Theoretical Studies of the Erosion of (100) and (111) Diamond

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Theoretical Studies of the Erosion of (100) and (111) Diamond Surfaces by Hyperthermal O(3P) Jeffrey T. Paci,*,†,‡ George C. Schatz,‡ and Timothy K. Minton§ †

Department of Chemistry, University of Victoria, P.O. Box 3065, Victoria, British Columbia, Canada V8W 3V6 Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, United States § Department of Chemistry and Biochemistry, Montana State University, Bozeman, Montana 59717, United States ‡

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ABSTRACT: Direct dynamics simulations, based on density functionalbased tight-binding theory with self-consistent charges and also on density functional theory, were used to investigate hyperthermal O(3P) atom collisions with (111) and (100) diamond surfaces. Surface functionalizations produced initially, shortly after the start of oxygen-atom exposure, and during steady-state conditions were investigated. Hydrogen atoms are removed from both surfaces by the incoming oxygen atoms, leading to hydroxyl radicals and water molecules. Both surfaces can be damaged by the incoming oxygen during the initial stages of exposure, resulting in the removal of carbon as CO2 molecules, and functionization of the surfaces with oxygen. The (111) surface is dominated by oxy radicals during steadystate exposure and also has a significant number of carbon atoms with dangling bonds. The (100) surface becomes nearly completely covered by ketone and ether functional groups. Its (2  1) reconstruction is opened in the process. Once covered, the (100) surface resists further erosion, presumably because the ether and ketone groups make the surface carbon atoms unattractive to incoming O atoms which act as electrophiles. Two mechanisms exist for the removal of carbon atoms from the (111) surface. The surface can become graphitized by incoming O atom impacts, and graphite is quickly eroded by hyperthermal O atoms. It can also be directly converted to CO2 as a β-scission-like process makes carbon atoms adjacent to oxy radicals susceptible to electrophilic attack.

I. INTRODUCTION Diamond thin films are candidates for use in low-Earth orbit (LEO), in device applications, and as protective coatings. This interest stems from their excellent mechanical, electrical, and thermal properties and the resistance of diamond to oxidative erosion.1,2 Such erosion considerations are critical because O(3P) is the dominant cause of chemical erosion in this region of the atmosphere of the Earth. This arises because O(3P) is the most abundant species in this region of space, and its diradical character and high energy tend to make collisions reactive. Because of the corotation of the Earth with the spacecraft, the relative velocity between the spacecraft and the O atoms in the outer atmosphere is 7.4 km/s, which makes the collision equivalent to an O atom with 4.5 eV of translational energy striking the leading edge of a spacecraft surface. Other potentially useful carbon-based materials, such as graphite and diamond-like carbon, have significantly higher erosion rates when exposed to oxygen.3 Although quite robust, diamond thin films do erode when exposed to oxygen under certain sets of conditions. Reactive ion etching (RIE) using oxygen-containing plasmas has been used to chemically etch polycrystalline diamond as a means of shaping and smoothing the material.3
6 Similarly, oxygen plasmas have been used to etch single-crystal diamond,7,8 with some of this work leading to a discussion of the need to find more anisotropic r 2011 American Chemical Society

etching techniques.9 Anisotropic etching in the context of this discussion refers to the preferential removal of atoms from a specific crystallographic plane. Its possibility has been demonstrated using a CO2/H2 plasma and processes involving reactiveion and microwave-plasma etching techniques.10 Ion beam etching, which is a specific type of RIE, using beams that either include oxygen or which collide with the sample in the presence of O2 have also been used to etch diamond. Etch rates suggest that the presence of oxygen causes etching to occur chemically rather than by way of sputtering.11
13 Other oxygencontaining gases have also been used.14 During the STS-8 space shuttle mission, (111)-oriented single-crystal diamond was exposed to the residual atmosphere in LEO.1 Subsequent analysis resulted in speculation that O-atom collisions resulted in the formation of functional groups and that they were likely composed of carbonyl and ether linkages.1 This speculation was supported by an earlier X-ray photoelectron spectroscopy-based study in which (110)-oriented single-crystal diamond was oxidized using nitric oxide.15 This study suggested that the process produced two surface oxide functionalities. Received: February 16, 2011 Revised: June 15, 2011 Published: June 16, 2011 14770

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CH4/H2 or CD4/D2 is often used as the growth material during the chemical vapor deposition of diamond thin films (see ref 16 for a description of the growth process that is most relevant to the present study). As a result, these films have hydrogen atoms terminating the diamond growth, i.e., capping what would otherwise be dangling bonds. It is well established that the first step of the reaction of O(3P) with alkanes is the abstraction of hydrogen2,17,18 RH + O f R + OH

ð1Þ

so it is expected that hydrogen abstraction from the diamond surfaces will play an important role. The formation of OH groups on the surface will also be important and may dominate early stages of the oxidation process.19 Some of the structures that might result from the oxidation of the diamond (100) and (111) surfaces have been investigated theoretically.20
24 In ref 24, the authors examine the stabilization that results from adding H atoms to a (100) surface that is (2  1)reconstructed, up to full surface coverage. The energetic consequences of substituting O atoms in ether as well as ketone arrangements was also explored. OH substitution and the addition of functional groups in various combinations were also described. This study suggested the types of functional groups expected and their arrangement, when H, O, and OH are available in the gas phase in non-negligible concentrations near the surface. It indicated that full coverage with ketone-like oxygen atoms is the most probable because of its associated barriers to formation, even though ketone coverage is not quite as stable as full ether coverage. The work by Larsson et al. in ref 23 suggests the same and indicates that the ketones will be present on an unreconstructed surface because the (2  1) arrangement is unstable when functionalized with O atoms. Larsson et al. also described the types of structures that might result from the oxidation of the (111) surface.23 They suggested that atop oxygen structures (oxy radicals) and bridge-type oxygen atoms (ethers) are possible on surfaces that are otherwise hydrogen-terminated. Follow-up work in ref 25 suggested that it is the atop structure that is by far the most important. The difference in the observed behavior of diamond (100) and (111) surfaces when exposed to hyperthermal O(3P) atoms is the primary focus of this work. When nanocrystalline and microcrystalline diamond films are exposed, (100) surfaces endure while (111) surfaces erode significantly.26 Eventually, the (100) surface erodes, but this may happen as reactions that start at the edge of a crystallite. Reference 27 indicates that this difference in etch rates has been observed in other experiments and is related to the effective stabilization of the (100) surface by oxygen functionalization. However, currently there is a limited understanding of the details of the chemistry involved in the erosion of both of these surfaces. In this work, we describe the results of direct dynamics simulations of O + diamond collisions based on the density functionalbased tight binding with self-consistent charges (SCC-DFTB) method28,29 and also with density functional theory, using the Perdew
Burke
Ernzerhof (PBE) functional30 with a double ζ plus polarization (DZP) orbital basis set. These calculations were performed to investigate the erosion of diamond (100) and (111) surfaces that is caused by exposure to hyperthermal O(3P), including changes in the erosion process, going from the early stages involving hydrogen-terminated surfaces to later stages involving oxygen-functionalized surfaces. This work builds upon our earlier study in which we described the corresponding

experiment and how the later erosion stages result in the removal of carbon from (111) surfaces, according to SCC-DFTB-based simulations.26

II. METHOD Following our earlier work,26 SCC-DFTB-based direct dynamics calculations were performed for this study; i.e., forces and energies were derived from SCC-DFTB28,29 calculations. The (100) and (111) surfaces of diamond were modeled, each taken to have 72 carbon atoms, forming slabs with six atomic layers. This was found to be the maximum thickness for which the calculations were computationally affordable. Electron spin was free to become polarized, but the total spin of the slab (oxidized or otherwise) plus the incoming O atom was fixed at two spin-up electrons. Spin
orbit interactions were not included, but in our past studies we have not found this to play an important role for high-energy collisions.31 In an extended system, it is still possible for spin-flips to occur. The Γ point was used to sample the Brillouin zone. Three-dimensional periodic boundary conditions were used. The two unit-cell vectors within the basal planes were optimized, so that the pristine diamond was under zero strain. Their lengths were chosen with considerations of minimizing the interaction of functional groups with those in neighboring virtual unit cells and to allow for surface relaxation and reconstruction. The lattice vector in the direction normal to the surfaces was set to 30 Å, a value large enough to prevent unrealistic interactions between neighboring unit cells in this direction. These unit cell vectors were fixed at these values for all of the simulations. In the (100) case, the back sides (the surfaces opposite the sides with which the incoming O atom collides) were (2  1) reconstructed, with the remaining dangling bonds terminated using hydrogen atoms. In the (111) case, the back sides were also hydrogen-terminated. Intramolecular trajectories were run at 298 K for the atoms in the slabs, and these trajectories were sampled at random to determine initial velocities and positions for all but the incoming O atom. Slabs were exposed to oxygen atoms traveling with 5 eV of translational energy. Normal incidence was considered, with impact locations chosen at random. Trajectories were propagated for 300 fs using a 10.0 au (0.24 fs) time step, on the lowest triplet potential-energy surface. Initial O-atom to diamond-surface separations of 10 au (5.3 Å) were used. Dynamics were followed as long as energy was conserved to within ∼ (0.01 eV/ atom. A fluence of 6  1019 oxygen atoms/cm2 (accumulated in ∼3.5 h) is typical of those used in the experiments described in ref 26. This corresponds to a fluence of 6  103 oxygen atoms/Å2 and can be compared to the fluence in a trajectory which is 1.3  10
2 oxygen atoms/Å2. To rectify the disparity between experimental and calculated fluence, we consider surfaces that are preoxidized to various levels, including surfaces that are close to steady state in oxygen coverage. A large number of trajectories were propagated, with different surface functionalizations, as described in Section III. There are nine states of O(3P) that arise by multiplying three spin states by the three orbital states. The O(3P) atomic term is split into three levels by spin
orbit interaction. The levels are 3 P2, 3P1, and 3P0, where 2, 1, and 0 are values of J, the total electronic angular momentum. At hyperthermal energies, the ground fine structure state 3P2 should project nearly randomly on the orbital states as the oxygen atom approaches the surface. So because there are three orbital states, 1/3 of the collisions will end up on the ground potential surface. 14771

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The Journal of Physical Chemistry C Smaller numbers of trajectories were propagated using forces and energies derived from PBE/DZP calculations. The Spanish initiative for electronic simulations with thousands of atoms (SIESTA) package32,33 was used. Pseudopotentials were of the Troullier
Martins-type,34,35 and they are available from the SIESTA homepage. The Γ point was used for the Brillouin zone sampling in these calculations as well, and a diagonalization was used to solve the Kohn
Sham equations. The unit cell vectors were the same as those used in the SCC-DFTB-based simulations, to allow for a direct comparison of the results of the two methods in cases when the same sets of initial conditions were used. The PBE/DZP-based simulations were very computationally time-consuming, even with system calls to SIESTA executed in parallel. The trajectories, which were propagated for ∼240 fs, each took up to approximately two months on four cores of modern Intel computer chips. Thus, the number of trajectories run based on PBE/DZP had to be limited, even though they may be more accurate than SCC-DFTB. Whenever possible, use was made of the electron density from the previous time step as a starting guess for the new density. Doing so usually greatly accelerates self-consistent field (SCF) convergence. SCF issues made it necessary to write software to detect problems and when appropriate make multiple attempts at convergence, at a given geometry, using different sets of simulation tools. SCC-DFTB and PBE/DZP are expected to predict bond lengths and angles to an accuracy of a few tenths of an angstrom and a few degrees, respectively, for the systems studied here. However, the barrier heights associated with the chemical reactions are unlikely to be predicted with the same high level of accuracy. Nevertheless, it is hoped that the use of the semiempirical method, SCC-DFTB, and a good basis set with the parameterfree density functional, PBE, will provide complementary information for these systems. As in our previous study on collisions between oxygen atoms and graphene,31 after the impact and/or adsorption of the colliding oxygen atom, the functionalized surfaces become vibrationally excited. Because the systems are not coupled to a thermal bath, this excitation results in an increase in temperature. The collisions cause the breaking and creation of new chemical bonds, so it is difficult to calculate the increase in temperature accurately. Coupling the systems to baths would be unrealistic because localized vibrational excitations are a critical aspect of the dynamics we simulated here. This is because they cause reactions to occur, as shock-waves caused by the incoming oxygen atom move outward from the location of impact, that would otherwise not take place. It is the confinement of the shock-waves by the finite slab sizes that causes the heating. These complications limit the propagation time for which trajectories can be accurately propagated. Therefore, we restrict our analysis to propagation times of ∼200 fs beyond the time at which the incoming O atom collides with the surface. Thus we expect these issues to have only a minor effect on the accuracy of the reported dynamics.

III. RESULTS AND DISCUSSION Trajectory calculations were run using different sets of surface functionalizations for both (111) and (100) surfaces. Models representing the surfaces prior to O-atom exposure, shortly after exposure has begun, and during steady-state conditions were examined. A. Pristine Surfaces. The diamond surfaces prior to exposure are expected to be terminated with hydrogen atoms and, in the

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Figure 1. Side view [panel (a)] and top view [panel (b)] of the pristine H-atom-terminated (111) diamond surface. Analogous images of the diamond (100) surface are shown in panels (c) and (d).

case of the (100) surfaces, (2  1) reconstructed. Surfaces representing these cases are shown in Figure 1. Twenty SCC-DFTBbased trajectories for each model were examined. These models were developed to explore the reactivity that might occur early in the erosion process. For the (100) surface, ten trajectories resulted in inelastic scattering, and eight produced OH radicals, leaving a surface carbon atom with a dangling bond. One trajectory made water. In another, the surface reconstruction was broken, forming an atop O atom. The local spin density on the oxygen atom showed an excess of ∼1 spin-up electron; it became doublet. The neighboring carbon atom with a dangling bond also had an excess of ∼1 spin-up electron. Thus, a spin flip would allow for ether formation. The O atom does not leave the surface because it used one of its excess spin-up electrons to form a covalent bond with a carbon atom, which had a spin-down electron to contribute. For the (111) surface, hydroxyl radicals were produced in 13 of the trajectories; water was produced in five; and inelastic scattering was observed in two. The hydrogen atoms on the (111) surface were more reactive than those on the (100) surface. Abstracting hydrogen from (111) leaves a carbon atom with a dangling bond and three unstrained C
C bonds with other sp3-hybridized carbon atoms. The abstraction of H atoms from the [(2  1)-reconstructed and H-atom terminated] (100) surface leaves carbon atoms with dangling bonds that have three strained sp3 bonds with neighboring carbon atoms. One would expect this to be a high-energy structure as compared to the analogous (111) surface structure and thus to require more energy to create, making it a less probable reaction. Regardless, these simulations suggest that when exposed to a hyperthermal O atom beam H atoms will be removed from both (111) and (100) surfaces. The unpaired electron spin as deemed from the Mulliken charges on the atoms at the ends of the trajectories was sometimes (approximately 30% of the trajectories) observed to accumulate in unrealistic locations. For example, it was observed to localize on (2  1)-reconstructed carbon atoms that were terminated with hydrogen atoms and on the H atom of a hydroxyl group. Also, it was absent from the O atom of hydroxyl groups and sometimes from (2  1)-reconstructed carbon atoms that had lost their hydrogen-atom termination. The connection of these spin density results to reaction mechanisms is not clear; however, this is one negative feature of the SCC-DFTB results. 14772

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Figure 2. Side view [panel (a)] and top view [panel (b)] of a partially oxidized (111) diamond surface. A partially oxidized diamond (100) surface is shown in panels (c) and (d).

Isotope effects were also investigated. Diamond films are sometimes grown using feed gases that include deuterium instead of hydrogen. The resulting deuterium-atom growth termination could play an important role because D atoms could slow abstraction reactions by a factor of more than 10 compared to H atoms.36 With this as motivation, we simulated O-atom collisions with the (100) and (111) diamond surfaces shown in Figure 1 but with deuterium in place of the hydrogen atoms. Twenty SCC-DFTB-based trajectories were run for each surface. In the (111) trajectories, hydroxyl radicals were formed 14 times and water was formed twice, while in the (100) trajectories hydroxyl radicals were formed in eight, water was formed in three, and a hydroxyl group was formed in one. The rest of the trajectories showed inelastic scattering, with the exception of one (100) trajectory that produced a ketone by way of a lattice-damaging mechanism described in Section III B2. These results suggest that deuterium like hydrogen is abstracted in a hyperthermal O-atom beam and thus does not play an important role in the steady-state erosion process. B. Partially Oxidized Surfaces. Motivated by the work in refs 23 and 25, we also exposed the (111) surface shown in Figure 2a to hyperthermal O atoms. The surface is comprised of two atop O atoms, one ether, and one hydroxyl group. Similarly, we modeled O atom collisions with the (100) surface shown in Figure 2b, which is a surface consistent with the findings of refs 23 and 24. This surface has two ketones, one ether, and a hydroxyl group. The ketones and ether exist on unreconstructed sites, as first described in ref 22. The hydroxyl group is attached to a (2  1)-reconstructed carbon atom. The remainder of the surface atoms are (2  1)-reconstructed. All other carbon atom valencies are satisfied with hydrogen atoms for both surfaces. These models were designed to capture the reactions that might occur shortly after the erosion process begins. Given sufficient time, atop oxygen atoms on a (111) surface like the one shown in Figure 2a may spontaneously abstract a neighboring hydrogen atom, forming a hydroxyl group and a carbon atom with a dangling bond. However, such a process is not expected to have important implications for the discussion below. 1. SCC-DFTB. One hundred trajectories based on SCC-DFTB were run for the (111) and (100) surfaces. Collisions with the (111) surface resulted in the ether group opening to become an atop O atom and a carbon atom radical in all but five of the trajectories. Thus, the barrier to the transformation is not large.

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W Reaction producing CO2 from an O-atom collision with Figure 3. b an oxidized (111) diamond surface, as illustrated using snapshots from a PBE/DZP-based trajectory. Following arrows clockwise: The incoming O atom (13.3 fs) collided with an atop O atom, pushing it aside (44.8 fs). The force of the collision broke a C
C bond, with the incoming O atom adding itself to the surface, forming an ether (71.4 fs). Another C
C bond broke (85.9 fs), followed by an O
C ether bond (105.2 fs). Finally, a C
C bond broke, releasing a CO2 molecule (157.2 fs). Click here for an animated view of this trajectory.

The observed instability of such ether groups has been previously reported.25 The reverse reaction, i.e., the subsequent conversion of the atop O atom to an ether group, was not observed. Oxygen molecules were produced in 22 of the (111) trajectories. In every case, they were produced by way of an Eley
Rideal (direct) mechanism. Their formation produced a dangling bond on the surface, which was in addition to the one created in almost all cases by the conversion of the ether to an atop O atom. These dangling bonds provide sites of enhanced reactivity. In seven cases, O2 molecules were subsequently adsorbed at dangling bonds, forming peroxy radicals. This enhanced reactivity also resulted in the formation of an atop O atom at the dangling bond formed by the conversion of the ether to an atop oxygen atom, in 14 of the trajectories. An H atom was displaced by the incoming O atom, resulting in the formation of a gaseous hydroxyl group, in more than half (51 of 100) of the trajectories. Also, an OH radical was formed, and inelastic scattering occurred, each in two trajectories. OH-mediated H-atom migration and peroxide formation were each observed in one trajectory. H atoms were frequently passed between atop O atoms which at least temporarily became OH groups. Similar behavior was observed previously in our molecular dynamics simulations of graphite oxide.37 Inelastic collisions were observed in 44 of the (100) surface trajectories. OH radicals formed in 25; water formed in 15; and an oxygen molecule was formed in one. Ketones formed in four, and OH groups formed in 11. Ether groups formed in three of the trajectories and appear to be stable; the ether that was on the surface before the collisions was never observed to open. Occasionally, H atoms were passed between O atoms which at least temporarily became OH groups. This meant that the carbon atoms that were part of the ketones became radicals when their O atoms became hydroxyl groups and that the O atoms that were initially part of an OH group became radicals. Overall, the (100) surface was less prone to oxidation than the (111) surface and more likely to cause inelastic scattering. 14773

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Figure 4. Electron-pushing diagram showing a plausible mechanism for the removal of carbon from the (111) diamond surface. An oxy radical with significant double bond character facilitates the formation of a CdO double bond on three occasions, in this process which is analogous to β-scission.38 Double arrows indicate resonance structures.

Nevertheless, hydrogen atoms were readily displaced from both surfaces. 2. PBE/DZP. Ten PBE/DZP-based trajectories were also run for each of the surfaces shown in Figure 2. For the (111) surface, the ether group became an atop O atom and a carbon atom radical during the initial geometry optimization, so whether or not this ether opened during the direct dynamics was not an issue. As in the SCC-DFTB case, this suggests that the barrier to this process is not large. Again, the reverse reaction was never observed. Oxygen molecules were produced in three of the ten (111)surface trajectories, by way of an Eley
Rideal mechanism, and the molecules were not subsequently physisorbed. Atop O atoms were produced in four of the trajectories, and a hydroxyl group and a hydroxyl radical were each formed in one. All of these reactions are consistent with what was observed in the SCC-DFTB-based trajectories. One (111)-surface trajectory showed damage to the diamond lattice, snapshots of which are shown in Figure 3. As is indicated in the figure, a CO2 molecule was produced within ∼120 fs of the collision. An electron pushing diagram illustrating a plausible reaction mechanism is presented in Figure 4. In the oxy radical there is a resonance structure (second diagram) that involves a CdO double bond. In this resonance structure, a carbon atom is susceptible to attack by the incoming O atom, which acts as an electrophile.2 For the (100) surface, OH radicals, ketones, ether and hydroxyl groups, and water were formed, consistent with the SCC-DFTB results. However, only one of the trajectories showed inelastic scattering, a rate significantly lower than that observed in the analogous SCC-DFTB-based simulations. Oxy radicals were also observed being formed. In two cases, H atoms were displaced by the incoming O atom, causing the H atom to leave the surface. In one, the incoming O atom collided with the H of a hydroxyl group and a hydrogen atom on the surface. The hydroxyl H was removed and departed the surface, and a new hydroxyl group was formed in place of the hydrogen atom that was initially tethered directly to the surface. In the other, a H atom was eliminated in a process that appeared to be a failed hydroxyl group-forming trajectory, in which the

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incoming O atom displaced a H atom from the surface. The process was somewhat similar to the higher-energy H-elimination mechanism for reactions between O(3P) and CH4, described in ref 39. Several trajectories showed some type of damage to the diamond lattice. One produces CO2 from the incoming O atom and a ketone group. Two trajectories showed ketone formation, resulting from the collision of the incoming oxygen atom with, and subsequent bonding to, a carbon atom in the second diamond layer. Two C
C bonds were broken, and a double bond was formed with the incoming O atom, to form the ketone. These simulations do not refer to the steady-state coverage of this surface as suggested by the high rate of H reactivity, so these may be transient processes. The surface which is mostly (2  1) reconstructed has the second diamond layer exposed, which may be the reason for its reactivity. Nevertheless, these simulations suggest that this largely reconstructed and hydrogen-terminated surface will erode layer-by-layer. No energy conservation problems were encountered during any of the PBE/DZP-based trajectories. At the ends of the trajectories, unpaired up- and down-electron spin was observed to accumulate at dangling bonds, on inelastically scattered O atoms, on the oxygen atoms of O2 molecules, etc. It appeared in reasonable locations, assuming global ground triplet electronic-state dynamics. A second set of pseudopotentials was used to repeat the 20 trajectories described above, to explore sensitivity to the parameters that they contain. Core radii of 1.15, 1.15, and 1.25 a0 were used for carbon, oxygen, and hydrogen, respectively, and nonlinear exchange-correlation correction pseudocore radii of 1.50 and 1.17 a0 were used for carbon and oxygen. For collisions with the (111) surface, the observed dynamics were qualitatively the same for both sets. For collisions with (100), the chemistry observed was often a function of the pseudopotentials. Both sets predicted the same kinds of reactivity but not necessarily for identical sets of initial conditions. C. Steady-State Coverages. The simulations described in previous subsections suggest that hydrogen atoms will be removed from both surfaces during the early stages of exposure to hyperthermal O atoms. Therefore, it is expected that hydrogenfree surfaces will dominate during most of the erosion process. Testing was performed to determine the (100) and (111) surface oxygen atom coverages that resulted in an approximately equal probability of incoming atom absorption and the incoming atom causing the removal of an oxygen atom already on the surface. These coverages were used as estimates of those that exist during steady-state O-atom exposures. No hydrogen atoms were included except those used to satisfy the valencies of atoms on the backsides of the slabs. Coverages of four, six, and eight O atoms on the surfaces, which have space for up to twelve O atoms, were examined. Functionalization locations were chosen at random. Twenty trajectories were propagated for each coverage. Eight O atoms on the (100) surface resulted in behavior that was below the steady-state criteria, so the addition of twelve O atoms was also examined. The coverages that most closely met the steady-state criteria were used in the trajectories described below and are shown in Figure 5. They are eight and twelve O atoms on the (111) and (100) surfaces, respectively. Full ketone coverage of the (100) surface has been previously reported to be energetically favorable.24 We did not consider surface roughness on a scale larger than a single diamond layer. Multilayer effects may be important in the erosion process,40,41 but their inclusion is beyond the scope of this work. 14774

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Figure 5. Side view [panel (a)] and top view [panel (b)] of a (111) diamond surface with steady-state O-atom coverage. An analogous diamond (100) surface is shown in panels (c) and (d).

1. SCC-DFTB. One hundred SCC-DFTB-based trajectories were run for each of the surfaces shown in Figure 5. The results were described in detail elsewhere,26 so only those most relevant to the current work are presented. Two processes that resulted in damage to the (111) surface were observed in the trajectories. One involved a partial graphitization in which a C
C bond between the second and third diamond layers was broken (see Figure 8 of ref 26). This occurred in five of 100 trajectories. The geometry change was such that it brought a carbon atom from the second diamond layer into the plane of the first. This change was such that the reverse process would seem to require the surmounting of a significant energy barrier. Graphite erodes quickly in a hyperthermal O-atom beam,31 so this graphitization process is expected to leave the diamond surface susceptible to erosion during subsequent O-atom collisions. Note that it is also possible that this propensity for graphitization is related to the thinness of the slab.26 A damage process which involved the removal of CO2 (see Figure 9 of ref 26) was also observed, in a trajectory propagated with slightly less than the steady-state coverage (six instead of eight precollision surface O atoms). It was similar to the one shown in Figure 3; i.e., it was driven by a β-scission-like process. Thus, these simulations suggest that the (111) surface is prone to erosion. No mechanism for the removal of carbon atoms was observed in the (100) trajectories. Inelastic scattering was the most probable collision event (see Figure 10 of ref 26). Sheet damage was observed in one of the trajectories; a partially detached carbonyl group was formed. However, given sufficient time, the carbonyl may have lain back down, reforming a ketone. The ketone reformation would almost certainly be barrierless, as it would satisfy four dangling bonds. This damage suggests that layer-by-layer erosion of the (100) surface may be possible. Nevertheless, the absence of a mechanism for carbon removal suggests that (100) is more erosion resistant than the (111) surface. 2. PBE/DZP. Sets of trajectory initial conditions, including all of those that resulted in particularly interesting chemistry during the SCC-DFTB-based calculations, were reused in PBE/DZPbased trajectories. Ten were rerun for (100) and ten for (111) surface collisions. This was done to determine if the two methods predict similar reactivity and especially to investigate the dynamics according to PBE/DZP which may be more accurate than those predicted by SCC-DFTB.

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W Reaction producing CO2 from an O-atom collision with Figure 6. b an oxidized (111) diamond surface, as illustrated using snapshots from a PBE/DZP-based trajectory. Following arrows clockwise: The incoming O atom (9.7 fs) strikes a carbon atom in the second diamond layer (46.0 fs). A C
C bond between the first and second diamond layers breaks (61.7 fs), followed by the breaking of a bond between the second and third diamond layers (93.1 fs). A new bond forms between this second-layer carbon atom and a neighboring atop oxygen atom (226.2 fs). Note that the PBCs satisfy the valencies of the carbon atoms at the left side of the slab. A C
C bond breaks, resulting in a tethered CO2 structure (243.1 fs). Click here for an animated view of this trajectory.

Collisions with the (111) surface usually resulted in the formation of additional atop O atom structures (seven of ten trajectories) or the formation of O2 molecules (two of ten trajectories). This suggests that the steady-state O-atom coverage may be somewhat higher than that predicted by SCC-DFTB. PBE/DZP otherwise predicted dynamics that appeared qualitatively similar to those predicted using SCC-DFTB. Damage to the carbon surface was observed in one of the (111) collision trajectories. Snapshots of this trajectory are shown in Figure 6. The final structure (see the 243.1 fs panel of Figure 6) contains the same tethered CO2 structure that went on to produce a CO2 molecule in Figure 3 (see the 85.9 fs panel of Figure 3). Thus, this damage suggests a mechanism for the removal of carbon from the (111) surface. During the trajectory shown in Figure 6, a C
C bond between the second and third diamond layers was broken (see the 61.7 and 93.1 fs panels). Its breakage releases the carbon atom that becomes part of the would-be CO2. Therefore, even though the trajectory does not result in graphitization, it does illustrate that C
C bonds necessary for graphitization are sometimes broken during PBE/DZP-based simulations, just as in those based on SCC-DFTB. Both the SCC-DFTB- and PBE/DZP-based trajectories showing the removal of carbon or the near removal of carbon suggest that it is CO2 not CO that leaves the (111) surface. After graphitization, both CO2 and CO are expected to be produced in a hyperthermal O-atom beam.31 Therefore, additional simulations and experiments looking for evidence of CO production would be helpful in determining whether direct reactions forming CO2 or graphitization followed by reactions transforming graphite to CO and CO2 dominate the erosion process. Experimental evidence of graphite formation suggests that the latter plays an important role.26 Pandey chain reconstruction42 of the (111) surface was not observed. This is a reconstruction of bare (111) surfaces, and it is not clear either in the experiments or in our calculations that the conditions needed for this to take place are present. We imagine 14775

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react with the carbon atoms of the surface. Thus, these simulations suggest a plausible explanation for its erosion resistance. The experiment26 that motivated this work used chemical vapor deposition diamond films, which contained microcrystallites whose surfaces were oriented randomly with respect to the overall surface normal. Therefore, individual crystal faces were oriented at almost any angle (from 0 to 90°) with respect to the incoming O atoms. We did not conduct an exhaustive study of (100) surfaces of all possible orientations, but as far as we could tell, the (100) faces did not react no matter what their orientation, with average incident beam energies of 5 and 7.5 eV. Note that in the experiments the beams had energy widths (fwhm) of about 1.5 and 2.0 eV, respectively, so a range of incidence energies was in fact probed. W Nondamaging O-atom collision with an oxidized (100) Figure 7. b diamond surface, as illustrated using snapshots from a PBE/DZP-based trajectory. Following arrows clockwise: The incoming O atom (9.7 fs) strikes a ketone oxygen atom, forming a peroxy radical (29.0 fs). The radical migrates to an adjacent O atom (33.9 fs), and the underlying carbon atom (2  1) reconstructs with a neighboring carbon atom (56.8 fs). The radical migrates to another adjacent ketone oxygen atom (96.8 fs). (2  1) carbon reconstruction bonds migrate (56.8, 96.8, and 243.1 fs), and a row of ketones is transformed into a row of ethers (243.1 fs). Click here for an animated view of this trajectory.

that the surface starts out with full hydrogen atom termination. As it is exposed to oxygen atoms, the hydrogen is gradually removed. At the same time, various oxygen atom functionalities are gradually added, so large areas of bare (111) surface do not arise. Pandey reconstruction makes for a more graphite-like surface, in which case our earlier work on graphite explains the chemistry.31 Collisions with the (100) surface resulted in the formation of O2 (four of ten trajectories), peroxy radical groups (four of ten), or peroxide rings (two of ten). Peroxy radical formation was accompanied by (2  1) reconstruction of a pair of carbon atoms (see Figure 7). Although PBE/DZP predicts that peroxy radical formation (see Figure 7) is a more probable event than SCC-DFTB, its formation is not suggestive of a mechanism for the removal of carbon, nor is the formation of peroxide rings. Instead, one might expect subsequent O-atom collisions with or near peroxide groups to result in the release of an O2 molecule, for example. Ether groups were often observed to form after O-atom impact. They appeared in nine of the ten trajectories and usually appeared in full rows (see the 243.1 fs panel of Figure 7). These groups were formed by having one of the ketone bonds break, the affected O atom move toward a neighboring C atom, and a new O
C bond form to that carbon. Reference 40 suggests that ether groups dominate the (100) surfaces at oxygen saturation coverages. Our PBE/DZP results indicate that this may be the case (see Figure 7). The incoming O atom appears to provide sufficient energy to overcome the barrier between the ketones which are energetically easier to form but less energetically stable than the ether groups.24 This is in contrast to the SCC-DFTB-based results in which this type of ketone to ether conversion was not observed. Regardless, both SCC-DFTB- and PBE/DZP-based simulations suggest that the (100) surface will be nearly fully covered by O-atoms during steady-state exposure. Neither suggested any mechanism for the removal of carbon. The electron-withdrawing effects of full ketone or ether coverage may leave few opportunities for the incoming O atom, which acts as an electrophile,2 to

IV. CONCLUSIONS Direct dynamics simulations based on forces and energies from SCC-DFTB and PBE/DZP calculations were performed to investigate hyperthermal collisions between O(3P) atoms and (111) and (100) diamond surfaces. (111) surfaces are expected to be hydrogen-terminated before O atom exposure, while (100) surfaces will be (2  1) reconstructed and hydrogen-terminated. Exposure to hyperthermal O atoms results in the conversion of these hydrogens to OH groups and in the removal of hydrogen as part of OH radicals and water in the early stages of the exposure. Both surfaces are soon stripped of hydrogen, and the surfaces become increasingly oxidized. The (2  1) reconstruction can be broken. The substitution of hydrogen with deuterium atoms has no significant impact on the dynamics. As the (111) surface becomes increasingly oxidized, oxy radicals begin to dominate, a finding consistent with earlier static density functional theory-based results.23 A significant concentration of carbon atoms with dangling bonds is also present. Oxygen molecules are frequently formed as incoming O atoms react with oxy radicals already on the surface by way of an Eley
Rideal mechanism. They are sometimes adsorbed at dangling bonds. The (100) surface becomes nearly fully covered with ketones and ethers as the oxidation process reaches its steady state. The surface reconstruction is broken in the process. Incoming O atoms, which act as electrophiles, damage both surfaces during the early stages of the erosion process. The (100) surface may erode layer-by-layer by producing CO2, while a significant concentration of hydrogen atoms remain at the surface. However, as additional ketone and ether groups form, they seem to act as a protective layer, preventing the electrophilic attack of underlying carbon. In this way, they act to significantly slow erosion. The (111) surface can erode by two mechanisms. Graphitization takes place, as bonds between the second and third diamond layers break, as a result of O-atom impact. Graphite is quickly eroded by hyperthermal O atoms. Processes related to β-scission in which oxy radicals leave adjacent carbon atoms susceptible to electrophilic attack also lead to carbon removal. These mechanisms make the (111) surface erode significantly more quickly than (100). W b

Web Enhanced Feature. Animated views of Figures 3, 6, and 7 are available in the HTML version of the paper.

’ ACKNOWLEDGMENT JTP thanks J. E. Wulff for insightful discussions. This work was supported by grants from the National Science Foundation 14776

dx.doi.org/10.1021/jp201563m |J. Phys. Chem. C 2011, 115, 14770–14777

The Journal of Physical Chemistry C (grants CHE-0943639 and CMMI-0856492). GCS was supported by AFOSR Grant FA9550-10-1-0205.

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