A density functional theory study of atomic oxygen and nitrogen adsorption over a-alumina ( 0001 )

The interaction of atomic oxygen and nitrogen on the (0001) surface of corundum (aalumina) is investigated from first-principles by means of periodic density functional calculations within the generalized gradient approximation. A large Al2O3 slab model (18 layers relaxing 10) ended with the most stable aluminum layer is used throughout the study. Geometries, adsorption energies and vibrational frequencies are calculated for several stationary points for two spin states at differents sites over an 1x1 unit cell. Two stable adsorption minima over Al or in a bridge between Al and O surface atoms are found for oxygen and nitrogen, without activation energies. The oxygen adsorption (e.g., Ead = 2.30 eV) seems to be much more important than for nitrogen (e.g., Ead = 1.23 eV). Transition states for oxygen surface diffusion are characterized and present not very high-energy barriers. The computed geometries and adsorption energies are consistent with similar adsorption theoretical studies and related experimental data for O, N or a-alumina. The present results along with our previous results for b-cristobalite do not support the assumption of an equal Ead for O and N over similar oxides, which is commonly used in some kinetic models to derive catalytic atomic recombination coefficients for atomic oxygen and nitrogen. The magnitude of O and N adsorption energies imply that Eley-Rideal and Langmuir-Hinshelwood reactions with these species will be exothermic, contrary to what happens for b-cristobalite.


Introduction
Aluminum oxide (Al 2 O 3 ), traditionally referred to as alumina, is a very important ceramic material of enormous technological importance with a wide range of applications, from electronics, optics, biomedical and mechanical engineering to catalyst support. Its high applicability is due to its enormous hardness (9 Mohs), extreme melting point (2327 ± 6 K) and excellent thermal (30 W•m -1 •K -1 at 373 K) and electrical (> 10 -12 ohm -1 •m -1 ) insulator behaviour 1 . In its crystalline form, called corundum, its hardness makes it suitable for use as an abrasive and as a component in cutting tools. Synthetic corundum is usually produced by the flame-fusion method (also called Verneuil process), allowing the production of large quantities of sapphire, rubies and other corundum gems. Langmuir-Hinshelwood (LH) atomic recombinations. Therefore, the first step in this theoretical approach will be the study of O and N adsorption over a-Al 2 O 3 (0001) surface in a similar way as we have recently carried out for b-cristobalite 17 , which is another oxide used in several TPSs 16 .
The central aim of our research in progress is the full theoretical study from first-principles of O and N recombination reactions over a-alumina (i.e., O + O ad , N + N ad , O + N ad or N + O ad ) in order to provide not only DFT information on the ground potential energy surfaces but also kinetic and dynamical data useful for next computational fluid dynamics (CFD) simulations about spacecraft flights. The present study will allow ascertaining the relative importance of O and N adsorption and also the magnitude of the unknown exothermicities (or endothermicities) for the different ER and LH processes involving these atomic species.
In the present work we have carried out DFT calculations for the O and N adsorption over aalumina (0001) with an Al-terminated first layer because this surface is the most stable according to experimental results 8 obtained by low-energy electron diffraction over different ended samples.
This information and some additional DFT calculations will be used in a following construction of an analytical potential energy surface for dynamical studies about atomic sticking and also for some ER or LH reactions involving O and N atoms.

Computational details
We have performed DFT calculations using the VASP code [18][19][20][21] , based on plane wave basis sets. The calculations reported here have been performed at the spin-polarized generalized gradient correction (GGA) level of density functional theory, using the Perdew-Wang 91 functional (PW91) [22][23] , which has been appropriate in similar studies 6,13,17 . The electron-ion interactions were described by using the projector-augmented-wave (PAW) technique [24][25] , particularly reliable for transition metals and oxides. We have also checked widely the correct energy cut-off (i.e., 500 eV) in several bulk and slab calculations.
Integration over the Brillouin zone was performed by using several k-points meshes to ensure the totally convergence in the results. Geometrical optimizations and vibrational frequencies were computed with an energy accuracy of 10 -6 eV.
In the adsorption studies we have used an 1x1 surface unit cell for the a-alumina (0001); 18 layers with an Al outermost layer formed the final slab model. Thus, to ensure the bulk behaviour, the last eight layers were kept fixed while the others were fully relaxed. The thickness between slabs (≈ 14 Å) was large enough to prevent significant interactions between them.
Several adsorption sites were characterized for both O and N adatoms. Spin magnetic moments were checked along with the corresponding analysis of a and b density of of states (DOS) in order to classify the structures as singlet, triplet, doublet or quartet.
Once determined the optimal geometry (without any symmetry restriccion) for each adsorption site, we calculated the Hessian matrix and its corresponding harmonic vibrational frequencies (ni) for the adatom. These can be approximately classified as two parallel and one perpendicular movement, keeping fixed the optimized slab geometry.

Bulk and slab calculations for the a-alumina
A primitive rombohedral unit cell can be used to describe a-alumina, with two Al 2 O 3 formula units ( space group). Nevertheless, more convenient is the hexagonal unit cell that contains 12 Al atoms and 18 O atoms (i.e., 6 Al 2 O 3 units). The hexagonal cell corresponds to a layered structure with six oxygen planes associated with aluminum planes above and below it, forming stochiometric triple layers (Fig. 1a). There are three O atoms and just one Al atom in each layer (  First of all, to obtain the optimal cell parameters, a complete optimization has been performed, including the minimization of both the force acting over each atom and the stress tensor allowing volume and shape relaxation. The optimal cell parameters (a=b and c) along with the two types of AlO distances and <OAlO angles (Fig. 1a) of the inner bulk structure are reported in Table   1 and compared with experimental data 28 . The agreement is quite good.
The slab model used consists of 18 layers; the first 10 were relaxed and the last 8 kept fixed to ensure the bulk behaviour. An interlayer relaxation (i.e., ∆d12, ∆d23,…) analysis is showed in Table 2. The most significant feature is the high inward relaxation of the surface plane (approx.  (Table 1) whereas much bigger <OAlO angles are achieved (i.e., <O Some authors have also remarked that this disagreement between experimental and theoretical first aluminum relaxation could be originated by the unfeasibility to obtain a real aluminum ended clean surface even at ultrahigh vacuum. It has been shown that an a-Al2O3 (0001) surface in equilibrium with an environment containing both oxygen and hydrogen species is fundamental for obtaining theoretical predictions consistent with experimental information 4 .
On the other hand, the Fermi energy obtained for the bulk model was 6.4 eV, which is lower than the experimental value of 8.7 eV 31 but much closer than another previous theoretical values (e.g., 5.8 eV 32 ).

Atomic oxygen adsorption on a-alumina
We have studied the adsorption of atomic oxygen on four different sites over the unit cell of a-Al2O3 (0001) (Fig. 1b) 13 , where the binding takes place mainly through the formation of a bond between one oxygen of the nitro group to an Al of the surface. Nevertheless, our calculated distances are still larger than the corresponding value in the gas-phase diatomic molecule (i.e., 1.6179 Å in ground 2 S + state 1 ), which presents a much higher bond dissociation energy (BDE = 5.2 ± 0.1 eV at 298 K 1 ). This fact is coherent with the lower BDEs obtained for both adsorption minima. Thus, in T1 the BDE (at 0 K) corresponds approximately to the calculated Ead as only one AlO bond is formed (Fig. 2c). This energy is close to the DFT binding energies (i.e., 0.83-1.13 eV) obtained for nitromethane on a-Al2O3 (0001) with mostly AlO bonding 13 .
In T2 minimum, the existence of two bonds (i.e., AlO and OO, Fig. 2d Despite the absence of experimental adsorption energies for atomic oxygen over alumina, the comparison with another oxides shows smaller adsorption energies (e.g., 2.0-2.5 eV on MgO(001) 33 or 3.7-5.9 eV on SiO2 (100) 17 ), although closer to MgO values, possibly because alumina is also an ionic oxide.
To analyze the electronic properties of both minima (T1 and T2), partial density of states projected onto the oxygen and aluminum atoms involved mainly in the bonds are presented for T1 in Fig. 3 and for T2 in Fig. 4, for both spin states. In T1 triplet, the 3pz states of Al (1)  and Al(1) 3px,y states, strengthening this bond. For T1 singlet this latter overlapping is a bit minor, which is consistent with its lower binding energy (or Ead).
In T2 singlet minimum the Oad 2px,y states and Al(1) 3px,y,z states participate principally in the AlO (bond) valence band, while Oad 2pz is moved to approximately 1 eV, with a less participation in agreement with the geometry obtained (Fig. 2d), which favoured more this kind of orbitalic overlapping. The major contribution into the less strong peroxo bond (1.554 Å of bond distance, Table 3) formed by Oad and O(1) seems to be given mostly by 2px,y states of both oxygens, as their 2pz states are separated each other around 1.5 eV (Fig. 4). For T2 triplet minimum it is observed a stronger overlapping of Al(1) and O(1) pz states (with more population of the a spin states in both atoms) at -15 eV giving place to a strong O(1)Al(1) bond and therefore, the other OadAl(1) bond should be weakened, producing a much less binding energy and Ead as observed (Table 3).
T1 and T2 structures are truly minima as we have verified by the analysis of harmonic vibrational frequencies (Table 3). In the case of adsorption of oxygen atom on T1 site, it is observed that the perpendicular frequency is much higher than the two parallel ones, and it is easy to understand this value according to the T1 minimum geometry; in T1 minimum, the distance between the O adatom and the first aluminum is practically the bulk distance (see Table 1) but differs from bulk structure in the location of neighbouring atoms; that is, in the bulk structure each aluminum atom is located in an octahedral hole coordinated to 6 O atoms (Fig. 2a) but in T1 the coordination is only four (Fig. 2c), with an Al and three O in almost the same plane. Therefore, the perpendicular frequency corresponds mainly to the OadAl stretching with a high value (541.3 cm -1 and 510.9 cm -1 for singlet and triplet states, respectively) because this is a strong bond whereas the parallel movements along the T1-T2 and T1-H lines have less frequencies due to the interactions with neighbour atoms in the same or in the deeper layers are clearly less important.
T2 structure, the most stable minimum, shows higher parallel frequencies than T1 minimum, because T2 has two short distances (i.e., O ad Al (1) and O ad O (1) ) and a small z Oad value, which is shorter than in T1 (e.g., 0.945 Å compared with 1.776 Å in singlet state), which means a stronger interaction for parallel movements to the surface (e.g., in the O ad -Al (1) direction).
B site is in between T1 and T2 minima. According to their vibrational frequencies (Table 3) it is a diffusion transition state in both spin states, connecting T1 and T2 minima in y direction (Fig.   1b). However, there is a great difference between singlet and triplet B ¹ structures; the B ¹ singlet is closer to T1 minimum and there is a low energy barrier (i.e., 0.06 eV for T1 ® B ¹ ® T2), corresponding to an exothermic diffusion path (Fig. 5). On the contrary, the B ¹ triplet structure is much closer to T2 minimum and now the diffusion process is endothermic, being the energy barrier somewhat higher than the endothermicity (i.e., 1.07 eV for T1 ® B ¹ ® T2) (Fig. 5). In the case of B ¹ triplet the imaginary frequency corresponds to a perpendicular movement to the surface (i.e., 551.9i cm -1 ), whereas in the case of B ¹ singlet it is parallel to the surface (i.e., 58.1i cm -1 ) and its value is clearly minor. This is consistent with the geometrical changes involved in both T1 ® T2 diffusion paths. Thus, in triplet state it involves mainly a big reduction of one OadO (1)  Hollow site is another transition state (H ¹ ) that connects also T1 and T2 but in the x direction ( Fig. 1b). Now the energetics for T1 ® H ¹ ® T2 diffusion is similar for both singlet and triplet states (Fig. 5), although there are several discrepancies respect the geometrical changes. In the triplet case, the distance between the oxygen adatom and the first aluminum atom is 1 Å higher (Table 3) than in the singlet state; thus the OadAl(1) interaction is much weaker in the triplet state and drives to obtain one stretching frequency that is a half of the obtained for the singlet state.
T1 ® H ¹ ® T2 path is endothermic for triplet state and exothermic for singlet state as it occurred for the alternative T1 ® B ¹ ® T2 path. Nevertheless, now the energy barriers are higher (i.e., 1.02 eV for singlet and 1.32 eV for triplet).
The information summarized in Fig. 5 could be interpreted as follows. When an oxygen atom collides with a a-Al2O3 (0001) surface it will be adsorbed (without any activation energy) mainly over an Al (T1 site) or one of the three equivalent oxygens (O1a, O1b, O1c) of O(1) layer (T2 sites). If it is initially adsorbed in T1 site, there will be two possibilities to migrate to the most stable T2 singlet minimum, being the path T1 ® B ¹ ® T2 the energetically most favourable. Nevertheless, it could be expected that both paths will be accessible at low atomic kinetic energies and moderate surface temperatures. On the other hand, the initial adsorption over one of the three equivalent T2 sites will be statistically more probable and will lead to the most stable singlet minima. The change from the initial atomic triplet state (arising from O( 3 P)) to the final T2 singlet state can be progressively produced when approaching the O atom to the surface. In fact, DFT calculations show no energy barrier to produce directly T1 and T2 minima when O( 3 P) becomes closer to these sites.
The diffusive processes of oxygen over a-Al2O3 (0001) surface are not too energetically demanding in opposite to what happens when oxygen atoms are adsorbed on another oxide as bcristobalite (100). In this latter case, we found strong diffusion energy barriers within the 3.0-6.6 interval 17 .

Nitrogen adsorption on a-alumina
In spite of the most relevant importance of oxygen interaction with the TPSs of spacecrafts due to its lower molecular energy dissociation and the main abundance of its molecular species in air in comparison to molecular nitrogen, we have also characterized the adsorption minima of nitrogen atoms over T1 and T2 sites for doublet and quartet states because this information is relevant for the study of the ER reactions that could be necessary in more acurate air kinetic simulations. Both, energetics and geometries are given in Table 4.
The NadAl distance in T2 doublet adsorption minimum (Table 4)  The NadO distance in T2 doublet adsorption minimum (Table 4) is much higher than the corresponding value for the gas-phase diatomic molecule (i.e., 1.1508 Å for NO (X 2 P1/2 1 ).
Nevertheless, this behaviour is quite similar to the one observed in the study of the N adsorption over the O face of b-cristobalite (100) for a bridge with two O atoms (i.e., dNO = 1.34-1.44 Å in B3 minimum 17 ).
Despite the existence of four stationary points, only a relatively stable minimum is found in T2 site for doublet state (1.23 eV of adsorption energy). A less stable minimum is found in T1 site for quartet state (only 0.4 eV of adsorption energy). Vibrational frequencies follow a similar behaviour as for oxygen adsorption, already explained in previous section. In this case transition states are not reported for this rather shallow minima, although several searches were unsuccessfully carried out.
The analysis of the two bond distances in T2 minimum points out that AlN bond should be stronger than NO bond in this structure, which has a high BDE of 6.546 ± 0.002 eV at 298 K for gas-phase NO (X 2 P1/2) molecule 1  The collision of nitrogen atom with a-Al2O3 (0001) surface will be much simpler than for oxygen atoms. Thus, only a significant adsorption minimum (T2) will have some influence on the dynamics of the collision in the case that pairing of two electrons of nitrogen can be achieved during the atomic approaching to the surface. This process will occur without any potential energy barrier.

Summary and conclusions
In The N adsorption over a-alumina on T1 and T2 sites is less important. Only a moderately stable minimum is found on T2 (doublet) (Ead = 1.23 eV). In T1 (quartet) a minor (physisorption) is observed (Ead = 0.40 eV).
The geometries, adsorption energies and binding energies for these stationary points can be understood comparing with available similar studies and related experimental data, and also by analysing the density of states. These results together with our previous DFT study for b-cristobalite do not support the old guess of an equal Ead for O and N over similar oxides, which has been used in some kinetic models to derive catalytic atomic recombination coefficients for oxygen and nitrogen 16 .
The DFT data obtained suggest that when an oxygen atom collides with an a-Al2O3 (0001) surface it will be adsorbed mainly over an Al (T1 site) or over one of the three equivalent oxygens (O1a, O1b, O1c) of O(1) layer (T2 sites). A probably fast surface diffusion will take place between both minima even at low atomic kinetic energies and moderate surface temperatures. Nevertheless, a dynamical study (e.g., with classical trajectories) should confirm this fact.
The stronger adsorption found for O in comparison with N could enhance more the oxygen Eley-Rideal reaction over a-alumina surface at several range temperatures.
The smaller oxygen and nitrogen adsorption energies for a-Al2O3 than for b-cristobalite (SiO2), means that O or N atomic recombination processes via the Eley-Rideal or Langmuir-Hinshelwood mechanisms (e.g., O + Oad ® O2(g) or Oad + Oad ® O2(g)) will be exothermic on a-

Figure 3
Partial DOS projected onto oxygen adatom and surface aluminum (Al (1)) for T1 minima (singlet and triplet state) over a-alumina. O 2s and 2p states and Al 3s and 3p states are shown.

Figure 4
Partial DOS projected onto oxygen adatom, surface aluminum (Al(1)) and surface oxygen (O(1)) for T2 minima (singlet and triplet state) over a-alumina. O 2s and 2p states and Al 3s and 3p states are shown.

Figure 5
Energy profile for all stationary points of oxygen adsorption over a-alumina (0001). Singlet   b) The first 10 layers are relaxed.