Initial-Stage Oxidation of Ni 3 Al(100) and -(110) from Ab Initio Thermodynamics

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1 ubs.acs.org/jpcc Initial-Stage Oxiation of 3 (100) an -(110) from Ab Initio Thermoynamics Likun Wang, Canying Cai, Yichun Zhou,*,, an Guangwen Zhou*, Hunan Provincial Key laboratory of Thin Film Materials an Devices, School of Materials Science an Engineering, Xiangtan University, Hunan , China Key Laboratory of Key Film Materials & ication for Equiment of Hunan Province, Xiangtan University, Hunan , China Deartment of Mechanical Engineering & Materials Science an Engineering Program, State University of New York at Binghamton, Binghamton, New York 13902, Unite States ABSTRACT: The microscoic mechanisms of the initial-stage oxiation of the 3 (100) an 3 (110) surfaces are comaratively stuie using ab initio calculations base on ensity-functional theory an thermoynamics consierations. The surface energies of the two surfaces as functions of aluminum an oxygen chemical otentials are constructe an show that the formation of any antisite efects is not favorable at the 3 (100) surface, whereas antisite efects are favorable at the 3 (110) surface. The surface hase iagrams of the 3 (100) an -(110) surfaces with ifferent antisite efects an at the various oxygen coverages are etermine. These results show that oxygen asortion enhances surface segregation at the initial stage of oxiation for both surfaces an that the 3 (100) surface is thermoynamically more favore to oxiize comletely at a lower oxygen coverage than the 3 (110) surface. 1. INTRODUCTION -base sueralloys are a class of technologically imortant intermetallic materials that rocess a high melting oint, low ensity, goo oxiation an corrosion resistance, an metal-like electrical an thermal conuctivities. 1,2 The unique combination of these roerties makes the -base alloys the material of choice for high-temerature alications, incluing chemical rocessing, ower generation, an aerosace roulsion. For instance, the volume fraction of the 3 is aroun 70% for the blaes an vanes of moern gas turbines as the reciitation strengthener an antioxiation hase in sueralloys. However, the surfaces of all -base alloys show strong chemical reactivity towar oxygen, an their ractical alications at elevate temeratures are still hinere by the cometitive oxiation of an that can revent the formation of a ense an rotective α- 2 O 3 layer. 3 The growth of a rotective aluminum oxie layer eens on the local reactivities of the alloy, which een on a number of convolute factors, incluing temerature, oxygen ressure, surface structure, an comosition. As a rototye of multicomonent surfaces, (100) an -(110) have been stuie extensively, 4 9 both exerimentally an theoretically, to unerstan the atomistic mechanism of the surface-oxiation-inuce 2 O 3 formation. Recently, the aluminum oxie film growth on (100) has been shown to rocee via the surface iffusion of atoms etache from substrate stes, 4 whereas the 2 O 3 growth on (110) involves the articiation of atoms sulie from the bulk, 5,6 emonstrating the strong eenence of the oxiation mechanism on the surface structure an crystallograhy orientation. On the theoretical sie, ensity-functional theory (DFT) calculations have been emloye to stuy oxygen asortion at the (100) 4 an (110) 7,8 surfaces an the reaction barriers of the initial stages of oxiation base on the electronic structure, atomic geometry, an energetic roerties. Furthermore, Liu et al. reorte their ab initio thermoynamics calculations for the oxiation mechanism of the intermetallic Ti 3 comoun, a relevant high-temerature alloy system. 10 By contrast, the theoretical stuy on the similarly imortant system of the intermetallic 3 comoun is much less with regar to its atomic-scale oxiation mechanism. Comare to the alloy, the 3 may be less oxiation resistant because it contains less an thus has a larger tenency to form less rotective multile oxies (e.g., 2 O 3, O) that involve the reistribution an segregation of an atoms in the substrate. While the classical Wagner s oxiation theory 11 rovies a general escrition of the oxiation behavior of binary alloys from a macroscoic oint of view that stiulates the correlation of the oxie formation with alloy comosition an activities of the metal an oxygen, the microscoic rocess initiating the selective oxiation of one comonent, commonly observe in most metal alloys exose to an oxiizing environment, still remains elusive. In the resent work, we reort a comarative stuy of DFT an the first-rinciles thermoynamics investigations of asortion of oxygen atoms at the 3 (100) an -(110) surfaces. Our aims are to fin Receive: May 15, 2017 Revise: August 14, 2017 Publishe: August 18, American Chemical Society 19191

2 The Journal of Physical Chemistry C Figure 1. Schematic to view of the 3 (100) an -(110) surfaces with ossible antisite efects for five cases: (a, f) the erfect surface, (b, g) the surface with one antisite efect [enote by 3 (100)-1, 3 (110)-1], (c, h) the surface with two antisite efects [enote by 3 (100)-2, 3 (110)-2], (, i) the surface with one antisite efect [enote by 3 (100)-1, 3 (110)-1], an (e, j) the surface with two antisite efects [enote by 3 (100)-2, 3 (110)-2]. Blue an ink sheres reresent an atoms in the surface layer, resectively. Light blue sheres reresent atoms in the secon (subsurface) layer. active surface sites for the asortion of oxygen an their eenence on the crystallograhic orientation for the selective oxiation of atoms, as well as to ientify the relative stability of the oxygenate surfaces as a function of the chemical otential of an O, from which we rovie a clear atomistic mechanism for the initial-stage oxiation of the 3 surfaces. 2. COMPUTATION METHODS 2.1. DFT Calculations. The ab initio calculations are base on DFT 12,13 an erforme with the VASP coe using rojector augmente wave (PAW) 17,18 otentials in conjunction with a lane-wave cut-off energy of 500 ev an PW91 generalize graient aroximation (GGA). 19 Electron smearing is carrie out following the Methfessel Paxton technique 20 with orer N = 1 an with of the smearing σ = 0.2. Self-consistent solutions are obtaine by emloying the (4 4 1) Monkhorst Pack 21 mesh in the Brillouin zone for the (2 2) surface unit cell. 3 has an orere cubic (L1 2 ) structure with the sace grou Pm3 m. Our calculate bulk lattice constant obtaine from the energy minimization of the bulk 3 unit cell using a Monkhorst Pack mesh of ( ) is Å, which is in goo agreement with the exerimental value of 3.57 Å 22 an with revious calculations. 23 The 3 (100) an -(110) surfaces are constructe by cleaving suercells mae from the bulk 3. Successive slabs with the (2 2) surface unit cell an five atomic layers are searate by a vacuum region of 15 Å. The atoms in the two bottom layers of the slab are fixe, while the to three layers of the slab are allowe to relax until the forces on each of them are less than 0.01 ev/å. The surface areas of the (2 2) surface unit cell are Å 2 for the 3 (100) surface an Å 2 for the 3 (110) surface, resectively. This means that the 3 (100) surface is more closely acke than the 3 (110) surface. To verify our values, we also relax the 3 (100) an 3 (110) slabs an comare the results with the reviously reorte calculate results. 23,24 The interlayer searation is measure by the ercentage of changes in relaxe istances an original istances. For the 3 (100) slab, our results show that after structural relaxation, the sacing change between the first an secon layers is 3.027% an that between the first an secon layers is 2.130%, which are similar to the reviously calculate values of 2.859% an 2.466%, 24 while slightly ifferent from the exerimental value of 2.809% for the first an secon layers an a larger ifference from the exerimental value of 1.124% for the first an secon layers. 25 For the 3 (110) slab, our results show that after structural relaxation, the sacing change between the first an secon layers is % an brween the first an secon layers is 9.992%, which are similar to the reviously calculate values of % an 9.618%, 23 with a slight ifference from the exerimental values of % an %. 26 The ercentage ifferences between the calculate an exerimental values are robably ue to the limite layers involve in the DFT calculations First-Princiles Atomistic Thermoynamics Calculations. We emloy a first-rinciles atomistic thermoynamic framework to assess the relative stability of the consiere surfaces as a function of the chemical otential of an O. The thermoynamic stability of a secifie surface eens on its surface energy. The following formulations emloye in our calculations are base on other works. 10,27 33 The surface energy (σ) can be calculate as 1 σ = ( S E N E N E N E 3 O O ) (1) where S is the surface area an E 3 is the total energy of the slab. E, E, an E O enote the chemical otential of,, an O, resectively. The number of,, an O atoms in the system is enote by N, N, an N O, resectively. We efine the relative surface energy (σ r ) of the 3 slab with the resence of antisite efects relative to that of the erfect 3 slab as σ = ( σ σ ) S r 3 3 = E E ( N N ) E ( N N ) E where σ is the surface energy of 3 slab without any antisite efects [shown in Figure 1a,f an efine as the erfect 3 (100) an -(110)]. σ is the surface energy of 3 slab with antisite efects but without oxygen atoms (any of the configurations shown in Figure 1b e,g j). E 3 an E 3 (2) 19192

3 The Journal of Physical Chemistry C enote the total energy of the erfect 3 slab an the configuration with antisite efects; N an N Ai enote, resectively, the number of an atoms in the erfect 3 slab. N an N Ai enote, resectively, the numbers of an atoms in the 3 slab with antisite efects. Figure 2 shows all ossible asortion sites for oxygen atoms on the erfect 3 (100) an 3 (110) surfaces: four on-to Figure 2. Schematic to view of the ossible asortion sites for O on (a) (100) an (b) (110) surfaces of 3. Re sheres reresent O atoms in the surface layer. Blue an ink sheres reresent an atoms in the surface layer, resectively. Light blue sheres reresent atoms in the secon (subsurface) layer. (O) sites, such as the on-to an on-to sites (labele as T1 T4); four 4-fol 2 2 hollow sites (labele as H1 H4); an eight brige sites incluing short-brige sites in the 3 (100) an an long-brige sites in 3 (110) (labele as B1 B8). For the 3 surfaces with antisite efects shown in Figure 1b e,g j, they have the same tyes of asortion sites as shown in Figure 2, soitisnot necessary to islay them here. In this work, the surface configurations with an without antisite efects are investigate sequentially uner ifferent oxygen coverages, an the most energetically stable surface configuration from the low oxygen coverage is subsequently use as a starting structure to etermine the next stable configuration from the higher oxygen coverage. The relative stability of the various O/ 3 (100) an O/ 3 (110) surfaces is analyze by calculating the average bining energy er oxygen atom. Here, we efine the oxygen coverage θ as the ratio of the number of the oxygen atoms to that of the atoms in the substrate surface layer. The unit of the oxygen coverage is monolayer (ML), an 1 ML is efine as four absorbe oxygen atoms er (2 2) surface cell. The average oxygen bining energy of the surface as a function of the oxygen coverage θ is calculate as 1 E( θ ) = { + N E [ E ( N N O/ E 3 3 ) O + ( N N ) E + N E ]} O O where E O/3 is the total energy of the O-asorbe 3 slab. Note that the oxygen bining energy efine by eq 3 inclues the change of the surface free energy when a surface antisite efect is involve. The surface hase iagrams of the 3 (100) an 3 (110) surfaces are esigne by the surface energy σ = E E ( N N ) E r O O/3 3 ( N N ) E N E O O Generally, the chemical otential of a secifie secies is equal at equilibrium in all contact hases, i.e., 3 alloys an molecular O 2. However, these chemical otentials are not simly the total energies of a certain atom or molecule. In orer to avoi the formation of metallic an hases, the chemical otentials of an must follow E E bulk an E E bulk. We articularly suose that the chemical otential of a secifie secies in the 3 surface is equal to that in bulk 3 ; the relation equation follows as 3E + E = E bulk 3. Thus, bulk the chemical otential of satisfies the constraint E E 3 3E. The chemical otential of O is allowe to vary with an uer limit etermine by the O 2 molecule, which is E O 1 E 2 O 2. Combing the results from our ab initio calculations for bulk 3, bulk, bulk, an molecular O 2, the ranges of the chemical otentials are etermine from our calculations to be ev < E < ev an ev < E O < 4.89 ev. (3) (4) Figure 3. Calculate surface energies of clean 3 (100) (a) an -(110) (b) with ifferent surface efects as functions of the chemical otential of

4 The Journal of Physical Chemistry C 3. RESULTS 3.1. Clean Surfaces of 3 (100) an 3 (110). We first investigate the relative stability of various atomic configurations of the clean 3 (100) surfaces (before oxygen asortion). Here, we consier the cases of the erfect surface without antisite efects [Figure 1a, referre to as 3 (100)] an surfaces with one an two antisite efects [Figure 1b,c, enote 3 (100)-1, 3 (100)-2] an one or two antisite efects [Figure 1,e, enote 3 (100)-1, 3 - (100)-2]. It shoul be note that the tomost surface layer of either 3 (100)-2 or 3 (100)-2 is comose of all atoms or all atoms. The calculate relative surface energies of the erfect surface an four 3 (100) surfaces with ifferent surface antisite efects (Figure 2a e) as the functions of E are shown in Figure 3a. We can observe that the erfect 3 (100) surface always has a lower surface energy than other surface configurations with the antisite efects. This fact inicates that the erfect 3 (100) surface is thermoynamically stable all the time before oxygen asortion. We then investigate the relative stability of the various atomic configurations of the clean 3 (110) surfaces. Here, we consier similarly the cases of the erfect surface without antisite efects [Figure 1f, referre to as 3 (110)] an surfaces with one an two antisite efects [Figure 1g,h, enote 3 (110)-1, 3 (110)-2] an one or two antisite efects [Figure 1i,j, enote 3 (110)-1, 3 - (110)-2]. The tomost surface layer of either 3 (110)- 2 or 3 (110)-2 is comose of all atoms or all atoms. The calculate relative surface energies of the erfect 3 (110) surface an four surfaces with the ifferent surface antisite efects (Figure 1g j) as the functions of E are shown in Figure 3b. We can observe that the 3 (110)-1 an 3 (110)-2 surfaces always have a higher surface energy than the erfect 3 (110) surface. This fact inicates that the segregation of atoms to the surface layer is thermoynamically unfavorable. On the other han, each of the other three surfaces [ 3 (110), 3 (110)-1, an 3 (110)-2] coul reresent the most stable configuration in some articular range of the chemical otential, which inicates that atoms ossibly segregate to the surface from the bulk naturally. In articular, the erfect 3 (110) surface is the lowest over the ominant range of the chemical otential of. At the slightly greater chemical otential, the 3 (110) surface with one antisite [ 3 (110)-1] is the most stable, suggesting that atoms can segregate to the surface layer of the substrate uner the -rich conition. Aitionally, the surface energy of the 3 (110)-2 has the lowest energy at very high chemical otential, that is, uner the extremely rich conition Asortion of Oxygen. The ossible oxygen asortion sites on the erfect 3 (100) an -(110) surfaces are shown in Figure 2. The 3 (100) an -(110) surfaces with antisite efects (as shown in Figure 1) have the same tye of surface sites for oxygen asortion as shown in Figure 2a,b, which are thus not islaye here. The number of calculate ossible oxygen asortion sites is significantly reuce by consiering the rotational an mirror symmetries of the system. Figure 4 shows the calculate average oxygen bining energies er oxygen atom as a function of the oxygen coverage for the most stable configuration of oxygen on the erfect 3 (100), 3 (100)-1, 3 (100)-2, 3 (100)-1, an 3 - Figure 4. Calculate bining energy er oxygen atom at the most stable asortion site as a function of the oxygen coverage for the O/ 3 (100), O/ 3 (100)-1, O/ 3 (100)-2, O/ 3 (100)- 1, an O/ 3 (100)-2 an O/ 3 (110), O/ 3 (110)-1, O/ 3 (110)-2, O/ 3 (110)-1, an O/ 3 (110)-2 surfaces. (100)-2 an the erfect 3 (110), 3 (110)-1, 3 (110)-2, 3 (110)-1, an 3 (110)-2. The bining energies for the oxygen with the ifferent antisite efects at the to layer of the 3 (100) an 3 (110) surfaces are always higher than that of the erfect 3 surfaces an the 3 surfaces with antisite efects, which means that the 3 (100) an 3 (110) surfaces with the ifferent antisite efects are unstable in the rocess of oxiation. The lowest oxygen bining energies for the 3 (100) surfaces coul be for the 3 (100)-1 or 3 (100)-2 surface in ifferent situations. Secifically, at the beginning oxygen coverage (0.25 ML), the bining energy of oxygen with the 3 (100)-1 surface is lower than that of the 3 (100)-2 surface. At the oxygen coverage of 0.5 ML, the oxygen bining energy for the 3 (100)-2 surface surasses that the 3 (100)-1 surface slightly. With increasing the oxygen coverage to 0.75 ML an then to 1 ML, the bining energy for the 3 (100)-2 suface becomes the lowest, an the ifference in the values of the bining energies of those two surfaces increases. As iscusse in section 3.1, the erfect 3 (100) surface reresents the most stable configuration among the clean surfaces with an without antisite efects, while in the rocess of oxiation the 3 (100) surfaces with ifferent antisite efects become 19194

5 The Journal of Physical Chemistry C Figure 5. Calculate three-imensional surface hase iagrams (a, b) an the corresoning two-imensional surface hase iagrams (c, ) at the ifferent surfaces of 3(100) an 3(110) as functions of E an EO. Each lane corresons to one of the teste surface configurations, an only the most stable configurations are consiere. 3(100) an 3(110) surfaces in the three-imensional surface hase iagram onto the two-imensional lane, we can obtain the corresoning two-imensional surface hase iagrams, which are shown in arts c an of Figure 5, resectively. For the 3(100) surface, we can observe that uner the O-oor conition, the erfect 3(100) is the most stable one. As the oxygen content increases, the 4O/3(100)-2 surface (corresoning to the O coverage of 1 ML) is the most stable configuration, which occuies the most art of the chemical otential sace. This suggests that O inuces the comlete surface segregation. Note that uner the O-rich conition, both 4O/3(100)-2 an 4O/3(100)-1 surfaces can be the most stable configuration, eening on the range of the chemical otential. The 4O/3(100)-1 configuration becomes the referre one when is almost oxiize in the area. Since the sace occuie by the 4O/ 3(100)-2 configuration (uner the O-rich conition) is much larger than that by the 4O/3(100)-1 configuration, the former is thermoynamically more favorable, imlying that all the atoms can be totally oxiize uring the oxiation rocess. the more stable configuration. The calculation results show that the asortion of oxygen can enhance the surface segregation of, resulting in the formation of the to surface layer with all the atoms. For 3(110), the oxygen bining energies for the 3(100)-2 surface are always the lowest. While the erfect 3(110) surface reresents the most stable configuration among the clean surfaces over the ominant chemical otentials, asortion of oxygen also enhances the surface segregation of, the same as for the 3(100) surfaces. Those results are similar to the surface segregation of boron uon hyrogen asortion on the Si(111) B surface.34, Surface Phase Diagram. In orer to further unerstan the oxiation characteristics of the 3 surfaces from the thermoynamics oint of view, we construct threeimensional surface hase iagrams of relative surface energies as functions of the chemical otentials of both E an EO for oxygen asortion on the ifferent 3(100) an 3(110) surfaces, as shown in arts a an b of Figure 5, resectively. Three imensional surface iagrams were reviously use to eluciate the oxiation mechanism of other similar systems.36,37 Projecting the lowest surface free energies of the ifferent 19195

6 The Journal of Physical Chemistry C Figure 6. Schematic sie views of the atomic structure of 1O/3(100)-1 (a), 2O/3(100)-2 (b), 3O/3(100)-2 (c), an 4O/ 3(100)-2 (), an 1O/3(110)-2 (e), 2O/3(110)-2 (f), 3O/3(110)-2 (g), an 4O/3(110)-2 (h). Re, blue, an ink/yellow sheres reresent O,, an atoms, resectively. 96.1, resectively. By contrast, the oxygen asortion on the 3(110) surface occurs referentially at the B1 site at the coverage of 0.25 ML with the most favorable configuration of 1O/3(110)-2. Figure 6e shows the fully relaxe structure with the asortion of the oxygen atom at the B1 site, where the oxygen atom bons with two neighboring atoms. The asortion of the first O atom causes the slight lateral relaxation of atoms in 1O/3(100)-1, while there are no obvious lateral or vertical shifts of the atoms in 1O/3(110)-2. For the next oxygen coverage (0.5 ML), the newly absorbe oxygen atom for the (100) surface stays referentially at the H4 site an the resulting most favorable configuration of 2O/ 3(100)-2 is shown in Figure 6b. It is interesting to note that the 2O/3(100)-1 is not the most favorable configuration. The asortion of two O atoms also causes the slight lateral relaxation of atoms in 2O/3(100)-2. For the (110) surface, the newly absorbe surface oxygen atom stays referentially at the B6 site, an the resulting most favorable configuration of 2O/3(110)-2 is shown in Figure 6f. It can be note from Figure 6f that the ositions of atoms in the fully relaxe structure of 2O/3(110)-2 change areciably, in which two of the atoms (labele as yellow atoms in Figure 6f) eviate from their original lateral ositions by nearly a quarter of the lattice constant an move uwar slightly, an the newly absorbe oxygen atom leas to a minor exansion of the to layer by 5.6% comare with the erfect 3(110). At the oxygen coverage of 0.75 ML, the newly asorbe oxygen on the (100) surface stays referentially at the B2 site in a tetraheral fashion. Figure 6c illustrates the fully relaxe structure of the resulting 3O/3(100)-2 configuration, which shows the lateral islacement of two atoms (labele as yellow atoms in Figure 6c) by nearly a quarter of the lattice constant. More imortantly, the oxygen atom that initially resies at H4 moves to B6 after the structure relaxation, resulting in 3.7% uwar movement of the to layer comare with the erfect 3(100). The newly asorbe oxygen on the (110) surface stays referentially at the B5 site in the tetraheral fashion, an Figure 6g shows the fully relaxe Similar to the 3(100) surface, the erfect 3(110) surface is the lowest uner the O-oor an -oor conitions. Uner the O-oor an -rich conitions, 3(110)-1 is the most stable configuration, an at the slightly greater chemical otentials, 3(110)-2 is the most stable, inicating that segregates to the surface naturally. As the oxygen content increases, we can observe that 3O/3(110)2 becomes the most stable configuration uner the -rich conition, incluing the area occuie by the 3(110)-1 surface, which means that O romotes the segregation from the substrate uring the oxiation rocess. On the O-rich chemical otential sace the surface hase iagram is occuie by 4O/3(110)-2 uner the -rich conition an by 3O/ 3(110)-2 uner the -oor conition, while the former occuies the far larger area. Uner the -oor conition, the erfect 3(110) is finally oxiize to 4O/3(110)-1 or 4O/3(110)-2; this also roves that O romotes the segregation from the substrate Comarison of the Oxiation Process of 3(100) an -(110). As we iscuss above, the surface configurations of 1O/3(100)-1, 2O/3(100)-2, 3O/3(100)-2, an 4O/3(100)-2 have the most negative oxygen bining energies at the ifferent oxygen coverages of 0.25, 0.5, 0.75, an 1 ML, resectively, for oxygen asortion on the 3(100) surface. The surface configurations of 1O/3(110)-2, 2O/3(110)-2, 3O/ 3(110)-2, an 4O/3(110)-2 have the most negative oxygen bining energies at the oxygen coverage of 0.25, 0.5, 0.75, an 1 ML, resectively, for oxygen asortion on the 3(110) surface. The atomic structures of those configurations from the sie view are islaye in Figure 6a g. Figure 6a shows the fully relaxe structure of the 1O/ 3(100)-1 configuration with the oxygen coverage of 0.25 ML. At this oxygen coverage, the oxygen atom asorbs referentially at the H1 site an bons with three neighboring atoms in a tetraheral fashion (note that it is not a comlete tetraheron ue to the lack of an atom at the to corner). The measure O bon lengths an O bon angles of this tetraheron are 1.87, 1.87, an 1.84 Å an 91.3, 91.3, 19196

7 The Journal of Physical Chemistry C Figure 7. Fully relaxe atomic structure of the 4O/3(100)-2 (2 2) suercell in the [011] (a) an [01 1] (b) sie view, 4O/3(110)-2 (2 2) suercell in the [001] (c) an [11 0] () sie view, an γ-2o3 in the [010] (e) an [100] (f) sie view. Re, blue, an ink sheres reresent O,, an atoms, resectively. 3(100)-2 structure in the [01 1] sie view an the bulk γ2o3 along the [100] sie view (Figure 7f), an both show similar corrugations in the ositions of an O atoms. The average O bon length is 1.82 Å in the O tetraherons in bulk γ-2o3, which is also close to the O bon lengths in the 4O/3(100)-2 configuration (the average O bon lengths of 1.79 Å). The ensities of an O in bulk γ2o3 are 0.1 an 0.15 atom/å2, resectively, while the surface ensities of an O atoms are 0.16 atom/å2 for both an O in 4O/3(100)-2. Comare to bulk γ-2o3, the 4O/ 3(100)-2 configuration has a higher ensity of oxygen atoms, suggesting that the to surface of 3(100) is comletely oxiize at this oxygen coverage. The higher ensity of in 4O/3(100)-2 causes a shorter O bon length comare to that of bulk γ-2o3. Figure 7c illustrates the fully relaxe structure of 4O/ 3(110)-2 along the [001] sie view, which shows that the surface heights of both an O atoms vary greatly, ifferent from the structure of the bulk γ-2o3 (Figure 7e). Figure 7 illustrates the fully relaxe structure of 4O/3(110)-2 along the [11 0] sie view, which shows that the O an atoms o not occuy the entire surface, leaving some oen area. The surface ensities of both an O are 0.11 atom/å2 in 4O/3(110)-2, which require the incororation of more oxygen atoms in orer to reach the same ensity of O in bulk γ2o3. Therefore, the 1 ML of oxygen coverage is still not sufficient to form a γ-2o3-like configuration, an more O atoms are require to asorb into the 4O/3(110)-2 surface. The average O bon length is 1.84 Å in the O structure of the resulting most favorable 3O/3(110)-2 configuration. The to layer has slight lateral an 7.9% uwar islacement comare with the erfect 3(110) surface. At the final oxygen coverage of 1 ML, the newly asorbe oxygen at the (100) surface stays favorably at the tetraheral site of H3. Figure 6 shows the fully relaxe structure of the resulting 4O/3(100)-2 configuration, from which the atoms in the to layer are measure to have unergone the uwar relaxation by 7.2% comare to the erfect 3(100) surface. For the 3(110) surface, the newly asorbe oxygen stays referentially at the tetraheral site of H4, an the fully relaxe structure of the most favorable 4O/3(100)-2 configuration is shown in Figure 6h. The oxygen asortion at the coverage results in the uwar elevation of the atoms in the to layer by 11.2% comare to the erfect 3(110) surface. We further comare the atomic structure of the most favorable configurations of the (100) an (110) surfaces at the oxygen coverage of 1 ML with the structure of bulk oxie.38 Figure 7a illustrates the atomic structure of the 4O/3(100)-2 surface in the [011] sie view, which shows that the atoms ten to locate at the searate atomic lanes to evelo a corrugate surface configuration, while most of the O atoms ten to have a similar surface height. For comarison, Figure 7e illustrates the bulk γ-2o3 along the [010] sie view, which shows that atoms locate at alternate atomic layers an O atoms locate at the same atomic lane, similar to the configuration shown in Figure 7a. Figure 7b shows the 4O/ 19197

8 The Journal of Physical Chemistry C Figure 8. Diffusion athway of 3(100) to evelo one surface antisite efect (a g) an then two surface antisite efects (g i). Diffusion athway of 3(110) to form one surface antisite efect (j ) an then two surface antisite efects ( r). Blue an ink sheres reresent an atoms, resectively. Our results further show that the oxygen asortion enhances the surface segregation, resulting in the formation of a comlete surface layer at the initial stage of oxiation for both surfaces. We reach this result by assuming a erfect 3 suercell slab unerneath the surface layer. This can be reasonable if one consiers the bulk as an infinite reservoir that can suly atoms to the surface layer while causing no changes in comosition itself. In reality, however, the oxygenasortion-inuce formation of antisite surface efects requires atom exchanges between the surface an subsurface region. Therefore, the subsurface region is also involve from the beginning of the oxiation rocess. As seen in Figure 8a, the formation of antisites at the (100) an (110) surfaces requires exchanges of atoms between the tomost an the thir layers, because the secon layer is ure. Therefore, our calculations involve the migration of atoms in the thir layer through the secon layer an then to tetraherons in 4O/3(110)-2 an the lower ensity of O leas to a larger O bon length. 4. DISCUSSION The DFT results escribe above show that the erfect surface is the most stable configuration for the 3(100) surface, whereas antisite efects ten to segregate at the 3(110) surface uner the nonoxiizing conitions. Such a ifference in the two surfaces can be attribute to two reasons. First, the (110) surface has a more oen structure than the more ensely acke (100) surface, suggesting that the segregation of larger atoms (i.e., ) to the (110) surface can be more favorable than to the (100) surface (the atomic raii for an are an nm, resectively). In aition, the interlayer sacing for the (110) surface is smaller than that for the (100) surface, which may also facilitate the segregation of atoms from the subsurface region to the outer surface

9 The Journal of Physical Chemistry C the tomost layer. In this rocess, an atom in the thir layer has to exchange the ositions, first with a atom in the secon layer an then with the atom in the surface layer. Figure 8a g islays the intermeiate snashots from the NEB-obtaine minimum energy reaction ath for the formation of an antisite on the 3 (100) surface. Figure 8a shows the erfect 3 (100) surface without any antisite efects. Figure 8b shows that the atomic exchange can be initiate by the inwar migration of the atom in the secon layer to an ajacent octaheral interstitial site between the secon an thir atomic layers (the octaheral site is more favorable than the tetraheral site because of its larger volume), which results in a vacant site in the secon layer. Figure 8c shows the migration of the atom in the thir layer to the vacant site in secon layer, an Figure 8 shows that the isloge atom in the octaheral site now moves to the vacant site in the thir layer. In this way, the atom in the thir layer moves to the secon layer by exchanging its site with the atom in the secon layer through the interstitial octaheral sites. Similarly, the atom in the secon layer exchanges with the atom in the first layer through the interstitial octaheral site between the first an secon layers, which eventually results in the formation of an antisite in the first layer (Figure 8 g). Figure 8h,i corresons to the configurations for the formation of the secon antisite on the (100) surface, which results in a ure surface layer. The formation of antisite efects on the 3 (110) surface can occur in the same way through the interstitial octaheral sites, as shown in Figure 8j r. It is worth mentioning that the resence of oint efects in a real samle can significantly facilitate such atom exchanges. We now consier the effect of oxygen asortion on the surface segregation of atoms. We calculate the system energy by asorbing four oxygen atoms into each of the intermeiate configurations (shown in Figure 8a r) at the hollow sites of the surface, which corresons to 1 ML of oxygen coverage, the highest oxygen coverage examine in our stuy. Figure 9 shows the total energy ifference of the intermeiate configurations with 1 ML of oxygen coverage. It can be seen that the oxygen asortion romotes segregation for both the (100) an (110) surfaces an such an effect is even stronger for 3 (110) because the system energy for the 3 (110) Figure 9. Comarison of the system energies for 3 (100) an 3 (110) before an after oxygen asortion onto the surface of the configurations shown in Figure 8a r surface is always lower than that for 3 (100). It can also be note from Figure 9 that the system energy for the 3 (110) surface with two antisite efects increases ramatically with the oxygen asortion (such an effect oes not show u for the (100) surface). This may be relate to the resence of ure layers in the subsurface region of the (110) surface. As shown in Figure 8r, the formation of two antisite surface efects results in three ure layers in the subsurface region, which may be highly unfavorable after the oxygen asortion an likely unergoes further comosition evolution by atom exchanges with eeer layers in the bulk. Further investigations to eluciate this comosition evolution are neee but are beyon the resent stuy. 5. CONCLUSION Using the DFT metho an thermoynamics calculations, we erform a comarative stuy of the oxygen asortion an thermoynamic stabilities of the various 3 (100) an 3 (110) surfaces. The relative surface energies of the clean 3 (100) an 3 (110) surfaces with ifferent surface antisite efects as functions of the chemical otential of are obtaine, an we fin that the erfect surface is the most stable configuration for the 3 (100) surface, whereas antisite efects ten to segregate at the (110) surface uner the nonoxiizing conitions. We have constructe the surface hase iagrams for the O 3 (100) an O 3 (110) surfaces with ifferent antisite efects uner ifferent oxygen coverages. The surface hase iagrams show that the oxygen asortion enhances the surface segregation, resulting in the formation of a comlete surface layer at the initial stage of oxiation. Comare with the O 3 (100) an O 3 - (110) surfaces, the 3 (100) surface is thermoynamically more favore to oxiize comletely at a lower oxygen coverage. AUTHOR INFORMATION Corresoning Authors *Y.Z. zhouyc@xtu.eu.cn. *G.Z. gzhou@binghamton.eu. ORCID Guangwen Zhou: X Notes The authors eclare no cometing financial interest. ACKNOWLEDGMENTS This work was suorte by the Hunre Talents Program of Hunan Province, China. The work at SUNY Binghamton was suorte by the U.S. Deartment of Energy, Office of Basic Energy Sciences, Division of Materials Sciences an Engineering uner Awar No. DE-SC REFERENCES (1) Miracle, D. B. The hysical an mechanical roerties of. Acta Metall. Mater. 1993, 41, (2) Davis, J. R. ASM Secialty Hanbook: ckel, Cobalt, an Their loys; ASM International: Materials Park, OH, (3) Finnis, M. W.; Lozovoi, A. Y.; avi, A. The oxiation of : What can we learn from ab Initio calculations? Annu. Rev. Mater. Res. 2005, 35, (4) Qin, H. L.; Chen, X. D.; Li, L.; Sutter, P. W.; Zhou, G. W. Oxiation-riven surface ynamics on (100). Proc. Natl. Aca. Sci. U. S. A. 2015, 112, E103 E109.

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