Adsorption and Diffusion of Oxygen Atoms on a Pt (211) Stepped

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Adsorption and Diffusion of Oxygen Atoms on a Pt(211) Stepped Surface Takafumi Ogawa, Akihide Kuwabara, Craig A.J. Fisher , Hiroki Moriwake, and Tomohiro Miwa J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp312535e • Publication Date (Web): 16 Apr 2013 Downloaded from http://pubs.acs.org on April 21, 2013

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The Journal of Physical Chemistry

Adsorption and Diffusion of Oxygen Atoms on a Pt(211) Stepped Surface Takafumi Ogawa,∗,† Akihide Kuwabara,† Craig A. J. Fisher,† Hiroki Moriwake,† and Tomohiro Miwa‡ Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi 456-8587, Japan, and Toyota Motor Corporation, 1, Toyota-cho, Toyota, Aichi 471-8572, Japan E-mail: [email protected]

Phone: +81-52-871-3500. Fax: +81-52-871-3599

∗ To

whom correspondence should be addressed Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya, Aichi 456-8587, Japan ‡ Toyota Motor Corporation, 1, Toyota-cho, Toyota, Aichi 471-8572, Japan † Nanostructures

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Abstract To clarify the influence of surface steps on the diffusion of adsorbed oxygen atoms on Pt, we have carried out density functional calculations of the adsorption of atomic oxygen on a Pt(211) stepped surface and the diffusion barriers between the adsorbed states. Comparison with Pt(111) and Pt(100) flat surfaces reveals that atomic oxygen is strongly bound at the ledge of the steps and weakly bound at the bottom of the steps. We show that the variation in the adsorption preferences correlates well with the d-band centers of the outermost Pt atoms on a clean Pt(211) surface. Although a high energy barrier of Ediff,⊥ = 1.36 eV is obtained for diffusion perpendicular to the step edge, the barrier lies within the range of experimental values. The energy barrier also depends on whether the O atom is ascending or descending the step, being about 0.3 eV lower in the case of the former. The barrier to diffusion parallel to the edge of Ediff,∥ = 0.73 eV is also higher compared to the equivalent barrier on a flat Pt(111) surface due to the deeper energy well at the ledge.

Keywords: Migration energy barrier; first principles calculation; density functional theory; nudged elastic band method; adsorption energy; d-band center


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Introduction Surface diffusion of adsorbed (chemisorbed) atomic oxygen on Pt electrodes is a fundamental and important step for many chemical reactions occurring at gas-solid interfaces. For example, at the Pt/YSZ (yttria-stabilized zirconia) composite electrodes used in zirconia oxygen sensors or solid oxide fuel cells, adsorbed atomic oxygen is generated on Pt particles by dissociative adsorption of oxygen molecules above 400 K 1,2 or spillover from the triple phase boundary which is induced by applying an electric potential or current in the context of electrochemical promotion of catalysis (EPOC). 3 Diffusion of the adsorbates is crucial to understanding the mechanism of EPOC 4 and identifying the rate-determining step of the electrode reaction; 5–8 however, the surface diffusion of oxygen is yet to be examined systematically at the atomistic level. Measurements of oxygen diffusion on Pt surfaces by field emission microscopy (FEM), 9 photoelectron emission microscopy (PEEM), 10,11 and scanning tunneling microscopy (STM) 12 provide diffusion energy barriers, Ediff , varying over a wide range from 0.43 eV to 1.73 eV. While STM enables individual atomic movements to be observed, PEEM and FEM measure collective diffusion on the micron scale. In the case of the latter, it is difficult to estimate Ediff because the number and size of step defects on the surface is unknown, there is uncertainty about how the diffusion model relates to adsorption and desorption of oxygen, and there is a lack of comparable theoretical data. On the other hand, measurement of laser-induced oxygen diffusion on stepped Pt(111) has provided some insight into oxygen diffusion in the vicinity of a surface step. 13 The development of density functional theory (DFT) and efficient methods for probing the minimum energy paths of reactions means it is now feasible to calculate Ediff directly; however, the diffusion barrier of an oxygen atom on a Pt surface has so far only been calculated for the case of flat Pt(111). 14 Surface diffusion, like surface adsorption, is generally affected by the presence of defects, both point defects such as vacancies and impurities, and extended defects such as steps. In particular, a surface step produces an additional barrier known as an Ehrlich-Schwoebel (ES) barrier, 15–17 which disturbs downhill diffusion of self-diffusing species and is related to the growth mechanism of films or pyramidal islands. The ES barrier to Pt atom diffusion on a Pt surface has been 3 ACS Paragon Plus Environment


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calculated by DFT 18 in order to interpret STM results for layer-by-layer growth. 19 The effect of the modeled ES barrier on macroscopic collective diffusion has also been investigated for O adsorbed on the W(110) 20 surface, as well as a generic model system. 21,22 The calculated diffusion coefficients based on modeled potential surfaces highlight the important influence steps have on macroscopic diffusion. Potential energy surfaces calculated from DFT can also be used in the first-principles study of macroscopic diffusion by combining them with kinetic Monte Carlo simulations. 23,24 In this paper, we examine adsorption of atomic oxygen on a simple Pt(111) vicinal-type surface, namely a Pt(211) surface, using DFT, and calculate the associated energy barriers between the adsorbed states. Our Pt(211) surface model consists of three atom columns comprising a Pt(111)type terrace and a Pt(100)-type step face; this model is often labeled Pt(s)-[3(111) × (100)]. This type of Pt(111) step (referred to as A-type) is found to be more prevalent compared to the Pt(s)[n(111) × (111)]-type step (B-type) in STM experiments. 19 Although oxygen adsorption on a Pt(211) surface has been studied previously, 25,26 a more systematic examination is required to calculate the associated migration energy barriers accurately. Comparison of the results with those from adsorption on flat surfaces can provide important insights into the catalytic behavior of Pt, so we also carried out and report calculations of adsorption and diffusion on flat Pt(111) and Pt(100) surfaces.

Calculation methods We obtain total energies and energy-minimized configurations using first-principles calculations based on DFT in the scheme of the plane-wave expansion and projector augmented wave method implemented in VASP. 27 The spin-dependent Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) is used for the exchange-correlation functional, 28 the Monkhorst-Pack (MP) grid method 29 for Brillouin zone sampling, and the first-order Methfessel-Paxton smearing method 30 with a width of 0.1 eV for occupation of eigenstates. For all calculations, 400 eV is


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used for the plane wave energy cutoff. During relaxation, forces on all atoms converged to at least within 0.02 eV/Å. All surface models were constructed from a Pt bulk crystal with lattice constant a = 3.976 Å. This result was obtained using a 10 × 10 × 10 k-mesh. The calculated lattice constants are larger by 1.4% than the experimental value of 3.96 Å, 31 as is typical for PBE-GGA calculations. Slabs with 9 atomic layers are used for Pt(111) and Pt(100) surfaces. In the latter case, we chose to use a square lattice rather than converting it to hexagonal symmetry 32 because here we are interested in comparing it with the step face of the Pt(211) surface. For the Pt(211) surface, the top layer is composed of three non-equivalent Pt atoms exposed to the vacuum in the surface unit cell, which we label Pt1, Pt2, and Pt3 as shown in Figure 1; a 9-layer slab model is used. For all surfaces, a vacuum spacing of 10 Å between the two surfaces is added and atoms in the top three layers are relaxed fully. We use a 4 × 4 unit cell for Pt(111), a 3 × 3 unit cell for Pt(100), and a ([ ] [ ]) ¯ 4 × 2 011¯ × 111 unit cell for Pt(211). Because the distance between periodic images of an adsorbate is greater than 9 Å in these models, they can be considered to be isolated adatoms, and thus the calculated energy barriers are suitable for analyzing tracer diffusion of the adsorbate. MP meshes in two dimensional planes parallel to the surface are 5 × 5 for Pt(111) and Pt(100), and 3 × 3 for Pt(211). These meshes are selected to give convergence in the total energies to within 0.01 eV. We define the adsorption energy using the energy of an isolated oxygen atom as reference. Charges on atoms are calculated from charge densities using Bader analysis. 33 The climbing image nudged elastic band (CI-NEB) 34,35 method is used to calculate diffusion barriers between adsorbed sites. The supplemental codes of CI-NEB for VASP and the code for Bader analysis are provided by the group of Henkelman. 36



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(a)

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(b) Pt1

Pt1 Pt2

Pt3 F2

Pt3

H Pt2

F1 EB

Pt3

T

Pt1

SB

[111]

Pt3

[211] [111]

[011]

Figure 1: (a) Top and (b) side views of sections of the Pt(211) surface model. Non-equivalent surface Pt atoms in the unit cell are labeled Pt1, Pt2, and Pt3. Possible adsorption sites for an oxygen atom are also shown in (a). SB, EB, and T stand for step-bridge, edge-bridge, and topon-edge sites, respectively. F and H sites correspond to three-fold fcc and hcp-hollow sites on the terrace, respectively.

Results Adsorption of oxygen atoms Symmetrically non-equivalent adsorption sites on Pt(211) are indicated in Figure 1 (a), and their associated adsorption energies calculated in this study are summarized in Table 1. The table also lists bond lengths dO−Pt between the adsorbed oxygen atom and nearest neighboring Pt atoms, their averages, d¯O−Pt , the magnetic moment of the adsorbed oxygen, and its effective ionic charge from Bader charge analysis. Of the various initial sites, 6 sites were found to represent stable adsorption sites after relaxation. The fcc-hollow sites (F1, F2) and hcp-hollow site (H) also exist on the Pt(111) terrace. The edge-bridge (EB) and edge-top (T) sites are located on the step-edge Pt atoms (Pt1). On the Pt(100) step face, only the step-bridge site (SB) is found to be stable. Table 1 also shows the results for isolated Pt(111) and Pt(100) surfaces. We first discuss adsorption on these two flat surfaces before comparing results with those for the stepped surface. The adsorption of oxygen on Pt(111) has been investigated extensively in the literature. We here focus on the consistency of our results with previous DFT calculations and experiments to gage the reliability of our method. The stable adsorption sites on Pt(111) are fcc-hollow, hcphollow, and top sites as shown in Table 1. The bridge site between fcc and hcp sites is unstable


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Table 1: Adsorption energies, Ead , individual and averaged distances between oxygen and nearest neighboring Pt, dO−Pt and d¯O−Pt , magnetic moment of oxygen, mO , and effective ionic charge of oxygen, QO , for Pt(211), Pt(111), and Pt(100) surfaces. Site labels Fcc and Hcp stand for fcc-hollow and hcp-hollow sites, respectively. Surface Pt(211)

Pt(111)

Pt(100)

Site Bridge (SB) Bridge (EB) Top (T) Fcc (F1) Hcp (H) Fcc (F2) Fcc Hcp Top Bridge Top

Ead [eV] dO−Pt [Å] -4.22 1.98,1.92 -4.85 1.95×2 -3.87 1.82 -4.53 2.06×3 -3.91 2.07, 2.03, 2.02 -4.00 2.06×2, 1.99 -4.62 2.05×3 -4.22 2.05×3 -3.35 1.83 -4.71 1.95×2 -3.58 1.81

d¯O−Pt [Å] 1.95 1.95 1.82 2.06 2.04 2.04 2.05 2.05 1.83 1.95 1.81

mO [µB ] QO [e] 0.00 -0.71 0.00 -0.74 0.57 -0.60 0.00 -0.78 0.00 -0.79 0.00 -0.76 0.00 -0.76 0.00 -0.75 0.68 -0.58 0.00 -0.72 0.00 -0.66

because the oxygen atom drops down into the more stable fcc position. The preferential adsorption at the fcc site on Pt(111) has been confirmed experimentally by STM. 37 Our results are in agreement with values of −4.59 eV for fcc and −4.29 eV for hcp obtained from previous calculations using PBE-GGA, 38 despite the difference in calculation conditions such as the degree of coverage and slab width. The coverage for the previous study was 0.11 ML, in contrast with 0.063 ML in our simulation. This agreement is perhaps not surprising, since in the previous study the adsorption energies were found to be almost independent of coverage up to about 0.25 ML. 38 For adsorption on the fcc site, other calculations using revised-PBE GGA (RPBE-GGA) and Perdew-Wang 91 GGA (PW91-GGA) functionals produced energies of −3.5 eV and −4.0 eV, respectively, for a coverage of 0.17 ML (i.e., less than 0.25 ML). 25 As shown from these data, the adsorption energy is sensitive to the choice of exchange-correlation functional. Of the functionals examined so far, RPBE-GGA is considered to produce the most reliable results. 39 Experiments produced corresponding values at the limit of zero coverage of −3.7 eV 40 and −4.1 or −4.3 eV. 41 Since the experimental values gradually increase with increasing coverage for the range of coverages considered here, the PBE functional is seen to overestimate the adsorption energy in the same way as for other gas adsorption systems. 39 The differences between fcc and



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hcp adsorption energies for all these calculations, including a local density approximation (LDA) study, 42 however, are consistently in the range of 0.4 − 0.5 eV. The large difference in energy between the two three-fold hollow sites cannot be attributed to the local features of coordinating atoms to the adsorbate (see dO−Pt in Table 1), but can be correlated with the d bonding states of subsurface Pt atoms. 42 This situation can better be seen using the differential charge density defined by ∆ρ (rr ) = ρPt+O (rr ) − (ρO (rr ) + ρPt (rr )) .

(1)

Here, ρPt+O (rr ) is the electron charge density of an examined oxygen-adsorbed Pt surface. Fixing the coordinates of the atoms, charge densities ρO (rr ) and ρPt (rr ) are calculated for the isolated oxygen atom without the Pt slab, and Pt surface system without the oxygen atom, respectively. Figure 2 shows the differential charge densities for fcc and hcp adsorption. Since adsorbed oxygen on Pt(111) attracts electrons, as shown by QO in Table 1, electrons in the Pt surface (down to some layer depth) are removed. ∆ρ of both adsorption sites extends from the adsorbed oxygen to the three nearest neighboring Pt atoms, PtNN . The difference appears in the bonding between PtNN and the subsurface (second layer) Pt atoms labeled αi for fcc and βi for hcp in Figure 2. In the case of fcc adsorption in Figure 2 (a), ∆ρ extends linearly to α1 and the calculated bond length between PtNN and α1 is shorter by about 1.9% than the bulk-Pt bond length. This bond strengthening is caused by removal of antibonding d electrons between the Pt atoms during adsorption. 42 On the other hand, in the case of hcp adsorption ∆ρ branches out in two directions from PtNN to β1 and β2 atoms, as seen in Figure 2 (b), and bonds between PtNN and βi increase relative to the bulk value. These results accord well with previous calculations. 42 On the square Pt(100) surface, our energies for the bridge and top sites are consistent with values of −4.62 eV (bridge) and −3.56 eV (top) obtained from PBE-GGA calculations, 38 but somewhat different to those of −3.809 eV (bridge) and −2.860 eV (top) from PW-GGA calculations. 43 The latter inconsistency may be attributed to the use of a 4 layer slab model in the earlier


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(b) Hcp-hollow

(a) Fcc-hollow

α1

β1

PtNN

α2

PtNN

α3

β2

β3

Figure 2: Isosurfaces of differential charge density for (a) fcc-hollow and (b) hcp-hollow adsorption on Pt(111) viewed from above. The red sphere in each figure is the adsorbed oxygen atom and other spheres are Pt atoms. The isosurface corresponds to ∆ρ (rr ) = ±0.01 electron/Å3 , where the yellow and blue surfaces represent positive and negative differential densities, respectively. αi and βi (i = 1, 2, 3) indicate positions of the subsurface Pt atoms next to the labeled PtNN . The Pt atom labeled β3 is located directly beneath the oxygen. study, which may have introduced spurious interactions by being too thin. The relative values between the two adsorption sites, however, are both around 1.0 eV. The four-fold hollow site on the Pt(100) surface is also a possible adsorption site and, during energy minimization calculations, we observed the adatom sitting on this position after relaxation, as previously reported. 38,43 However, when searching for the minimum energy path as in CI-NEB calculations, no energy barrier between the bridge and hollow sites was found. Indeed, the four-fold hollow site corresponds to the saddle point, and is not actually a stable adsorption site. Relaxation of the same configurations with a stricter criterion of 0.001 eV/Å resulted dropping to the bridge site. This result suggests the energy surface around the four-fold hollow site is relatively flat, and previous reports of it being a stable adsorption site most likely are an artifact of the energy-minimization procedure used, particularly of the convergence criterion were insufficiently strict. Our results show the utility of CI-NEB calculations for avoiding these difficulties, allowing to be identified with greater confidence. On Pt(211), the most favorable adsorption site was found to be the EB site, consistent with experimental results from high-resolution electron energy loss spectroscopy (HREELS). 2 ∆ρ for the EB adsorption is shown in Figure 3. From the top and side views, the charge-density deviation ¯ is found to extend over the (111) plane which includes the adsorbed oxygen, as seen in the sliced view in Figure 3 (c). Within this plane, two-fold chains in the density differential can be seen, one of which is on the line passing through PtNN and the neighboring Pt atom labeled γ1 . Assuming 9 ACS Paragon Plus Environment


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(a) Top view

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(b) Side view

[111]

[211] [011]

[111]

(c) Sliced view PtNN 1

2 [211] [011]

Figure 3: (a) Top, (b) side, and (c) sliced views of the differential charge density isosurface for edge-bridge adsorption on Pt(211). The conditions are the same as in Figure 2. In (a), only the top ¯ Pt layer is represented. The sliced view in (c) shows the (111) plane corresponding to the dashed rectangles in (a) and (b). In (c), γ1 and γ2 indicate subsurface Pt atoms next to PtNN . the origin of this deviation is the same as in the case of fcc adsorption on Pt(111), the bond length between PtNN and γ1 should shorten. Indeed our calculation indicates a 3.3% decrease in the bond length between PtNN and γ1 , while the bond length between PtNN and γ2 increases by 0.8% relative to the bulk value. EB values are consistent with previous studies, 25,26 as summarized in The calculated Ead − Ead

Table 2. The averaged distances d¯O−Pt are similar for the same type of adsorption sites on each surface, as seen in Table 1. Roughly speaking, d¯O−Pt decreases by 0.1 Å for each increase in coordination number of the adsorption site. The two top sites on Pt(211) and Pt(111) retain their magnetic moments, while for all other adsorption configurations the magnetic moment of the isolated oxygen atom disappears. The calculated ionic charge of oxygen indicates that oxygen adsorbed on the Pt surface is always negatively ionized. These results reveal that only atoms adsorbed on the top adsorption sites on Pt(111) and Pt(211) retain their isolated atomic character due to their retention of unfilled p orbitals. In contrast, all other adsorbed oxygen atoms form closed shells by bonding to Pt atoms. 10 ACS Paragon Plus Environment

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EB in units of eV for different oxygen adsorption sites on Table 2: Comparison of Ead − Ead Pt(211). In all calculations the preferred site is the edge-bridge (EB) site. Labels for adsorption sites are the same as in Table 1.

Site SB T F1 H F2

PBE-GGA RPBE(this work) GGA 25 0.63 0.98 0.32 0.4 0.94 1.0 0.85 1.0

PW91GGA 25

LDA 26

0.3 0.8 0.9

0.34

-1.9 0.6

Pt1

Pt1

F2 SB

∆Ead [eV]

0.4

H

0.2

F1

-2.0

0.0 EB

εd-EF [eV]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


EB Pt2

-0.2 Pt3

T

T

-0.4

-2.1 0

2

4

6

8

x-xEB [Å]

¯ Figure 4: ∆Ead and εd − EF as a function of the x coordinate along [111]. xEB is the coordinate of the adsorbed edge-bridge oxygen atom. εd was obtained from the projected density of states. To visualize the trends in the adsorption energies more clearly, we define the relative adsorption energy ∆Ead as step

flat ∆Ead = Ead − Ead .

(2)

flat is E Here, Ead ad of the corresponding site on the corresponding flat surface, i.e., Pt(111) or

Pt(100). We label the sites on the Pt(111) terrace F1, H, and F2, and the sites on the Pt(100) step face SB, EB, and T in the Pt(211) model in the same manner as described earlier. In Figure ¯ 4, ∆Ead is plotted as a function of distance from the EB site in the [111] direction (Figure 1). This plot shows that the step edge is preferred by oxygen during adsorption, while the bottom of the step is relatively unfavorable. Adsorption preferences on transition metal surfaces can be frequently described in terms of 11 ACS Paragon Plus Environment


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Table 3: Possible diffusion paths for an adsorbed oxygen atom on Pt(211), Pt(111), and Pt(100) and the corresponding diffusion barrier Ediff . Path label P⊥ P∥F1 P∥SB P(111) P(100)

Path EB→F1→H→F2→SB→EB EB→F1→EB EB→SB→EB Fcc→Hcp→Fcc Bridge→Bridge

Ediff [eV] 1.36 0.73 0.85 0.58 0.51

a hybridization model between the d-band of the transition metal and the valence orbitals of the adsorbate, 44,45 the basis of the Newns-Anderson model. 46 The main prediction of this theory is that a higher d-band center energy leads to lower adsorption energy. In our case, the d-band centers,

εd , of Pt1, Pt2, and Pt3 at the clean Pt(211) surface (in Figure 1) , obtained from projected density of states and plotted in Figure 4, show a clear correlation with ∆Ead . Our results thus confirm the validity of the d-band model in the interpretation of the adsorption preferences around the step in the Pt system.

Diffusion barriers for adsorbed oxygen atoms In Table 3, the diffusion barriers between the most favorable adsorption sites are listed for feasible pathways on Pt(211), Pt(111), and Pt(100) surfaces. The top three rows in the table show the data for possible paths on Pt(211). The diffusion paths perpendicular to the edge, P⊥ , and parallel to the edge, P∥SB and P∥F1 , are presented schematically in Figure 5. P(111) and P(100) stand for paths on Pt(111) and Pt(100), respectively. On Pt(111), oxygen diffuses via the bridge site between fcc and hcp sites, but the saddle point is slightly shifted towards the hcp site from the geometric center of the two Pt atoms neighboring the bridge site. The calculated value of 0.58 eV for P(111) is in agreement with a previously reported value of 0.55 eV. 14 The agreement between the STM result 12 and the previous DFT result has already been discussed by Bogicevic. 14 The difference between the relatively low STM value of Ediff = 0.41 eV and the DFT values can be attributed to the way the prefactor was estimated.


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EB

Pt1

Pt3 Pt2 EB

EB

[111]

Pt1

Pt3 [011]

Figure 5: Diffusion paths of an oxygen atom on a Pt(211) surface. The labels of the three paths correspond to those in Table 3. The cause of the discrepancy with the much higher value of 1.73 eV obtained from FEM measurements 9 on the Pt(111) surface is not entirely clear, but may be attributable to the presence of defects on the surfaces. The saddle point along P(100) is the four-fold hollow site and the diffusion barrier on the path is lower by 0.07 eV than that on Pt(111). Figure 6 shows the calculated potential energy surface for the path P⊥ corresponding to diffusion of atomic oxygen from one EB site to another across a terrace on Pt(211). This reveals that the energy of the adsorbed oxygen is raised near the bottom of the step. This increase is thought to result from modifications to the electronic structure of Pt atoms near the step in the same way as discussed above for adsorption energies. The diffusion barrier, Ediff , of 1.36 eV over the step along P⊥ is more than twice as large as the barrier on the Pt(111) terrace of Pt(211). We note that the barrier along P⊥ is significantly lower (by more than 2.0 eV) than the barriers for diffusion of oxygen into subsurface layers calculated for Pt(111) and Pt(100). 38 There are two possible paths, P∥F1 and P∥SB , for diffusion parallel to the edge on Pt(211). Of the two diffusion paths, P∥F1 is more favorable than P∥SB by 0.12 eV. This also reflects the adsorption preference around a step as presented in Figure 6. The anisotropic difference in barrier energies between P⊥ and P∥F1 of 0.53 eV shows that a large electron redistribution in Pt occurs in the direction normal to the step. Our calculated Ediff for P⊥ may be the upper limit for the diffusion barrier on the Pt(111) 13 ACS Paragon Plus Environment


1.4 1.2

E-EEB [eV]

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1.0 H

0.8

F2

0.6

SB

0.4 0.2

F1

EB

EB 0.0 0

1

2

3

4

5

6

x-xEB [Å] Figure 6: Potential energy barriers encountered by an oxygen atom on a Pt(211) surface along the ¯ path P⊥ as a function of the distance along [111]. surface, so the FEM value of 1.73 eV 9 is difficult to reconcile with our results by invoking the effects of defects alone. However, more recent PEEM experiments produced values of 0.84 eV and 0.51 eV for Ediff on Pt(111) via a simple Fickian diffusion model and numerical reactiondiffusion model, respectively, 10 which are close to our calculated diffusion barrier on the Pt(111) flat-terrace surface than on the step-dense surface. Laser-induced diffusion experiments estimated the diffusion barrier from a bound edge-bridge oxygen to a terrace site to be ≈ 0.8 eV. 13 This compares well with our calculated value for a jump from an EB to F1 site of 0.73 eV. The calculated potential surface for atomic oxygen on Pt(211) is different from the ES barrier because trapping sites for the oxygen atoms exist on the edge as opposed to the situation for selfadsorption on Pt steps. Even in the latter case, the potential profile can be more complex than the original ES barrier model. 47 Figure 7 depicts schematically the proposed diffusion barrier model for oxygen diffusion over A-type steps examined in this study. The terrace barrier ET is ≈ 0.6 eV, the same as diffusion on Pt(111). Energy lowering at the step edge affects the barrier between the terrace site and edge-bridge trapping site by EE1 ≈ 0.15 eV, and the trapping energy at the edgebridge site by EE2 ≈ 0.3 eV. The energy increase at the step bottom adds to the barrier between the terrace site and edge-bridge site by EB ≈ 0.5 eV. These changes in diffusion barriers show that the effects surface steps have on diffusion are strongly related to the different adsorption energies,


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EB EE1

ET EE2

EB

Figure 7: Model energy barriers (upper) for oxygen diffusion on a Pt(111) stepped surface in the direction perpendicular to the step. The terrace adsorption sites (fcc-hollows on Pt(111)) and step edge-bridge (EB) sites are shown in the lower diagram. ET is the diffusion barrier on the terrace. EE1 and EE2 correspond to energy lowering effects at the step edge, while EB reflects the increase in energy at the step bottom. ∆Ead , in the vicinity of the step. In this model, the diffusion barrier varies depending on whether the O atom is ascending or descending the step (by ≈ 0.3 eV), indicating that diffusion of oxygen atoms occurs more easily up the step than down it. The calculated energy barriers are limited to the discussion of tracer diffusion, but these results can be used in the further study of collective diffusion by combining with lattice model calculations.

Conclusions We have examined the differences in adsorption energies of atomic oxygen on a Pt(211) stepped surface based on DFT calculations by comparison with adsorption on ideally flat Pt(111) and Pt(100) surfaces; the step edge is an energetically favorable adsorption site, while the step bottom is unfavorable. The change in adsorption energy with position correlates well with the d-band centers of Pt atoms on a pristine Pt(211) surface. It is thus confirmed that d-band centers act as a good indicator for adsorption preferences on a defective platinum surface that includes steps. Starting from the preferred adsorption sites, the energy barriers to oxygen atom diffusion on Pt(211) have also been calculated. Diffusion along the step edge is increased by 0.15 eV relative to that



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on the Pt(111) terrace surface on account of the higher stability of the edge-bridge site. On the other hand, diffusion perpendicular to the step edge has a high energy barrier of 1.36 eV, but is consistent with experimental measurements. Oxygen diffusion over steps is thus possible at high temperatures even on surfaces with a high density of steps. Based on detailed energy surface calculations, a simple barrier model for diffusion in the direction perpendicular to the step ledge has been proposed.

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1.4

[111]

1.2

E-EEB [eV]

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EB

1.0

H

0.8

F2

0.6

SB

0.4 0.2

[211]

EB'

F1

EB

EB'

0.0 0

[111]

1

2

3-

4

5

Coordinate in direction [Å] x-x[111][Å]

Edge Bridge (EB) adsorption

EB


6

Adsorption and Diffusion of Oxygen Atoms on a Pt (211) Stepped

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