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Reconstruction of TiAl Intermetallic Surfaces: A Combined STM and DFT Study Mazharul M. Islam,†,§ Anne-Ga€elle Noumet,†,‡ Frederic Wiame,† Marie-Pierre Bacos,‡ Boubakar Diawara,† Vincent Maurice,*,† and Philippe Marcus*,† †
Laboratoire de Physico-Chimie des Surfaces, CNRS (UMR 7045), Ecole Nationale Superieure de Chimie de Paris (Chimie-ParisTech), 11 rue Pierre et Marie Curie, 75005 Paris, France ‡ ONERA, Departement Materiaux Metalliques et Procedes, BP 72-29 avenue de la Division Leclerc, 92322 Ch^atillon Cedex, France ABSTRACT: The structure of the γ-TiAl(111) alloy surface was studied with combined experimental and theoretical approaches. The experimental scanning tunneling microscopy (STM) images indicate surface reconstruction with a (2 2) superstructure as a result of Al depletion of the alloy surface after preparation. The atomic protrusions form a zigzag pattern oriented along the direction of the shorter surface unit vector of the (2 2) supercell, that is, the [101] direction. The theoretical investigations performed with molecular dynamics in combination with simulated annealing based on the density functional theory (DFT) show that the surface starts to reconstruct at temperatures higher than 950 K, in agreement with the experimental annealing temperature. Geometric analysis and simulated STM images obtained from periodic DFT calculations show that the atomic protrusions forming the zigzag patterns correspond to Al atoms of the reconstructed topmost plane. The persistence of the reconstructed structure up to the simulated melting temperature of 1800 K shows the high stability of Al vacancies injected in the topmost plane of the alloy.
1. INTRODUCTION TiAl-based intermetallic alloys are developed as promising materials for gas turbine applications at high temperature in jet engines and energy production systems due to their high melting point, low density, and outstanding mechanical properties.1-8 The introduction of these alloys as rotating parts is limited by their insufficient oxidation resistance in hot corrosive or oxidative environments1,9-12 and by the detrimental effect of the oxidation mechanisms on the mechanical properties of the bulk.13-15 Different doping elements, such as Nb, are added to the binary TiAl alloy to improve the ductility at lower temperatures and to increase the oxidation resistance.2,10,15-19 Surface properties, such as hardness and wear resistance, may be improved by surface modification.20-23 To better understand the oxidation properties of these alloys, several studies of the initial stages of oxidation have been carried out on polycrystalline surfaces24-30 and, more seldom, on singlecrystalline surfaces.31-33 However, to our knowledge, only one study including the structure of the oxide-free TiAl alloy surface has been reported so far.34 There, it was shown by quantitative low energy electron diffraction (QLEED) that chemical reconstruction of the (010) surface was observed after cleaning by Ar bombardment and postannealing at 1175 K, producing a (1 1) structure with the Ti atoms of the topmost plane substituted by Al atoms. Here, we report a joint experimental and theoretical investigation of the atomic structure of the γ-TiAl(111) surface. For the first time, the surface structure of the nonoxidized alloy was r 2011 American Chemical Society
investigated experimentally by scanning tunneling microscopy (STM) at the atomic scale. The surface reconstruction observed experimentally was investigated theoretically by finite temperature molecular dynamics (MD) calculations in combination with simulated annealing (SA) at the density functional theory (DFT) level. The reconstructed surface was further characterized by calculating STM images based on the DFT approach.
2. METHODS 2.1. Experimental Details. The experiments were performed in an ultra-high-vacuum (UHV) system (base pressure below 110-10 mbar) equipped with scanning tunneling microscopy/spectroscopy (STM/STS, Omicron STM1 with SCALA system) and with facilities for surface chemical control by Auger electron spectroscopy (AES, Riber CMA OPC105) and structural control by low energy electron diffraction (LEED, Riber OPD304) as well as argon ion sputtering, annealing, and gas dosing of the sample. All the presented STM images were recorded at room temperature in constant current mode. No filtering was used. Background plane subtraction was applied, and linear drift correction was performed when needed. A TiAl single crystal (not available commercially) was provided by Pr. M. Yamagushi (Department of Materials and Engineering, University of Tokyo). Its bulk composition (at. %) was Ti50Al46.5Nb3Received: October 27, 2010 Revised: January 12, 2011 Published: February 07, 2011 3372
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The Journal of Physical Chemistry C Si0.5. The lower content in Al was due to some mixing of the predominant γ-TiAl phase with the R2-Ti3Al phase (biphasic crystal). The predominance of large grains of the γ phase and their orientation along the (111) direction were controlled by Laue back diffraction. These large γ-TiAl grains were then positioned in the center of the sample cut by spark machining, thus allowing facile and unambiguous positioning of the AES, LEED, and STM analyses on the γ phase. The presence of Nb at a doping level was originally intended to study its effect on the oxidation properties,35 but it was observed to not influence the data reported here, as shown below. Si was present at a contamination level and was also observed to not influence the data. The bulk structure of the γ-TiAl phase is of the L10 type, most often referred to as face-centered tetragonal. Its space group is P4/mmm with a = 0.398 nm and c = 0.406 nm at equiatomic composition,36 giving a c/a ratio of 1.022. This compound has a large homogeneity range, with the aluminum content varying between 50 and 70 at. % at high temperatures. The (111) orientation corresponds approximately to a hexagonal bulk termination with alternating close-packed rows of Al and Ti, and a Ti50Al50 composition if bulk-terminated. The sample surface was prepared by mechanical polishing with a diamond spray with a final grading of 0.25 μm. In UHV, the γ-TiAl(111) surface was treated by repeated cycles of argon ion bombardment (p(Ar) = 1 10-5 mbar, 1 keV energy, ∼2 μA sample current) and annealing under UHV at temperatures ranging from 1000 to 1100 K (instrumental limit). A cumulated annealing time of ∼130 h was necessary to produce the atomically flat terraces presented below. After surface preparation, traces of O (OKLL at 506 eV) were detected by AES, but Nb (NbMNN at 167 eV) and Si (SiLVV at 90 eV) were at or below the detection limit (Figure 1). Small amounts of C (CKLL at 272 eV) could still be observed but were impossible to thoroughly remove at the limited annealing temperature of 1100 K and even after surface oxidation at 900 K in p(O2) = 1 10-7 mbar.35 2.2. Computational Details. The surface reconstruction of TiAl was investigated by periodic calculations using the DFT MD in combination with the simulated annealing (SA) approach. The GGA-based Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional37 was employed using VASP.38-40 The projector-augmented wave (PAW) potentials41,42 were used for the core electron representation, whereas the valence electrons were represented by the energy cutoff Ecut = 240 eV as converged for the bulk TiAl optimization. On the basis of the optimized bulk structure (optimized lattice parameters, a = 0.400 nm and c = 0.408 nm), a (2 2) supercell was constructed for the γ-TiAl(111) surface with increasing the number of TiAl layers. Several SA calculations were performed with different high temperatures from 800 to 2200 K as described previously.43-45 Four-layer slabs (sufficient to stabilize the surface energy33) of TiAl were employed, keeping the two bottom layers frozen in order to simulate the bulk. STM images were simulated using the TersoffHamann46 approach, which provides a reliable qualitative picture of the surface topography. In this method, the surface is treated exactly, while the tip is modeled as a locally spherical potential well. The tunneling current is proportional to the surface local density of states (LDOS) at the Fermi level and at the position of the STM tip.
3. RESULTS AND DISCUSSION 3.1. Experimental STM Data. Figure 2 shows STM images of the terrace and step topography obtained after surface preparation
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Figure 1. AES spectrum of the sputter cleaned and annealed TiAl surface.
Figure 2. STM images of the sputter cleaned and annealed γ-TiAl(111) surface revealing the terrace topography. (a) Topographic image (0.5 V sample bias voltage, 0.5 nA tunneling current). (b) Profile along the line marker in (a). (c) Current difference image associated with (a).
and evidences the good crystalline quality of the annealed surface. The step height was measured to be 0.21 ( 0.02 nm, as shown by the line profile in Figure 2b, in very good agreement with the reticular distance of the (111) planes (0.232 nm from the bulk parameters) and indicating a monatomic step height. Wide (up to 50 nm) terraces were observed to be interspaced by series of much narrower terraces (∼3 nm). The current difference image (image of the difference between the preset and measured tunnelling currents) shown in Figure 2c reveals the atomic corrugation on the terraces. A periodic structure is observed to cover completely the terraces, evidencing long-range structural order at the surface. The image in Figure 2c also better highlights the defects assigned to residual 3373
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Figure 3. (a, b) Atomically resolved STM topographic images of the terraces of the γ-TiAl(111) surface: (a) 0.01 V, 4.0 nA and (b) 0.03 V, 1.0 nA. The unit cell of the periodic structure is marked in (a) and (b). The zigzag pattern formed by the atomic protrusions is better resolved in (b).
contamination. The bright spots (one is pointed out by an arrow) on the terraces and along the steps are assigned to oxide traces, and the dark spots (one is circled) are assigned to islands of C contamination. Figure 3 shows two STM images obtained on the terraces, one of them being atomically resolved. The periodic structure is confirmed as well as the discontinuities caused by the darker islands assigned to the traces of contaminants. The unit cell (marked) is rectangular with measured parameters of 0.99 ( 0.05 and 0.57 ( 0.03 nm (after distortion corrections). This unit cell is in very good agreement with a (2 2) supercell (with a size of 0.991 nm 0.568 nm), indicating the formation of a (2 2) superstructure at the surface of the alloy. The LEED data confirmed the formation of a (2 2) superstructure, however, with a weak contrast pointing to the nonperfect ordering of the surface, in agreement with the STM data in Figure 2c. Among the possible causes of formation of the (2 2) superstructure are the surface segregation of Nb and Si present in the bulk, the presence of contaminants adsorbed on the surface, or the surface enrichment in one of the main alloying elements (Ti or Al). The dimensions of the (2 2) supercell impose a surface concentration of at least one impurity atom per cell (12.5 at. %) to form the superstructure. This excludes the segregation of Nb and Si because these elements were at or below the detection limit of AES estimated to be ∼2-3 at. % (Figure 1). This also excludes that the superstructure results from the O traces too little to be reasonably associated with it. The C traces could not be eliminated even after surface oxidation, whereas the surface structure was drastically changed.35 This high stability of C traces is consistent with their assignment to dispersed titanium carbide particles, as previously observed with XPS on these TiAl alloys,30,31 which supports the assignment of the islands observed by STM to the C contamination. The remaining possible origin for the superstructure is then the surface enrichment of the alloy in Ti or Al, as previously
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observed for the (010) surface, but after annealing at 1175 K and producing no superstructure.34 Our previous XPS studies performed on Nb-free TiAl revealed enrichment in Ti of the surface after preparation assigned to the preferential sputtering of Al caused ion bombardment.30 This was also observed by XPS on the Nb-doped alloy used in the present study for which the surface concentration in Ti, averaged over all atomic planes corresponding to the escape depth of the photoelectrons, was calculated to stabilize at ∼60 at. % (average surface composition of Ti60Al35Nb5 with a dispersion of 1-2 at. %) after argon ion sputtering, followed by annealing for 4 h at 1000 K.35 Aluminum segregation was observed by AES after the longer annealing required for the STM study with the AlLMM (68 eV) to TiLMM (416 eV) peak-to-peak height ratio typically of 0.82 after annealing for 4 h at 1000 K and increasing to 1.13 after the cumulated time of 130 h at 1000-1100 K. Using the surface concentration measured after 4 h at 1000 K as a reference and determined by XPS to be Ti60Al35Nb5, the surface concentration, averaged over all atomic planes corresponding to the escape depth of the Auger electrons,, is calculated to be Ti53Al42Nb5 after 130 h at 1000-1100 K, or Ti55Al45 if we exclude the Nb content. Thus, it appears that, although annealing causes Al segregation like that observed on the (010) surface34 and in agreement with the general trend observed for aluminides,47 surface enrichment in Ti partially subsists after annealing of the alloy at 1000-1100 K and must be at the origin of the formation of the (2 2) superstructure on the TiAl(111) surface. Figure 3b also reveals the details of the surface atomic structure. It can be seen that the observed atomic protrusions form a zigzag pattern oriented along the direction of the shorter unit vector of the (2 2) supercell, that is, the [101] direction. The STM images are very sensitive to tip effects and tunneling conditions, as can be noticed from the comparison of panels a and b in Figure 3 (from the same area). The nearest-neighbor distance between the protrusions, averaged over several images giving the same pattern, is 0.40 ( 0.04 nm, which results in a zigzag angle varying from 75° to 100°. This zigzag pattern has been superimposed on the unreconstructed structure of the alloy surface, and no fit is obtained with the bulklike atomic positions. This shows that a simple substitution of the Al surface atoms by Ti atoms cannot reproduce the structural pattern evidenced by STM and, thus, that surface reconstruction, including restructuring, and not only chemical substitution of the surface atoms, as previously reported for the (010) surface after annealing at 1175 K,34 must be considered in addition to the Al depletion to describe the surface structure observed in our study. 3.2. DFT Study. DFT calculations were performed to simulate the surface atomic structure of the γ-TiAl(111) alloy observed by STM. The models were built by removing every two aluminum rows in the topmost plane of the bulk-terminated surface. By this way, the surface becomes Ti-enriched to 66 at. %. For the calibration of temperature, we have done several SA calculations at different high temperatures from 800 to 2200 K. It was observed that the surface starts to reconstruct by restructuring at temperatures higher than 950 K and melt at temperature highers than 1800 K. These are in good agreement with the experimental annealing temperature, 1000-1100 K in our experiment, and the melting temperature, 1753 K, from the phase diagram.48 The surface reconstruction is stable up to 1750 K in our simulation. Out of many simulated structures, we show here two structures that were obtained by SA calculations at 1000 and 1700 K (Figure 4). In both cases, the surface is 3374
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Figure 4. MD SA calculation (a) (2 2) starting structure containing two rows of Al vacancies in the topmost plane (side view), (b) structure at 1000 K (top view), and (c) structure at 1700 K (top view). The red lines mark the zigzag patterns. Gray and blue spheres represent the Al and Ti atoms, respectively.
Table 1. Calculated and Experimental Atomic Distances (nm) and Angles (°) of the Zigzag Structure of the Reconstructed TiAl(111) Surface zig-zag Al-Al
distance/angle d1 (nm) d2 (nm) angle (°)
Ti-Ti (1)
d1 (nm) d2 (nm) angle (°)
Ti-Ti (2)
MD calculation at 1000 K 0.375 0.432 99 0.294 0.332 120
d1 (nm)
0.372
d2 (nm) angle (°)
0.420 108
reconstructed to form zigzag patterns joining the Al or Ti atoms as marked. The surface reconstructions persist near the melting temperature. In the following, we discuss only the structure simulated at 1000 K, close to the annealing temperature of our experiment. Table 1 compiles the nearest-neighbor distances (d1 and d2) and angles between the atomic protrusions forming the three different zigzag patterns identified in the simulated topmost planes. One is an Al-Al zigzag marked in Figure 4b, and the other two are the Ti-Ti zigzag patterns, Ti-Ti(1) and TiTi(2), also marked in Figure 4b. It is observed that the Al-Al zigzag distance and angle values show the best agreement with the experimental observation. The average distance for the Al-Al zigzag is 0.404 nm, and the zigzag angle is 99° (experimental distance and angle are 0.40 ( 0.04 nm and 75-100°, respectively). For the Ti-Ti(1) and Ti-Ti(2) zigzag patterns, the average distance and angle values are 0.313 nm and 120°, and 0.396 nm and 108°, respectively. This shows that the zigzag protruding pattern observed in the experimental image can be assigned to the Al atoms of the topmost plane. We have simulated the STM image obtained from periodic DFT calculations as presented in Figure 5. Figure 5a shows top and side views of the reconstructed surface with the zigzag pattern joining Al atoms as marked. The STM image shown in
Figure 5. (a) Top and side views of the γ-TiAl(111) surface at 1000 K (only the first and second layers are shown). The yellow and dark blue spheres represent the top layer Al and Ti atoms, respectively, whereas the gray and sky blue spheres represent the second layer Al and Ti atoms, respectively. (b) DFT STM image obtained at a bias voltage of 0.5 V. The zigzag pattern formed by the Al atoms is marked. (c) Close-up of the experimental STM image with the zigzag pattern and unit cell marked.
Figure 5b has been simulated at a bias voltage of þ0.5 V. For comparison, we show in Figure 5c a close-up of the experimental STM image. It can be seen that the zigzag pattern joining Al atoms in the simulated image reproduces the feature observed in the experimental image, thus confirming the assignment deduced from the geometrical considerations. Here, it should be noted that the DFT STM image had to be simulated at a higher bias voltage (þ0.5 V) than that used experimentally (þ0.03 V) for contrast enhancement. The main difference between simulation and experiment is that the DFT approach does not take into account the electronic structure of 3375
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The Journal of Physical Chemistry C the STM tip, which can have a huge effect on the experimental measurement and may account for the difference observed here. It should be emphasized that this investigation on the γ-TiAl(111) surface was also performed by employing various other models, such as (i) vacancy-free surfaces and (ii) Tienriched surfaces due to the substitution of Al atoms by Ti or due to the addition of Ti ad-atoms. Neither of these models resulted in any surface reconstruction by restructuring or formation of zigzag patterns and could account for the observed structure. Thus, we conclude that the surface depletion in Al caused by preferential sputtering is at the origin of the surface reconstruction observed on this alloy surface despite some Al segregation after postannealing at 1000-1100 K. The Al vacancies injected in the topmost plane are highly stable because the reconstruction persists up to the melting temperature of the alloy, according to our simulation. These data are in line with our previous findings that Al vacancies injected by the selective growth of an ultrathin aluminum oxide film can be trapped in the topmost surface plane and clustered at the oxide/alloy interface to initiate voiding.32,33 The present study shows that Al vacancies can also be trapped in the topmost plane at the oxide-free alloy surface stabilized by surface reconstruction, rather than being annihilated by diffusion into the bulk of the alloy.
4. CONCLUSION The structure of the oxide-free γ-TiAl(111) surface has been investigated for the first time by joint experimental and theoretical approaches. Surface reconstruction forming a (2 2) superstructure was evidenced by STM after surface preparation by Ar sputtering and UHV annealing at 1000-1100 K. A zigzag atomic protruding pattern oriented along the [101] direction characterizes the reconstructed alloy surface enriched in Ti due to the preferential sputtering of Al by Ar bombardment and despite Al segregation upon annealing. DFT MD calculations were performed with (2 2) supercells of the bulklike terminated γ-TiAl(111) surface containing two Al vacancies in the topmost plane and at simulated annealing temperatures ranging from 800 to 2200 K. The simulated temperatures for reconstruction by restructuring and melting of 950 and 1800 K, respectively, are in good agreement with the experimental annealing temperature (1000-1100 K) and the melting temperature (1753 K). The surface reconstruction is shown to be stable up to 1750 K by the simulation. The surface reconstruction simulated by DFT MD is characterized by the formation of zigzag structures, as observed experimentally. The simulated STM images obtained from periodic DFT calculations show that the atomic protrusions reproduce zigzag patterns oriented along the [101] direction. The average interatomic distance in the Al-Al zigzag is 0.404 nm with an angle of 99°, in agreement with the experimental values, showing that the experimentally observed zigzag patterns can be associated with the Al atoms. These data show that the surface reconstruction results from the presence of Al vacancies injected by preferential sputtering of the Al atoms during surface preparation. The Al/Ti ratio at the reconstructed (2 2) surface is 1:2 due to Ti enrichment at the topmost plane. The persistence of the surface reconstruction at high annealing temperatures shows a high stability of the Al surface vacancies in the topmost plane, with no annihilation by diffusion in the bulk.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (V.M.),
[email protected] (P.M.). Present Addresses §
Institut f€ur Physikalische and Theoretische Chemie, Universit€at Bonn, Wegelerstrasse 12, 53115 Bonn, Germany.
’ ACKNOWLEDGMENT A postdoctoral grant of the French Ministry of Research for the support of M. M. I. is acknowledged. ’ REFERENCES (1) Kim, Y.-W.; Dimiduk, D. M. JOM 1991, 43, 40. (2) Froes, F. H.; Suryanarayana, C.; Eliezer, D. J. Mater. Sci. 1992, 27, 5113. (3) Yamaguchi, M.; Inui, H.; Ito, K. Acta Mater. 2000, 48, 307. (4) Clemens, H.; Kestler, H. Adv. Eng. Mater. 2000, 2, 551. (5) Wu, X. Intermetallics 2006, 14, 1114. (6) Lasalmonie, A. Intermetallics 2006, 14, 1123. (7) Imayev, R. M.; Imayev, V. M.; Oehring, M.; Appel, F. Intermetallics 2007, 15, 451. (8) Sung, S. Y.; Kim, Y. J. Intermetallics 2007, 15, 468. (9) Rahmel, A.; Quadakkers, W. J.; Sch€utze, M. Mater. Corros. 1995, 46, 271. (10) Lang, C.; Sch€utze, M. Mater. Corros. 1997, 48, 13. (11) Dettenwanger, F.; Schumann, E.; R€uhle, M.; Rakowski, J.; Meier, G. H. Oxid. Met. 1998, 50, 269. (12) Li, X. Y.; Taniguchi, S. Intermetallics 2004, 12, 11. (13) Appel, F.; Brossmann, U.; Christoph, U.; Eggert, S.; Janschek, P.; Lorenz, U.; Mullauer, J.; Oehring, M.; Paul, J. D. H. Adv. Eng. Mater. 2000, 2, 699. (14) Li, X. Y.; Taniguchi, S. Intermetallics 2005, 13, 683. (15) Bacos, M. P.; Morel, A.; Naveos, S.; Bachelier-Locq, A.; Josso, P.; Thomas, M. Intermetallics 2006, 14, 102. (16) Tian, W. H.; Nemoto, M. Intermetallics 1997, 5, 237. (17) Taniguchi, S.; Uesaki, K.; Zhu, Y.-C.; Zhang, H.-X.; Shibata, T. Mater. Sci. Eng., A 1998, 249, 223. (18) Fergus, J. W. Mater. Sci. Eng., A 2002, 338, 108. (19) Maurice, V.; Noumet, A.-G.; Zanna, S.; Josso, P.; Bacos, M.-P.; Marcus, P. Acta Mater. 2008, 56, 3963. (20) Boonruang, C.; Thongtem, S. Appl. Surf. Sci. 2009, 256, 484. (21) Narksitipan, S.; Thongtem, T.; McNallan, M.; Thongtem, S. Appl. Surf. Sci. 2006, 252, 8510. (22) Zhao, B.; Sun, J.; Wu, J. S.; Yuan, Z. X. Scr. Mater. 2002, 46, 581. (23) Yang, W. J.; Sekino, T.; Shim, K. B.; Niihara, K.; Auh, K. H. Thin Solid Films 2005, 473, 252. (24) Shanabarger, M. R. Mater. Sci. Eng., A 1992, 153, 608. (25) Shanabarger, M. R. Appl. Surf. Sci. 1998, 134, 176. (26) Taylor, T. N.; Paffett, M. T. Mater. Sci. Eng., A 1992, 153, 584. (27) Geng, J.; Gantner, G.; Oelhafen, P.; Datta, P. K. Appl. Surf. Sci. 2000, 158, 64. (28) Schmiedgen, M.; Graat, P. C. J.; Baretsky, B.; Mittemeijer, E. J. Thin Solid Films 2002, 415, 114. (29) Kovacs, K.; Perczel, I. V.; Josepovits, V. K.; Kiss, G.; Reti, F.; Deak, P. Appl. Surf. Sci. 2002, 200, 185. (30) Maurice, V.; Despert, G.; Zanna, S.; Josso, P.; Bacos, M.-P.; Marcus, P. Acta Mater. 2007, 55, 3315. (31) Maurice, V.; Despert, G.; Zanna, S.; Josso, P.; Bacos, M.-P.; Marcus, P. Surf. Sci. 2005, 596, 61. (32) Maurice, V.; Despert, G.; Zanna, S.; Josso, P.; Bacos, M.-P.; Marcus, P. Nat. Mater. 2004, 3, 687. (33) Islam, M. M.; Diawara, B.; Maurice, V.; Marcus, P. J. Phys. Chem. C 2009, 113, 9978. 3376
dx.doi.org/10.1021/jp110278t |J. Phys. Chem. C 2011, 115, 3372–3377
The Journal of Physical Chemistry C
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(34) Wang, C. P.; Kim, S. K.; Jona, F.; Strongin, D. R.; Sheu, B. R.; Marcus, P. M. Surf. Rev. Lett. 1995, 2, 183. (35) Noumet, A.-G. Niobium effects on titanium aluminide oxidation mechanisms. Ph.D. Thesis, Universite Pierre et Marie Curie (Paris VI), Paris, 2006. (36) Elliott, R. P.; Rostoker, W. Acta Metall. 1954, 2, 884. (37) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (38) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558. (39) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 48, 13115. (40) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251. (41) Kresse, G.; Joubert, J. Phys. Rev. B 1999, 59, 1758. (42) Bl€ochl, P. E. Phys. Rev. B 1994, 50, 17953. (43) Kresse, G.; Bergermayer, W.; Podloucky, R.; Lundgren, E.; Koller, R.; Schmid, M.; Varga, P. Appl. Phys. A: Mater. Sci. Process. 2003, 76, 701. (44) Islam, M. M.; Diawara, B.; Maurice, V.; Marcus, P. Surf. Sci. 2009, 603, 2087. (45) Islam, M. M.; Diawara, B.; Maurice, V.; Marcus, P. Surf. Sci. 2010, 604, 1516. (46) Tersoff, J.; Hamann, D. R. Phys. Rev. B 1985, 31, 805. (47) Franchy, R. Surf. Sci. Rep. 2000, 38, 195. (48) McCullough, C.; Valencia, J. J.; Levi, C. G.; Mehrabran, R. Acta Mater. 1989, 37, 1321.
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