J. Phys. Chem. C 2009, 113, 18321–18330
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Carbon Adsorption and Absorption in the (111) L12 Fe3Al Surface Gustavo E. Ramı´rez-Caballero,†,‡ Perla B. Balbuena,*,† Paula R. Alonso,§ Pablo H. Gargano,§ and Gerardo H. Rubiolo§,| Department of Chemical Engineering, Texas A&M UniVersity, College Station, Texas 77843, Departamento Materiales, GIDAT, and Instituto Sa´bato, UniVersidad Nacional de San Martı´n, Comisio´n Nacional de Energı´a Ato´mica, AVda Gral Paz 1499, San Martı´n, Pcia de Buenos Aires, Argentina, and Consejo Nacional de InVestigaciones Cientı´ficas y Tecnolo´gicas, Argentina ReceiVed: July 21, 2009; ReVised Manuscript ReceiVed: September 3, 2009
Density functional theory is used to investigate the adsorption of carbon on the (111) surface of the L12 Fe3Al structure under various carbon coverages and the absorption in interstitial sites of the subsurface. Surface reconstruction is observed after carbon is adsorbed on the surface, and as carbon coverage increases carbon structures are formed in most cases with enhanced adsorption energies. C structures evolve, becoming sp3like at intermediate coverage, and at much higher coverage sp2 networks form a graphene sheet that separates from the metal surface. The surface Fe magnetic moments are decreased in the presence of C, and the change is dependent on the position of the adsorbed C atom. At low C coverage, C interacting with Fe has an induced magnetic moment on the order of 0.15 µB that becomes reduced as C-C structures are formed. The interstitial octahedral sites of the first interlayer below the surface are the most stable sites for carbon absorption, where carbon is more stable than when adsorbed on the surface at the same total coverage. Carbon diffusion from the surface to the subsurface at low coverage has a barrier of 0.99 eV, but the barrier is significantly reduced to 0.33 eV at higher C surface coverage. Strong lattice distortions occur due to the incorporation of carbon on the surface and subsurface, giving some insights into possible carburization pathways of the L12 F3Al phase. 1. Introduction Fe-Al-based alloys are materials being tested for several different applications in chemical, petrochemical, and electric power generation industrial plants. The main applications are in tubing of boilers, vapor generators, refinery ovens, and heat exchangers at high and low pressures. Fe-Al-based alloys offer some advantages due to their low cost, low density, and excellent resistance to oxidation and sulfidizing environments at high temperatures1-4 due to formation of a protective layer on the alloy surface. In this way, Fe-Al alloys hold promise as a replacement to stainless steels for use in harsh environments.5 Despite these attractive properties, it is still necessary to improve the mechanical properties6 and carburization resistance at high temperatures.7 Carburization may take place when iron or iron-based alloys are immersed in carbon atmospheres at high temperatures. It is initiated by carbon absorption into the subsurface, which reacts with the substrate, forming carbides such as Fe3C.8 Changes in microstructure may lead to undesirable mechanical and thermodynamic properties.8,9 When immersed in environments that are supersaturated with carbon, iron alloys can even experience corrosion by metal dusting.10 Iron-rich Fe-Al alloys exhibit the presence of A2 RFe(Al) solid solution (which dissolves up to 45 atom % Al) and the fcc γFe (Al) solid solution limited to 1.3 atom % Al. An increase * To whom correspondence should be addressed. E-mail: balbuena@ tamu.edu. † Texas A&M University. ‡ Permanent address: Departamento de Ingenieria Quimica, Universidad Industrial de Santander, Bucaramanga, Colombia. § Universidad Nacional de San Martı´n. | Consejo Nacional de Investigaciones Cientı´ficas y Tecnolo´gicas.
in aluminum content leads to formation of Fe3Al phase, with D03 structure, stable until almost 550 °C.11 The Fe3Al intermetallic compound with D03 structure has been extensively studied, and there are several reviews related to its properties.5,6,12-16 However, alloying Fe-Al with carbon produces a structural change from the bcc-based D03 structure resulting in formation of the fcc-based perovskite-type κ-phase Fe3AlCx with E21 structure.7,17-20 An analogous perovskite structure can be found in the Ni-Al system, where Ni3Al with L12 structure gives rise to Ni3AlCx when alloyed with carbon.19,20 It is thus of interest to reveal whether the presence of an fcc compound favors or disadvantages carbon deposition and its subsequent erosion process. Schneider and Zhang21 studied using electron backscattered diffraction the precipitation of κ (Fe3AlC) compound in a R-Fe(Al) matrix with a composition of Fe-15 atom % Al exposed to a strong carburizing atmosphere and discussed experimental work from other authors suggesting nucleation and growth of the κ phase in contact with γFe (Al,C). The κ(Fe3AlC) compound can be considered as an ordered fcc arrangement of Fe and Al of type L12, with C atoms in the octahedral interstices. A perfect atomic arrangement of this type would correspond to the formula Fe3AlC. However, this stoichiometry has never been observed. Palm and Inden17 established that the κ phase may be considered as an ordered solid solution stabilized by carbon rather than regarding it as a carbide, and they proposed the formula Fe4-yAlyCx for this phase where x may vary between 0.8 and 1.2 and y between 0.42 and 0.71. A recent density functional theory (DFT) study related to the structure of the κ-Fe3AlC perovskite22 reported the properties of this structure compared to those of the intermetallic Fe3AlL12. In particular, this work revealed differences in spin effects
10.1021/jp907148q CCC: $40.75 2009 American Chemical Society Published on Web 09/23/2009
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Figure 1. Possible adsorption sites on the Fe3Al surface: (red) Fe, (blue) Al.
on the vibrational properties of the L12-Fe3Al system obtained by the spin-generalized gradient (SGGA) and generalized gradient (GGA) approximations; these differences were shown to become negligible when the L12-Fe3Al system interacts with carbon atoms. Other related DFT work focused on Fe3C bulk properties and surface stability,9 CO adsorption and dissociation on Fe surfaces,23 diffusion and dissolution of carbon in ferrite and austenite,24 and Fe-Al-C phase diagram assessment.25 On the assumption that a composition of γFe (Al,C) close to the stoichiometric Fe3AlC could favor κ (Fe3AlC) formation, in this work we analyze the thermodynamics of carbon adsorption and absorption in the L12 Fe3Al structure and the minimum-energy pathways for migration of carbon atom from the surface to the subsurface. 2. Computational and System Details Calculations were performed within the DFT framework using the Vienna ab initio simulation package (VASP),26-29 based on plane wave basis sets. Electron-ion interactions are described using the projector-augmented wave (PAW) method,30 which was expanded within a plane wave basis set up to a cutoff energy of 400 eV. Electron exchange and correlation effects were described by the Perdew-Burke-Ernzerhof (PBE)31,32 GGAtype exchange correlation function. Spin polarization was included in every simulation. The convergence criterion for the electronic self-consistent iteration was set to 10-4 eV, and the forces were converged to 0.01 eV/Å. A Fe3Al (1,1,1) surface with L12 crystal structure was modeled using 2 × 2 supercells with a total of 24 atoms. A (111) surface plane was chosen because it has the highest concentration of atoms per unit area for an fcc structure, which is analogous to a L12 structure. To our knowledge, the surface energies of L12-Fe3Al structures have not been reported; the (111) plane in a L12 structure forms a stoichiometric surface. Segregation energies for Fe and Al atoms in the (111) surface of the L12 structure obtained using a recently reported methodology33 revealed antisegregation behavior with segregated structures being 1.3 and 0.58 eV less stable (for segregation of Fe and Al, respectively) than the nonsegregated stoichiometric
Figure 2. fcc-Fe3 and hcp-Fe3 hollow sites have strong adsorption energies due to formation of Fe3C structures. The image illustrates the phenomenon observed during the simulation when C was initially located on fcc-Fe2Al or hcp-Fe2Al sites. The arrows indicate the migration of the C atom from its initial position to the stable site. The carbon atom in the figure is adsorbed on the most stable hcp-Fe3 location.
Figure 3. Geometry of relaxed configurations of adsorbed C: (a) clean surface, (b) fcc-Fe3 and hcp-Fe3, and (c) top-Al. (Red) Fe. (Blue) Al. (Yellow) C atoms.
structure. Brillouin zone integration was performed using 9 × 9 × 1 a Monkhorst Pack grid34 and a Methfessel-Paxton35 smearing of 0.2 eV. The system consists of a six-layer slab model; the two layers at the bottom of the slab were fixed, whereas the other four layers were allowed to relax. The slab was taken as infinite in the x and y directions and finite in the z direction; periodic boundary conditions were used in the three directions. A vacuum space of 12 Å was included in the cell to separate the slab from those at the upper and lower cells, thus ensuring no interactions between the adsorbed species and the bottom surface of the next slab. The optimum bulk lattice constant and the magnetic moment of L12-Fe3Al were determined as 3.65 Å and 2.30 µB/Fe at., in agreement with those recently reported.22 Adsorption (on the surface) and absorption (in the subsurface) of carbon were simulated on the L12-Fe3Al surface and between layers. Top, bridge, fcc, and hcp sites were tested for adsorption of carbon at several coverages. During these calculations we allowed ion relaxation, while cell shape and volume where kept constant. From 1 to 8 carbon atoms on the surface corresponding to 1/4-2 monolayer (ML) were used to evaluate the interactions between carbon atoms and the L12-Fe3Al surface. For absorption, octahedral and tetrahedral interstices sites were studied. The adsorption or absorption energies, Ead or ab, of carbon were calculated using the following equation
TABLE 1: Calculated Adsorption Energies (in eV; see Figure 1 for a description of sites) and Magnetic Moments µB (in Bohr’s magneton per iron atom) Averaged over All Fe Atoms in the Slab (〈µB〉), and Per Surface atom on the L12 Fe3Al Surface (carbon coverage is 1/4 ML) carbon location on surface
adsorption energy (eV)
〈µB〉/ (Fe at.)
Fe on surface-1, µB
Fe on surface-2, µB
Fe on surface-3, µB
Al on surface, µB
carbon, µB
clean surface fcc-Fe3 hcp-Fe3 top-Al
-7.23 -7.45 -0.78
2.35 2.24 2.18 2.35
2.53 1.83 1.57 2.59
2.42 1.66 1.35 2.49
2.47 1.74 1.46 2.54
-0.10 -0.07 -0.06 -0.06
-0.14 -0.15 -0.009
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Ead or ab ) Eslab with adsorbed or absorbed C - (Eclean slab + N · Ecarbon) N where Eslab with adsorbed or absorbed C stands for the total energy of the interacting L12-Fe3Al surface with N adsorbed or absorbed C atoms, Eclean slab is the total energy of the bare L12-Fe3Al slab, and Ecarbon is the energy of gas-phase C in the ground state. This calculation was done breaking the symmetry of the unit cell. Negative Ead or ab values indicate favorable (exothermic) adsorption or absorption. The energies and paths of diffusion processes presented in this study were calculated using the modified climbing image method,36,37 a variation of the nudged elastic band (NEB) method38 implemented in VASP. This method allows finding saddle points and minimum-energy paths between known initial and final positions of a diffusion process. 3. Adsorption of Carbon on the Surface 3.1. One Carbon Atom on the Surface. Simulations were performed with one carbon atom on the surface at a time, initially located on hcp, fcc, bridge, and top positions. The various possible sites are indicated in Figure 1. After relaxation, stable adsorption locations were found on fcc-Fe3, hcp-Fe3, and top-Al sites, which indicates considerable surface selectivity. Table 1 shows that when comparing the adsorption energy per C atom on hcp-Fe3, fcc-Fe3, and top-Al sites, the first one is the strongest followed by fcc-Fe3. On the other hand, fcc-Fe2Al and hcp-Fe2Al hollow sites were found to be not stable; the simulation allows observing migration of
carbon atoms from their initial position to the hcp-Fe3 and fccFe3 hollow sites leading to formation of Fe3C structures (Figure 2). Table 1 indicates that the magnetic moments of the L12-Fe3Al surface atoms change significantly with the presence of adsorbed carbon. On the clean surface (Figure 3a), all the magnetic moments of the surface atoms are higher than that of the average of the slab, 〈µB〉, and the Al atom gets a weak induced magnetic moment coupling antiferromagnetically to the Fe atoms. When carbon is added on the fcc site, where it is surrounded by 3 Fe atoms (Figure 3b), µΒ of the surface iron atoms decreases significantly with respect to the respective slab average; this decrease correlates with the elongation of the Fe-Fe distances (Table 2) and with an induced magnetization of the C atom, which has been observed experimentally39 and theoretically.40 The effect is larger when C is on the hcp site, where the Fe-Fe distances are longer and the magnetic moment of C is slightly enhanced. Note that the induced magnetic moment on C is much larger than that on the Al atom. In contrast, when C is on top of the Al atom (Figure 3c), the magnetic moments of the Fe surface atoms are larger than the slab average and no appreciable magnetization is detected on the carbon atom. The Fe-C bond lengths are 1.81 Å for the fcc sites and 1.80 Å for the hcp sites; in the top-Al location, the bond length between the Al and the C atom is 1.92 Å. 3.2. Adsorption of Carbon on the Surface at Higher Coverage. When more than one C atom is initially located on the surface, carbon atom migration was observed from its initial position to either one of the fcc or hcp stable sites; thus, the two referred stable positions act as attractor points that conglomerate additional C atoms to favor formation of C
TABLE 2: Geometrical Parameters of Final Configurations after Relaxing C in Several Locationsa surface clean surface fcc-Fe3 hcp-Fe3 top-Al clean surface with grapheneb a
Fe1-Fe2 Fe2-Fe3 Fe3-Al Fe1-Al Fe1-Fe3 Fe1-Fe2-Fe3 Fe1-Al-Fe3 Al-Fe1-Fe2 Al-Fe3-Fe2 2.54 2.63 2.73 2.49 2.58
2.54 2.63 2.73 2.49 2.58
2.60 2.58 2.58 2.58 2.59
2.60 2.58 2.58 2.58 2.59
2.54 2.63 2.73 2.49 2.58
60.0 60.0 60.0 60.0 60.0
58.52 61.07 63.80 57.53 59.63
120.36 119.39 118.04 121.21 119.83
120.36 119.39 118.04 121.21 119.83
C coverage is 1/4 ML. Distances in Angstroms and angles in degrees. b Clean surface with graphene is discussed in the next section.
Figure 4. During the DFT optimization, two C atoms each initially forming bonds with two Fe and one Al atoms (a) migrate to a bridge site where each of them bonds with two Fe atoms (the Fe-C bond length is 2.00 Å), and also they form a surface C-C bond of length 1.35 Å (double bond), as shown in b. (c and d) Final configurations for 3 and 4 C atoms on the surface, respectively. In all cases the adsorbates induce surface reconstruction as depicted in e for the case of 4 C atoms where buckling of Al atoms is clearly observed.
Figure 5. (a and b) Structures formed when 5 C atoms are on the surface, with initial positions listed in Table 3: (a) isolated C is on the fcc Fe3 site; (b) isolated C is on the hcp Fe3 site. (c and d) Six and 7 atoms forming chains and chains with alternating rings, respectively. Graphene formation: (e) Side view of the relaxed geometry showing the complete separation of a graphene layer from the L12-Fe3Al surface; this separation is 4.00 Å. (f) Top view of the final system showing formation of a graphene structure. The bond distance between carbon atoms is 1.49 Å. The Fe-Fe distances in the first surface layer under graphene are elongated with respect to a similar relaxed surface without graphene, and the C-C distances are also longer than those in pure graphene.
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TABLE 3: Number of Carbons on the Surface, Their Respective Initial Positions before Relaxation, Calculated Adsorption Energies Per Carbon Atom, and Magnetic Moments (in Bohr’s magneton per iron atom)a number of carbon atoms 2 2 3 3 3 3 4 4 4 4 5 5 6 7 8
position before relaxation
adsorption energy (eV)
formation of carbon structures after relaxation
〈µB〉/ (at. Fe)
Fe on surface-1 µB
1C hcp-Fe3,1C fcc-Fe3 2 C fcc-Fe2Al 1C hcp-Fe3, 2C hcp-Fe2Al 1C fcc-Fe3, 2C fcc-Fe2Al 1C hcp-Fe3, 1C fccFe3, 1C fcc-Fe2-Al 1C hcp-Fe3, 1C fccFe3, 1C hcp-Fe2-Al 1C hcp-Fe3, 3C hcp-Fe2Al 1C fcc-Fe3, 3C fcc-Fe2Al 1C hcp-Fe3, 1C fccFe3, 2C fcc-Fe2Al 1C hcp-Fe3, 1C fccFe3, 2C hcp-Fe2Al 1C fcc-Fe3, 3C fcc-Fe2Al, 1C hcp-Fe3 1C hcp-Fe3, 3C hcp-Fe2Al, 1C fcc-Fe3 1C fcc-Fe3, 3C fcc-Fe2Al, 1C hcp-Fe3, 1C hcp-Fe2Al 1C fcc-Fe3, 3C fcc-Fe2Al, 1C hcp-Fe3, 2C hcp-Fe2Al 1C fcc-Fe3, 3C fcc-Fe2Al, 1C hcp-Fe3, 3C hcp-Fe2Al
-7.29 -6.91 -6.06 -6.71 -6.99
no yes no yes yes
1.91 2.30 1.79 2.26 1.90
0.64 2.30 0.20 1.99 0.32
0.64 1.74 0.13 2.02 0.58
0.65 2.30 0.20 1.96 0.58
-7.02
yes
1.88
0.40
0.52
0.40
-5.67 -6.51 -6.71
no yes yes
1.79 2.11 1.97
0.20 1.23 1.19
0.20 1.27 1.18
0.20 1.19 -0.08
-6.72
yes
1.97
0.47
0.93
0.93
-6.40
yes
2.00
0.89
0.92
0.86
-6.48
yes
1.88
0.55
0.60
0.51
-6.90
yes
1.78
0.27
-0.08
0.27
-7.12
yes
1.85
0.66
0.67
-0.036
-7.57
yes
2.35
2.45
2.50
2.39
Fe on surface-2 µB
Fe on surface-3 µB
a 〈µB〉 is averaged over all Fe atoms in the slab, and the other magnetic moments correspond to each surface Fe atom. Formation of carbon structures after relaxation means that at least one carbon-carbon bond was formed after relaxation. Structures are shown in Figures 4 and 5, except for the last two structures of 3C atoms and the last two structures of 4 C atoms that are included as Supporting Information (Figure 2S). Table 3S in the Supporting Information lists the magnetic moments of the Al and C atoms.
Figure 6. Interstitial sites underneath the Fe3Al surface: (a) octahedral Fe6; (b) octahedral Fe4Al2; (c) tetrahedral Fe3, Al above; (d) tetrahedral Fe3, Al below; (e) tetrahedral Fe2Al, Fe above; (f) tetrahedral Fe2Al, Fe below.
structures as illustrated in Figure 4 for cases of 2, 3, and 4 atoms on the surface. At higher coverage, increasingly complex carbon networks are formed as illustrated in Figure 5. In the particular case of eight C atoms (2 ML) initially adsorbed on the fcc and hcp surface sites, we observed formation of a graphene-like structure that becomes completely separated from the L12-Fe3Al surface, (Figure 5e and 5f). The separation between the surface and the graphene layer is 4.00 Å; this separation was measured with respect to Fe atoms from the surface, since the Fe and Al atoms in the surface are not totally coplanar, as seen in Figure 5e; the separation distance agrees fairly well with the 3.8 Å calculated for graphene over Co.41 The relaxed Fe-Fe interatomic distances of the surface under graphene (2.58 Å) are longer than those found in a clean surface (2.54 Å), whereas the Fe-Al distances remain 2.60 Å for the clean surface and for the surface under graphene. In addition, the calculated C-C bond length in the surface with graphene is 1.49 Å, which is longer than the C-C bond length of free graphene, 1.43 Å, obtained with the same method/basis set using VASP. These differences between bond lengths are attributed to the mismatch between the lattice constants of the surface and that of graphene. The adsorption
site shown in Figure 5f corresponds to “ring top” with a metal atom in the center of the ring on the subsurface layer. Alternative structures for graphene adsorption have been tested. As found in previous studies for graphene on Ni42 and Co,41 ring-fcc and ring-hcp are stable structures (-7.73 eV); in addition, a graphene plane in the ring-bridge configuration was found adsorbed with identical energy. These three graphene structures were separated by 3.98, 3.99, and 4.02 Å from the metal surface. However, the same three structures were tested at closer distances from the surface, and it was found that another minimum exists at a separation of 2.15 Å for the fcc-ring structure and 2.16 Å for the hcp-ring structure, with adsorption energies of -7.78 eV. The corresponding structures are provided as Supporting Information (Figure 1S). Similar stable structures at closer distances were found by Swart et al. for graphene in ring-fcc, ring-hcp, and ring-bridge configurations interacting with Co(111).41 Although DFT is known to give a poor description of weak dispersion interactions, the C-metal interactions in Figures 4 and 5 do not fall in this category, since they are known to be dominated by electrostatic interactions,43 except the case of graphene formation when the separation distance is on the order of 4 Å (Figure 5e and 5f and Figure 1S).
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TABLE 4: Calculated Absorption Energies (in eV) and Magnetic Moments µB (in Bohr’s magneton per iron atom)a carbon location 1-2 2-3 3-4 1-2 2-3 3-4 1-2 2-3 3-4 2-3 3-4 1-2
layers, layers, layers, layers, layers, layers, layers, layers, layers, layers, layers, layers,
octahedral Fe6 octahedral Fe6 octahedral Fe6 octahedral Fe4Al2 octahedral Fe4Al2 octahedral Fe4Al2 tetrahedral Al above tetrahedral Al above tetrahedral Al above tetrahedral Al below tetrahedral Al below octahedral Fe5Alb
absorption energy (eV) 〈µB〉/(Fe at.) Fe-1 µB Fe-2 µB Fe-3 µB Fe-4 µB Fe-5 µB Fe-6 µB carbon µB -7.80 -7.88 -7.79 -6.77 -6.41 -6.41 -5.59 -3.07 -4.64 -4.60 -4.47 -7.19
2.19 2.18 2.17 2.28 2.25 2.27 2.29 2.24 2.24 2.18 2.27 2.20
2.24 2.53 2.53 2.04 1.85 1.87 1.78 1.61 1.63 1.81 1.63 2.01
1.94 2.42 2.41 2.04 1.85 1.87 1.78 1.62 1.61 1.82 1.66 2.01
2.09 2.47 2.47 1.92 1.89 1.88 1.78 1.60 1.62 1.82 1.61 1.80
1.83 1.81 2.36 1.92 1.89 1.88
1.91 1.86 2.38
1.83
1.83
1.75 1.76 2.35
-0.15 -0.16 -0.16 -0.07 -0.08 -0.08 -0.06 -0.05 -0.06 -0.16 -0.05 -0.12
a 〈µB〉 is an average over all Fe atoms in the slab, and the other values correspond to the Fe and C atoms interacting in a given subsurface site. The magnetic moments of the Al atoms are provided as Supporting Information (Table 4S). b See text and Figure 7 for a description of the subsurface reconstruction.
Figure 7. (a) Top view of the initial carbon location: one carbon atom in the tetrahedral location between the surface and the subsurface with a Fe atom below. (b) Top view of the final carbon location after relaxation: surface reconstruction. (c) The final position of carbon is an octahedral location that does not belong to the L12 crystal structure.
Table 3 shows the adsorption energies of C atoms at increasing coverage. At low coverage, from one to four C atoms, if C atoms do not form structures, the average adsorption energy decreases as more atoms are being added; this is because once one of the most stable sites (hcp-Fe3) is occupied, occupancy of two or three of the neighbor Fe2Al sites can occur without formation of C-C bond; however with weaker adsorption energies. Stronger adsorption energies can be found at constant C coverage when C-C bonds are formed. In the case of 3 C atoms, C-C bond formation can take place under several conditions. For example, if the fcc-Fe3 site is occupied, addition of C to the less stable neighboring fcc Fe2Al sites causes formation of the 3-atom ring structure shown in Figure 4c. Moreover, alternative structures may be formed with two C atoms initially located on the most stable hcp-Fe3 and fcc-Fe3 sites and the third C atom on the less stable fcc-Fe2Al or hcpFe2Al sites. In both cases, the C located on the less stable site moves closer to one of the atoms in a stable site and forms a C-C chain of two atoms while the third atom remains isolated. These structures (short chain + isolated adsorbed atom) are more stable than the ring of 3 atoms. Similarly, a chain of 3 C atoms can be formed, leaving one isolated C atom in one of the stable sites, and these structures are also more stable than the ring of three atoms and the isolated adsorbed C atom shown in Figure 4d and 4e. Images of the adsorbed chains + isolated atoms are reported as Supporting Information (Figure 2S), and adsorption energies and magnetic moments are included in Table 3. For 5 C atoms, we found the structures shown in Figure 5a and 5b, having the weakest adsorption energies, although we do not discard formation of alternative stable configurations at this coverage. When the coverage is higher than 5 atoms, the adsorption energy becomes stronger with increasing coverage, reflecting the strength of the C-C interactions being formed.
C adsorption on the (111) L12 Fe3Al surface has some similarities with that occurring on other metal surfaces. For example, formation of carbon clusters such as C3 rings, short chains, and C4 structures have been reported on Ni (111) surfaces,42 and stable chains have been found on stepped (211) Co surfaces.44 Formation of graphene parallel to the metal surface has also been reported on Ni (111)42 and Co (111)41 and even in stepped Co(211) surfaces where it grows parallel to the (100) plane.44 However, the presence of the Al atoms on the (111) L12 Fe3Al surface imparts special characteristics to the adsorption and absorption processes. For example, there are greater energy differences between the possible adsorption sites, with the 3-fold Fe3 sites being the preferred ones. Also, although surface reconstruction occurs in other metal surfaces such as Ni(111),42 Al atoms are easily displaced by the strong C-Fe interaction as illustrated in Figure 4e. Table 3 also shows that the surface magnetic moment changes under different carbon coverage; in most cases, the moments of the individual Fe atoms are decreased with respect to the slab average, except when the graphene-like layer lifts off the surface as shown in Figure 5. Formation of C structures restores the magnetic moments of the surface Fe atoms to higher values, as a consequence of the reduction on the induced magnetization on the C atom because of the decrease of the C-Fe interactions. This can be clearly observed in the adsorption of 2, 3, and 4 C atoms where if a C network is formed as in Figure 4 the magnetic moments of the surface Fe atoms are only slightly below the slab average, whereas when no C-C bond is formed, the values are much lower than the slab average. In Figure 4d, the only C atom that is not forming C-C bonds has the largest magnetic moment (-0.15 µB). As the number of C bonds on the surface increases, the magnetic moment of the Fe surface atoms becomes further reduced, possibly due to the spin transfer to the C atoms, whose magnetic moment (reported as Supporting Information, Table 3S) is on the order of 0.03 µB/C atom. On the other hand, comparison of the adsorption energies at constant coverage for adsorption of individual atoms vs formation of networks reveals interesting features. For example, for 2C atoms adsorbed, the adsorption becomes weaker when the C-C bond is formed on the surface, whereas the opposite trend is found for the cases of 3 and 4 C atoms adsorbed. A closer look to the spin transfer (Table 3S, Supporting Information) indicates that a weaker adsorption results when the magnetic moments of the adsorbed C atoms forming C-C bonds are of the same sign (ferromagnetic coupling) as those of the Fe atoms, while antiferromagnetic coupling is found in the cases of 3 and 4 adsorbed C atoms forming structures (Figure 4c and 4d).
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TABLE 5: Main Geometric Distances (dij in Angstroms) between Atoms i and j Corresponding to an Octahedral Intersticea octahedral interstitial location
d16
d13
d14
d15
d26
d23
d24
d25
d63
d34
d45
d56
avg
1-2 layers Fe6 2-3 layers Fe6 3-4 layers Fe6 1-2 layers Fe4Al2 2-3 layers Fe4Al2 3-4 layers Fe4Al2 1-2 layers Fe5Al
2.54 2.56 2.59 2.60 2.58 2.58 2.67
2.50 2.60 2.57 2.73 2.56 2.59 3.05
2.50 2.60 2.57 2.73 2.56 2.59 3.05
2.54 2.56 2.59 2.60 2.58 2.58 2.67
2.50 2.60 2.57 2.57 2.59 2.60 2.70
2.60 2.57 2.58 2.58 2.58 2.58 2.65
2.60 2.57 2.58 2.58 2.58 2.58 2.65
2.50 2.60 2.57 2.57 2.59 2.60 2.70
2.50 2.60 2.57 2.50 2.60 2.57 2.70
2.61 2.57 2.58 2.56 2.59 2.58 2.61
2.50 2.60 2.57 2.50 2.60 2.57 2.70
2.54 2.56 2.59 2.62 2.61 2.57 2.69
2.54 2.58 2.58 2.60 2.59 2.58 2.74
a
Atoms labeled as in Figure 8a, 8b, and 8e.
TABLE 6: Main Geometric Distances (dij in Angstroms) between Atoms i and j Corresponding to a Tetrahedral Intersticea tetrahedral interstitial location 1-2 2-3 3-4 1-2 2-3 3-4 a
layers layers layers layers layers layers
Al Al Al Al Al Al
above above above below below below
TABLE 8: Difference (δij in Å) between Distances dij of a Tetrahedral Interstice in a Clean Surface (Table 6) and That with One C Atom Insidea
d12
d13
d14
d23
d34
d42
avg
2.73 2.56 2.58 2.57 2.59 2.60
2.73 2.56 2.58 2.57 2.59 2.60
2.73 2.56 2.58 2.57 2.59 2.60
2.56 2.59 2.58 2.62 2.61 2.57
2.56 2.59 2.58 2.62 2.61 2.57
2.56 2.59 2.58 2.62 2.61 2.57
2.65 2.58 2.58 2.60 2.60 2.59
tetrahedral interstitial location
δ12
δ13
δ14
δ23
δ34
δ42
avg
1-2 2-3 3-4 2-3 3-4
0.78 0.70 0.70 0.68 0.64
0.78 0.70 0.70 0.68 0.64
0.78 0.70 0.70 0.68 0.64
0.06 0.11 0.10 0.10 0.13
0.06 0.11 0.10 0.10 0.13
0.06 0.11 0.10 0.10 0.13
0.42 0.41 0.40 0.39 0.39
a
layers layers layers layers layers
Al Al Al Al Al
above above above below below
The indexes i and j correspond to the labels in Figure 8c.
Atoms labeled as in Figure 8c.
atoms followed by octahedral interstices with C surrounded by four Fe and two Al atoms, whereas tetrahedral interstices with an Al atom above or below the impurity have the weakest absorption energies. The trend in absorption energies follows that found for Fe4C, where the octahedral interstitials were also found to be more stable than the tetrahedral ones.45 For a given subsurface site, the absorption energies vary slightly with the position of the interstice relative to the surface, but more variation is observed in the magnetic moments. The magnetic moments of the Fe atoms in the octahedral Fe6 (Figure 6a) are on average lower than the slab average, and the carbon atom receives an induced magnetization similar to that found for the adsorption of one C atom on fcc and hcp sites (Table 1). As shown in Tables 7 and 8, the Fe-Fe distances are elongated after C insertion in the subsurface, and the expansion is larger when the interstice is located between the first and second layers. Consequently, larger Fe magnetic moments are found as the interstice is located deeper into the inner layers. Compared with the octahedral Fe6 case, the induced magnetization on the C atom is reduced to one-half when C is located in the octahedral site containing 4 Fe and 2 Al atoms (Figure 6b), possibly due to the lowered C-Fe interaction evidenced by the weaker absorption energies. The magnetic moments on the Fe atoms are also slightly lower than those on the Fe6 site. In the tetrahedral site having an Al atom on top (Figure 6c), the C magnetization is comparable to that in the octahedral Fe4Al2, although the adsorption energies of the tetrahedral site are much weaker, and the magnetic moments of the Fe atoms also decrease, due to the much larger expansion of the Fe-Fe distances found in these sites (Table 8). Both tetrahedral sites
Moreover, the isolated carbon atom in Figure 4d has the strongest magnetic moment (-0.15 µB), revealing a strong C-Fe interaction in agreement with the larger adsorption energy compared to the case where no structures are formed. For 5 C atoms adsorbed, the configurations shown in Figure 5 and 5b yield similar magnetization on the carbon atoms and Al atoms; in both cases, four C atoms form a sp3-like structure, where the C atom “on top” exhibits ferromagnetic coupling with the Fe atoms, whereas the other C atoms are antiferromagnetically coupled. 4. Carbon Atoms in the Subsurface 4.1. Absorption. The L12 crystal structure has four interstices in both octahedral and tetrahedral positions between the two layers. Up to eight C atoms per interlayer can be hosted in those subsurface sites. In each of these interstices a C atom was added; after relaxation, the binding energy and the geometrical changes due to the impurity presence were calculated. Figure 6 shows several possible interstitial locations in the L12 crystal structure, and Table 4 displays their respective binding energies and magnetic moments. In octahedral sites only two locations are different from four possible, while all possible tetrahedral locations are different. The C atoms were located between the first and second layers, second and third layers, and third and fourth layers, where the first and second layers are the surface and subsurface and the fifth and sixth layers are the bottom layers of the slab which are fixed representing the bulk. The results in Table 4 show a trend of highest absorption energies in octahedral interstices with C surrounded by six Fe
TABLE 7: Difference (δij in Å) between Distances dij of an Octahedral Interstice in a Clean Surface (Table 5) and That with One C Atom Insidea octahedral interstitial location
δ16
δ13
δ14
δ15
δ26
δ23
δ24
δ25
δ63
δ34
δ45
δ56
avg
1-2 layers Fe6 2-3 layers Fe6 3-4 layers Fe6 1-2 layers Fe4Al2 2-3 layers Fe4Al2 3-4 layers Fe4Al2
0.17 0.15 0.16 0.09 0.21 0.19
0.12 0.11 0.11 0.09 0.11 0.12
0.12 0.11 0.11 0.09 0.11 0.12
0.17 0.15 0.16 0.09 0.21 0.19
0.17 0.15 0.16 0.15 0.10 0.13
0.12 0.11 0.11 0.09 0.11 0.12
0.12 0.11 0.11 0.09 0.11 0.12
0.17 0.15 0.16 0.09 0.21 0.19
0.17 0.15 0.16 0.15 0.10 0.13
0.11 0.11 0.11 0.02 0.03 0.03
0.17 0.15 0.16 0.15 0.10 0.13
0.19 0.11 0.11 0.07 0.02 0.04
0.15 0.13 0.14 0.10 0.12 0.13
a
The indexes i and j correspond to the labels in Figure 8a and 8b.
Absorption in the (111) L12 Fe3Al Surface
J. Phys. Chem. C, Vol. 113, No. 42, 2009 18327
Figure 8. Schematic representation of octahedral and tetrahedral subsurface sites, indicating labeling of the corresponding atoms involved in each site: (a) octahedral Fe6; (b) octahedral Fe4Al2; (c) tetrahedral with an Al atom above or below; (d) tetrahedral with a Fe atom above or below; (e) octahedral Fe5Al found after reconstruction.
Figure 9. Large tetragonal distortion. Table 8 shows the displacements of the Al atom due to the presence of the C atom.
show similar magnetization patterns except for one of the C atoms showing an unusually higher magnetization compared to the other similar sites. We suspect that this is due to a particular configuration where C interacts strongly with its neighbor Fe atoms, but we were not able to confirm this. Moreover, tetrahedral interstices with Fe atoms above or below the impurity (Figure 6e and 6f) were found to be unstable; during relaxation, the C atom spontaneously diffused to an octahedral interstice surrounded by 6 Fe atoms. Two special cases were observed: when a C atom was located in a tetrahedral interstice between the first and the second layers with an Fe atom below the impurity, in the relaxed system the surface layer was displaced, forming a new interstitial location for the impurity which does not correspond to an interstitial location of the L12 crystal structure; the binding energy for this new interstitial location where the C atom is surrounded by 5 Fe and 1 Al atoms is -7.19 eV (Figure 7). In a second special case, when the C atom was located in a tetrahedral position between the first and the second layers with an Al atom below the impurity (Figure 6d), the C atom during relaxation spontaneously diffused toward the surface hcp-Fe3 adsorption site; as shown in the previous section, this hcp-Fe3 location has the strongest adsorption energy. Note that the magnetic moments of this case follow the same pattern as those of the octahedral sites. Previous experimental studies are controversial with respect to the magnetic nature of the single-phase κ-Fe3AlCx alloys. For example, the compound has been reported as ferromagnetic;46 however, other studies indicate that the κ phase is not magnetic.47,48 Our results reveal a clear change of the Fe magnetic moments due to their interaction with C atoms, as evidenced by the variation of magnetic moments depending on the C location on the surface or subsurface (Tables 1, 3, and 4); however, most of the magnetic moments of the surface Fe atoms (Table 3) interacting with adsorbed carbon at high coverage are much lower than those calculated by Maugis et al. for the bulk κ-Fe3AlC phase (1.12 µB/at.Fe),25 whereas higher values are found for the surface Fe atoms interacting with C at low coverage or when C is in the subsurface (at low coverage). We note that the bulk κ-Fe3AlC phase has a larger lattice constant (3.75 Å) than that of the Fe3Al phase (3.65 Å) simulated in this work.
Figure 10. (a) Initial location for diffusion with 1/4 ML total C coverage. (b) Initial location for diffusion with 5/4 ML. The diffusing C atom is in the center of the figure. It is not bonded to any other C atom, and it is in the same location as the C atom with 1/4 ML. (c) Starting location for the chosen diffusion path, fcc-Fe3. The energy barrier for diffusion is related to the size of the hollow site.
4.2. Surface Deformation. In order to estimate the deformation caused by the presence of C in the subsurface, the main geometrical distances of octahedral and tetrahedral sites were measured before and after the impurity addition and then compared. Tables 5 and 6 show the interstitial side distances represented in Figure 8 when the subsurfaces do not haVe carbon impurities. It is observed that between the first and the second layers the octahedral interstice surrounded by six Fe atoms has shorter side distances than those of an octahedral interstice surrounded by four Fe and two Al, due to the elongated Fe-Al distances. In other interlayers the differences of interstitial side distances between the two octahedral sites are less pronounced. A similar observation is found in the tetrahedral site when Al is on the surface. Tables 7 and 8 show the differences of side distances of interstices caused by C addition. It can be concluded that addition of carbon impurity in tetrahedral interstices causes higher structural deformation than that produced when carbon is absorbed in the most stable octahedral interstices. A lattice expansion is expected upon carburization of the L12 Fe3Al in agreement with the larger lattice constant calculated for the bulk stoichiometric κ-Fe3AlC phase.25 Table 8 shows large differences in characteristic distances between a clean surface and that with one C atom in the subsurface, located in tetrahedral interstitial locations (Figure 9); these large differences are produced by displacements of Al atoms in the z direction due to the C atom presence; similar large tetragonal distortions which may play an important role in the mechanical and physical properties of these materials have been reported experimentally and theoretically.45,49,50 5. Diffusion Process On the basis of the adsorption and absorption studies a possible path of C surface penetration into the subsurface was chosen. Among the three stable adsorption locations, fcc-Fe3, hcp-Fe3, and top-Al, the fcc-Fe3 hollow site is the best candidate as the initial location for C diffusion, since an octahedral interstice composed of six Fe atoms is located right underneath
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Ramı´rez-Caballero et al.
Figure 11. Minimum-energy path for carbon surface penetration in the L12-Fe3Al surface with 0.25 ML of carbon coverage. The pictures correspond to the initial state, transition state, and final state during the diffusion process. The reaction coordinate follows successive images from the starting to the end point along the reaction path and could be expressed as a combination of distances between the migrating C and its closest Fe atoms. Note the strong surface reconstruction; additional images are provided as Supporting Information (Figure 3S).
Figure 12. Minimum-energy pathway for carbon migration into the subsurface in the L12-Fe3Al surface with 1.25 ML of surface carbon coverage. The pictures correspond to the initial state, transition state, and final state during the diffusion process. The reaction coordinate follows successive images from the starting to the end point along the reaction path, being a combination of geometrical changes dominated by the distances between the migrating carbon atom and its closest Fe atoms.
the fcc site and there is a favorable difference of the binding energy between the adsorbed and the absorbed location for diffusion, -7.23 and -7.45 eV, respectively. In contrast, the top-Al site is not a feasible initial location, and the hcp-Fe3 hollow site has an unstable tetrahedral location underneath (first to second layers, with Al below). As described in the previous section, a C atom located in this interstice during relaxation spontaneously diffused outside the surface to the hcp-Fe3 adsorbed location. It is clear that the diffusion energy barrier for the chosen surface-subsurface migration path would depend on the size of the space defined by the three Fe atoms of the fcc hollow site. It was observed that this size is affected by carbon coverage on the surface; the presence of other C atoms on the surface
may cause surface stress and affect interatomic distances on the surface layer; therefore, higher surface carbon coverage may favor carbon migration into the subsurface. In order to prove this statement, a diffusion process was simulated using nudged elastic band techniques for two cases: with the same initial and final path locations but under different C coverage. The first case has one C atom, which is the atom that penetrates into the subsurface (Figure 10a); the second case has four additional C atoms adsorbed on the surface (Figure 10b). Figure 11 shows the calculated minimum-energy path (MEP) of carbon migration from the surface into the subsurface for the system with a carbon coverage of 0.25 ML; the diffusion barrier is 0.99 eV. All images of the calculated diffusion pathways are provided as Supporting Information (Figure 3S).
Absorption in the (111) L12 Fe3Al Surface
J. Phys. Chem. C, Vol. 113, No. 42, 2009 18329 6. Conclusions
Figure 13. Transition-state structures found during calculation of the minimum-energy path for carbon surface penetration in the L12-Fe3Al surface: (a) with 0.25 ML of carbon coverage; (b) with 1.25 ML of carbon coverage. Table 9 displays the geometry of the transition-state structures; bond distances in Angstroms and angles in degrees.
TABLE 9: Geometric Distances between i and j Atoms (dij in Angstroms) in the Hollow Site That the C Atom Crosses during Diffusion, and Surface-Subsurface Distance (in Angstroms)a total C coverage
d12
d23
d31
d14
d24
d34
0.25 ML 2.63 2.63 2.63 1.81 1.81 1.81 1.25 ML 2.71 2.71 2.71 1.76 1.76 176 a
surface-subsurface distance 2.08 2.06
Atom labels are given in Figure 10c.
From Figure 11 it is observed that the carbon atom initially located in a hollow site moves in the direction of one of the Fe-Fe bridge sites, causing the rupture of that bond and forming a linear Fe-C-Fe chain as seen in the transition state. In the next steps the C atom gradually moves down toward the interstitial site, while the surface atoms tend to reaccommodate close to their initial locations. Similar diffusion barriers have been reported also for C diffusion in Fe-containing systems different than the L12-Fe3Al surface: A similar diffusion barrier of 0.99 eV was reported for the diffusion of diluted carbon in an fcc Fe bulk system;24 this agreement of diffusion barriers may reflect the fact that the carbon diffusion process occurred, always having Fe atoms as nearest neighbors. However, this MEP is not symmetrical, and the C atom breaks symmetry during the diffusion path. Experimental measurements of carbon diffusion in ferrite in the temperature range of 238-473 K reported a diffusion barrier of 0.87 eV,51 and in austenite with 0.1 wt % concentration of carbon a diffusion barrier of 1.60 eV was reported.52,53 We note that the magnitude of the energy barrier is also influenced by the energy cost of the strong surface reconstruction. On the other hand, when the carbon coverage increases to 1.25 ML the diffusion barrier decreases to 0.33 eV, and it was observed that the carbon atom penetrates the surface through the hollow site following an almost linear diffusion path; these results confirm that the presence of more carbons adsorbed on the surface produce a surface deformation, facilitating the path of carbon penetration lowering the diffusion barriers. Figure 12 shows the minimum-energy path of this process and also the structures of the initial state, transition state, and final state. Figure 13 shows the transition-state structures for both diffusion processes; the transition-state structure of the system with 0.25 ML of carbon coverage has the carbon nearly perfectly collinear between Fe1 and Fe2, whereas for the system with 1.25 ML carbon coverage, the carbon atom is coplanar with Fe1, Fe2, and Fe3.
Examination of possible mechanisms of incorporation of C atoms to a L12 Fe3Al surface reveals surface reconstruction effects when carbon atoms are adsorbed on the surface due to their strong affinity to Fe atoms and to formation of highly interconnected carbon networks. At higher C coverage, graphene sheets grow parallel to the (111) surface, causing surface reconstruction with elongated Fe-Fe distances and C-C distances in the graphene structure longer than those of isolated graphene due to the mismatch between the geometries of graphene and the metal surface. Various alternative configurations of graphene are found, the most stable being the ring-fcc and ring-hcp, in agreement with those found on Co and Ni surfaces. Carbon is also very stable when absorbed into the subsurface, especially in the octahedral sites where a C atom is surrounded by six iron atoms. The diffusion from the surface to the subsurface has a barrier of 0.99 eV at 0.25 ML of C but is reduced to 0.33 eV when the coverage increases to 1.25 ML. Previous experimental studies are controversial with respect to the magnetic nature of the single-phase κ-Fe3AlCx alloys. Therefore, it is important to investigate how the presence of C atoms modifies the magnetic properties of the Fe atoms. In this work, we follow the variation of the magnetic moments of Fe atoms and those induced on the C atoms as the carburization process takes place. The calculated magnetic moments of the carburized surface are reduced with respect to that of L12 Fe3Al, and they are found to be dependent on the specific location of the carbon atoms on the surface; however, they are still higher on average than the values calculated for the bulk stoichiometric κ-Fe3AlC phase, which has a larger lattice constant than the L12 Fe3Al phase.25 When C adsorbs on the surface without forming C-C bonds, there is an induced magnetic moment on the carbon atoms that couple antiferromagnetically to the surface iron atoms, resulting in high adsorption energies; similarly, when C-C networks are formed, if carbon is antiferromagnetically coupled to iron the adsorption energies are stronger than in cases where a ferromagnetic coupling is found. The local magnetic moments per C atom decrease as the number of C-C interactions increase and become negligible when a graphene surface is formed and separates from the metal surface. A lattice expansion is found after carburization, which is significant when C occupies the subsurface tetrahedral sites, but it is much smaller when the carbon atoms are located in the most stable subsurface octahedral sites. The stoichiometric κ-Fe3AlC phase has never been found experimentally, and it is speculated that the Fe/Al ratio is different than 3:1; in addition, there could be other defects such as the existence of “antisites” where Al and Fe sites are exchanged. All of these variations may influence the physical and chemical properties of the carburized phase. Our study provides initial insights about the effects of carbon on the L12 Fe3Al phase, which is closest in structure to the perovskite κ-Fe3AlC phase. Further experimental and theoretical studies are needed to clarify the nature of the nonstoichiometric κ-Fe4-yAlyCx phases. Supporting Information Available: Images and equilibrium distances of graphene structures ring-fcc, ring-hcp, and ringbridge at two different distances from the surface; alternative structures for clusters of 3C and 4C atoms adsorbed in p(2 × 2) cells listed in Table 3 but not shown in Figures 4 and 5; magnetic moments of C and Al atoms corresponding to all the adsorption structures included in Table 3; magnetic moments of Al atoms involved in subsurface absorption sites; intermediate images of the diffusion pathways discussed in the text and
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Figures 11 and 12. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgment. This work was partially supported by the U.S. Department of Energy, under grant DE- FG02-06ER15836, and by Secretarı´a de Ciencia y Tecnologı´a del Gobierno Argentino, under grant BID 1728/OC-AR, PICT No 38240 (program 2007-2009), and the UNSAM, under grant 28/C046 (program 2007/2008). Computational resources from the TAMU Supercomputer Facility and the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC03-76SF00098, are gratefully acknowledged. References and Notes (1) Krein, R.; Schneider, A.; Sauthoff, G.; Frommeyer, G. Microstructure and mechanical properties of Fe3Al-based alloys with strengthening boride precipitates. Intermetallics 2007, 15, 1172. (2) Sykes, C.; Bampfylde, J. W. The physical properties of ironaluminum alloys. J. Iron Steel Inst. 1934, 130, 389. (3) DeVan, J. H.; Tortorelli, P. F. The oxidation sulfidation behavior of iron-alloys containing 16-40 AT-degrees Aluminum. Corros. Sci. 1993, 35, 1065. (4) Tortorelli, P. F.; DeVan, J. H. In Processing, properties, and applications of iron aluminides; Schneibel, J. H., Crimp, M. A., Eds.; TMS: Warrendale, PA, 1994; p 257. (5) Garima Sharma; Limaye, P. K.; Ramanujan, R. V.; Sundararaman, M.; Prabhu, N. Dry-sliding wear studies of Fe3Al-ordered intermetallic alloy. Mater. Sci. Eng., A 2004, 386, 408. (6) Falat, L.; Schneider, A.; Sauthoff, G.; Frommeyer, G. Mechanical properties of Fe-Al-M-C (M ) Ti, V, Nb, Ta) alloys with strengthening carbides and Laves phase. Intermetallics 2005, 13, 1256. (7) Schneider, A.; Zhang, J. Metal dusting of ferritic Fe-Al-M-C (M ) Ti, V, Nb, Ta) alloys in CO-H2-H2O gas mixtures at 650 °C. Mater. Corros. 2003, 54, 778. (8) Grabke, H. J. Thermodynamics, mechanisms and kinetics of metal dusting. Mater. Corros. 1998, 49, 303. (9) Chiou, W. C.; Carter, E. A. Structure and stability of Fe3Ccementite surfaces from first principles. Surf. Sci. 2003, 530, 88. (10) Chun, C. M.; Mumford, J. D.; Ramanarayanan, T. A. Mechanisms of metal dusting corrosion of iron. J. Electrochem. Soc. 2002, 149, B348. (11) Palm, M. Concepts derived from phase diagram studies for the strengthening of Fe-Al-based alloys. Intermetallics 2005, 13, 1286. (12) McKamey, C. G.; Devan, J. H.; Tortorelli, P. F.; Sikka, V. K. A Review of Recent Developments in Fe3al-Based Alloys. J. Mater. Res. 1991, 6, 1779. (13) Stoloff, N. S. Iron aluminides: present status and future prospects. Mater. Sci. Eng., A: Struct. Mater. Prop. Microstruct. Process. 1998, 258, 1. (14) Baligidad, R. G.; Radhakrishna, A.; Datta, A.; Rao, V. V. R. Effect of molybdenum addition on structure and properties of high carbon Fe3Al based intermetallic alloy. Mater. Sci. Eng., A: Struct. Mater. Prop. Microstruct. Process. 2001, 313, 117. (15) Garima Sharma; Kishore, R.; Sundararaman, M.; Ramanujan, R. V. Superplastic deformation studies in Fe-28Al-3Cr intermetallic alloy. Mater. Sci. Eng., A 2006, 419, 144. (16) Zhu, S. M.; Guan, X. S.; Shibata, K.; Iwasaki, K. Microstructure and mechanical and tribological properties of high carbon Fe3Al and FeAl intermetallic alloys. Mater. Trans. 2002, 43, 36. (17) Palm, M.; Inden, G. Experimental-Determination of PhaseEquilibria in the Fe-Al-C System. Intermetallics 1995, 3, 443. (18) Baligidad, R. G.; Radhakrishna, A. Effect of carbon content on elevated temperature stability and tensile properties of Fe-8.5 Al Alloys. Mater. Sci. Eng., A 2000, 281, 143. (19) Sanders, W.; Sauthoff, G. Deformation behaviour of perovskitetype phases in the system Fe-Ni-Al-C 0.2. Deformation behaviour of a two phase Fe3AlCO0.45 alloy. Intermetallics 1997, 5, 377. (20) Sanders, W.; Sauthoff, G. Deformation behaviour of perovskitetype phases in the system Fe-Ni-Al-C 0.1. Strength and ductility of Ni3AlCx and Fe3AlCx alloys with various microstructures. Intermetallics 1997, 5, 361. (21) Schneider, A.; Zhang, J. Orientation relationship between a ferritic matrix and kappa-phase (Fe3AlCx) precipitates formed during metal dusting of Fe-15Al. Intermetallics 2005, 13, 1332. (22) Connetable, D.; Maugis, P. First principle calculations of the K-Fe3AlC perovskite and iron-aluminium intermetallics. Intermetallics 2008, 16, 345.
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