Alloy Interfaces

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9978

2009, 113, 9978–9981 Published on Web 05/13/2009

Atomistic Modeling of Voiding Mechanisms at Oxide/Alloy Interfaces Mazharul M. Islam,* Boubakar Diawara,* Vincent Maurice,* and Philippe Marcus* Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR 7045), Ecole Nationale Supe´rieure de Chimie de Paris (Chimie ParisTech), UniVersite´ Pierre et Marie Curie, 11 rue Pierre et Marie Curie, 75005 Paris, France ReceiVed: April 10, 2009

For the first time, voiding mechanisms resulting from the condensation of atomic vacancies injected at oxide/ alloy interfaces by the growth of oxide layers have been studied by means of periodic density functional theory (DFT) calculations. Several interfaces were built by superimposing ultrathin films of alumina on the γ-TiAl(111) surface, and their relative stabilities were compared by calculating the interface energy variation. The formation energy of single Ti or Al vacancies and clustered and dispersed ensembles of 2Ti + 1Al or 2Al + 1Ti vacancies injected into the alloy were calculated. The results show that it is easier to inject the vacancies into the oxide/alloy interface than into the bare alloy surface and into the bulk alloy. The injected vacancies, trapped at the oxide/alloy interface, condense in the topmost plane of the alloy to form 2D clusters. The minimization of the coordination number of the vacancies with metal atoms of the alloy and O atoms of the overlaying oxide favors vacancy condensation and interfacial voiding. The data are relevant for a detailed understanding of the adherence and breakdown of protective oxide films and the lifetime of metallic materials. The fate of metallic vacancies injected at oxide/metal interfaces by the growth of oxide layers is critical for the corrosion protection provided by surface oxides and for the lifetime of the metallic material in many applications. Vacancy condensation can lead to interfacial voiding, thus weakening the adherence and promoting the breakdown of the protective oxide. Interfacial voiding typically occurs on aluminide intermetallic alloys (NiAl, FeAl) used in jet engines1 as the result of the growth mechanism of alumina layers.2-6 A fundamental understanding of the mechanisms of interfacial vacancy condensation requires atomic-scale observations of the buried interfacial defects, extremely difficult when thick oxide and/or rough interfaces are produced but accessible in the very first stages of growth when the oxide is still ultrathin.7,8 Ultrathin alumina films on intermetallic alloys are widely studied as nanotemplates to support model catalysts, but the structural details of the oxide/alloy interfaces remain difficult to resolve and control.9-16 Recent combined experimental and theoretical investigations on NiAl(110)13,15 and Ni3Al(111)16 concluded that the films (two O layer thick and O-terminated) have an overall stoichiometric Al/O ratio (1:1.3) higher than that of Al2O3 (1:1.5), and they are largely distorted with respect to bulk alumina structures. An unmodified alloy surface at the interface with the oxide was proposed, assuming perfect rehomogenization of the alloy surface after oxidation and thereby disregarding the possible structural modifications induced by vacancy injection. In contrast, modifications of the alloy surface underneath of the ultrathin alumina layer have been reported on TiAl substrates.7,17,18 Owing to a slow self-diffusion * To whom correspondence should be addressed. E-mail: rana-islam@ enscp.fr (M.M.I.); [email protected] (B.D.); vincent-maurice@enscp. fr (V.M.); [email protected] (P.M.). Phone: +33 1 44276736. Fax: +33 1 46340753.

10.1021/jp903331w CCC: $40.75

in the bulk alloy, a fraction of the atomic vacancies injected in the alloy would be trapped at the interface between the two-three O layer thick alumina film and a γ-TiAl(111) surface. The self-assembly of the vacancies would form interfacial vacancy clusters (containing up to six missing atoms each) arranged periodically to produce arrays of triangular twodimensional nanocavities.7,17 Here, we report the atomistic modeling of the stabilization of these vacancies and their self-assembly to form clusters and initiate voiding at the interface between an alumina film (γlike as inferred from the experimental growth temperature of 650 °C7,17) and a γ-TiAl(111) substrate (Ti50Al50 composition and L10 structure) with ab initio periodic DFT calculations. The GGA-based Perdew-Burke-Ernzerhof exchange-correlation functional19,20 was employed as implemented in VASP.21 Full geometry optimization was performed using PAW potentials22,23 and the energy cutoff of Ecut ) 400 eV (as optimized by calculations for bulk Al2O3) for the core and valence electrons, respectively. To our knowledge, this is the first atomistic modeling of oxide/alloy interfaces that addresses the fate of injected vacancies and voiding mechanisms. It gives insight into the atomic composition of the vacancy clusters, the driving force for vacancy condensation, and the local bonding configuration at the interface, which are difficult to obtain from experiments. A (2 × 4) supercell (as ) 11.4 Å, bs ) 11.2 Å) of the primitive TiAl(111) surface unit cell consisting of four atomic layers was used as a coincidence cell to build the interface. The oxide films were cut from the (111)-oriented nondefective and defective spinel γ-Al2O3 bulk structures24 containing two Al layers and two O layers and were O-terminated. Using the parameter of 11.2 Å for γ-Al2O3(111), the lattice mismatch with the TiAl(111) slab was only 1.8% (along a). The resulting  2009 American Chemical Society

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J. Phys. Chem. C, Vol. 113, No. 23, 2009 9979

Figure 1. (a,b,c) Defective and (d,e,f) nondefective spinel models of alumina thin films on γ-TiAl(111) before (a,d) and after (b,c,e,f) full structural optimization without (b,e) and with (c,f) an interfacial trivacancy cluster (2 Ti + 1 Al) (side view). Blue, gray, and red spheres represent Ti, Al, and O atoms, respectively. Only the first atomic layer out of four layers of the TiAl alloy surface is shown. The trivacancy interfacial clusters are marked by the pink spheres in the topmost plane of the alloy (c,f). Interfacial oxygen atoms marked in green and light blue and pointed to in (b,c) are relocated to minimize lost bonding with the vacancy cluster.

TABLE 1: Interface Stabilization Energy (∆γ) for Defective and Nondefective Spinel Models of Alumina Thin Films Having Octahedral or Mixed Octahedral-Tetrahedral Al Planes at the Interface with the γ -TiAl(111) Surface alumina type/alloy def spinel/TiAl(111) nondef spinel/TiAl(111)

interface plane

∆γ (eV/Å2)

octa octa-tetra octa octa-tetra

-2.63 -2.49 -2.40 -2.58

interface structures contained 52 (defective spinel alumina) or 56 atoms (nondefective spinel alumina) in the oxide and 64 atoms in the alloy and were separated by a vacuum gap of 15 Å (Figure 1). For each alumina structure, two possible terminations of the oxide, corresponding to an octahedral Al layer or to a mixed octahedral-tetrahedral Al layer, were considered at the interface with the alloy. The Al/O stoichiometric ratio was 1:1.6 with the defective spinel model, in agreement with the experimental value of 1:1.6 ( 0.1 for this system.7,17 The higher value of 1:1.3, obtained with the nondefective spinel model, equals that obtained for Al2O3 thin film on NiAl (1:1.33).13 The stability of each structure was assessed by calculating the interface energy variation ∆γ in the grand canonical ensemble as defined by13

∆γ ) (Eoxide/alloy-slab - Ealloy-slab - NAlµAl - NOµO)/Area (1) where NO (NAl) is the number of O (Al) atoms in the oxide film, E is the slab energy, and µO (µAl) is the chemical potential for O (Al) atoms as calculated from the formation energy of the oxygen molecule25 (bulk aluminum crystal26). The interfaces with the octahedral and mixed octahedral-tetrahedral Al layers are more stable for the models built from the defective and nondefective spinel alumina structures, respectively (Table 1). Both were used for further investigation of the bonding analysis and vacancy formation. Marked reconstruction characterizes the interface built from the defective spinel alumina (Figure 1b). Interlayer mixing is observed in the interfacial region where four O atoms have moved down from the oxide film to form new bonds with Al and Ti atoms extracted from the topmost alloy plane at interatomic distances of 2.05 and 1.85 Å, respectively. In the subsurface region of the oxide film, the coordination around

Al atoms has changed. The Al atoms which were four-fold or six-fold coordinated before optimization (Figure 1a) are fivefold coordinated after reconstruction (Figure 1b). Much less distortion characterizes the interface built from the nondefective spinel alumina (Figure 1e). Four Al atoms have moved from the interface layer to the top region of the oxide film to give a mixed layer of four-fold- and six-fold-coordinated Al atoms. Different configurations of the metallic vacancies were considered, such as single vacancies consisting of one Ti or one Al missing atom, triangular clusters consisting of 2Ti + 1Al (Figure 1) or 2Al + 1Ti nearest-neighbor missing atoms and ensembles of 2Ti + 1Al or 2Al + 1Ti dispersed missing atoms. The triangles of three vacancies are first approximations of the clusters containing up to six vacancies deduced from the experimental study.7 Investigation of larger clusters would have required larger coincidence cells, which was not possible with the available computational resources. The defect formation energy (∆E) was calculated as ∆E ) RDE + µ,27 where RDE is the raw defect energy defined as the energy difference of the system with and without defects and µ is the chemical potential of aluminum or titanium obtained from the calculated formation energy of the respective bulk metal. The results are compiled in Table 2. By using the chemical potential obtained from a different equation,27 we have obtained the same hierarchy in the calculated ∆E values. The calculated vacancy formation energy in bulk TiAl is smaller for Ti than that for Al, in agreement with experimental measurements.28 The calculated value of 1.81-1.82 eV for single vacancies is in reasonable agreement with the experimental value of 1.41 ( 0.06 eV.28 It is also observed that Ti vacancies are easier to form at the vacuum/γ-TiAl(111) and Al2O3/γ-TiAl(111) interfaces, showing that this chemical selectivity also applies at the bare surface and at the oxide/alloy interface. Note that in the case of the selective formation of alumina at the surface of the alloy, Al vacancies are injected in the metal, although their formations cost more energy than those of Ti vacancies. The segregation of Ti vacancies from the bulk can however result from the nonreciprocal self-diffusion of Al and Ti (Kirkendall effect).4 The data in Table 2 reveal several stabilization effects. First, it is shown that, independent of their chemical identity, the vacancy formation is easier at the bare surface of the alloy than that in the bulk of the alloy, as expected from a simple argument of coordination number minimization (9 with nearest neighbors

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TABLE 2: Comparison of the Vacancy Formation Energy (eV) for Single Vacancies, Trivacancy Clusters, and Dispersed Trivacancies in Bulk γ-TiAl, at the Bare γ-TiAl(111) Surface, and at the Interface between Defective and Nondefective Spinel Models of Alumina Thin Films and the γ-TiAl(111) Surfacea vacancy type single (Ti) single (Al) cluster (2Ti + 1Al) cluster (2Al + 1Ti) dispersed (1Ti + 1Al + 1Ti) dispersed (1Al + 1Ti + 1Al) a

bulk TiAl

TiAl(111) surface

def. spinel/TiAl(111) nondef. spinel/TiAl(111) interface interface

2 × 2 × 2 3 × 3 × 3 experiment28 2 × 4 × 1 2 × 4 × 2

2×4×1

2×4×1

1.41 ( 0.06

0.78 1.46 2.88 2.93 3.10 3.40

0.88 1.70 3.00 3.74 3.34 4.15

1.82 2.75 6.05 7.25

1.81 2.74 5.96 7.02

0.93 1.93 3.14 3.92

0.95 1.97 3.19 3.96

The multiples of the bulk and surface unit cells used for calculations are indicated.

at the surface versus 12 in the bulk). Second, the formation of the vacancies is easier at the oxide/alloy interface than that at the vacuum/alloy interface, independent of the alumina structure used to model the oxide. This stabilization effect of the oxide/ alloy interface demonstrates that the vacancies forced into the alloy surface by the growth mechanism of the oxide can be trapped at the oxide/alloy interface. Third, irrespective of the nature of the vacancies and of the alumina structure, the clusters of three vacancies are easier to form than the ensembles of three dispersed vacancies. The minimization of the coordination number of the missing atoms is also expected to act as a driving force for the clustering of vacancies since the coordination number is 20 for the clusters of 3 vacancies but 27 for the ensembles of 3 dispersed vacancies. This stabilization effect demonstrated by the DFT modeling confirms the experimental assumption7 that the vacancies trapped at the oxide/alloy interface self-assemble to form vacancy clusters. The bonding analysis of the reconstructed interface (built from the defective spinel alumina) including vacancy clusters shows that the atomic positions in the topmost region of the oxide film remain nearly unchanged (Figure 1b,c). However, there is a significant change of the positions of two O atoms neighboring the vacancy clusters in the interfacial region. The O atom, marked in green and pointed to, has lost two bonds with two missing Ti atoms and, as a result, gets closer to an Al atom of the oxide film with a bond distance shortened from 2.1 to 1.84 Å. The O atom, marked in light blue and pointed to, has lost one bond with a missing Ti atom and one bond with a missing Al atom. It also gets closer to an Al atom of the oxide film with a bond distance shortened from 2.94 to 1.99 Å and thereby changes the local coordination of Al from five-fold to six-fold (Figure 1c). This local reconstruction is attributed to the strength of the oxygen-metal bonds broken by the inclusion of the metallic vacancies in the interface. In the case of the slightly distorted interface (built from the nondefective spinel alumina), the clustering of the atomic vacancies at the interface has less effect on the geometry (Figure 1e,f). At the interface, the Al atoms of the oxide film have lost bonds with the missing Ti and Al atoms. However, this has little influence on the structure of the interface and oxide film since the coordination around Al atoms in the film remains unchanged and the Al-O bond distance variation is less than 0.1 Å. This is attributed to the weaker strength of the aluminum-metal bonds broken by the inclusion of the vacancies in this interface. We expect that larger vacancy clusters could form at this type of interface following the same criteria. In summary, we have constructed atomistic models of the interface between a two O layer thick film of alumina with different structures and a γ-TiAl(111) substrate and performed a quantum chemical DFT investigation of the insertion of atomic

vacancies and their self-assembly to form clusters and initiate voiding at the oxide/alloy interface. Nearly equal stabilization of the surface energy can be obtained by interfacing the alloy with defective or nondefective spinel alumina cuts terminated by an Al layer at the interface. Significant reconstruction characterized by interlayer mixing and changes of local coordination or relaxation of the atomic positions was observed depending on the structure of the oxide films. For all interfaces, the insertion of atomic vacancies was found to cost less energy at the oxide/alloy interface than that at the vacuum/alloy interface and that in the bulk of the alloy. The formation of clusters of nearest-neighbor vacancies was found to be easier than that of an equal number of dispersed atomic vacancies of the same chemical nature. These data show that the injected vacancies, whose annihilation by self-diffusion toward the bulk alloy is slow, are stabilized by trapping in the topmost atomic plane of the alloy at the oxide/alloy interface. We conclude that the minimization of the coordination number of the vacancies with metal atoms of the alloy and oxygen atoms of the oxide layer promotes interfacial voiding by vacancy stabilization and condensation. Acknowledgment. M.M.I. thanks the French Ministry of Research for the support of a postdoctoral grant. The authors are grateful to Professor Thomas Bredow for fruitful discussion. Computing facilities by CCRE (University P. et M. Curie, Paris) and the National French IDRIS Center are acknowledged. References and Notes (1) Padture, N. P.; Gell, M.; Jordan, E. H. Science 2002, 296, 280. (2) Presscott, R.; Mitchell, D. F.; Graham, M. J.; Doychak, J. Corros. Sci. 1995, 37, 1341. (3) Pint, B. A. Oxid. Met. 1997, 48, 303. (4) Grabke, H. J. Intermetallics 1999, 7, 1153. (5) Rivoaland, L.; Maurice, V.; Josso, P.; Bacos, M.-P.; Marcus, P. Oxid. Met. 2003, 60, 159. (6) Hou, P. J. Am. Ceram. Soc. 2003, 86, 660. (7) Maurice, V.; Despert, G.; Zanna, S.; Bacos, M.-P.; Marcus, P. Nat. Mater. 2004, 3, 687. (8) Wang, C. M.; Baer, D. R.; Thomas, D. E.; Amonette, J. E.; Anthony, J.; Qiang, Y.; Duscher, G. J. Appl. Phys. 2005, 98, 094308. (9) Baumer, M.; Freund, H.-J. Prog. Surf. Sci. 1999, 61, 127. (10) Franchy, R. Surf. Sci. Rep. 2000, 38, 195. (11) Stierle, A.; Renner, F.; Streitel, R.; Dosch, H.; Durbe, W.; Cowie, B. C. Science 2004, 303, 1652. (12) Qin, F.; Magtoto, N. P.; Kelber, J. A.; Jennison, D. R. J. Mol. Catal., A: Chem. 2005, 228, 83. (13) Kresse, G.; Schmid, M.; Napetsching, E.; Shishkin, M.; Ko¨hler, L.; Varga, P. Science 2005, 308, 1440. (14) Kulawik, M.; Nilius, N.; Freund, H.-J. Phys. ReV. Lett. 2006, 96, 036103. (15) Schmid, M.; Shishkin, M.; Kresse, G.; Napetsching, E.; Varga, P.; Kulawik, M.; Nilius, N.; Rust, H.-P.; Freund, H.-J. Phys. ReV. Lett. 2006, 97, 046101.

Letters (16) Schmid, M.; Kresse, G.; Buchsbaum, A.; Napetsching, E.; Gritschender, S.; Reichling, M.; Varga, P. Phys. ReV. Lett. 2007, 99, 196104. (17) Maurice, V.; Despert, G.; Zanna, S.; Josso, P.; Bacos, M.-P.; Marcus, P. Surf. Sci. 2005, 596, 61. (18) Maurice, V.; Despert, G.; Zanna, S.; Josso, P.; Bacos, M.-P.; Marcus, P. Acta Mater. 2007, 55, 3315. (19) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (20) Perdew, J. P.; et al. Phys. ReV. B 1992, 46, 6671. (21) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251. (22) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953.

J. Phys. Chem. C, Vol. 113, No. 23, 2009 9981 (23) Kresse, G.; Joubert, J. Phys. ReV. B 1999, 59, 1758. (24) Gutie´rrez, G.; Taga, A.; Hohansson, B. Phys. ReV. B 2001, 65, 012101. (25) Bottin, F.; Finocchi, F.; Noguera, C. Phys. ReV. B 2003, 68, 035418. (26) Hagen, M.; Finnis, M. W. Philos. Mag. A 1998, 77, 447. (27) Woodward, C.; Kajihara, S.; Yang, L. H. Phys. ReV. B 1998, 57, 13459. (28) Brossmann, U.; Wu¨rschum, R.; Badura, K.; Schaefer, H.-E. Phys. ReV. B 1994, 49, 6457.

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