J. Phys. Chem. C 2010, 114, 7045–7053
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Water Adsorption on Native and Hydrogenated Diamond (001) Surfaces O. Manelli,†,‡ S. Corni,‡ and M. C. Righi*,†,‡ Dipartimento di Fisica, UniVersita` di Modena e Reggio Emilia, Modena, Italy, and Centro S3, CNR-Istituto di Nanoscienze, Modena, Italy ReceiVed: NoVember 18, 2009; ReVised Manuscript ReceiVed: February 26, 2010
Understanding water interaction with diamond surfaces is fundamental for applications in tribology, device technology, and microelectronics operating in biological environments. In this paper, we provide a full microscopic description of the interaction of water with diamond (001) surfaces. We performed ab initio calculations within the framework of density functional theory including long-range van der Waals interactions. We considered both native and hydrogenated surfaces. We calculated the structure and the energetics for molecular and dissociative adsorption, and in the case of exothermic processes, we determined the energy barriers for dissociation. Our results allow prediction of the formation of water islands on native surfaces that grow along and perpendicularly to dimer rows. Moreover, they highlight the role played by the water coverage in determining the adsorption mode (physisorption or dissociation), suggesting an explanation for experimental results on similar Si(001) surfaces. Finally, we provide an understanding on the mechanism of carbon dangling bond passivation by water which is the key factor in determining the excellent tribological performances of diamond in humid environments as measured in experiments. Introduction Water interaction with diamond is an interesting problem of fundamental chemistry, which is also important for practical applications. Diamond is, in fact, a biocompatible material presenting an extremely good stability and a full compatibility with microelectronics processing methods. The combination of these properties renders diamond highly promising for integration of DNA and other biological materials with microelectronics.1 In addition, diamond presents unique electronic properties such as the negative electron affinity of the hydrogenated surface and its p-type conductivity. Remarkably, these properties depend on the interaction with water.2 Moreover, thanks to the outstanding mechanical and frictional properties, diamond is receiving a lot of attention for tribological applications.3 Diamond, artificially grown by chemical vapor deposition (CVD), is used for coating of tools and automotive components and is considered a very promising material for micro/nanoscale applications such as MEMS/NEMS.4 The tribological performances of diamond highly depend on the air humidity. While diamond films obtained by CVD are mostly hydrogen terminated, carbon dangling bonds (DBs) can be produced by mechanical rubbing.5 The presence of DBs can cause a significant friction increase as observed in vacuum and in dry conditions,6 and it has been recently demonstrated by spectroscopic analysis that the ultralow coefficient of friction (COF) of diamond in humid environments is due to DB passivation by water molecules.7 In this paper, we investigate the microscopic mechanisms of diamond surface passivation by water. It is known from experiments that water adsorbs both on the clean and on the hydrogenated diamond surfaces. In the experiment by A. Laikhtman and collaborators,8 after exposure to water vapor at room temperature, the oxygen peak was * To whom correspondence should be addressed. E-mail: mcrighi@ unimore.it. † Universita` di Modena e Reggio Emilia. ‡ INFM-CNR National Research Center on nanoStructures and bioSystems at Surfaces (S3).
detected by X-ray photoelectron spectroscopy (XPS) both on bare and fully hydrogenated samples, with a larger area on the bare one. To distinguish between molecular and dissociative adsorption, the samples were annealed at 300 °C. The oxygen peak disappeared on the hydrogenated surface, while it remained stable on the bare surface, indicating the presence of chemical bonding. Dissociative adsorption at room temperature9 and oxidation at high temperatures10 were reported by other authors that analyzed the C(001) surface. In the present study, we consider the (001) surfaces, since the CVD growth is usually performed in the [001] direction to obtain smoother surfaces. Despite its importance, the problem of water interaction with diamond has been little investigated by theory. The only ab initio study on the interaction between water and the C(001) surface we are aware of is based on a cluster model of the surface consisting of one dimer.11 The predictions obtained with this model, which are the absence of a molecular adsorption state and a high energy barrier for molecular dissociation, are in disagreement with the experimental observations abovedescribed. Water interaction with the hydrogenated H-C(001) surface has been studied by K. Larsson et al. who investigated the electron transfer mechanism that gives rise to the surface conductivity,12 and by H. X. Young and coauthors who simulated the adsorption of an isolated water molecule on a selected surface location.13 We performed a comprehensive study of water interaction with the (001) surface of diamond, taking into consideration the bare surface, the fully hydrogenated surface, and hydrogenated surfaces containing DBs in different concentrations. We studied both molecular adsorption and dissociative adsorption. The calculations were repeated for different water coverages: we found that the molecule-surface interaction is highly affected by the presence of already adsorbed molecules. In particular, the activation energies for dissociation can decrease by 1 order of magnitude from the isolated molecule to the full coverage conditions. The calculations were performed in the framework of the density functional theory (DFT), by also
10.1021/jp910971e 2010 American Chemical Society Published on Web 03/25/2010
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Figure 1. Top view representation of the water-C(001) adsorbate system at the different water coverages considered. The condition of full coverage [θx ) 1, θy ) 1] (a) is simulated by using a (2 × 1) cell; lower coverages [θx ) 1, θy ) 0.5] (b) and [θx ) 0.5, θy ) 1] (c) are simulated by means of (2 × 2) and (4 × 1) cells, respectively. The use of a (4 × 4) cell allows one to mimic a condition [θx ) 0.5, θy ) 0.25] where the molecule is almost isolated from its periodic replicas (d).
including the long-range van der Waals (vdW) interactions (DFT+vdW in the following). The importance of considering the nonlocal interactions is highlighted by comparing the DFT+vdw results with the DFT ones. We discuss our findings in relation to the experimental knowledge on water interaction with diamond, and we consider their implications in the tribological problem. Methods We performed plane-wave pseudopotential first principles calculations based on DFT with the QUANTUM ESPRESSO software.14 The approximation for the exchange-correlation functional was selected by performing test calculations on the structural and electronic properties of bulk diamond: we compared the local density approximation (LDA) to the generalized gradient approximation (GGA) in two different parametrizations: PW9115 and PBE.16 The results obtained with PBE turned out to be in closest agreement with experiments.17 It is well-known that DFT in the LDA or GGA approximations fails in describing nonlocal interactions such as the longrange vdW interactions. Because of the fundamental role played by the vdW interactions in many systems, a great effort has been made in developing approaches to remedy the deficiency of current DFT formalism.18–26 In the DFT+LAPs method, this is accomplished by adding local atomic potentials (LAPs) in the local part of the pseudopotential.27 The simplicity of this approach along with its accuracy in describing the interaction energies of a large variety of complexes dominated by both vdW and hydrogen-bonding interactions induced us to adopt the DFT+LAPs to study water adsorption on diamond surfaces. However, it should be kept in mind that the DFT+LAPs has never been used to study adsorption on solid surfaces and screening effects (by diamond dielectric function) are not treated
by DFT+LAPs. Many works on molecular adsorption based on different DFT+vdW schemes have recently appeared in the literature.28–33 Discussing the merit of the DFT+LAPs in quantitatively describing the adsorption energies is beyond the scope of this paper; our aim is to investigate the effects of the inclusion of the vdW interactions on the adsorption trends. This is accomplished by comparing the DFT and DFT+LAPs results. For the first kind of calculations, we used ultrasoft pseudopotentials generated with the PBE approximation and a cutoff energy for plane-wave expansion of 30 Ry. For the second kind of calculations, we used revPBE34+LAPs norm-conserving pseudopotentials27 and a cutoff energy of 100 Ry.35 Diamond surfaces were modeled using periodic supercells containing a slab of 12 diamond layers and a vacuum region 15 Å thick. In order to simulate different water coverages, we adopted supercells having different in-plane dimensions; in particular, we considered (2 × 1), (2 × 2), (4 × 1), and (4 × 4) 2D cells. A top view representation of the water coverage realized on the C(001) surface by adopting a (2 × 1) cell is presented in Figure 1a. This condition, consisting of one water molecule per carbon dimer, will be referred to as the full coverage condition. Figure 1b-d shows situations of different coverages along the [110] and [1j10] directions (from now on referred to as x and y directions) realized by adopting the wider 2D cells. We tested the accuracy of the surface calculations with respect to the number of k points adopted to sample the Brillouin zone (BZ) by comparing the results obtained with Monkhorst-Pack36 (MP) grids of different density. The result of this comparison37 along with the gain of computational resources motivated our choice of considering a 4 × 8 × 1 MP grid to sample the (2 × 1) cell. Equivalent MP grids were used to sample the BZ of the larger 2D cells.
Water Adsorption on Diamond (001) Surfaces As anticipated in the Introduction, we studied the interaction of water with diamond taking into consideration the bare (dimer reconstructed) C(001) surface, the fully (mono)hydrogenated H-C(001) surface, and hydrogenated surfaces containing different concentrations of carbon dangling bonds (DBs). We studied both molecular and dissociative adsorption. The most stable configuration for the molecular adsorption was identified by calculating the molecule adsorption energy for different lateral positions and orientations with respect to the underlying surface. We adopted a homogeneous grid of eight points with 1.26 Å spacing to construct the potential energy surface (PES) experienced by a water molecule on the C(001) surface at full coverage conditions. The optimization of the adsorbate geometry at each grid point was performed by relaxing all the system degrees of freedom except for the slab bottom layer and the (x, y) coordinates of the oxygen atom. In this way, the molecule, initially positioned at 2 Å distance from the surface, could rotate and translate along the z direction. The system configuration identified as the PES absolute minimum was further relaxed removing the constraint on the lateral coordinates of the oxygen atom. The PES calculation was then repeated for different initial molecular orientations. In particular, we considered the orientations obtained by aligning one OH bond of the molecule along the y direction, and then by considering the molecular axis along the x, y, and z directions. In the latter case, we took into consideration the two possible situations for a vertical disposition of the molecule: one with hydrogen atoms pointing toward the surface, the other with the oxygen atom pointing toward the surface. Molecular adsorption at different water coverages and for different degrees of surface hydrogenation was investigated by partial PES calculations, i.e., sampling those positions and orientations that were considered the most relevant on the basis of the information acquired by the complete PES calculation previously described. The analysis on the effects of coverage and surface termination in molecular adsorption was performed by comparing the molecular adsorption energies Emol ads of the most stable configuramol is obtained from supercell tions identified on each surface. Eads mol tot tot tot total energies as Eads ) Esurf+H2O - (Etot surf + EH2O), where Esurf+H2O is the energy of the supercell containing the diamond slab and tot is the energy of the same supercell the adsorbed molecule, Esurf containing only the optimized diamond slab, and EHtot2O is the energy of an isolated water molecule, calculated in a cubic mol can be supercell of 20 Å edge. At not too low coverages, Eads decomposed in one contribution originating from the interaction between the coadsorbed molecules (EH2O-H2O) and one contribution coming from the molecule-surface interaction (EH2O-surf). The former can be obtained by comparing the energy of a water molecule in the adsorbed configuration to the energy of the isolated water molecule. The energy of the molecule in the adsorbed configuration is obtained from the supercell calculation performed for the adsorbate system by excluding the diamond slab while leaving the water molecule fixed in its optimized adsorption configuration. Physisorption is by definition governed by nonbonded interactions, such as dispersion, electrostatic, and polarization. The surfaces studied in this work involve somewhat polar bonds (the C-H bonds of the hydrogenated surface) and polarizable bonds (such as the C-C dimer bonds of the reconstructed C(001) surface, which involve a polarizable π-electron cloud). Therefore, we considered it useful to perform the Lo¨wdin population analysis38 in order to identify the charge displacement occurring in such bonds, and how this is modified upon water adsorption. This is done by preliminarily projecting the elec-
J. Phys. Chem. C, Vol. 114, No. 15, 2010 7047 tronic wave functions on a localized basis set. Since the latter spans a smaller space than the original plane-wave basis set, a small portion of the total charge is lacking. Such portion is called the spilling parameter. In our calculations, we obtained a small value for the spilling parameter, corresponding to 0.5% of the total charge. As a next step in the investigation of water adsorption on diamond surfaces, we considered the process of dissociative adsorption. We took into consideration dissociation from the molecular adsorption states identified as the most stable. The dis energy of the dissociation reaction can be derived as ER ) Eads mol dis - Eads , where Eads is the energy for the dissociative adsorption mol defined above. No zero-point calculated in analogy with Eads energy correction has been done. Since the number of bonds between H and heavy atoms (C and O) is the same in reactants dis and products, such corrections should largely cancel out in Eads and ER. For exothermic processes (ER < 0), we calculated the reaction path by means of the nudged elastic band (NEB) method.39 The NEB algorithm allows one to identify the minimum energy path (MEP) and the associated energy barrier for a transition from a given initial to a given final state. A set of 3N-dimensional images of the system is generated between the end point configurations. A spring interaction between adjacent images is added to ensure continuity to the path, thus mimicking an elastic band. An optimization of the band, involving the minimization of the forces acting on the images brings the band to the MEP. We used this algorithm in its optimized version, including the “improved tangent estimate”40 and “climbing the image”41 in conjunction with the ab initio calculations. Vibrational zero point energy effects are not included in our calculations. We do not expect they can qualitatively modify the dissociative adsorption energy picture, although they may affect the exact values of Eads dis . For adsorption involving hydrogen transfer with low energy barriers, hydrogen delocalization may occur; this quantum delocalization is the subject of on-going work in our lab. Results Molecular Adsorption. The C(001) surface presents a (2 × 1) reconstruction constituted of carbon dimers lying along the [110] direction. The calculated dimer length (1.387 Å) is shorter than the carbon bond length in bulk diamond (1.543 Å), indicating the existence of a CdC double bond. The most stable configuration for molecular adsorption identified on the C(001) surface at full water coverage is shown in Figure 1a in a top view representation and in Figure 2a in a lateral view representation. Water molecules molecularly adsorb above the surface trenches at 2.0 Å equilibrium distance from the plane containing carbon dimers. The molecule is tilted with one OH bond pointing toward the C atom of a dimer and the other OH bond almost parallel to the y direction. The dimer length is almost unchanged (1% longer than on the clean surface) as well as the water bond lengths (2% longer than in the isolated molecule). This observation along with the molecule-surface distances reported in Figure 2a indicate the absence of any chemical interaction between the surface and the water molecule. Water adsorption occurs through electrostatic and vdW interactions, as can be seen in the first row of Table 1 where the DFT+LAPs energies are reported along with the water-induced polarization of carbon dimers. Water molecular adsorption is highly favored at the high coverage considered. It is possible to observe that a significant contribution to the adsorption energy (-16 kJ/mol over -41 kJ/mol) comes from the water-water interaction energy (EH2O-H2O). In fact, in conditions of full coverage along the
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Figure 2. The most stable configurations for molecular adsorption on the clean (hydrogenated) surface at full coverage [θx ) 1, θy ) 1] and at extremely low coverage [θx ) 0.5, θy ) 0.25] conditions are reported in panels a and b (c and d), respectively. The optimized adsorption configurations obtained for water interaction with one and two DBs on hydrogenated surfaces are represented in panels e and f, respectively. The reported distances are in Å.
TABLE 1: Results for Molecular Adsorption Obtained by the DFT+LAPs Approach, Which Includes the van der Waals Interactionsa surface C(001)
[θx, θy] [1,1] [1, 0.5] [0.5, 1] [0.5, 0.25]
H-C(001)
[1, 1]
2DBs/H-C(001)
[0.5, 0.25] [0.5, 0.5]
1DB/H-C(001)
[0.5, 0.5]
mol Eads
EH2O-H2O
EH2O-surf
dz
δC1, δC2
δC3, δC4
-41 (-22) -29 (-13) -35 (-20) -20 (-8) -25 (-19) (-9) -32 (-18) -35 (-19)
-16 (-16) -3 (-5) -15 (-14) -1 (-0) -17 (-16) (0.00)
-25 (-6) -26 (-8) -19 (-6) -19 (-8) -8 (-3) (-9)
2.0 (2.5) 1.8 (2.6) 2.3 (2.5) 2.2 (2.6) 2.2 (2.8) (2.5) 1.6 (2.2) 1.6 (1.9)
+0.12,-0.11 (+0.07,-0.04) +0.15,-0.15 (+0.06,-0.03) +0.04-0.02 (+0.020.00) +0.01,+0.02 (+0.01,+0.02)
+0.06-0.01 (+0.050.00) +0.07,-0.01 (+0.05,0.00)
a
mol The DFT-PBE results are also reported in parentheses for comparison. The adsorption energy Eads (kJ/mol) per molecule, reported as a function of the water coverage [θx, θy], is analyzed by separating the contribution coming from the molecule-molecule interaction EH2O-H2O (kJ/mol) from the contribution due to the molecule-surface interaction EH2O-surf (kJ/mol). (The calculation of EH2O-H2O (see method) is not meaningful for the partially hydrogenated surfaces, where the molecular structure is deformed due to the interaction with DBs.) The distance dz of the oxygen atom from the topmost layer is reported in Å. The presence of water induces a polarization on the carbon dimers of the C(001) surface; this can be appreciated by looking at the differences δ (e) of the valence charge and the calculated charge of the C atoms of the dimers (the atoms are labeled according to Figure 2a,b).
trenches (θy ) 1), hydrogen bonds are established among the periodic replicas of the molecule separated by the short edge of the (2 × 1) cell, 2.52 Å long. The remaining part of the adsorption energy, representing the molecule-surface interaction energy (EH2O-surf), is mostly due to the interaction between the water dipole and the induced dipole on the surface. A water molecule approaching the C(001) surface induces a polarization on carbon dimers. The C atom closer to hydrogen presents, in fact, an extra charge δC2 ) -0.11e with respect to its valence charge, while the C atom closer to oxygen is subjected to a slight charge depletion, δC1 ) +0.12e. At full water coverage along the direction of dimers (θx ) 1), the polarization of dimers is efficiently realized by the cooperative action of molecules adsorbed at adjacent trenches. To investigate the effects of coverage, we repeated partial PES calculations adopting wider supercells. We halved first the
water density along the y direction (Figure 1b) and then along the x direction (Figure 1c); finally, a condition that approximates an isolated molecule on the surface was investigated (Figure 1d). Physisorption above the trenches turned out to be the most favorable adsorption location also in reduced coverage conditions. We can see in the second row of Table 1 that the molecule-molecule interaction energy (EH2O-H2O) drastically decreases by reducing the water coverage along the y direction; thus, the intermolecular interaction occurs mainly along the direction of dimer rows. Once the lateral hydrogen bonds are removed, the molecule optimizes its position relative to the surface getting closer to it and inducing a stronger dimer polarization. On the contrary, a reduced coverage along the x direction cancels the cooperative action of adjacent molecules in polarizing the carbon dimers as can be seen by comparing the δC values of the [1,1] and [0.5,1] coverages in Table 1. This
Water Adsorption on Diamond (001) Surfaces weakens the molecule-surface attraction, as can be seen from the decreased value of EH2O-surf and from the increased dz distance reported in the third row of Table 1. The optimized adsorption configuration for the isolated molecule is presented in Figure 2b. The adsorption distances and the energy are higher than at high coverage, indicating that isolated molecules are more weakly bonded to the surface. We can conclude the analysis on molecular adsorption at the C(001) surface by observing that it is always favored, with adsorption energies ranging from -41 kJ/mol at full coverage to -21 kJ/mol in the case of isolated molecules. In particular, the full coverage along the direction of dimer rows (θy ) 1) favors intermolecular interactions, and the full coverage along the direction perpendicular to dimer rows (θx ) 1) favors the cooperative polarization of surface dimers, enhancing the attraction between the surface and the water molecules. It is worth mentioning that the use of the DFT+LAPs approach turned out to be essential for capturing the effect of coverage on the molecule-surface interaction. We can see in Table 1 that the results obtained by the DFT-PBE calculation (reported in parentheses) do not reproduce correctly the water-surface energies, the adsorption distances, and the dimer polarization. Not even the changes of energies and distances as a function of coverage are reproduced. Only the water-water energy is in agreement with the DFT+LAPs calculations, as expected since these interactions should be dominated by hydrogen bonding, with dispersion interactions playing only a minor role. The most important adsorbate by which diamond surfaces can be terminated is hydrogen. It is the dominating species in CVD processes; thus, diamond surfaces obtained by this growth technique are found in the hydrogen terminated state.42 First principles calculations of surface energy showed that the H-C(001) surface is more stable than the clean C(001) one.43 In the hydrogenated surface, the carbon atoms remain arranged in dimer rows as in the clean diamond surface, and only the π-bond between the dimer atoms is replaced by a covalent bond to one hydrogen at each surface atom. The bond lengths we calculated by the DFT+LAPs approach are lC-C ) 1.627 Å and lC-H ) 1.10 Å. Due to the different electronegativities of C and H, the CH bonds are polar to some extent. We calculated a charge depletion on each hydrogen atom δH ) +0.16e and an extra charge δC ) -0.12e on each carbon atom. The optimized configurations obtained for water adsorption on the HsC(001) surface at full coverage and in the limit of isolated molecule are shown in Figure 2c and d, respectively. We can see that the molecule orientation on the hydrogenated surface is different from that obtained on the clean one: due to the interaction with the hydrogen layer, the water molecule presents the hydrogens pointing toward the vacuum, and the oxygen toward the surface, in agreement with ref 12. This is more evident in the configuration of Figure 2d, where the extremely low coverage limit allows for an optimized adsorption geometry with respect to the full coverage limit where hydrogen bonds are established along the y direction. The calculated geometrical parameters indicate that the surface bonds and the molecule geometry are almost unperturbed by the reciprocal interaction, and that molecular adsorption on the hydrogenated surface occurs thorough long-range interactions as for the clean surface. However, adsorption interactions on the HsC(001) surface are weaker than on the C(001) surface, as can be seen from the adsorption energies and equilibrium distances reported mol ) -25 kJ/mol is in Table 1. At full coverage conditions, Eads almost half of the value obtained for the clean surface in the
J. Phys. Chem. C, Vol. 114, No. 15, 2010 7049 same conditions. Since the molecule-molecule interaction energy is almost unchanged, we conclude that the molecule-surface attraction is weaker for the hydrogenated surface than for the clean surface. This is also evident from the calculated atomic charges of the surface CH bonds that are almost unchanged by the presence of the adsorbed molecule: the water-induced polarization of the surface is less effective on HsC(001) than on C(001) because the charge displacements that can be induced on the CdC bonds are higher than those on the CsH and CsC bonds. We now move our discussion to water interaction with hydrogenated diamond surfaces containing dangling bonds (DBs). Spectroscopic analysis of diamond surfaces after tribological tests in dry conditions revealed that carbon DBs are produced at hydrogenated diamond surfaces by the surface rubbing, and can cause a great increase of friction forces and wear.5,6 We analyzed the situations of one water molecule interacting with one and with two carbon dangling bonds (1DB and 2DBs). In the latter case, the DBs were considered to belong to different dimers, as the situation of a water molecule interacting with a clean carbon dimer has already been considered in the context of the analysis performed for the C(001) surface. The calculations were performed by considering the spin polarization and adopting (4 × 2) cells where fully saturated dimers separate the DB along the y direction, avoiding in this way the formation of delocalized DB wave functions as observed for infinite-length DB wires.44 The optimized adsorption structures obtained for water interaction with 1DB and with 2DBs are shown in Figure 2e,f. We can observe a change in the molecule orientation with respect to the fully hydrogenated case; the molecule is tilted so as to point one OH bond in the direction of the carbon DB. We explored the possibility of oxygen-carbon interaction by considering as an initial structure the one presenting the oxygen atom closest to the carbon dimer. During the relaxation processes, the molecule rotated until one of the two hydrogen atoms got in the proximity of the unsaturated carbon, as in Figure 2e,f. The close distance between the water hydrogen and the carbon atom presenting the DB (Figure 2e,f), along with the slight length increase of the OH bond pointing toward the surface (which is 4% longer than for a molecule in vacuum), suggests that the interaction may have a partial covalent character. Indeed, the energies obtained for water adsorption mol ) -32 on hydrogenated surfaces where DBs are present (Eads mol kJ/mol for 2DBs/H-C(001) and Eads ) -35 kJ/mol for 1DB/ H-C(001)) are lower than the adsorption energy calculated at the same water coverage (θx ) 0.5, θy ) 0.5) on the clean surface Emol ads ) -22 kJ/mol. This latter data was calculated within the same computational scheme adopted for the DB-containing systems. To further characterize the water interaction with DBs, we analyzed the electronic structure of the system. In particular, we calculated the projected density of states for the various atoms directly involved in the interaction (H and O of water, closest surface C). The results for the interacting system and for the water molecule and the surface isolated from each other are reported in parts a and b of Figure 3, respectively. For the sake of clarity, only the majority spin pdos is shown. In the C pdos, the narrow peak at -1.2 eV corresponds to the dangling bond state, that is in fact localized on this C atom. In passing from the pdos of the isolated subsystems (panel a) to those of the interacting system, a small, but detectable, pdos of water atoms in correspondence with the dangling bond peak of C arise. Other changes are also visible in the water peak around -9
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Figure 3. Projected density of states (PDOS) for the atoms involved in the water-surface interaction for the hydrogenated surface exposing an isolated dangling bond (1DB/H-C(001)). Panel a refers to noninteracting water and surface, while panel b refers to the interacting system. The PDOS energy scale has been shifted to have EFermi ) 0 eV. Only the majority spin component of the PDOS is shown.
eV, that splits into two peaks. The presence of peaks at the same energy for the pdos of C, H, and O reveals the existence of electronic states delocalized on these three atoms, and it is thus indicative of a partial covalent character. However, judging by the rather asymmetric nature of water-surface orbital mixing, the extent of such covalent character is certainly very small. Dissociative Adsorption. We consider in this section the process of surface passivation by water dissociation. This process, which has not yet received a theoretical description, is particularly relevant for the implications on diamond tribology. As anticipated in the Introduction, the saturation of carbon DBs is considered the key factor in determining the excellent tribological performances of diamond in humid environments.7 Indeed, water (or hydroxyl-containing molecules such as glycerol45,46) is attracting interest as a possible environmentalfriendly lubricant for carbon-based materials.47,48 We consider first water dissociation on the clean C(001) as being representative of hydrogen depleted areas. Then, we study water dissociation on hydrogenated surfaces presenting a smaller density of carbon DBs. Dissociation of water on defective sites in graphene has been shown to have activation barriers lower than half the value for the dissociation of bulk water. This has been suggested to be relevant for H2 production.49 It has been shown in the previous section that the most stable configuration for water molecular adsorption on the C(001) surface is along the surface trenches. Since the molecule-surface interaction turned out to be influenced little by the water density along the trench, we studied the process of water dissociation for θy ) 1 and variable θx. The initial and final states of the dissociative reaction at θx ) 1 are represented in the left and right panels of Figure 4a, respectively. The dimer length in the dissociatively adsorbed structure lC-C ) 1.625 Å indicates that the double CdC bond is broken when new C-H and C-OH bonds are formed. The dissociative adsorption energy per dis ) molecule calculated within the DFT+LAPs approach is Eads -322 kJ/mol. This energy includes the formation energy of the chemical bonds and the interaction energy between the H and OH fragments attached to neighboring carbon dimers. As can be seen in Table 2, the value obtained by DFT-PBE slightly differs from the DFT+LAPs result most likely because the interfragment interactions are underestimated by DFT-PBE. At coverages of θx < 1, molecular dissociation produces a partial passivation of the diamond surface. Locally, the chemisorption of a water molecule can occur on only one dimer (Figure 4b50)
Manelli et al. or between two different dimers (Figure 4c), respectively. We can see that in the second situation two DBs per molecule are produced on the surface upon dissociative adsorption, and the adsorption energy calculated for the configuration of Figure 4c points to a less favorable adsorption than those of Figure 4a,b51 (Table 2). All of the considered dissociative processes are however exothermic with reaction energies ER ranging from about -290 kJ/mol when water dissociative adsorption does not produce DBs to -125 kJ/mol when DBs are produced. We calculated the energy barriers associated to the dissociative processes considered above, and we found that they are highly influenced by the water coverage. We can in fact observe in Table 2 that EA ) 6 kJ/mol for θx ) 1, while for θx < 1 the activation energies are more than 1 order of magnitude higher. The small activation energy calculated for θx ) 1 is a result of the cooperative action of the molecules located in adjacent trenches that chemically interact with the same carbon dimer during their contemporary dissociation. We explored other mechanisms for dissociation at full coverage by considering a situation presenting two molecules per cell: one dissociated and one undissociated (Figure 4d, left). During the relaxation process, we observed the spontaneous dissociation of the initially undissociated molecule: by approaching the surface, the molecule splits into two fragments that saturate the carbon DBs originally present at the two sides of the trench. Thus, in a situation where water molecules are already dissociatively adsorbed giving rise to partial dimer saturation, incoming water molecules spontaneously dissociate and complete the dimer saturation. As a final step in the analysis of DBs passivation by water dissociative adsorption, we consider the process of molecular dissociation on partially hydrogenated surfaces. The precursor states represented in Figure 4e,f (left) are those identified in the section devoted to molecular adsorption. When two adjacent DBs are available on the surface, both the H- and OHfragments of a dissociating molecule can bind to the surface, as in Figure 4e (right). The corresponding dissociative adsorption dis energy Eads ) -373 kJ/mol and reaction energy ER ) -341 kJ/mol indicate that the process is energetically favored and highly exothermic. The activation energy calculated for the dissociative process of Figure 4e (EA ) 11 kJ/mol) is lower than those obtained at the same water coverage on the clean surface (EA ) 78 and 88 kJ/mol), indicating that dissociative adsorption is more easily activated when the CdC double bonds are already broken. In the presence of isolated DBs, the molecule cannot be fully chemisorbed: only one fragment can be accommodated on the surface, and the other one remains floating above the surface. We considered both the cases of hydrogen and hydroxyl incorporation (Figure 4f,g), and we found that both of the processes are endothermic (see Table 2), although the incorporation of H is much less unfavorable than the incorporation of a hydroxyl group. This result indicates that the passivation of isolated DBs by water dissociation requires at least two steps: in the first, endothermic, the DB is passivated by incorporating a water H into the surface; then, the remaining hydroxyl migrates on the surface (possibly exchanging other H atoms with the surface) until it finds another DB to passivate. The overall process is highly exothermic (with ER comparable to the case with two DBs in Table 2), and the endothermic nature of the first step (ER ) 28 kJ/mol) is probably not enough to completely inhibit it at room temperature. In any case, even if the dissociative passivation of the DBs does not take place, the
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Figure 4. Dissociative processes on the clean and partially hydrogenated surfaces. The initial states of the reactions are represented on the left and the final states on the right. The energetics of the processes is reported in Table 2. dis TABLE 2: Dissociative Adsorption Energies Eads (kJ/mol) per Molecule Calculated within the DFT+vdW Approach (in Parentheses within DFT-PBE) Corresponding to the Adsorption Configurations Represented in Figure 4 (right)a
surface C(001)
[1, 1] [0.5, 1] [0.5, 1]
2DBs/H-C(001) 1DB/H-C(001)
dis Eads
ER
EA
process
-322 (-285) (-284) -165 (-130) -373 -7 +76
-281 (-262) (-267) -130 (-107) -342 +28 +111
6 (6) (78) 65 (88) b
Figure 4a
[θx, θy]
[0.5, 0.5] [0.5, 0.5]
Figure 4b Figure 4c Figure 4e Figure 4f Figure 4g
a The reaction energy ER (kJ/mol) is obtained as the difference between the initial (Figure 4, left) and the final (Figure 4, right) states of the dissociation processes. The activation energies EA (kJ/ mol) are reported for exothermic processes. b The energy barrier obtained in conditions of [0.5, 1] water coverage is EA ) 10 kJ/mol.
reactivity of these surface sites is reduced by the molecular adsorption discussed in the previous section. Discussion and Conclusions The following observations can be derived from the analysis of the above presented results. (i) Molecular adsorption is favored both on the hydrogenated and on the bare surfaces, with more favorable binding on the
bare surface. This result is in agreement with the experimental observations by A. Laikhtman and coauthors who performed the XPS analysis of the hydrogenated and the bare surface after exposure to water vapor at room temperature, and found a higher concentration of water on the bare surface. Our results indicate that this is due to a stronger molecule-surface interaction because the clean carbon dimers are polarized by water molecules. (ii) The PES calculated for molecular adsorption on the clean surface is rather smooth: the adsorption energy obtained for the most favorable location, which is above the surface trenches, is about 16 kJ/mol lower than for locations above the dimer rows which correspond to the PES maxima. The energy barriers for molecular diffusion are lower than the maximum PES corrugation; thus, the precursor state of molecular adsorption is delocalized at room temperature. According to our results, which show that the adsorption energy per molecule is lower at high coverage than at low coverage, a diffusing molecule will bind in the proximity of a surface region where other molecules are already adsorbed. This is because of a twofold reason: the molecule experiences a stronger attraction by dimers that are already polarized and can form hydrogen bonds with other adsorbed molecules. The energy gain due to the enhanced molecule-surface and molecule-molecule attraction will promote molecular adsorption along dimers in the first case and perpendicular to dimers in the second case. Thus, we do not
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expect a homogeneous wetting of the surface but water islands that grow preferentially along and perpendicularly to dimer rows. (ii) Dissociative adsorption on the clean surface, as well as molecular adsorption, is highly influenced by the coverage: the energy barrier calculated for the dissociation of a water molecule in the presence of other molecules adsorbed in the adjacent trenches is more than 1 order of magnitude lower than the energy barriers calculated for the dissociation of a molecule within an isolated trench or within an isolated dimer. Furthermore, we observed a spontaneous dissociation when an incoming molecule interacts with the DBs of dimers decorated with fragments of already dissociated molecules. Thus, at high water coverage, initial dissociative processes can be easily activated even at room temperature, as observed experimentally,8,9 and they can give rise to chains of dissociative processes that produce a quick surface passivation. On the contrary, below a saturation coverage, we expect nondissociative adsorption or rare events of dissociation at ordinary temperatures. A similar coveragedependent behavior was observed for water adsorption on the silicon (001) surface,52,53 and the question on how the coverage could alter the adsorption mode remained open.54 According to our results, the energy barriers for dissociation are substantially decreased thanks to the cooperative action of neighboring molecules. Theoretical studies based on cluster models for the surface, such as that performed by Y. Okamoto where an isolated molecule interacts with an isolated dimer,11 cannot capture this effect. Indeed, the energy barrier estimated for molecular dissociation (108 kJ/mol) in that work resembles the one we obtained for the case of dissociative adsorption within an isolated dimer (88 kJ/mol). (iii) Carbon dangling bonds are present in diamond films obtained by CVD if processes to achieve a full surface hydrogenation are not carried out and can be produced during the tribological process. The study of water interaction with partially hydrogenated surfaces revealed that two adjacent dangling bonds are needed for one-step dissociative adsorption. Dissociative reactions with isolated dangling bonds are in fact endothermic processes; to make the overall process energetically favorable, a second reaction step is necessary where the water radical produced by the isolated DB passivation migrates on the surface until it finds another DB to passivate. Obviously, the probability of this second step decreases when the number of DBs decreases. Therefore, we can speculate on a possible crossover between two regimes: for high DB concentrations, passivation takes place by dissociative adsorption, either on adjacent DBs or via the two-step process mentioned above. At low DB concentration, the reactivity of these sites can be reduced by molecular adsorption. In fact, the adsorption structures and energetics suggest that this is a relatively stable adsorption state, also thanks to a (weak) covalent character seen by analyzing the projected density of states. As regards the tribological problem, we can observe that our findings support the interpretation of the high sensitivity of the COF of diamond to the air humidity as the result of surface passivation. We have in fact shown that surface regions with a high density of carbon DBs, locally resembling the clean surface, can be readily passivated if the ambient air has a sufficient high relative humidity. Furthermore, a water molecule can bind to DBs of hydrogenated surfaces, and when adjacent DBs are present, it can dissociatively adsorb, producing a considerable decrease of the surface energy. (iv) By performing a comparative analysis of the results obtained for molecular adsorption within the DFT-PBE and DFT+LAPs approaches, we can observe that DFT-PBE predicts
Manelli et al. a significantly weaker binding. The discrepancy of the results increases with the degree of surface polarizability. By neglecting the vdW interactions, the average adsorption energy is underestimated by 23% in the case of the fully hydrogenated surface and by 50% for the clean surface. In the same way, the average equilibrium distances obtained without the inclusion of the vdW interactions are overestimated (by 23% in the case of the clean surface) and they do not vary as a function of coverage. Thus, the inclusion of the vdW interactions turned out to be essential for understanding the effect of coverage in enhancing the molecule-surface attraction. On the contrary, the energetics associated to hydrogen bonding is similar in the two approaches, as well as the qualitative behavior of the energy barriers calculated for molecular dissociation at different coverages. Acknowledgment. This work is partially supported by MIUR through PRIN 2007 BL78N3 and by INFM-CNR through the Parallel Computing Initiative. S.C. acknowledges the EU for funding under the FP6-NEST-028331 project PROSURF. The calculations were performed using the supercomputing facilities at CINECA Bologna, Italy. References and Notes (1) Yang, W.; Auciello, O.; Butler, J. E.; Cai, W.; Carlisle, J. A.; Gerbi, J. E.; Gruen, D. M.; Knickerbocker, T.; Lasseter, T. L.; Russell, J. N.; Smith, L. M.; Hamers, R. J. Nat. Mater. 2002, 1, 253. (2) Chakrapani, V.; Angus, J. C.; Anderson, A. B.; Wolter, S. D.; Stoner, B. R.; Sumanasekera, G. U. Science 2007, 318, 1424. (3) Grierson, D. S.; Carpick, R. W. Nanotoday 2007, 2 (5), 12. (4) Auciello, O.; Birrell, J.; Carlisle, J. A.; Gerbi, J. E.; Xiao, X.; Peng, B.; Espinosa, H. D. J. Phys.: Condens. Matter 2004, 16, R539. (5) Gao, G. T.; Mikulski, P. T.; Chateauneuf, G. M.; Harrison, J. A. J. Phys. Chem. B 2003, 107, 11082. (6) van den Oetelaar, R. J. A.; Flipse, C. F. J. Surf. Sci. 1997, 384, L828. (7) Konicek, A. R.; Grierson, D. S.; Gilbert, P. U. P. A.; Sawyer, W. G.; Sumant, A. V.; Carpick, R. W. Phys. ReV. Lett. 2008, 100, 235502. (8) Laikhtman, A.; Lafosse, A.; Le Coat, Y.; Azria, R.; Hoffman, A. Surf. Sci. 2004, 551, 99. (9) Gao, X.; Liu, L.; Qi, D.; Chen, S.; Wee, A. T. S.; Ouyang, T.; Loh, K. P.; Yu, X.; Moser, H. O. J. Phys. Chem. C 2008, 112, 2487. (10) Struck, L. M.; D’Evelyn, P. J. Vac. Sci. Technol., A 1993, 11, 1992. (11) Okamoto, Y. Phys. ReV. B 1998, 58, 6760. (12) Larsson, K.; Ristein, J. J. Phys. Chem. B 2005, 109, 10304. (13) Young, H. X.; Yu, Y.; Xu, L. F.; Gu, C. Z. J. Phys.: Conf. Ser. 2006, 29, 145. (14) Giannozzi, P. et al. J. Phys. Condensed Matter 2009, 21, 395502. (15) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (16) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (17) Zilibotti, G.; Righi, M. C.; Ferrario, M. Phys. ReV. B 2009, 79, 075420. (18) Kohn, W.; Meir, Y.; Makarov, D. E. Phys. ReV. Lett. 1998, 80, 4153. (19) Fuchs, M.; Gonze, X. Phys. ReV. B 2002, 65, 235109. (20) Rydberg, H.; Dion, M.; Jacobson, N.; Schro¨der, E.; Hyldgaard, P.; Simak, S. I.; Langreth, D. C.; Lundqvist, B. I. Phys. ReV. Lett. 2003, 91, 126402. (21) Dion, M.; Rydberg, H.; Schro¨der, E.; Langreth, D. C.; Lundqvist, B. I. Phys. ReV. Lett. 2004, 92, 246401. (22) von Lilienfeld, O. A.; Tavernelli, I.; Rothlisberger, U.; Sebastiani, D. Phys. ReV. Lett. 2004, 93, 153004. (23) Thonhauser, T.; Cooper, V. R.; Li, S.; Puzder, A.; Hyldgaard, P.; Langreth, D. C. Phys. ReV. B 2007, 76, 125112. (24) Silvestrelli, P. L. Phys. ReV. Lett. 2008, 100, 053002. (25) Harl, J.; Kresse, G. Phys. ReV. B 2008, 77, 045136. (26) Misquitta, A. J.; Jeziorski, B.; Szalewicz, K. Phys. ReV. Lett. 2003, 91, 033201. (27) Sun, Y. Y.; Kim, Y.-H.; Lee, K.; Zhang, S. B. J. Chem. Phys. 2008, 129, 154102. (28) Ortmann, F.; Schmidt, W. G.; Bechstedt, F. Phys. ReV. Lett. 2005, 95, 186101. (29) Chakarova-Ka¨ck, S. D.; Schro¨der, E.; Lundqvist, B. I.; Langreth, D. C. Phys. ReV. Lett. 2006, 96, 146107. (30) Rohlfing, M.; Bredow, T. Phys. ReV. Lett. 2008, 101, 266106.
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