Mechanisms of Initial Oxidation of the Co (0001) and Cr (110) Surfaces

Mar 16, 2010 - Mechanisms of Initial Oxidation of the Co(0001) and Cr(110) Surfaces ... D-28359 Bremen, Germany, Fraunhofer Institute for Mechanics of...
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Mechanisms of Initial Oxidation of the Co(0001) and Cr(110) Surfaces Janina Zimmermann*,†,‡ and Lucio Colombi Ciacchi†,§ Hybrid Materials Interfaces Group, Faculty of Production Engineering and Bremen Center for Computational Materials Science, UniVersity of Bremen, D-28359 Bremen, Germany, Fraunhofer Institute for Mechanics of Materials IWM, D-79108 Freiburg, Germany and Fraunhofer Institute for Manufacturing Technology and Applied Materials Research IFAM, D-28359 Bremen, Germany ReceiVed: January 15, 2010

Despite the fundamental importance of metal surface oxidation in a number of emerging fields such as catalysis, microelectronics, and biosensor technology, a comprehensive picture of the processes leading to the growth of thin oxide layers at low temperature is still lacking. In this work, we employ advanced first-principles molecular dynamics based on density-functional theory to investigate the early oxidation stages of the Co(0001) and Cr(110) surfaces and observe surprisingly different chemical mechanisms governed by a delicate balance between thermodynamical and kinetic effects. On cobalt, oxide nucleation occurs via an early place-exchange of the metal atoms of the surface layer with oxygen atoms of dissociatively adsorbing O2 molecules. Further development of the oxide takes place according to a kinetically constrained reaction path, which leads to pseudoamorphous structures bearing evident Co3O4-like magnetic, electronic and structural properties. These results help to rationalize a number of low-temperature experimental data for the (0001) and other Co surface orientations. In contrast, chromium oxidizes along a thermodynamically stable path involving the formation of perfect oxygen ad-layers, which strongly reduce the reactivity of the surface toward further oxygen adsorption. Only the thermally activated extraction of Cr atoms off the metal surface and the unexpected formation of chromate-like precursory structures initiates the experimentally observed layer-by-layer growth of epitaxial Cr2O3 oxide films. 1. Introduction The oxidation of metal and semiconductor surfaces at low temperature is of fundamental importance in a variety of fields where functional or mechanical devices are in contact with oxidizingenvironments.Theseincludenanowiresensorstructures,1,2 fuel cell electrodes,3 catalytically active nanoparticles,4 and biomechanical implants.5 Because of the constraints imposed by the increasing demand for miniaturization of such structures, a control over the oxidation processes on the atomic scale is highly desirable, yet the knowledge of the dynamical evolution of the atomic and electronic structure of the surfaces during oxygen chemisorption reactions is still very limited. This is due to the small time and size scales of the reactions, which preclude their direct experimental observation. Moreover, the frequent occurrence of metastable superficial oxide structures6,7 prevents the use of thermodynamic data or equilibrium phase diagrams to interpret and predict the mechanisms of surface oxidation. Accurate dynamical investigations of model systems by means of state-of-the-art quantum mechanical modeling are thus required, as presented here for the case of Co(0001) and Cr(110). Since the early works on the theory of surface oxidation,8,9 considerable attention has been devoted to narrow-band 3d transition metals. Among these, cobalt and chromium pose a special challenge to theoretical investigations due to the magnetic ordering present in the bulk, in the unoxidized surface, and in their most stable oxides. Interest in the study of Co and Cr derives from their frequent use either in binary CoCr alloys * E-mail: [email protected]. † University of Bremen. ‡ Fraunhofer Institute for Mechanics of Materials IWM. § Fraunhofer Institute for Manufacturing Technology and Applied Materials Research IFAM.

or in multicomponent alloys in combination with Fe, Ni, Mn and other elements. The high reactivity of Co/Cr surfaces toward oxygen plays a key role in technological applications, ranging from perpendicular magnetic recording media10,11 to orthopedic implants12 and heterogeneous catalysis.13,14 In particular, Cr is one of the most established alloying elements for corrosion protection. Experimental studies (mainly photoelectron spectroscopy and electron diffraction) reveal that the oxidation of Co(0001) leads to different species depending on the temperature. At or above 300 K, oxygen diffuses into the bulk and forms CoO, followed by oxidation of CoO to Co3O4 by a nucleation and growth mechanism.15,16 At lower temperatures, the oxidation starts immediately with formation of a Co3O4-like oxide.17,18 The same phenomenon has been observed also for other Co surface orientations.19,20 However, whether the structures formed in the initial oxidation stage present amorphous or crystalline character remains unclear. Instead, it is well-known from experimental data that chromium surfaces oxidize with formation of a thin film of Cr2O3 over a wide temperature range. The oxide film exhibits a limiting thickness which is strongly temperature dependent, indicating that the oxidation process may be controlled by Crion diffusion.21 At low temperatures, the initial oxidation of Cr(110) has been suggested to proceed by formation of a disordered Cr2O3 layer with a saturation coverage below 1 nm.22 However, it remains unclear whether the disorder is due to the presence of water in the oxide23 or to the scarce mobility for atomic oxygen, which prevents the formation of ordered overlayers,24 as instead observed at 300 K.25 Above room temperature, several works report on the epitaxial growth of R-Cr2O3 (0001)||Cr (110) thin films.21,23,26 The assumption of a

10.1021/jp1004105  2010 American Chemical Society Published on Web 03/16/2010

Oxidation of the Co(0001) and Cr(110) Surfaces layer-by-layer growth mechanism is supported by the absence of roughening at the surface and the metal/oxide interface. However, because of the intrinsic limitations of experimental techniques and the absence of theoretical works, little is known about the initial oxidation mechanisms and the structural, chemical and magnetic properties of the native oxide films on Co and Cr. In the present work, we aim to elucidate and compare the mechanisms of oxide nucleation on the pure Co(0001) and Cr(110) surfaces on the basis of first-principles molecular dynamics simulations (FPMD) within density-functional theory (DFT). This technique has provided a deep insight into the initial oxidation stages of metal and semiconductor surfaces,27-30 complementing experimental data with predictions about structural details and reaction pathways in the low-temperature oxidation regime. Here we find that oxide nucleation on cobalt occurs via the early place-exchange of metal and oxygen atoms and the growth of an open, pseudoamorphous oxide structure with evident Co3O4-like features. These results are in excellent agreement with the available low-temperature experimental data. Instead, chromium oxidizes in a layer-by-layer fashion via formation of perfect oxygen ad-layers. Interestingly, the growth of Cr2O3 thin films is preceded by the formation of chromatelike structures with overoxidized Cr atoms, resulting from the high supply of oxygen in the initial oxidation phase combined with the limited diffusion of Cr ions. 2. Methods Description of the Model Systems. The Co(0001) and the Cr(110) surfaces are modeled by a rectangular hcp-(3×23) and a bcc-(3×22) surface unit cell, respectively, both including 12 surface atoms. All simulations are performed with periodically repeated cells consisting of a slab of six stacked metal layers separated by a vacuum gap of the same thickness in the x direction perpendicular to the surface. Computational Details. Our calculations are performed within the framework of DFT using the PW91 generalized gradient approximation (GGA) to the exchange-correlation functional,31 under periodic boundary conditions. Both the minimization of the electronic states and the molecular dynamics simulations are performed using the Car-Parrinello (CP) method32 on the basis of special algorithms developed to treat metallic systems.33,34 We use the projector augmented wave (PAW) method35 to represent the interaction between valence electrons and core ions, as implemented in the LAUTREC code.36 The generated PAW data sets treat 9 explicit valence electrons for cobalt, 8 semicore and 6 valence electrons for chromium, and 6 valence electrons for oxygen. The included projectors for the s, p, and d angular momentum channels are 3, 2, 2 for cobalt, 3, 3, 2 for chromium, and 2, 2, 0 for oxygen (see also ref 37). The wave functions are expanded in plane waves up to a kinetic energy cutoff of 540 eV at the (0, 0.25, 0.25) point in the Brillouin zone. The electronic states are occupied according to a Fermi-Dirac distribution using a smearing width of 0.1 eV. All calculations are performed within a spin-polarized formalism without any spin constraint. Atomic charges are computed according to a Bader decomposition of the charge density using the grid-based algorithm of Henkelman et al.38 All simulations are performed with the adsorption of oxygen molecules only on one surface of the slab, hence inducing a surface-dipole and an electrostatic asymmetry in the supercell. In order to circumvent the build-up of an artificial uniform electric field across the vacuum region due to periodic boundary conditions, we apply a dipole correction consisting of an external field that instantaneously compensates

J. Phys. Chem. C, Vol. 114, No. 14, 2010 6615 the artificial field (see e.g. refs 39 and 40). This translates into a step of the electrostatic potential in the middle of the vacuum region, whose height provides the value of the work function difference between the oxidized and the bare surfaces. For each system, the computed values of the work function of the bare surfaces lie within ( 0.005 eV, irrespective of the oxidation state of the opposite surfaces. These amount to 5.0 eV for Co(0001) and 4.9 eV for Cr(110), compared to the experimental values of 5.0 and 4.5 eV, respectively.41 Electron Minimization and Magnetic Ordering. The systems considered in the present work are characterized by a magnetic order and therefore by a complex potential energy landscape. This fact requires special care for the electronic structure calculations in order to achieve convergence and find the correct magnetic ground state. Using a CP damped dynamics scheme, we apply a very slow quenching of the electronic temperature, which always leads to convergency using a sufficiently small time step of generally 2.5 au and never exceeding 3.0 au. Prior to minimization, the wave functions are either randomly initialized or initialized as atomic orbitals imposing an initial magnetic ordering to the metal atoms. For each system, we perform different initializations checking the existence of different magnetic solutions (throughout this paper we illustrate the magnetic orderings bearing the lowest total energy). The total energy differences among these are about one order of magnitude smaller than the differences between different atomic configurations (i.e., never more than 0.2 eV per simulation cell). In the consecutive FMPD simulations of the oxidation reactions of each surface, we pay attention to the consistency between the magnetic structure at the end of a simulation and at the beginning of the following one. The ground state of bulk Co in the hcp lattice is ferromagnetic with a computed magnetic moment of 1.60 Bohr Magnetons (to be compared with the experimental value of 1.58 µB42). For bulk Cr, using a bcc cubic cell we find an antiferromagnetic ground state and a magnetic moment per atom of 1.02 µB. While the experimental magnetic ground state is a longitudinal spindensity wave with an incommensurate wave vector,43 our magnetic solution is in agreement with a number of previous electronic structure calculations at the DFT level using a simple bcc cell structure (see, e.g., ref 44). The correct magnetic ordering is also found for the bulk oxides Co3O4 and Cr2O3, whose main properties are summarized in ref 45. We note that our calculations are performed at the standard GGA level, which results in a severe underestimation of the band gap of Co3O4 and Cr2O3. However, the magnetic ordering, the energetics and the structural features of the oxides are correctly reproduced. Due to the well-known overestimation of the binding energy of O2 within DFT,46 the total energy of O2 is derived from total energy calculations of bulk Co and Co3O4 and the experimental value of the enthalpy of formation ∆Hf0(Co3O4) ) -106 kcal per O2 mole,47 according to: EO2 ) 1/2ECo3O4 - 3/2ECo ∆Hf0(Co3O4). With this value of EO2, the computed enthalpy of formation of Cr2O3 is -169 kcal/mol, to be compared with the experimental value of 181 kcal per O2 mole.47 Molecular Dynamics Strategies. All FPMD simulations are performed starting from fully relaxed systems without imposing initial velocities to any atom. The time-step of 2.5-3.0 au used for electronic minimization also maintains the adiabaticity between the electronic and ionic degrees of freedom during the MD simulations. Unless otherwise stated, we perform microcanonical MD simulations. Where required, control of the simulation temperature is achieved through a velocity rescaling of the ions, with typical heating or cooling rates of the order of

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Figure 1. Selected final snapshots of ten consecutive FPMD simulations of the initial oxide formation on the Co(0001) surface. Cobalt atoms are shown in blue and oxygen atoms in red, the oxygen coverage of each snapshot is indicated. The isosurfaces illustrate regions of positive (gray) and negative (yellow) spin density. Arrows indicate oxygen atoms carrying a net magnetic moment.

300 K/ps. The atoms of the outermost surface layer not involved in the oxidation reactions are kept fixed during the dynamical simulations but not during the static relaxations. After the geometry optimizations all force components on the unconstrained atoms are less than 0.05 eV/Å. 3. Results 3.1. Oxidation of Co(0001). FPMD Simulations. We begin our study with consecutive FPMD simulations of the adsorption of oxygen molecules on the Co(0001) surface, reaching a final coverage of 1.67 ML (Figure 1). In the first simulation, a single oxygen molecule, initially at rest, is placed at a distance of about 2.8 Å over the fully relaxed surface, i.e., at virtually 0 K, and the system is let free to evolve according to a microcanonical CP dynamics. The molecule is attracted by the surface, binds initially to two Co atoms, and dissociates spontaneously through the same “hot atom” dissociative mechanism already observed for Al,27 Si,28 Ti,48 and TiN,30 as shown schematically in Figure 2a. The process is characterized by electron donation from the metal atoms into the antibonding π* and σ* orbitals of O2.27 This is reflected in the evolution of the total charge of the two oxygen atoms and leads to evident oscillations in the spin density while the O atoms migrate over the magnetic metal surface, as shown in Figure 2b. The reaction is highly exothermic and comprises a large release of kinetic energy which is distributed from the O atoms to the metal substrate during the following few picoseconds. After quenching of the atomic motion, the O atoms are stably adsorbed at fcc adsorption sites with a Co-O distance of 1.84 Å, as shown in Figure 1a. Starting from this configuration, a further nine O2 molecules are placed one at a time above the surface, and FPMD simulations are performed until an initial oxide layer develops on the metal substrate. The final snapshots of the simulations after atomic relaxation are shown in Figure 1a-h. With increasing coverage, repulsion of incoming O2 molecules takes place. Adsorption for coverages higher than 0.5 ML occurs only if the oxygen molecules are initially placed

Figure 2. Analysis of the adsorption of O2 on a bare Co(0001) surface (a and b) and on a bare Cr(110) surface (c and d). Left: Evolution of the O-O distance and of the height of the center of mass of the O atoms with respect to the average height of the surface. Right: Evolution of the spin density and of the atomic charge integrated within the Bader region associated with both O atoms.

close enough to the surface (about 1.5 Å), promoting the formation of covalent bonds. With the adsorption of a fourth O2 molecule (0.67 ML) a cobalt atom leaves the surface plane, being extracted by an oxygen atom that remains bound on top of it, as shown in Figure 1c. In the subsequent simulation (to reach a coverage of 0.83 ML), a dioxygen molecule adsorbs on the surface but does not dissociate spontaneously. We thus gradually increase the simulation temperature to ∼600 K. The thermal motion of the surface leads to an increased amplitude of the O2 stretching mode until the bond length becomes large enough to enable partial filling of the σ* antibonding molecular orbital. This results in the dissociation of O2 after 1.9 ps and incorporation of O atoms below the surface plane, filling a vacancy left by an outcoming cobalt atom (Figure 1d). Similarly, up to a coverage of 1.67 ML, the energy released upon dissociation of O2 activates place exchanges between the surface

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Figure 3. (a) Calculated density of states of the Co atoms of the surface layer for selected oxygen coverages during FPMD simulations. The coverage is indicated on the left. The majority (minority) spin manifold is plotted with solid (dashed) lines. (b and c) LDOS of two 4fcoordinated Co atoms of the outer oxide structure of the FPMD system at 1.67 ML (dashed lines) and LDOS of a Co atom on a tetrahedral site in bulk Co3O4 (red lines). The peaks in the LDOS corresponding to the t2g and eg orbitals are labeled. Positive (negative) values indicate majority (minority) spin.

Co atoms and the incoming oxygen atoms. Interestingly, the oxidation process so far involves exclusively metal atoms of the topmost layer of the metal surface, while the atoms of the subsurface layer remain in their original lattice position. The final oxide layer obtained is characterized by an apparently disordered, rather open structure with a thickness of about 0.6 nm, and the presence of further potentially reactive sites for O2 adsorption. Properties of Oxidized Cobalt (1.67 ML). The Co atoms of both metallic cobalt and its stable oxides CoO and Co3O4 display a net magnetic moment. While antiferromagnetic ordering is present in the oxides, metallic Co is ferromagnetic. The ferromagnetic ordering is preserved on the atoms of the bare Co(0001) surface, where the magnetic moment is enhanced by 6%. In our FPMD simulations, we observe a gradual decrease of the magnetic moment of the surface Co atoms going from the blank surface (1.7 µB per Co atom) to the system with a coverage of 0.67 ML (1.0 µB per Co atom, on average). The event of Co/O place exchange that occurs at a coverage of 0.83 ML (Figure 1d) is characterized by a spin reversal for some of the Co atoms and by the initiation of an antiferromagnetic ordering in the formed Co-O network, indicative of a first “nucleation” of oxide on the surface. The adsorption of further oxygen molecules leads to development of an antiferromagnetic oxide structure (see Figure 1e-h). The overall evolution of the magnetization of the oxide film with increasing O coverage is also clearly reflected in the density of states spectra of the Co surface atoms during the oxidation (Figure 3a). Our calculated layer-projected DOS for the blank Co(0001) surface (whose spectrum agrees very well with previous calculations49) presents a clear spin asymmetry consistent with its ferromagnetism. During the oxidation, the spin asymmetry is still visible at intermediate coverages due to the magnetic rearrangement associated with oxide nucleation, but vanishes at 1.5 ML, when an antiferromagnetic ordering is established in the oxide structure. A characteristic feature of the DOS evolution is the appearance and growth of a peak centered around -6 eV which emerges above the DOS of the clean surface after the initial oxygen adsorption. This characteristic peak arises from the oxygen 2p orbitals and is always

Figure 4. (a) Bader charges of all Co atoms of the FPMD system (1.67 ML) with respect to their number of nearest-neighbor oxygen atoms. For comparison, the charges on the Co atoms of bulk Co3O4 and bulk CoO are shown in blue and green, respectively. (b) Distribution of the Co-O distances for the surface Co atoms of the FPMD system with coverage 1.67 ML as well as for bulk Co3O4 and CoO.

observed in spectroscopic investigation of the valence band evolution during oxidation of Co(0001).17,50 In the oxide film at 1.67 ML, Co atoms are coordinated by at most four O neighbors. For comparison, the Co2+ ions in bulk CoO are 6-fold (6f) coordinated within octahedral sites, while Co2+ and Co3+ ions in Co3O4 occupy tetrahedral and octahedral sites, respectively. Indeed, the local DOS (LDOS) of several 4f-coordinated atoms in the oxide layer presents features very similar to the Co2+ ions in Co3O4, which are in a 3d7 high spin state with four paired electrons in the eg orbitals and three unpaired electrons in the higher-energy t2g orbitals (Figure 3b). More evidence of Co3O4 -like features in the oxidized FPMD system at 1.67 ML is provided by an analysis of the Co Bader charges and the distribution of the Co-O distances in the oxide layer, compared with those of the bulk oxides (Figure 4). In particular, the distance distribution of the FMPD system presents a broad nearest-neighbor peak centered around 1.84 Å, which includes also the distance of 1.93 Å of Co3O4, and is far from the distance of 2.12 Å of CoO. The charge values increase roughly linearly with the number of O first-neighbors (Figure 4a), and reach values of 1.4 to 1.6 electrons for the 4fcoordinated Co atoms. The agreement with the Bader charge 1.45e of the Co atoms on 4f-coordinated sites in Co3O4 is excellent. For comparison, the charge of the 6f-coordinated Co atoms in CoO is lower (1.3e), despite the higher coordination. Notably, no 6f-coordinated Co atoms are present in the FPMD system at this oxygen coverage, and none of the atoms present

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Figure 5. Selected final snapshots for FPMD simulations of the initial oxide formation on the Cr(110) surface, labeled with the corresponding oxygen coverages. Cr atoms are shown in green and O atoms in red. (a) Snapshot after a MD simulation leading to stably adsorbed, undissociated molecular oxygen. (b and c) Final snapshots from a simulation series (called MD1) performed without temperature constraint. (d-f) Final snapshots from a second simulation series (called MD2) after the adsorption of five, six, and seven O2 molecules, respectively. The isosurfaces illustrate regions of positive (gray) and negative (yellow) spin density.

features similar to the octahedral sites in bulk Co3O4. The latter would present a 3+ formal oxidation state with paired electrons in the t2g orbitals and empty eg orbitals, thus leading to absence of magnetization and a formal charge of 1.6e. 3.2. Oxidation of Cr(110). FPMD Simulations. The initial oxidation of the bcc Cr(110) surface is modeled following the same procedure as for the Co(0001) surface. As in the case of cobalt, the initial oxidation is characterized by spontaneous adsorption and dissociation of O2 molecules on the surface (Figure 2c,d). An distinctive feature of the oxidation of chromium is the absence of place exchange mechanisms between metal and oxygen up to a coverage of 0.67 ML, where the oxygen atoms are stably adsorbed on both “hollow” and “bridge” surface sites. As a consequence of the strong surface dipole arising from the donation of electronic charge from the metal to oxygen, the reactivity of the surface toward further reactions is considerably reduced. Several attempts of adsorbing a fifth O2 molecule lead to its desorption from the surface. In one simulation, a molecule remains chemisorbed in an end-on configuration roughly perpendicular to the surface without dissociating, as shown in Figure 5a. In another simulation, an O2 molecule adsorbs and dissociates leading not only to formation of an oxygen ad-layer on an almost perfectly flat Cr(110) surface, as shown in Figure 5b, but also to a further decrease of the surface reactivity. Adsorption of a new molecule occurs only after forcing the formation of covalent bonds by placing the molecule close to the surface, with initial Cr-O distances as in Cr2O3. In this case, the heat released during the molecular dissociation induces the extraction of a Cr atom out of the surface. The Cr atom is lifted by about 2.4 Å over the surface plane, remains bound to the surface via three O atoms, and coordinates a fourth O atom “on top” (Figure 5c). The obtained tetrahedral coordination shell strongly resembles the structure of a chromate ion CrO42-, bound to the (110) surface layer. This first set of simulations (path MD1) is characterized by the formation of stable, saturated structures which do not present

reactive sites for further adsorption and incorporation of O2. Thus, in order to promote oxide nucleation, we repeat the simulation leading to a coverage of 0.83 ML by gradually increasing the temperature to about 800 K within the first 0.6 ps and annealing the system for 1.2 ps (path MD2). The effect of thermal motion combined with the heat released during O2 dissociation leads to extraction of two Cr atoms out of the surface at 0.83 ML. After quenching of the atomic motion, these are both coordinated to four oxygen atoms sharing one of them, as shown in Figure 5d. The vacancies left behind by the outgoing Cr atoms enable an oxygen atom to be incorporated in the surface plane. In the following simulation, dissociation of O2 occurs only after heating and annealing the system at 850 K for 3.6 ps. This and the next simulation lead to incorporation of a single O atom underneath the surface, but not to extraction of other Cr atoms from the surface. Figure 5e-f shows the final snapshots at 1.0 and 1.17 ML. In the final structure, the two extracted Cr atoms are located at the centers of two cornersharing oxygen tetrahedra, forming a structure resembling a dichromate ion Cr2O72-. Again, no evident sites for further O2 adsorption are present. Properties of Oxidized Chromium (1.17 ML). Along the MD1 reaction path, the antiferromagnetic ordering of the bccCr lattice is preserved also after oxygen adsorption and after extraction of a single Cr atoms from the surface (see Figure 5c). In the MD2 path, the two Cr atoms extracted from the surface display an antiferromagnetic coupling when directly bound together (as in Figure 5d,e), and a ferromagnetic coupling when connected through a bridging oxygen atom (Figure 5f). As for cobalt, the magnetic moments of the surface atoms decrease gradually going from the blank surface (1.76 µB) to the system with a perfect oxygen ad-layer at 0.83 ML (0.85 µB on average). Finally, extraction of a Cr atom above the surface layer partially restores the magnetic moments of the surface atoms, presenting absolute values between 0.9 and 1.3 µB. An

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Figure 6. Density of states projected on single Cr and O atoms. (a) From bottom to top: a Cr atom of the clean Cr(110) surface layer; the same Cr atom after adsorption of an ad-layer of oxygen; the Cr atom in the chromate-like structure shown in Figure 5c; one Cr atom of the dichromate-like structure shown in Figure 5f; a Cr atom of bulk Cr2O3 (red). (b) From bottom to top: DOS of an O2 molecule in vacuum; DOS of an adsorbed O2 molecule as shown in Figure 5a; DOS projected on an O atom adsorbed on the surface layer; DOS of an oxygen atom bound on top on an extracted Cr atom, as shown in Figure 5c; DOS of an O atom of bulk Cr2O3 (red). The majority (minority) spin mainfold is indicated by solid (dashed) lines.

exception is represented by the extracted 4-fold (4f) coordinated Cr atom, whose magnetic moment (1.8 µB) is considerably higher. These features are reflected in the DOS projected on four relevant types of Cr atoms appearing in our FPMD simulations, compared with bulk Cr2O3 (Figure 6a). In the clean Cr(110) surface, the d band is clearly visible between -0.5 and -2.5 eV and presents a net magnetization (Figure 6a, bottom), in excellent agreement with previous works.51,52 After adsorption of a perfect monolayer of oxygen, the DOS of the same Cr atom shows an appreciable decrease in the occupation of the majority band due to electron donation to oxygen. The vanishing differences between majority and minority spin manifolds reflect the lowering of the magnetic moment of Cr after oxygen adsorption. The features appearing between -4 and -8 eV originate from the p orbitals of oxygen. Moreover, the DOS projected on the Cr atoms extracted from the surface both in MD1 and MD2 (denoted as “similar CrO42- ” and “similar Cr2O72-” in Figure 6a) present an almost complete depletion of the minority spin manifold between -3 and 0 eV, which can be found also in the DOS of Cr3+ in bulk Cr2O3 (see Figure 6a, top). For the latter, the peaks of the half-filled t2g orbitals (majority spin) at -1.0 eV are clearly visible, together with the peaks above the Fermi level for the unoccupied orbitals t2g (minority spin) and eg. However, in our FPMD system, the extracted Cr atoms present a lower occupation of the majority spin manifold with respect to Cr3+ in Cr2O3, suggesting an oxidation state higher than 3+. A high oxidation state is confirmed also by the calculated atomic Bader charges, indicated besides the corresponding DOS in Figure 6a. All Cr atoms extracted above the surface layer present atomic charges which are considerably higher than those of the underlying Cr atoms in the surface layer, and also higher than Cr in Cr2O3. These features are clearly visible in Figure 7a, where the Bader charges of all Cr atoms in the oxidized structure at 1.17 ML (MD2) are reported as a function of the number of nearest-neighbor oxygen atoms. For comparison, also

Figure 7. (a) Bader charges of all Cr atoms of the FPMD system (1.17 ML, see Figure 5f) as a function of their number of nearestneighbor O atoms. For comparison, the Cr charges of bulk Cr2O3 (red) and of isolated dichromate Cr2O72- (violet) are shown. (b) Distribution of the Cr-O distances for the oxygen-coordinated Cr atoms of the FPMD system with coverage 1.17 ML, as well as for bulk Cr2O3 and Cr2O72-.

the calculated values for bulk Cr2O3 and for an isolated dichromate Cr2O72- molecule are shown. The two extracted Cr atoms in the FPMD system, which are both 4f-coordinated, present charge values approaching those of the isolated dichromate structure (2.1e), rather than those of bulk Cr2O3 (1.7e). A similar trend emerges also from the radial distribution function (RDF) of the Cr-O distances in the oxidized system compared with those of bulk Cr2O3 and dichromate, shown in Figure 7b. The shortest distance (1.57 Å) in the FPMD system, due to the bonds between either extracted Cr atoms and their respective on-top, dangling oxygen atoms (see Figure 5f), is analogous to the shortest bond length for the calculated relaxed structure of an isolated dichromate ion (1.63 Å). The distances between these two Cr atoms and their shared oxygen atom amount to 1.77 Å both for our FPMD system and for dichromate. On the contrary, no clear association to the RDF peaks of bulk Cr2O3 can be performed. Finally, different kind of oxygen atoms are observed in our FPMD systems. First, in several MD simulations at coverages 0.67-0.83 ML we observe the presence of molecular oxygen, stably adsorbed in an end-on configuration over the surface. The DOS of adsorbed O2 compared with an O2 molecule in vacuum is shown in Figure 6b (bottom). The association of the peaks is unambiguous. They show the filling of the antibonding π* orbitals of the minority spin in the case of adsorbed O2. This arises from electron donation of the underlying metal and leads to an almost full quenching of the magnetic moment of

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Figure 9. Topmost layers of the monocline simulation supercell for an R-Cr2O3(0001)||Cr(110) structure after static relaxation, including 12 Cr surface atoms. The oxygen coverage is 2.0 ML.

Figure 8. Energetic gain after the consecutive adsorption of O2 molecules on the Co(0001) and Cr(110) surfaces as a function of the oxygen coverage. Solid lines with filled symbols represent the FPMD systems, while solid lines with empty circles denote perfect oxygen ad-layers. The dashed lines indicate the enthalpy of formation per O2 for the bulk oxides Cr2O3 and Co3O4.

the molecule. Moreover, two adsorbed oxygen atomic species are shown in Figure 6b. The DOS of an isolated oxygen atom (O top) on top on an extracted Cr atom is characterized by a strong and narrow, slightly spin-polarized double peak between -3.5 and -4.2 eV, whose presence is also visible in the spectrum of the neighboring Cr atom (panel a, middle). Instead, the DOS of O atoms at hollow sites on the surface layer (O ads.) displays a broad feature between -4 and -8 eV, the same as observed in the oxidation of cobalt (see Figure 3a). Interestingly, the DOS of O in Cr2O3 presents features of both kinds of surface O atoms. Additionally, it exhibits a feature between -0.6 and 2 eV, which can be clearly attributed to the d band of the neighboring Cr atom. 3.3. Oxidation Energetics. Energy Profiles of the Oxidation Process. The calculated energetic gain for the simulated oxidation reactions as a function of the oxygen coverage is illustrated in Figure 8. For comparison, we include in the graph dashed lines representing the enthalpy of formation per O2 for the bulk oxides Cr2O3 and Co3O4. Along with the results obtained with FPMD, we plot the energies of perfect oxygen ad-layers at 1.0, 1.5, and 2.0 ML. At 1.0 ML the O atoms are placed in 3-fold hollow surface sites. The lowest-energy systems at 1.5 ML are then obtained with surface and subsurface oxygen coverages of (0.5 ML, 1.0 ML) and (1.0 ML, 0.5 ML) for Co and Cr, respectively. The 2.0 ML system for Co corresponds to a configuration (1.0 ML, 1.0 ML). For Cr, the lowest energy at 2.0 ML is obtained for the atomistic model proposed in ref 23 on the basis of experimental LEED and STM data. In this work, the authors found a clear evidence for an epitaxial R-Cr2O3(0001)||Cr(110) structure consisting of 1.0 ML oxygen adsorbed on the substrate, a double Cr intermediate layer and a second oxygen layer, finally terminated by a Cr cation plane. After DFT relaxation, the intermediate double Cr layer rearranges forming a flat plane as shown in Figure 9. The energy profile related to the oxidation process presents substantial qualitative and quantitative differences for Co and Cr. For cobalt, the FPMD data and the data for a perfect ad-

Figure 10. Evolution of the work function with respect to the bare surface as a function of the oxygen coverage, for the following systems: (left) cobalt (0001) surface, both for the MD simulations and for perfect oxygen ad-layer systems and (right) chromium (110) surface, for MD2 (see text) and for perfect oxygen ad-layers.

layer coincide up to a coverage of 0.5 ML. From here on, the extraction of cobalt atoms from the surface layer at 0.67 ML and the incorporation of oxygen atoms at 0.83 ML lead to energetically less favorable structures compared to a perfect O ad-layer. However, the FPMD structures become more stable than the perfect systems at coverages higher than 1.17 ML. A striking feature at higher coverages is that the slope of the interpolated FPMD curve clearly approaches the one of the Co3O4 line, denoting that the energy gain upon adsorption and incorporation of new O2 molecules in the oxide film is as high as the enthalpy of formation of bulk Co3O4. In the case of chromium, the energy curves for the FPMD systems and for the perfect oxygen layers are almost superimposed up to a coverage of 1.0 ML, as shown in Figure 8. In particular, the events of initial oxide nucleation observed in the FPMD simulations (MD2) do not lead to formation of energetically metastable structures as instead observed for cobalt. The energy differences between the FPMD structures and the perfect O ad-layers are as little as 0.1 eV per simulation supercell (the differences at low coverages are due to adsorption on hollow or bridge sites in the two cases). While no spontaneous oxide growth could be observed in the FPMD systems, the energy gain associated with the formation of ideal expitaxial layers at 1.5 and 2.0 ML approaches the slope of the Cr2O3 line. This seems to confirm the experimental finding that Cr(110) oxidizes according to a layer-by-layer mechanism with formation of a crystalline oxide film in epitaxy with the substrate23 and terminated by Cr atoms. Interestingly, lifting a Cr atom from the surface plane to a position above a 1.0 ML oxygen ad-layer is associated with an increase in energy by 1.3 eV. On the contrary, at 2.0 ML the Cr-terminated structure shown in Figure

Oxidation of the Co(0001) and Cr(110) Surfaces 9 is 2.6 eV lower in energy than a corresponding O-terminated structure with a full Cr layer between the O layers. Changes of the Work Functions during Oxidation. The energetic behavior of the considered systems and their oxidation mechanisms are directly reflected in the changes of the work function ∆Φ upon oxidation. After initial oxygen adsorption, the d-orbital depletion of the surface metal atoms and the charge transfer into the p orbital of the O atoms gives rise to a strong surface dipole and decreases its reactivity, thus inhibiting further oxygen adsorption. As shown in Figure 10, the formation of perfect O ad-layers leads to a steady increase of ∆Φ, with maxima of 1.8 and 2.3 eV obtained at a coverage of 1.0 ML on Co and Cr, respectively. Instead, the onset of oxide nucleation by place exchange between metal and oxygen observed in the FPMD simulations is characterized by a sudden drop of the work function. For cobalt, this event occurs at 0.67 ML and leads to a decrease of ∆Φ, which remains fairly stable around the value 0.65 eV during the subsequent oxide growth. This is in excellent agreement with experimental data showing that ∆Φ never exceeds 0.6 eV17 after exposure of Co(0001) to oxygen. This seems to rule out the possibility of oxidation via formation of a perfect oxygen layer. For chromium, the drop in ∆Φ occurs at a higher coverage, accordingly to the later onset of oxide formation at 0.83 and 1.0 ML for the MD2 and MD1 systems. The introduction of subsurface O atoms leads to a substantial decrease of ∆Φ also in the case of perfect ad-layers. In particular, ∆Φ becomes negative for the model system R-Cr2O3(0001)||Cr(110), which is attributed to the termination of the oxide by Cr atoms. Consistently, an initial increase in ∆Φ and a sudden drop toward negative values has been found also by experimental measurements for Cr(110) at low oxygen exposures, before crystalline Cr2O3 starts growing.53 We note that a Cr termination of oxide structures in the very initial stage of the oxidation process (at coverages lower than 2.0 ML) is never observed in our FPMD simulations. Here, instead, the accumulation of a large amount of O atoms before oxide nucleation leads to oxidation states higher than 3+ for the Cr atoms that first leave the surface, and with the frequent occurrence of onefold-coordinated O atoms on top of Cr ions, consistent with relatively high ∆Φ values at about 1.0 ML. 4. Discussion Features of the Initial Oxidation of Co. In our simulations we observe that Co(0001) oxidizes spontaneously at low temperatures, following a metal-oxygen exchange mechanism which initiates the growth of an amorphous, antiferromagnetic oxide. The onset of oxide formation at 0.67 ML is characterized by extraction of Co atoms off the surface layer, followed by the incorporation of oxygen underneath the surface. This is in agreement with experimental data, which estimate that oxygen starts dissolving underneath the surface layer at approximately 0.5 ML.17 At the coverage 0.83 ML, we first observe a spin reversal for some Co atoms in the oxide network, and increasing the O coverage eventually leads to cancelation of the spin polarization in the oxide at 1.5 ML. This is consistent with the antiferromagnetic ordering of the two stable oxides CoO and Co3O4, which are expected to form on cobalt on exposure to air,17,50 and is confirmed by spin-resolved photoemission data showing a total loss of the spin polarization already in the initial stage of Co(0001) oxidation.19 Indeed, within a well-developed oxide network, next-nearest neighbor Co atoms are known to couple via an antiferromagnetic superexchange interaction of the type Co2+-O-Co2+ or Co3+-O-Co3+,54 which is also at

J. Phys. Chem. C, Vol. 114, No. 14, 2010 6621 the origin of the antiferromagnetic ground state of CoO and Co3O4.55,56 The antiferromagnetic superexchange interaction is characterized by a vanishing magnetic moment of the bridging oxygen atom, as visible in all our simulations. Moreover, in accordance with photoelectron spectroscopy experiments,50 we find that the nonoxidized Co substrate underneath the oxide film is still ferromagnetic. At the metal/ oxide interface, O atoms which bridge the metal substrate with Co atoms of the oxide layer with the same spin direction are characterized by non-negligible spin density, reaching values of about 0.4 µB. Indeed, mixing of the d orbitals of the Co ions with the p orbital of the oxygen atom leads to an induced magnetic moment on oxygen aligned to those of the neighboring, ferromagnetically coupled Co atoms (highlighted by arrows in Figure 1e-h). This feature is in accordance with experimental results for Co(0001),50 and has been predicted also by theoretical calculations for the ferromagnetic fcc-Co(100) and Fe(001) surfaces.19,57 In particular, the spectroscopic signature indicative of spin-polarization on oxygen is found to decrease with increasing oxygen exposure.58 This is consistent with the development of an antiferromagnetic oxide of increasing thickness, while ferromagnetic ordering remains localized at the metal/oxide interface. In the low-temperature regime, the slow diffusion of oxygen into the bulk is expected to lead to initial formation of the oxygen rich phase Co3O4, rather than of CoO. Indeed, by analyzing the distribution of Co-O distances and atomic charges, the local density of states on several Co atoms, and the overall energetics of the oxidation process, we found that the formed oxide layer at coverages of about 1.67 ML strongly resembles Co3O4. The emergence of Co3O4-like features during low-temperature oxidation is strongly supported by experimental investigation of the Co(0001) surface and of other surface orientations.17-20 Features of the Initial Oxidation of Cr. The initial oxidation of Cr(110) is characterized by rapid dissociative chemisorption of O2 molecules and their ordered arrangement on stable adsorption sites of the surface. Differently from the case of Co, a spontaneous metal/oxygen exchange process does not take place, leading to saturation of the reactive surface sites at coverages of 0.83-1.0 ML. At low temperatures, O2 molecules can stably adsorb in molecular form, and Cr atoms are only observed to leave the surface plane if O2 dissociation is forced either by simulated high-temperature annealing or by placing the molecule extremely close to Cr surface atoms. In a number of independent FPMD simulations, one or two Cr atoms are extracted from the surface and arrange in tetrahedrally coordinated O shells which bear structural and electronic features of chromate or dichromate ions (see Figure 5). However, even this process does not recover the reactivity of the surface, so that successive adsorption steps are strongly inhibited. It is a remarkable fact that experimental Auger spectra also report a surface saturation coverage at low temperature (120 K) which has been estimated to be about 1.0 ML.24 The authors argued that, within this temperature range, the adatom mobility is considerably lower than at room temperature and diffusion of oxygen atoms into the Cr-lattice is kinetically inhibited. In particular, they ruled out the existence of subsurface oxygen. As a consequence, the surface sites available for dissociative adsorption decrease with increasing coverage and features of molecular O2 ad-species have been detected by vibrational spectroscopy.25 The O2 ad-species are believed to be stable only at low temperatures and to coexist with dissociatively chemisorbed oxygen ad-atoms. As confirmed by

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our simulations, they are supposed to bind to Cr via only one atom and be tilted with respect to the direction normal to the surface. The presence of chemisorbed O2 molecules has been confirmed by photoemission spectroscopy studies, which reveal a weak spectral feature at ∼-7.5 eV.22,25 In fact, our calculated density of states projected on an O2 molecule stably adsorbed on the surface during the FMPD simulations reveals a peak at exactly -7.5 eV (see Figure 6b), making the correspondence with the experimental results unambiguous. Mechanisms of Oxide Formation on Co and Cr. The initial oxidation of Co(0001) and Cr(110) clearly manifest different features and seem to occur along two distinct pathways, as revealed by the structural details and the energetics of the oxidation process obtained in the FPMD simulations. The behavior of cobalt is similar to what found in the case of Al(111),27 Si(100),28 and Ti(0001).48 Namely, the large heat developed by the dissociation reaction of O2 leads to strong structural rearrangements of the surface and initiates the spontaneous formation of a noncrystalline oxide layer at oxygen coverages around 0.6 ML. Initially, the formed oxide structures are metastable with respect to an ideal ad-layer of adsorbed oxygen on the surface. They are, however, necessary precursors for the subsequent growth of a stable thicker oxide, since the incorporation of subsurface O atoms after the formation of perfect O ad-layers becomes unfavorable at coverages larger than about 1.2 ML (Figure 8). Instead, at the same or higher coverages the energy gain of the reaction of novel O2 molecules with the disordered oxide layer is almost equal to the enthalpy of formation of bulk Co3O4. This agrees well with the close matching of the distribution of Co-O distances, LDOS, and Bader charges between the FPMD systems and bulk Co3O4, as outlined above. In the case of Cr(110), upon reaction with O2, we observe the clear tendency of formation of an almost perfect O ad-layer up to saturation of the surface reactivity. Oxygen/metal exchange processes take place only in simulations at high temperatures (∼800 K), leading to structures whose energies differ only very slightly from those of ideal O ad-layers and do not present free sites for reactions with new O2 molecules. Further oxide growth becomes thus limited by the thermally activated extraction of Cr ions from the surface. Notably, the diffusion of Cr atoms across a perfect ML of oxygen to form a Cr-terminated surface is not favored at this oxygen coverage. Instead, the strong enrichment in adsorbed oxygen prior to the extraction of Cr atoms is responsible for the formation of chromate and dichromate-like structures where the ions present oxidation states higher than 3+ and are terminated by single O atoms. A side view of the system discloses regular, alternating layers formed uniquely by Cr or O atoms, which can be considered as precursors to the development of Cr2O3. This process is expected to take place on a longer time-scale than achievable by FPMD, and to involve the diffusion of further Cr atoms from the metal substrates into the overoxidized layer. Experimental data obtained at or above room temperature reveal that further oxide growth proceeds with formation of an epitaxial R-Cr2O3(0001)||Cr(110) layer up to a temperaturedependent limiting thickness.23,26 In perfect agreement with the experimental evidence, our R-Cr2O3(0001)||Cr(110) model structure at 2.0 ML of oxygen is stably terminated by Cr atoms, which accounts for a decrease of the work function below the value of the pure metal surface. The energy gain associated with the development of this structure approaches the enthalpy of formation of bulk Cr2O3. On the basis of these findings, we suggest that the oxidation of Cr(110) proceeds also at low

Zimmermann and Ciacchi temperature in a layer-by-layer mode which follows closely a thermodynamically stable path along the potential energy minimum surface. An interesting feature common to both Co and Cr is the fact that the onset of oxide formation is observed to take place exactly at the O coverage where the energy gained by formation of perfect O ad-layers becomes less than the enthalpy of formation of the bulk oxides (see Figure 8). In both cases, the growth of the oxide structures promoted by this initial oxide “nucleation” event proceeds with energy gains approaching the enthalpy of formation of the bulk oxides already at coverages of about 2.0 ML. Further work will be necessary to investigate whether this feature is peculiar of the systems investigated here or is more generally shared by other pure metal surfaces. 5. Summary In summary, we have found that pure Co and Cr oxidize according to very different mechanisms, which agree well with the available experimental studies while providing novel chemical details of the reaction pathways and the thin-layer oxide structures. Oxide nucleation on cobalt initially follows a metastable, kinetically driven path that results from the high heat release during the dissociation of O2. The early placeexchange of metal and oxygen atoms leads to the growth of an open, pseudoamorphous oxide structure with evident Co3O4like features. Instead, the oxidation of Cr(110) occurs along an energy path close to thermodynamic equilibrium and limited by Cr-ion diffusion already in the earliest oxidation stages. After the formation of perfect oxygen ad-layers, the extraction of Cr atoms results in overoxidized chromate-like structures, which seem to be precursors for the subsequent layer-by-layer growth of Cr2O3 thin films in epitaxy with the metal surface. Acknowledgment. We acknowledge useful discussions with A. Dianat and M. Bobeth. All calculations have been performed using the computer resources of the Zentrum fu¨r Informationstechnologie und Hochleistungsrechnung (ZIH) at the University of Dresden (Germany). This work has been funded by the Deutschen Forschungsgemeinschaft under Grants CI-144/1 and CI-144/2. References and Notes (1) Stern, E.; Klemic, J. F.; Routenberg, D. A.; Wyrembak, P. N.; Turner-Evans, D. B.; Hamilton, A. D.; LaVan, D. A.; Fahmy, T. M.; Reed, M. A. Nature 2007, 445, 519–522. (2) Park, S. K.; Hong, Y. K.; Lee, Y. B.; Bae, S. W.; Joo, J. Curr. Appl. Phys. 2009, 9, 847–851. (3) Strmcnik, D.; Kodama, K.; van der Vliet, D.; Greeley, J.; Stamenkovic, V. R.; Markovic´, N. M. Nat. Chem. 2009, 1, 466–472. (4) Lim, B.; Jiang, M.; Camargo, P. H. C.; Cho, E. C.; Tao, J.; Lu, X.; Zhu, Y.; Xia, Y. Science 2009, 324, 1302–1305. (5) Larsson, C.; Thomsen, P.; Aronsson, B. O.; Rodahl, M.; Lausmaa, J.; Kasemo, B.; Ericson, L. E. Biomaterials 1996, 17, 605–616. (6) Reuter, K.; Stampfl, C.; Ganduglia-Pirovano, M. V.; Scheffler, M. Chem. Phys. Lett. 2002, 352, 311–317. (7) Klikovits, J.; Napetschnig, E.; Schmid, M.; Seriani, N.; Dubay, O.; Kresse, G.; Varga, P. Phys. ReV. B 2007, 76, 045405. (8) Wagner, C. Z. Phys. Chem. 1933, B21, 25–41. (9) Cabrera, N.; Mott, N. F. Rep. Prog. Phys. 1949, 12, 163–184. (10) Futamoto, M.; Hirayama, Y.; Honda, Y.; Kikukawa, A.; Tanahashi, K.; Ishikawa, A. J. Magn. Magn. Mater. 2001, 235, 281–288. (11) Khan, M. R.; Fisher, R. D.; Heiman, N.; Pressesky, J. IEEE Trans. Magn. 1988, 24, 2985–2987. (12) Milosˇev, I.; Strehblow, H.-H. Electrochim. Acta 2003, 48, 2767– 2774. (13) Gupta, K. S.; Mehta, R. K.; Sharma, A. K.; Mudgal, P. K.; Bansal, S. P. Transit. Metal Chem. 2008, 33, 809–817. (14) Andrieux, J.; Swierczynski, D.; Laversenne, L.; Garron, A.; Bennici, S.; Goutaudier, C.; Miele, P.; Auroux, A.; Bonnetot, B. Int. J. Hydrogen Energ. 2009, 34, 938–951.

Oxidation of the Co(0001) and Cr(110) Surfaces (15) Bridge, M. E.; Lambert, R. M. Surf. Sci. 1979, 82, 413–424. (16) Martin, M.; Koops, U.; Lakshmi, N. Solid State Ion. 2004, 172, 357–363. (17) Castro, G. R.; Ku¨ppers, J. Surf. Sci. 1982, 123, 456–470. (18) Getzlaff, M.; Bansmann, J.; Scho¨nhense, G. J. Electron Spectrosc. Relat. Phenom. 1996, 77, 197–207. (19) Clemens, W.; Vescovo, E.; Kachel, T.; Carbone, C.; Eberhardt, W. Phys. ReV. B 1992, 46, 4198–4204. (20) Grellner, F.; Klingenberg, B.; Borgmann, D.; Wedler, G. J. Electron Spectrosc. Relat. Phenom. 1995, 71, 107–115. (21) Stierle, A.; Zabel, H. Europhys. Lett. 1997, 37, 365–370. (22) Komeda, T.; Sakisaka, Y.; Onchi, M.; Kato, H.; Suzuki, S.; Edamoto, K.; Aiura, Y. Phys. ReV. B 1988, 38, 7345–7348. (23) Maurice, V.; Cadot, S.; Marcus, P. Surf. Sci. 2000, 458, 195–215. (24) Shinn, N. D.; Madey, T. E. Surf. Sci. 1986, 173, 379–394. (25) Shinn, N. D.; Madey, T. E. Surf. Sci. 1986, 176, 635–652. (26) Stierle, A.; Bo¨deker, P.; Zabel, H. Surf. Sci. 1995, 327, 9–16. (27) Colombi Ciacchi, L.; Payne, M. C. Phys. ReV. Lett. 2004, 92, 176104. (28) Colombi Ciacchi, L.; Payne, M. C. Phys. ReV. Lett. 2005, 95, 196101. (29) Colombi Ciacchi, L. Int. J. Mater. Res. 2007, 98, 708–716. (30) Zimmermann, J.; Finnis, M. W.; Colombi Ciacchi, L. J. Chem. Phys. 2009, 130, 134714. (31) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244–13249. (32) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471–2474. (33) VandeVondele, J.; De Vita, A. Phys. ReV. B 1999, 60, 13241– 13244. (34) Stengel, M.; De Vita, A. Phys. ReV. B 2000, 62, 15283–15286. (35) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953–17979. (36) De Vita, A.; Canning, A.; Galli, G.; Gygi, G.; Mauri, F.; Car, R. EPFL Supercomput. ReV. 1994, 6, 22–27. (37) Dianat, A.; Zimmermann, J.; Seriani, N.; Bobeth, M.; Pompe, W.; Colombi Ciacchi, L. Surf. Sci. 2008, 602, 876–884.

J. Phys. Chem. C, Vol. 114, No. 14, 2010 6623 (38) Henkelman, G.; Arnaldsoon, A.; Jønsoon, H. Comput. Mater. Sci. 2006, 36, 354–360. (39) Neugebauer, J.; Scheffler, M. Phys. ReV. B 1992, 46, 16067–16080. (40) Bengtsson, L. Phys. ReV. B 1999, 59, 12301–12304. (41) Michaelson, H. B. J. Appl. Phys. 1977, 48, 4729–4733. (42) Meyer, H. P.; Sucksmith, W. Proc. R. Soc. London 1951, 207, 427– 446. (43) Corliss, L. M.; Hastings, J. M.; Weiss, R. J. Phys. ReV. Lett. 1959, 3, 211–212. (44) Cˇerny´, M.; Pokluda, J.; Sˇob, M.; Fria´k, M.; Sˇandera, P. Phys. ReV. B 2003, 67, 035116. (45) Zimmermann, J.; Colombi Ciacchi, L. In High Performance Computing in Science and Engineering ’07; Nagel, W. E., Kro¨ner, D., Resch, M., Eds.; Springer-Verlag: Berlin, Germany, 2008; pp 173-186. (46) Giannozzi, P.; Car, R.; Scoles, G. J. Chem. Phys. 2003, 118, 1003– 1006. (47) CRC Handbook of Chemistry and Physics, 89th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2008-2009. (48) Schneider, J.; Colombi Ciacchi, L. Surf. Sci., accepted. (49) Ma, S. H.; Zu, X. T.; Jiao, Z. Y.; Xiao, H. Y. Eur. Phys. J. B 2008, 61, 319–324. (50) Getzlaff, M.; Bansmann, J.; Scho¨nhense, G. J. Magn. Magn. Mater. 1995, 140, 729–730. (51) Victora, R. H.; Falicov, L. M. Phys. ReV. B 1985, 31, 7335–7343. (52) Sung, S. S.; Hoffmann, R. J. Am. Chem. Soc. 1985, 107, 578–584. (53) Sakisaka, Y.; Kato, H.; Onchi, M. Surf. Sci. 1982, 120, 150–170. (54) Troyanchuk, I. O.; Lobanovsky, L. S.; Khalyavin, D. D.; Pastushonok, S. N.; Szymczak, H. J. Magn. Magn. Mater. 2000, 210, 63–72. (55) Roth, W. L. J. Phys. Chem. Solids 1964, 25, 1–10. (56) Staemmler, V.; Fink, K. Chem. Phys. 2002, 278, 79–87. (57) Huang, H.; Hermanson, J. Phys. ReV. B 1985, 32, 6312–6318. (58) Fo¨rster, S.; Baum, G.; Mu¨ller, M.; Steidl, H. Phys. ReV. B 2002, 66, 134427.

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