defined by the total hydrogen yield YH 1 ± 0.2 per impact hydrogen atom ejected in the form of either hydrogen atoms, molecules or as hydrocarbons. Such surface preparations were done separately for each impact energy and type of particle, requiring fluences of impact particles typically in the range of 1000–2000 impacts per case. The particle-surface simulations at a given impact energy were then performed on a number of surfaces with various cumulated fluences, with thousands of impact trajectories until satisfactory statistical weights of the desired results were achieved. In the present work we apply the same approach, extending it over a range of surface temperatures T (300– 1000 K). The surface is modeled by a cell of amorphous deuterated carbon (a-C:D) with linear dimensions of approximately 2.5 nm and of about 2500 atoms. The initial, ‘‘virgin’’ cell was created by succession of heating (to 104 K) and annealing (to 300 K) a carbon bulk (randomly hydrogenated to about 0.4 of H/C). Such a ‘‘virgin’’ cell, with applied 2D periodic boundary conditions, was then heated to a desired temperature by a Langevin thermostat, and relaxed for 100 ps. Keeping the surface thermostated at a chosen T, the surface was cumulatively bombarded by deuterium atoms at various ener-
Our results for the total carbon sputtering are fairly constant across the considered temperature range, while available experiments in this impact energy and temperature range show a slow increase of the yield, peaking in range of 600–700 K, followed by a steeper decrease with increase of T. A typical case is shown in Fig. 2, for the impact of 15 eV/D. Although the calculated data agree in magnitude with the measurements of Balden et al. [7] within the margin of 50%, even oscillating around the experimental data, the trend of increase toward the 600–700 K peak is missing. We have observed in simulations a mild increase of the threefold-coordinated and the adequate drop of the fourfold-coordinated carbon with increase of temperature, as was the case in [5], but this was not enough to significantly influence the sputtering chemistry. Thus, we hypothesize that increase of the carbon sputtering yield towards the peak value in the experiments could be assigned to the thermally increased diffusion of volatile molecules and atoms. Namely, the chemistry of the sputtering mainly happens at the end of the collision cascade of an impact atom, when it is almost thermalized. The higher impact energy means a deeper penetration, resulting in higher sensitivity to the diffusion rate and therefore the stronger dependence on the surface temperature, as confirmed in the temperature/energy dependences of the measured methane sputtering [9]. The drop of the available experimental yields with temperature above 800 K, we attribute to the intensive thermally induced diffusion and desorption of hydrogen from the surface. However, the thermal processes evolve at time scales much longer than ps–ns considered by molecular dynamics, which is a possible explanation for absence of a clear peak in our results, as well as absence of a more essential drop at high temperatures. We postulate that the hydrogen content of the surface is the precursor for the
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J. Dadras, P.S. Krstic / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
chemical sputtering, and we will illustrate at the end of this section by a numerical experiment that the loss of hydrogen can be a cause for the reduced sputtering at higher temperatures. A 3D plot of the carbon sputtering yields as a function of both surface temperature and impact energy is presented in Fig. 3, and compared with available experimental data of Balden et al. [7]. This figure illustrates comprehensively the general trends of both measured and simulated data in the considered ranges of impact energy and surface temperatures. The calculated data stay acceptably close (within 50%) to the measured yields at temperatures below 700 K, though without showing a particular trend. At temperatures above about 800 K (as was also the case in Fig. 2) our results do not follow the trend of the measured data to decrease with temperature. However, a drop is seen in the case of 50 eV, which we consider an exception to the rule possibly caused by the fact that 50 eV is the border line of applicability of the REBO potential. As discussed above, we hypothesize that the reason for the measured drop in the sputtering yield at higher temperatures is thermally stimulated diffusion and desorption of hydrogen from the surface, which are evolving at the time scales out of the capabilities of molecular dynamics. We note that recent experimental results of Doerner at al. [16] show a strong release of D from carbon upon heating, a process that starts already at 500 K. At 1 eV impact our simulations produce total carbon yields below 103, in agreement with our previous modeling [13], as well as with modeling of Salonen et al. [5]. Chemical erosion of amorphous carbon induced by thermal hydrogen atoms, which can reach significant yields [9], evolves at much longer time scales, not reachable by the molecular dynamics. In order to speed up the deuterium desorption we overheat the hydrogen in the simulation cell to 5000 K (while keeping the carbon frozen, to prevent the cell ‘‘exploding’’). We let the surface relax and thermostat it for 100 ps to its original temperature, and then repeat the sputtering simulations with such a prepared surface. This process was repeated for various lengths of time of over-heating until agreements with experiments of [7] were reached. Fig. 4(a–c) shows our results for the sputtering yields by employing the above method for 15 eV, 20 eV, and 30 eV impact energies. This illustrates well the hypothesized reason for the drop of measured sputtering yields. Using the same surfaces, we also make predictions of the methane and acetylene sputtering yields at Fig. 4 (d–f), which give the ‘‘corrected’’ values in the range 800–1000 K. We note that emission of methyl is strongly dependent on the sp3 hybridization content in the surface [12], which is not warranted by our method of stimulated release of hydrogen, and that these predictions should be accepted here with caution.
Fig. 3. 3D plot of the carbon sputtering yield as a function of both surface temperature and energy of the impacting particle, compared to experimental data from [7] (hollow stars).
Fig. 4. The total carbon sputtering yields after stimulated reduction of deuterium (filled circles), experiments [7] (stars), and results without the forced D reduction (hollow circles), for various impact energies (a–c). Predictions for methane and acetylene sputtering yields (d–f) for high surface temperatures, after the stimulated reduction of deuterium (filled triangles and squares) and original results (hollow triangles and squares).
Finally, the needed reductions of the hydrogen content are shown in Fig. 5, running between 5% and 30% for D/D0, where D is the amount of deuterium atoms in the simulation cell after over-heating and D0 is the number of deuterium atoms before over-heating (i.e. immediately after being cumulatively bombarded). To explain the deviation of the point at 900 K for Ei=30 eV from the trends of 15 and 20 eV we note in Fig. 4(c) that, unlike the cases for 15 and 20 eV, the original (not-corrected) sputtering yield for 900 K is noticeably below those at 800 and 1000 K. The ‘‘right’’ contents of D at temperatures between 800–1000 K for fitting the total carbon yields with experimental values in [7] were found after trying superheating for various durations of time, resulting in various D/D0 and various sputtering rates until the agreement with measurement was reached. It is also interesting to compare the rate of the thermally induced decrease of the deuterium content in carbon obtained by this ‘‘trial-and-error’’ method and those
Fig. 5. Reduction of deuterium from the simulation cell by over-heating. Shown are the fractions (a) D/D0, obtained by trial-and-error simulations of the carbon yield to agree with the experiments of [7] at various impact energies. (b) D/C, after and prior to the forced deuterium reduction by over-heating. Thermally induced deuterium release rate from measurements of Doerner et al. [15] is shown by symbols.
J. Dadras, P.S. Krstic / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
obtained in [16] by fitting to the measured D content. The slope of D/C (or D/D0 here, since C content was kept constant during the over-heating) is from [16] proportional to exp (2268/T), presented with -symbols in Fig. 5. 3. Conclusions We have used classical molecular dynamic simulations to model chemical sputtering from a-C:D surfaces, prepared at various surface temperatures in the range of 300–1000 K, bombarded by deuterium atoms for a range of impact energies, 1–50 eV. Our results do not show a temperature dependent peak in the sputtering yields that has been observed in beam-surface experiments [6–8]. We hypothesize that the reason for this disagreement between experiment and simulation lies in the incapability to model thermally induced stimulated processes of diffusion and desorption, which evolve at time scales beyond those that can be described by MD (which is only applicable for a range between ps and ns). By over-heating the simulation cell we forced partial release of deuterium from the cell, and find by trial-and-error the deuterium release fractions by fitting carbon sputtering yields to experimental data in [7]. Acknowledgements We acknowledge support of the Office of Fusion Energy Science, U.S. Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC, of the LDRD program of the Oak Ridge National Laboratory, and of DOE INCITE program. The data were obtained at the ORNL computational resources of the National Center of Computational Sciences.
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References [1] E. Marmar, S. Allen, M. Bell, et. al., Report of the Burning Plasma Organization Panel on Planning for US Participation in ITER, (2008). [2] C.P.C. Wong, Innovative tokamak DEMO first wall and divertor material concepts, J. Nucl. Mater. 390–391 (2009) 1026–1028. [3] R. Andreani et al., Fusion Eng. Des. 81 (2006) 25–32. [4] P. Norajitraa et al., Divertor conceptual designs for a fusion power plant, Fusion Eng. Des. 83 (2008) 893–902. [5] E. Salonen, K. Nordlund, J. Keinonen, C.H. Wu, Bond-breaking mechanism of sputtering, Europhys. Lett. 52 (5) (2000) 504–510. [6] B.V. Mech, A.A. Haasz, J.W. Davis, Isotopic effects in hydrocarbon formation due to low-energy H+/D+ impact on graphite, J. Nucl. Mater. 255 (1998) 153– 164. [7] M. Balden, J. Roth, New weight-loss measurements of the chemical erosion yields of carbon materials under hydrogen ion bombardment, J. Nucl. Mater. 280 (2000) 39–44. [8] F.W. Meyer, P.R. Harris, H. Zhang, W. Jacob, T. Schwarz-Selinger, U. von Toussaint, J. Nucl. Mater. (2010), doi:10.1016/j.jnucmat.2010.08.037. [9] W. Jacob, J. Roth, Sputtering by Particle Bombardment, in: R. Behrisch, W. Eckstein (Eds.), Chemical Sputtering, vol.110, Springer, Berlin, 2007, pp. 329– 400 (Topics in Applied Physics). [10] P.S. Krstic, C.O. Reinhold, S.J. Stuart, Chemical sputtering by impact of excited molecules, European Physics Letters 77 (2007) 33002. [11] S.J. Stuart, P.S. Krstic, T.A. Embry, C.O. Reinhold, Methane production by deuterium impact at carbon surfaces, Nuclear Instruments and Methods in Physics Research B 255 (2007) 202–207. [12] P.S. Krstic, C.O. Reinhold, S.J. Stuart, Chemical sputtering from amorphous carbon under bombardment by deuterium atoms and molecules, New J. Phys. 9 (209) (2007). [13] P.S. Krstic, C.O. Reinhold, S.J. Stuart, Energy and angle spectra of sputtered particles for low-energy deuterium impact of deuterated amorphous carbon, J. Appl. Phys. 104 (2008) 103308. [14] C.O. Reinhold, P.S. Krstic, S.J. Stuart, H. Zhang, P.R. Harris, F.W. Meyer, J. Nucl. Mat. 401 (2010) 1. [15] D.W. Brenner, O.A. Shenderova, J.A. Harrison, et al., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys.: Condens. Matter 14 (2002) 783–802. [16] R.P. Doerner, M.J. Baldwin, G.De. Temmerman, et al., Codeposition of deuterium with ITER materials, Nucl. Fusion 49 (2009) 035002.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Chemical sputtering of deuterated carbon surfaces at various surface temperatures Jonny Dadras a,⇑, Predrag S. Krstic a,b a b
Department of Physics & Astronomy, University of Tennessee, Knoxville, TN 37996, United States Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, United States
a r t i c l e
i n f o
Article history: Received 11 November 2010 Received in revised form 27 December 2010 Available online 5 January 2011 Keywords: Molecular dynamics Chemical sputtering Temperature dependence Amorphous carbon Erosion Deuterated surface
a b s t r a c t The chemical sputtering of deuterated amorphous carbon (a-C:D) surfaces irradiated by 1–50 eV deuterium atoms at surface temperatures between 300 and 1000 K was studied using classical molecular dynamics. A quasi-stationary state was reached by cumulative bombardment for each energy and temperature. Results were compared with available experimental data and previous modeling results and the applicability of molecular dynamics for thermally generated processes was discussed. An attempt is made to correct the absence of the thermally stimulated desorption/degassing of hydrogen from the MD simulations, which evolve at the longer time scales. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Many current and future fusion reactors (e.g. ITER, DEMO) rely on carbon based plasma-facing materials, either for divertor plates (ITER) or as a possible substrate for deposited metal layers [1]. Sputtering of hydrocarbons, besides eroding the plasma-facing walls and components, pollutes the plasma, degrading reactor performance. Tritium retention in carbon walls or in deposited carbon layers of a D–T reactor creates an issue of fusion radioactive waste. While the surfaces of the near-future pulsed experimental fusion machine (ITER) are kept cold, close to room temperature, the temperatures of the plasma-exposed surfaces in reactors that would be capable of energy conversion (DEMO) have to be elevated, possibly to 1000 K [2–4]. This motivates our study of the sputtering yield as function of surface temperature, for surfaces bombarded by hydrogen particles in the least described chemical sputtering energy range (i.e. below 50 eV). There are few theoretical/simulation studies of sputtering yields in this energy region. Salonen et al. [5] obtained results for a virgin (i.e. not cumulatively bombarded) a-C:T surface (tritiated to T/ C = 0.4) irradiated by tritium atoms following a Maxwell–Boltzmann distribution of impact energies with Erms = 10 eV, and for a range of incident angles. The authors of [5] found a noticeable peak in the sputtering yield around 900 K, claiming that this peak persists also for other surfaces composed of different hydrogen
⇑ Corresponding author. Tel.: +1 865 385 3949. E-mail address: [email protected] (J. Dadras). 0168-583X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.12.082
isotopes. We were unable to reproduce their results with a ‘‘virgin’’ surface at the single impact energy of 10 eV (see Fig. 1). The temperature dependence of the chemical sputtering yield of graphite bombarded by D (or H) has been studied experimentally by Mech et al. [6] and Balden et al. [7]. The authors of [6] used a beam of Dþ 2 and employed a quadrupole mass spectrometer to find the yield of carbon atoms, Ychem, from the yield of a collection of ejected stable hydrocarbons Ychem = ((CH4 + 2(C2H2 + C2H4 + C2H6) + 3(C3H6 + C3H8))/H. In [7] a beam of Dþ 3 ions was used, and the total chemical erosion was determined from a weight loss measurement. As can be seen in Fig. 2, the results of [7] are about five times larger than those of [6]. Both the difference in impacting molecular ions and of the method of erosion measurements could cause a discrepancy in these experiments [8]. The measurements show a noticeable peak in the sputtering yield at around 600– 700 K. We note that our calculation of the total carbon erosion yields in Fig. 2 include all ejected hydrocarbons CxDy which satisfy x 6 4, and are in a better agreement with measurements of Balden et al. [7]. Further details on the various experimental and theoretical aspects of the chemical sputtering, including its dependence on the surface temperature can be found in [9] and references therein. Our previous work [10–14] has demonstrated that classical molecular dynamic (MD) simulations using the Brenner–Tersoff reactive empirical bond-order (REBO) potential [15] could produce results in agreement with experimental data on specific hydrocarbon (methane and acetylene) chemical sputtering yields for a range of incident atom energies for surfaces at room temperature. The key element of that success has been mimicking as much as
J. Dadras, P.S. Krstic / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
Fig. 1. Comparison of carbon sputtering yields from simulations [5] for a plasma bombarding an a-C:T surface (triangles) with results of this work for a virgin a-C:D surface bombarded by 10 eV deuterium (squares). Error bars of the current results show the standard error obtained from one surface, the data from reference [5] show the standard error from six different surfaces.
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gies, in the range Ei = 1–50 eV. For each T and Ei, six surfaces which underwent between 1000 and 2000 impacts (where they reached the quasi-steady state) were selected for the sputtering simulations. The motion of atoms in the bottom 2 Å of the simulation cell was frozen in the direction of impact (Z), to prevent motion of the whole cell. Finally, each of the chosen cumulatively bombarded surfaces was relaxed for 100 ps. A surface, prepared by cumulative bombardment, is used for the sputtering simulation by a D atom of appropriate energy, impacting normally to the surface, at a random location in the plane (X,Y) of the simulation cell interface. The simulation is allowed to run for at least 30 ps, to collect all sputtered particles, and during that time no thermostat is applied. The surface is then reset and this process is repeated for 4800 random impact trajectories. Total number of trajectories used in this work, for all considered impact energies and surface temperatures exceeds seven million. Sputtering yields are calculated and averaged over all trajectories, followed by averaging over the six different surfaces at a given T and Ei. The reported error bars in this paper in most cases reflect the standard error of dispersion of the results across these six surfaces. It is noted that the results from the surfaces which turned out not to be in the steady state (total hydrogen yield differed from unity by more than 20%) are not taken into account. Our total sputtering yield, reported in this paper is a sum over all hydrocarbon CnDm (and carbon, Cn) sputtering yields for n 6 4, supported by most of the experiments on the chemical sputtering of carbon. As shown in our previous work [10–13], and in particular in [14], the MD simulations using the REBO potential seem to significantly overestimate contributions of heavier hydrocarbons. In Section 2 we present and analyze our results, comparing them with available experimental data, followed by our conclusions.
2. Results
Fig. 2. Comparison of sputtering yields for surfaces bombarded by 15 eV deuterium as a function of surface temperature. Experimental data [6] (hollow squares) and [7] (stars); present simulations (filled circles) with error bars representing standard error obtained from six different surfaces.
possible the conditions in ion-surface experiments. This was achieved by cumulatively bombarding the surface until a quasisteady-state is reached, defined by the total hydrogen yield YH 1 ± 0.2 per impact hydrogen atom ejected in the form of either hydrogen atoms, molecules or as hydrocarbons. Such surface preparations were done separately for each impact energy and type of particle, requiring fluences of impact particles typically in the range of 1000–2000 impacts per case. The particle-surface simulations at a given impact energy were then performed on a number of surfaces with various cumulated fluences, with thousands of impact trajectories until satisfactory statistical weights of the desired results were achieved. In the present work we apply the same approach, extending it over a range of surface temperatures T (300– 1000 K). The surface is modeled by a cell of amorphous deuterated carbon (a-C:D) with linear dimensions of approximately 2.5 nm and of about 2500 atoms. The initial, ‘‘virgin’’ cell was created by succession of heating (to 104 K) and annealing (to 300 K) a carbon bulk (randomly hydrogenated to about 0.4 of H/C). Such a ‘‘virgin’’ cell, with applied 2D periodic boundary conditions, was then heated to a desired temperature by a Langevin thermostat, and relaxed for 100 ps. Keeping the surface thermostated at a chosen T, the surface was cumulatively bombarded by deuterium atoms at various ener-
Our results for the total carbon sputtering are fairly constant across the considered temperature range, while available experiments in this impact energy and temperature range show a slow increase of the yield, peaking in range of 600–700 K, followed by a steeper decrease with increase of T. A typical case is shown in Fig. 2, for the impact of 15 eV/D. Although the calculated data agree in magnitude with the measurements of Balden et al. [7] within the margin of 50%, even oscillating around the experimental data, the trend of increase toward the 600–700 K peak is missing. We have observed in simulations a mild increase of the threefold-coordinated and the adequate drop of the fourfold-coordinated carbon with increase of temperature, as was the case in [5], but this was not enough to significantly influence the sputtering chemistry. Thus, we hypothesize that increase of the carbon sputtering yield towards the peak value in the experiments could be assigned to the thermally increased diffusion of volatile molecules and atoms. Namely, the chemistry of the sputtering mainly happens at the end of the collision cascade of an impact atom, when it is almost thermalized. The higher impact energy means a deeper penetration, resulting in higher sensitivity to the diffusion rate and therefore the stronger dependence on the surface temperature, as confirmed in the temperature/energy dependences of the measured methane sputtering [9]. The drop of the available experimental yields with temperature above 800 K, we attribute to the intensive thermally induced diffusion and desorption of hydrogen from the surface. However, the thermal processes evolve at time scales much longer than ps–ns considered by molecular dynamics, which is a possible explanation for absence of a clear peak in our results, as well as absence of a more essential drop at high temperatures. We postulate that the hydrogen content of the surface is the precursor for the
1282
J. Dadras, P.S. Krstic / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
chemical sputtering, and we will illustrate at the end of this section by a numerical experiment that the loss of hydrogen can be a cause for the reduced sputtering at higher temperatures. A 3D plot of the carbon sputtering yields as a function of both surface temperature and impact energy is presented in Fig. 3, and compared with available experimental data of Balden et al. [7]. This figure illustrates comprehensively the general trends of both measured and simulated data in the considered ranges of impact energy and surface temperatures. The calculated data stay acceptably close (within 50%) to the measured yields at temperatures below 700 K, though without showing a particular trend. At temperatures above about 800 K (as was also the case in Fig. 2) our results do not follow the trend of the measured data to decrease with temperature. However, a drop is seen in the case of 50 eV, which we consider an exception to the rule possibly caused by the fact that 50 eV is the border line of applicability of the REBO potential. As discussed above, we hypothesize that the reason for the measured drop in the sputtering yield at higher temperatures is thermally stimulated diffusion and desorption of hydrogen from the surface, which are evolving at the time scales out of the capabilities of molecular dynamics. We note that recent experimental results of Doerner at al. [16] show a strong release of D from carbon upon heating, a process that starts already at 500 K. At 1 eV impact our simulations produce total carbon yields below 103, in agreement with our previous modeling [13], as well as with modeling of Salonen et al. [5]. Chemical erosion of amorphous carbon induced by thermal hydrogen atoms, which can reach significant yields [9], evolves at much longer time scales, not reachable by the molecular dynamics. In order to speed up the deuterium desorption we overheat the hydrogen in the simulation cell to 5000 K (while keeping the carbon frozen, to prevent the cell ‘‘exploding’’). We let the surface relax and thermostat it for 100 ps to its original temperature, and then repeat the sputtering simulations with such a prepared surface. This process was repeated for various lengths of time of over-heating until agreements with experiments of [7] were reached. Fig. 4(a–c) shows our results for the sputtering yields by employing the above method for 15 eV, 20 eV, and 30 eV impact energies. This illustrates well the hypothesized reason for the drop of measured sputtering yields. Using the same surfaces, we also make predictions of the methane and acetylene sputtering yields at Fig. 4 (d–f), which give the ‘‘corrected’’ values in the range 800–1000 K. We note that emission of methyl is strongly dependent on the sp3 hybridization content in the surface [12], which is not warranted by our method of stimulated release of hydrogen, and that these predictions should be accepted here with caution.
Fig. 3. 3D plot of the carbon sputtering yield as a function of both surface temperature and energy of the impacting particle, compared to experimental data from [7] (hollow stars).
Fig. 4. The total carbon sputtering yields after stimulated reduction of deuterium (filled circles), experiments [7] (stars), and results without the forced D reduction (hollow circles), for various impact energies (a–c). Predictions for methane and acetylene sputtering yields (d–f) for high surface temperatures, after the stimulated reduction of deuterium (filled triangles and squares) and original results (hollow triangles and squares).
Finally, the needed reductions of the hydrogen content are shown in Fig. 5, running between 5% and 30% for D/D0, where D is the amount of deuterium atoms in the simulation cell after over-heating and D0 is the number of deuterium atoms before over-heating (i.e. immediately after being cumulatively bombarded). To explain the deviation of the point at 900 K for Ei=30 eV from the trends of 15 and 20 eV we note in Fig. 4(c) that, unlike the cases for 15 and 20 eV, the original (not-corrected) sputtering yield for 900 K is noticeably below those at 800 and 1000 K. The ‘‘right’’ contents of D at temperatures between 800–1000 K for fitting the total carbon yields with experimental values in [7] were found after trying superheating for various durations of time, resulting in various D/D0 and various sputtering rates until the agreement with measurement was reached. It is also interesting to compare the rate of the thermally induced decrease of the deuterium content in carbon obtained by this ‘‘trial-and-error’’ method and those
Fig. 5. Reduction of deuterium from the simulation cell by over-heating. Shown are the fractions (a) D/D0, obtained by trial-and-error simulations of the carbon yield to agree with the experiments of [7] at various impact energies. (b) D/C, after and prior to the forced deuterium reduction by over-heating. Thermally induced deuterium release rate from measurements of Doerner et al. [15] is shown by symbols.
J. Dadras, P.S. Krstic / Nuclear Instruments and Methods in Physics Research B 269 (2011) 1280–1283
obtained in [16] by fitting to the measured D content. The slope of D/C (or D/D0 here, since C content was kept constant during the over-heating) is from [16] proportional to exp (2268/T), presented with -symbols in Fig. 5. 3. Conclusions We have used classical molecular dynamic simulations to model chemical sputtering from a-C:D surfaces, prepared at various surface temperatures in the range of 300–1000 K, bombarded by deuterium atoms for a range of impact energies, 1–50 eV. Our results do not show a temperature dependent peak in the sputtering yields that has been observed in beam-surface experiments [6–8]. We hypothesize that the reason for this disagreement between experiment and simulation lies in the incapability to model thermally induced stimulated processes of diffusion and desorption, which evolve at time scales beyond those that can be described by MD (which is only applicable for a range between ps and ns). By over-heating the simulation cell we forced partial release of deuterium from the cell, and find by trial-and-error the deuterium release fractions by fitting carbon sputtering yields to experimental data in [7]. Acknowledgements We acknowledge support of the Office of Fusion Energy Science, U.S. Department of Energy, under Contract DE-AC05-00OR22725 with UT-Battelle, LLC, of the LDRD program of the Oak Ridge National Laboratory, and of DOE INCITE program. The data were obtained at the ORNL computational resources of the National Center of Computational Sciences.
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References [1] E. Marmar, S. Allen, M. Bell, et. al., Report of the Burning Plasma Organization Panel on Planning for US Participation in ITER, (2008). [2] C.P.C. Wong, Innovative tokamak DEMO first wall and divertor material concepts, J. Nucl. Mater. 390–391 (2009) 1026–1028. [3] R. Andreani et al., Fusion Eng. Des. 81 (2006) 25–32. [4] P. Norajitraa et al., Divertor conceptual designs for a fusion power plant, Fusion Eng. Des. 83 (2008) 893–902. [5] E. Salonen, K. Nordlund, J. Keinonen, C.H. Wu, Bond-breaking mechanism of sputtering, Europhys. Lett. 52 (5) (2000) 504–510. [6] B.V. Mech, A.A. Haasz, J.W. Davis, Isotopic effects in hydrocarbon formation due to low-energy H+/D+ impact on graphite, J. Nucl. Mater. 255 (1998) 153– 164. [7] M. Balden, J. Roth, New weight-loss measurements of the chemical erosion yields of carbon materials under hydrogen ion bombardment, J. Nucl. Mater. 280 (2000) 39–44. [8] F.W. Meyer, P.R. Harris, H. Zhang, W. Jacob, T. Schwarz-Selinger, U. von Toussaint, J. Nucl. Mater. (2010), doi:10.1016/j.jnucmat.2010.08.037. [9] W. Jacob, J. Roth, Sputtering by Particle Bombardment, in: R. Behrisch, W. Eckstein (Eds.), Chemical Sputtering, vol.110, Springer, Berlin, 2007, pp. 329– 400 (Topics in Applied Physics). [10] P.S. Krstic, C.O. Reinhold, S.J. Stuart, Chemical sputtering by impact of excited molecules, European Physics Letters 77 (2007) 33002. [11] S.J. Stuart, P.S. Krstic, T.A. Embry, C.O. Reinhold, Methane production by deuterium impact at carbon surfaces, Nuclear Instruments and Methods in Physics Research B 255 (2007) 202–207. [12] P.S. Krstic, C.O. Reinhold, S.J. Stuart, Chemical sputtering from amorphous carbon under bombardment by deuterium atoms and molecules, New J. Phys. 9 (209) (2007). [13] P.S. Krstic, C.O. Reinhold, S.J. Stuart, Energy and angle spectra of sputtered particles for low-energy deuterium impact of deuterated amorphous carbon, J. Appl. Phys. 104 (2008) 103308. [14] C.O. Reinhold, P.S. Krstic, S.J. Stuart, H. Zhang, P.R. Harris, F.W. Meyer, J. Nucl. Mat. 401 (2010) 1. [15] D.W. Brenner, O.A. Shenderova, J.A. Harrison, et al., A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, J. Phys.: Condens. Matter 14 (2002) 783–802. [16] R.P. Doerner, M.J. Baldwin, G.De. Temmerman, et al., Codeposition of deuterium with ITER materials, Nucl. Fusion 49 (2009) 035002.