Computational Studies of the Adsorption and Diffusion of Hydrogen on

J. Phys. Chem. C 2008, 112, 3667-3678

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Computational Studies of the Adsorption and Diffusion of Hydrogen on Fe-Co Alloy Surfaces John M. H. Lo and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, Calgary, Alberta, T2N 1N4 Canada ReceiVed: July 6, 2007; In Final Form: NoVember 26, 2007

Studies of the dissociative adsorption of H2 and surface diffusion of H atoms on FeCo(110) using periodic density functional theory and a slab model are reported. It is found that the bcc Fe-Co alloy in B2 phase favors the exposure of (110) plane under cleavage. The H2 molecule is adsorbed on FeCo(110) via the dissociative mechanism where H-H bond scission over an OT-Co site kinetically is the most feasible, possessing an energy barrier of merely 1.5 kcal/mol, much lower than that for the corresponding H2 adsorption on Fe(100) and Fe(110). Upon adsorption, H atoms prefer the TF-Co and TF-Fe sites so that the highest degree of coordination with the surface atoms can be achieved. The calculations reveal that H atoms may diffuse easily over the FeCo(110) surface; the rate-determining step is the migration across a SB site which requires that an activation barrier of about 4.2 kcal/mol be overcome. It is noticed that the diffusive motion TF-Fe f TF-Fe is dominant at room temperature, while at higher temperatures the diffusion TF-Fe f TF-Co prevails.

1. Introduction Iron and cobalt are the two metals most commonly used as catalysts in the industrial Fischer-Tropsch (F-T) synthesis in which CO is hydrogenated to alkanes, alkenes and various oxygenates. Despite superior F-T activity, both metals exhibit some drawbacks that restrict their practical application. While Fe is found to favor the production of oxygen-containing hydrocarbons1 and the water-gas shift reaction forming H2O, it suffers from the formation and accumulation of carbide on the surface that suppresses its catalytic activity. On the other hand, Co shows low ability to produce surface cobalt carbide that may poison the catalyst, but favors only the long-chain olefins and non-oxygenates.2 Consequently, it is desirable to search out a family of catalysts that possess all the preferred catalytic properties while all flaws can be eliminated. A logical solution to this problem is the binary alloy of Fe and Co. The cooperativity of metals has been an issue of extensive studies in organometallic chemistry and catalysis. It is believed that complexes engaging two metal types display not only the reactivity originated from individual metals but also novel functionalities resulting from the synergistic interaction between them. For instance, the use of a Ti(IV)-Rh(I) complex, compared to the traditional Wilkinson Rh(I) catalyst, can enhance the turnover frequencies by an order of magnitude and shorten the reaction time3 of the catalytic intramolecular hydroacylation of styrene 2-carboxaldehyde and 3-phenyl-4pentenal. A similar approach has been found to be successful in heterogeneous catalysis. Alloying on the surface layer of Ni bulk with a small amount of Au significantly suppresses the formation of graphite on the surface of catalyst, and helps maintain its conversion activity during the course of the steamreforming process of n-butane.4 The reactivity and selectivity of Fe-Co alloy toward F-T synthesis have been investigated by various experimental * Corresponding author. E-mail: [email protected].

methods. In the series of studies by Butt et al.,5-8 the silicasupported Fe-Co alloys demonstrate a strong resistance against carburization and a higher selectivity toward water-gas shift reaction and olefin formation than pure Fe and Co catalysts. The replacement of silica support by early transition metal oxides, such as TiO29,10 or ZrO2,11 and Y Zeolite7,8 enhances the CO conversion and shifts the selectivity to higher molecular weight hydrocarbons. The spectacular properties of Fe-Co alloys have been attributed to the synergism of Fe and Co on the alloy surface.5 It is proposed that the presence of neighboring Co centers destabilizes the Fe carbide formed from the CO dissociation, thus impeding the carburization that poisons the catalyst. Unfortunately, no justification of the role of electronic interaction between Fe and Co in this process is yet available. Additionally, the reasons for the high activity of Fe-Co alloys in the water-gas shift reaction and the facile synthesis of longchain olefins are unknown. Therefore, theoretical investigations, which may provide an alternative avenue to acquire insights at the molecular level into the accounts of these issues, become appealing. In this study, the interaction of hydrogen with the surface of Fe-Co alloy, which constitutes the early stage of the FischerTropsch synthesis, was investigated using the first-principle density functional theory (DFT) calculations. In particular, the adsorption process of hydrogen and its subsequent migration over the FeCo(110) surface were explored. In this work, the site preference of the adsorption of H and the associated energetics were determined. Meanwhile, the favorable diffusion channels of adsorbed H atoms on the alloy surface were computed. From this data the corresponding diffusion coefficients were calculated. 2. Computational Details All calculations were performed employing the DFT method implemented in the Vienna ab initio Simulation Package

10.1021/jp075294q CCC: $40.75 © 2008 American Chemical Society Published on Web 02/19/2008

3668 J. Phys. Chem. C, Vol. 112, No. 10, 2008 (VASP).12-14 In order to have the proper description of a twodimensional extended array of metal atoms, periodic boundary conditions were used throughout the study. The calculations were done using the spin-polarized generalized gradient approximation (GGA) of the Perdew, Burke and Ernzerhof (PBE) functional15,16 with the projector augmented wave (PAW) method of Blo¨chl17,18 that describes the electron-ion interaction. The one-electron pseudo-orbitals that were used to construct the wave functions were expanded with a kinetic energy cutoff of 400 eV, and the k-points were sampled by the MonkhorstPack scheme.19 Electron smearing with a smearing width of 0.1 eV was utilized via the Methfessel-Paxton technique20 to allow for better convergence during the geometry optimization. In this study, the stationary points and the transition states associated with the adsorbed H atoms were identified through vibrational frequency calculations. To determine the vibrational frequencies, the Hessian matrix was computed using the finite difference method and harmonic approximation, with a step size of 0.02 Å. The frozen phonon approximation was adopted in which the metal atoms were fixed at the relaxed geometries. The minimum energy paths concerning the adsorption of H2 and the diffusion of adsorbed H atoms were obtained by the nudged elastic band (NEB) method of Jo´nsson and coworkers.21,22 In this approach, both the activation energy and the geometries of intermediate states (images) connecting the initial state (reactants) and the final state (products) were obtained via the simultaneous energy minimization of these discretized images with the restriction of atomic motion on the hyperplane perpendicular to the reaction path. In these NEB calculations, eight images were employed and a force constraint of 0.01 eV/Å was applied to determine the convergence of geometries. 3. Results and Discussion 3.1. Calculations of Bulk and Fe-Co Surfaces. The structural features of Fe-Co alloys have been extensively studied by experiments23-30 and theoretical calculations31-37 because of their peculiar properties that the magnetization varies as a function of the composition of Co and possesses a maximum at about 30 atomic % Co. Many stable intermetallic phases of Fe-Co alloys with a wide range of Co concentration have been observed based on electrochemical and spectroscopic measurements.38,39 At low temperatures, Fe-Co alloys are ferromagnetic and adopt the bcc-based ferrite structure, which undergoes a phase transition to the fcc-based austenite structures at about 900 °C. The bcc Fe-Co alloys are composed of both the ordered B2 (CsCl) phase and disordered R-phase for the range of 25 to 75 atomic % Fe, in which the alloy with equiatomic composition (FeCo) possesses the highest enthalpy of formation according to recent DFT and cluster expansion calculations.37 Consequently, the present work only focused on the phenomena of adsorption and diffusion of H atoms on the surface of the CsCl-B2 phase of FeCo. The experimental lattice constant of the ordered bcc FeCo alloy is 2.8571 Å, as deduced from the binary phase diagram.40 The polarized neutron diffraction measurement yielded the local magnetic moments of 2.921 and 1.623 µB for Fe and Co, respectively.41 In the present work, the equilibrium lattice constant for the bulk FeCo alloy was found to be 2.8418 Å using the k-point mesh of 11 × 11 × 11. This value differs from the experimental quantity by only 0.5%. The corresponding average magnetic moment was 2.23 µB, which is in very good agreement with the values obtained by neutron diffraction (2.27µB)41 and theoretical calculations (2.2842 and 2.18 µB34).

Lo and Ziegler TABLE 1: Surface Energies of Fe-Co Alloys (in J/m2) plane

6×6×6

8×8×8

(100) (110) (111)

2.633 2.391 2.710

2.586 2.363 2.706

Nevetheless, the computed bulk modulus of 2.05 mbar is much smaller than the experimental value (2.47 mbar)42 although it is closer to the value (2.26 mbar) determined by the augmentedspherical-wave method;34 the discrepancy may be attributed to the smaller computed lattice constant compared to the experimental value. To determine the highest possible surface exposure on which the adsorption of hydrogen may occur, the surface energies for the three lowest Miller-indexed Fe-Co planes were calculated. The surface energy was defined as the energy required to cleave the bulk FeCo along a particular plane, and was computed according to the following relation:43

Esurf )

Etot(slab) - nEtot(bulk) 2A

(1)

In this equation, E(slab) and E(bulk) refer to the energies of the metal slab and the bulk respectively. n is the total number of bcc Fe-Co unit cells contained in the slab, and A is the area of the plane generated in the cleavage. Using eq 1, the surface energies for the (100), (110) and (111) planes of Fe-Co alloys were obtained for 6 × 6 × 6 and 8 × 8 × 8 k-point meshes and are summarized in Table 1. As shown, the lowest surface energy is observed for the (110) plane, suggesting that this plane is most likely formed during the surface cleavage of Fe-Co alloy. This trend is in line with the results from the X-ray diffraction that indicate the strong (110) texture of the Fe-Co lattice.29 It is worth noting that the computed surface energies decrease slightly with the larger sizes of k-point mesh, and no significant relaxation and reconstruction have been observed. In these calculations, the Fe-Co slab with 8 layers was employed to compute Esurf. It has been observed in the case of Fe that Esurf converges within 0.01 J/m2 when a 9-layer slab is used.43 Accordingly, it is believed that the present order of surface energies (110) < (100) < (111) for the Fe-Co alloy should be reliable. In the subsequent calculations regarding the adsorption and diffusion processes of H atoms, the surface was modeled by a 4-layer slab of the c(2 × 2) supercell, with the lattice parameter shown previously (2.8418 Å). In order to reduce the computational cost, a 6 × 6 × 1 k-point grid was chosen; this grid has been proven to yield the same lattice constant as that obtained using a finer 11 × 11 × 11 mesh. Adsorption was assumed merely on one side of the slab, and a vacuum layer of 10 Å was inserted between two slabs so as to minimize the induced dipole interactions due to the presence of adsorbates. In all calculations, the H atoms and the top two layers of Fe and Co atoms were allowed to relax, while the remaining atoms were fixed at their bulk-optimized positions. The geometry optimizations were performed with the force tolerance of 0.01 eV/Å; an ion relaxation was completed when all forces were smaller than this threshold. 3.2. Adsorption of H Atoms on the FeCo(110) Surface. There exist four adsorption sites on the (110) surface of pure Fe: one-fold (OT), short-bridge (SB), long-bridge (LB) and three-fold (TF) sites, as identified by the low-energy electron diffraction (LEED) experiments.44 On the FeCo(110) surface, three additional sites are found which are due to the replacement of 50% Fe atoms by Co. Each group of the OT, SB and TF

Adsorption and Diffusion of Hydrogen on Fe-Co Alloys

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Figure 1. H adsorption sites on FeCo(100). Key: open circles, Co; striped circles, Fe; black circles, H.

sites is split into two subsets, one corresponding to the adsorption on Fe, the other one on Co. The resulting seven adsorption sites as well as the nomenclature adopted in this work are illustrated in Figure 1. The adsorption of H atoms on these seven sites of the FeCo(110) surface has been investigated for the surface coverage of 0.125, 0.250 and 0.500 ML, which correspond to one, two and four H atoms adsorbed on the c(2 × 2) supercell respectively. Two types of binding energies were reported for the adsorbed H atoms:

Ead1 ) Ead2 )

NEH + Eslab - E(slab+H) N

(1/2)NEH2 + Eslab - E(slab+H) N

(2) (3)

which were computed with respect to either isolated H atom (Ead1) or isolated H2 molecule (Ead2). In these equations, N is the number of adsorbed H atoms on the slab surface, Eslab the total energy of the slab, and E(slab+H) the total energy of the slab-adsorbate system. The energies of isolated H (EH) and H2 molecule (EH2) were computed by assuming an H atom or H2 molecule enclosed in a 10 × 10 × 10 Å3 simulation box. The positive Ead1 and Ead2 indicate the stabilized adsorption of H atoms relative to the separated slab and adsorbate. Table 2 shows the calculated adsorption energies and the structural information of various adsorption modes of H atom on the FeCo(110) surface at the 0.125 ML coverage. As can been seen, all adsorption modes are energetically favorable with respect to an isolated H atom; however, adsorption on the OTFe site becomes slightly disfavored with respect to the isolated H2 molecule. Both LEED and DFT-GGA calculations have illustrated that the TF sites of Fe(110) are most preferred for the H adsorption with the coverage below 1 ML.44,45 The same site preference has also been observed in the case of FeCo(110); the TF-Co and TF-Fe sites are among the most favorable for H adsorption while the other sites lie 4 to 19 kcal/mol above them. Frequency calculations reveal that these TF sites are true minima, yet the bridge sites (SB, LB-Co and LB-Fe) are actually the transition states connecting these TF sites. The OT sites are classified as the second-order saddle points, each of which possesses two imaginary frequencies. These assignments are consistent with those deduced from the PAW-PBE calculations of Jiang and Carter for the Fe(110) surface.45 The computed frequencies of 1074 and 1172 cm-1 for TF-Co and TF-Fe sites are similar to the experimental value of 1060 cm-1 for the H-surface stretching on the Fe(110) surface,46 possibly due to the similar structure at the TF sites. The site preference of H is found to be positively correlated to the degree of coordination of an H atom to the surface atoms forming the adsorption site; at the most favorable TF site, H is coordinated to three surface

metal atoms while it is only bound to two metal atoms at the less preferred SB or LB site. The effects of zero-point energy (ZPE) corrections to the adsorption energies and site preference for H atoms on FeCo(110) have been explored, because of the small mass of H. Table 3 contains the zero-energy corrected binding energies of H atoms at 0.125 ML coverage. It can been seen that the influences of ZPE are not very significant; generally the adsorption energies are reduced by less than 4 kcal/mol when ZPE are taken into account. Moreover, the same trend of relative stability retains; the TF-Co and TF-Fe sites are still the most preferred. Interestingly, the relative stability SB > LB-Fe is reversed by the inclusion of ZPE, but the energy separation is again negligible (250 K).

TABLE 4: Diffusion Barriers (in kcal/mol), Attempt Frequencies (in THz) and Diffusion Prefactors (in cm2/s) for the Migration of H on the FeCo(110) Surface at Various Temperatures pathway

diffusion temp attempt barriers (K) frequency

TF-Co f LB-Fe f TF-Co

3.07

TF-Co f SB f TF-Fe

3.30

TF-Fe f LB-Co f TF-Fe

0.22

TF-Fe f SB f TF-Co

2.73

423 473 523 1000 423 473 523 1000 423 473 523 1000 423 473 523 1000

13.31 13.41 13.51 13.96 11.67 11.92 12.13 13.06 20.53 19.98 19.60 18.39 14.27 14.36 14.45 14.93

diffusion prefactor 1.83 × 10-5 3.08 × 10-5 4.71 × 10-5 3.20 × 10-4 2.67 × 10-5 4.57 × 10-5 7.07 × 10-5 5.00 × 10-4 5.15 × 10-4 5.34 × 10-4 5.51 × 10-4 6.51 × 10-4 5.36 × 10-5 8.57 × 10-5 1.26 × 10-4 7.05 × 10-4

the H atom into the vibrational state that can either lead to a successful hopping or allow for an effective tunneling through a high barrier. The rates for the four diffusion pathways have been calculated for the temperature range 423-1000 K using eq 5, and the results are plotted in Figure 13(a). It can been seen that the diffusion rate for pathway 3 remains the fastest for the whole spectrum of temperatures under investigation. The estimated

npν(T)l2 2d

(7)

in which l is the jump length of H atom between the adsorption sites, d the dimension of diffusion (in this case, d ) 2), and np the number of equivalent diffusion paths. One may see that there is no obvious relation between the diffusion prefactor and the associated barrier; for example, the diffusion pathway 2 has a higher D0 than that for pathway 1 although its ∆E is higher than the latter one. This can be rationalized by considering the facts that D0 is independent of ∆E and the jump length l for pathway 2 is longer than that for pathway 1. The diffusion coefficients D of H atoms associated with these four hopping pathways in terms of temperature have also been computed. Figure 13(b) depicts the resulting Arrhenius plot for T > 423 K. An intriguing phenomenon is observed among the diffusion coefficients for pathway 3 where it turns out to be the most dominant for the temperature range considered in this work (i.e., 423-1000 K). As in the case of ΓHA TST, the surprising change of D for this pathway is greatly influenced by the temperature-dependent exponential term exp(-∆E/kBT). While D does not vary significantly for pathway 3 due to its small ∆E, the variations for the other three pathways are remarkable. Therefore, the trend reverses in this temperature region where the diffusion coefficient for pathway 3 surpasses those for the other three routes. In terms of the activation barriers, one may argue that, at rather low temperature, the diffusion of H atoms via pathway 3 is fast since the H atoms at TF sites are the least bound. On the other hand, at sufficiently high temperatures where H atoms can move freely on the surface, the diffusive motions via the SB sites would predominate because of the longest jump length. Because of the rather low diffusion barriers and light weight of H atom, quantum tunneling may play a significant role in surface diffusion on FeCo(110). Quantum tunneling diffusion of H on Ni(100) and Ni(111) surfaces has been studied experimentally by Lin and Gomer58 using the fluctuation method and theoretically by Zhu.59 They discovered that the tunneling is accomplished via electron-phonon coupling, and the resulting diffusion prefactors DT are in a magnitude of 10-10 cm2/s for temperatures below 200 K. Since this work only considers the diffusion of H atoms on FeCo(110) at temperatures above 400 K, and the computed D0 are greater than DT by several orders of magnitude, it is reasonable to simply neglect the effects of the quantum tunneling on the calculated diffusion coefficients and prefactors.

Adsorption and Diffusion of Hydrogen on Fe-Co Alloys 4. Conclusions The phenomena of dissociative adsorption of H2 and diffusion of H atoms on the FeCo(110) surface have been studied using periodic density functional theory in the generalized gradient approximation, incorporated with the PBE functional and projector-augmented wave method. The metal surface was modeled by a four-layer, c(2 × 2) supercell. The current study has demonstrated that the (110) surface of the binary Fe-Co alloy is the most exposed plane with a surface energy of 2.363 J/m2. On the (110) surface, seven adsorption modes for H atoms were identified. It was found that only the TF-Co and TF-Fe modes are stable, while the others correspond to either transition states or higher-order saddle points of the potential energy surface. The computed binding energies of the H atoms at these two sites are comparable to those for H adsorption on pure Fe(110) surface. It is interesting, however, to note that H prefers the adsorption with the highest number of coordination to Co atoms. This phenomenon is attributed to the band transfer between Co and Fe during the alloying process, which causes the higher occupation of Fe spin-up 3d band and the weaker Fe-H bond compared to Co-H bond. In addition to the relative binding energies of H atoms on different adsorption sites, their dependence on surface coverage has also been investigated. A decreasing trend was noticed for all kinds of adsorption modes. The TF-Co and TF-Fe modes remain the most favorable up to the 0.500 ML coverage. At high surface coverage, several hybrid adsorption modes, such as TF-Fe/TF-Co and LB-Co/LB-Fe, have been studied; however, their stabilities are found lower than the “pure-bleed” TF-Co, TF-Fe, LB-Co and LB-Fe counterparts. Six dissociative adsorption channels of H2 onto the FeCo(110) surface have been considered. It is found that the dissociation over an OT-Co site is the most kinetically viable process, having a barrier of only 1.5 kcal/mol, a value much smaller than that for H2 adsorption on Fe(110). The smaller barrier may result from the stronger interaction of H2 with Co that lowers the energy of the associated transition state. Another feasible pathway involves the dissociation of H2 over a TF-Fe site; its activation energy is about 1.9 kcal/mol. Similarly, the rather low barrier is the consequence of the interaction of H2 with the two Co atoms at the TF-Fe site which stabilizes the transition state structure. Both channels regarding the dissociation over an LB site are found to be the most unlikely, even though the measured barriers are between 3.0 and 4.4 kcal/mol. Finally, the diffusion of adsorbed H atoms on the FeCo(110) surface at low surface coverage has also been studied. Four possible diffusive motions have been explored. The attempt frequencies and thus the hopping frequencies for all four processes are high, among which the TF-Fe f TF-Fe motion is the fastest due to its extremely small barrier. The diffusion prefactors of these four pathways have been computed; in general, they agree fairly well with the accepted “usual value” of 0.001 cm2/s. At temperatures around 500 K, the diffusion TF-Fe f TF-Fe is most prominent; for a higher temperature regime, however, the other pathways become equally important because of their large jump lengths. It is no doubt that the H adsorption and diffusion on FeCo(110) discussed in this work only constitute a part of the early stage of the F-T synthesis, and a thorough understanding of the Fe-Co catalyzed F-T synthesis requires the exploration of CO adsorption and dissociation, as well as the C-H bond formation on this surface. Work in this line is currently underway.

J. Phys. Chem. C, Vol. 112, No. 10, 2008 3677 Acknowledgment. Financial support by Alberta Ingenuity Funds and the computer resources by the Western Canada Research Grid and the department of chemistry at the University of Calgary are gratefully acknowledged. T.Z. thanks the Canadian Government for a Canada Research Chair in Theoretical Inorganic Chemistry. References and Notes (1) Schulz, H. Appl. Catal. A 1999, 186, 3. (2) Bartholomew, C. H.; Farrauto, R. J. Fundamentals of Industrial Catalytic Processes; Wiley-Interscience: New York, 2006; pp 398-464. (3) Morgan, J. P.; Kundu, K.; Doyle, M. P. Chem. Commun. 2005, 3307. (4) Besenbacher, F.; Chorkendorff, I.; Calusen, B. S.; Hammer, B.; Molenbroek, A. M.; Norskov, J. K.; Stensgaard, I. Science 1998, 279, 1913. (5) Amelse, J. A.; Schwartz, L. H.; Butt, J. B. J. Catal. 1981, 72, 95. (6) Arcuri, K. B.; Schwartz, L. H.; Piotrowski, R. D.; Butt, J. B. J. Catal. 1984, 85, 349. (7) Lin, T. A.; Schwartz, L. H.; Butt, J. B. J. Catal. 1986, 97, 177. (8) Butt, J. B.; Lin, T. A.; Schwartz, L. H. J. Catal. 1986, 97, 261. (9) Arai, H.; Mitsuishi, K.; Seiyama, T. Chem. Lett. 1984, 13, 1291. (10) Ishihara, T.; Eguchi, K.; Arai, H. Appl. Catal. 1987, 30, 225. (11) Bi, Y. H.; Dalai, A. K. Can. J. Chem. Eng. 2003, 81, 230. (12) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. (13) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15. (14) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (15) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (16) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Phys. ReV. B 1999, 59, 7413. (17) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953. (18) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (19) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (20) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616. (21) Mills, G.; Jo´nsson, H. Phys. ReV. Lett. 1994, 72, 1124. (22) Mills, G.; Jo´nsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 305. (23) Fine, M. E.; Ellis, W. C. Trans. Am. Inst. Mining Met. Eng. 1948, 175, 742. (24) Collins, M. F.; Forsyth, J. B. Philos. Mag. 1963, 8, 401. (25) Bardos, D. I. J. Appl. Phys. 1969, 40, 1371. (26) Spooner, S.; Lynn, J. W.; Cable, J. W. AIP Conf. Proc. 1971, 5, 1415. (27) Rajkovic, M.; Buckley, R. A. Met. Sci. 1981, 15, 21. (28) Raynor, G. V.; Rivlin, V. G. Int. Met. ReV. 1983, 28, 211. (29) Vasko, V. A.; Kim, M.; Mryasov, O.; Sapozhnikov, V.; Minor, M. K.; Freeman, A. J.; Kief, M. T. Appl. Phys. Lett. 2006, 89, 092502. (30) Fu, Y.; Miyao, T.; Cao, J. W.; Yang, Z.; Matsumoto, M.; Liu, X. X.; Morisako, A. J. Magn. Magn. Mater. 2007, 308, 165. (31) Schwarz, K.; Mohn, P.; Blaha, P.; Ku¨bler, J. J. Phys F: Met. Phys. 1984, 14, 2659. (32) Richter, R.; Eschrig, H. J. Phys F: Met. Phys. 1988, 18, 1813. (33) James, P.; Eriksson, O.; Johansson, B.; Abrikosov, I. A. Phys. ReV. B 1999, 59, 419. (34) Qiu, S. L.; Marcus, P. M.; Moruzzi, V. L. J. Appl. Phys. 1999, 85, 4839. (35) Paduani, C.; Krause, J. C. J. Appl. Phys. 1999, 86, 578. (36) MacLaren, J. M.; Schulthess, T. C.; Butler, W. H.; Sutton, R.; McHenry, M. J. Appl. Phys. 1999, 85, 4833. (37) Dı´az-Ortiz, A.; Drautz, R.; Fa¨hnle, M.; Dosch, H.; Sanchez, J. M. Phys. ReV. B 2006, 73, 224208. (38) Masumoto, H.; Saito, H.; Shinozaki, M. Sci. Rep. Res. Inst. Tohoku UniV. A 1954, 6, 523. (39) Wojcik, M.; Jay, J. P.; Panissod, P.; Jedryka, J.; Langouche, G. Z. Phys. B: Condens. Matter 1997, 103, 5. (40) Ohnuma, I.; Enoki, H.; Ikeda, O.; Kainuma, R.; Ohtani, H.; Sundman, B.; Ishida, K. Acta Mater. 2002, 50, 379. (41) Di Fabrizio, E.; Mazzone, G.; Petrillo, C.; Sacchetti, F. Phys. ReV. B 1989, 40, 9502. (42) Liu, A. Y.; Singh, D. J. Phys. ReV. B 1992, 46, 11145. (43) Spencer, M. J. S.; Hung, A.; Snook, I. K.; Yarovsky, I. Surf. Sci. 2002, 513, 389. (44) Moritz, W.; Imbihl, R.; Behm, R. J.; Ertl, G.; Matsushima, T. J. Chem. Phys. 1985, 83, 1959. (45) Jiang, D. E.; Carter, E. A. Surf. Sci. 2003, 547, 85. (46) Baro, A. M.; Erley, W. Surf. Sci. 1981, 112, L759. (47) Hammer, L.; Landskron, H.; Nichtl-Pecher, W.; Fricke, A.; Heinz, K.; Mu¨ller, K. Phys. ReV. B 1993, 47, 15969. (48) Faglioni, F.; Goddard, W. A., III. J. Chem. Phys. 2005, 122, 014704. (49) Stibor, A.; Kresse, G.; Eichler, A.; Hafner, J. Surf. Sci. 2002, 507510, 99.

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