Structure and Stability of Hydrated Î²-MnO2 Surfaces - American

Article pubs.acs.org/JPCC

Structure and Stability of Hydrated β-MnO2 Surfaces Gloria A. E. Oxford* and Anne M. Chaka† Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States ABSTRACT: Hydration of the β-MnO2 (110), (100), and (101) surfaces is investigated using a combination of periodic density functional theory and ab initio thermodynamics. Fully hydrated surfaces are found to be significantly more stable than the stoichiometric ones up to temperatures in the range of 650 to 730 K at ambient oxygen and water partial pressures. A mixture of molecular and dissociative water adsorption is predicted to occur on the (110) and (101) surfaces, while the (100) surface does not dissociate water. Changes in surface reactivity upon water adsorption are explored via partial density of states analysis. Differences in surface relaxations and vibrational spectra are discussed and can be used to identify the type of adsorption mode.

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INTRODUCTION Manganese oxides are commonly found throughout the environment and have been recognized for their technological significance for centuries.1 In recent times, the advantages of using manganese oxides in batteries,2−5 catalysis,2,6−8 water treatment,9,10 and sensors11 have been widely explored. The importance of manganese oxides in the geochemical cycling of heavy metal ions has also been the subject of numerous studies given their high adsorption capacities and oxidative abilities.12−16 β-MnO2 (pyrolusite), a principal component in alkaline batteries,3,4 is the most stable and abundant polymorph of manganese dioxide.1 As such, it can be expected to play a nontrivial role in geochemical processes. β-MnO2 is a rutiletype mineral formed from edge-sharing chains of Mn4+O6 octahedra linked via their corners. It is found in the P42/ mnm space group with lattice constants a = 4.4041 Å and c = 2.8765 Å.17 Natural β-MnO2 is usually pseudomorphous after γ-MnOOH. Several transmission electron microscopy reports noted the presence of cracks parallel to the {010} planes18,19 or rhombic holes20 in pseudomorphous pyrolusite, which were proposed to result from the transformation of γ-MnOOH into β-MnO2. These structural characteristics of natural pyrolusite provide large surface area and high reactivity,18 likely increasing its role in geochemical processes. Its specific interactions with environmental contaminants (or reactants in catalytic applications) depend on the relevant surface structure and composition under environmental conditions because these aspects of the surface influence its reactivity. Yet, structural analyses of β-MnO2 surfaces have been few, resulting in a lack of knowledge about its surface chemistry and possible modes of interaction with adsorbates. To date, β-MnO2 surface studies have mostly focused on the surface composition by identifying the manganese oxidation state and oxygen species present via X-ray photoelectron spectroscopy (XPS). Oku et al.21 and Rosso and Hochella22 examined powdered samples in UHV and found Mn4+ and O2− This article not subject to U.S. Copyright. Published 2012 by the American Chemical Society

at the surface. Rosso and Hochella also noted two additional peaks in the O 1s spectra at 530.75 and 532.75 eV, which were labeled “adventitious species” and may have been due to adsorbed water or hydroxyl groups. A recent study investigated the epitaxial growth of β-MnO2 on LaAlO3 and MgO (001) surfaces.23 XPS detected Mn4+ and Mn3+ at the β-MnO2 surface as well as O2− and a contaminate oxygen species proposed to be adsorbed water. Pyrolusite was also grown epitaxially on the rutile TiO2 (110) surface.24 After six bilayers, a second phase was introduced, and therefore, characterization of the surface was impeded. In none of these studies was atomic-level detail of the surface obtained. Recent computational efforts have focused on detailed structural analysis of β-MnO2 surfaces and may help to interpret experimental data in future work.25,26 Maphanga et al.25 used rigid-ion interatomic potentials to model low-index surfaces of pyrolusite and compared their relative energies and reducibilities. Density functional theory (DFT) has also been applied to the study of β-MnO2 (110), (100), and (101) surfaces.26 In that work, surface reconstructions and redox behavior of the three surfaces were described, and the stoichiometric surfaces were found to be the most stable over a wide range of temperatures and oxygen partial pressures. While these results may be compared to experiments where water is excluded from the system, they lack applicability to environmental conditions at which water will certainly be present. In this work, we present a combination of periodic DFT calculations and ab initio thermodynamics that explores hydration of the β-MnO2 (110), (100), and (101) surfaces. On the (110) and (101) surfaces, a mixture of different adsorption modes are predicted to be observed under ambient conditions. The (100) surface, however, prefers molecular adsorption. Received: March 8, 2012 Revised: May 7, 2012 Published: May 9, 2012 11589

dx.doi.org/10.1021/jp302268m | J. Phys. Chem. C 2012, 116, 11589−11605

The Journal of Physical Chemistry C

Article

Partial density of states (PDOS) calculations elucidate differences in surface reactivity before and after water adsorption on the clean surfaces. Surface reconstructions are discussed in detail, and vibrational spectral modes are given, which may be useful to experimentalists studying hydrated β‑MnO2 surfaces.

The DFT total energies of the hydrated surface slab, stoichiometric surface slab, and gas-phase H2O were used for gas EHslab2O, Eclean slab , and EH2O, respectively. The adsorption energy was then normalized by the number of adsorbed water molecules per slab, NH2O. Surface free energies give relative stabilities of the surfaces under varying environmental conditions and were calculated with ab initio thermodynamics. This method has been applied to identify and predict surface terminations and surface redox behavior as a function of temperature and pressure for a wide range of minerals.26,34−49 Details of the theory are given below in the context of hydrated β-MnO2 surfaces. The underlying assumption of ab initio thermodynamics is the existence of a chemical and thermal equilibrium between the surface, the bulk oxide, and a gas-phase reservoir. The surface free energy, γ, for a slab with two equivalent surfaces in contact with the gas-phase reservoir is

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METHODS Periodic DFT calculations were carried out in DMol3 27−29 using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE).30 Atomic orbitals were described with a double-numeric-plus-polarization basis set. The optimizations were performed using a real-space cutoff of 3.5 Å. As shown in our recent study,26 this methodology yields an antiferromagnetic (AFM) arrangement of the manganese spins as the ground state, in agreement with experimental results,31,32 and was therefore employed in this work. The optimized bulk lattice constants were a = b = 4.4569 Å and c = 2.8823 Å, within +1.2% and +0.2% error, respectively, of the experimentally determined lattice constants as previously reported.26 Following the approach utilized in our earlier work,26 the (110) surface was modeled as a five-metal-layer slab, and (7 × 4 × 1) k points in a Monkhorst−Pack grid were used for a (1 × 1) surface cell. The (100) and (101) surfaces required seven-metal-layer slabs and (1 × 4 × 7) and (4 × 4 × 1) Monkhorst−Pack grids, respectively, for (1 × 1) surface cells. The surfaces of the slabs were related by inversion symmetry and were separated by a double vacuum of 10 Å. This vacuum was determined to be sufficient to avoid interactions between slabs, all of which were nonpolar. All atom positions were fully relaxed during the optimization procedure. A convergence criterion of 0.01 eV/Å was used for the forces. To verify location of true minima and calculate vibrational frequencies, the frozen phonon method33 as implemented in DMol3 was employed with a step size of 0.53 pm (0.01 bohr). Because the stoichiometric terminations of the (110), (100), and (101) surfaces were calculated to be the most thermodynamically stable over a wide range of environmental conditions using ab initio thermodynamics,26 hydration of these surfaces was explored. Various initial configurations of molecularly and/or dissociatively adsorbed water were considered on each surface. It should be noted that the search of configurational space was not exhaustive and lower-energy surfaces than those found here may exist. Initially, hydration of the (1 × 1) surface cell was modeled, providing information in the monolayer (1 ML) coverage regime. To determine how adsorption energies and surface free energies change with coverage, quarter monolayer (0.25 ML) coverage was also examined by starting with the lowest-energy configurations at 1 ML, removing 75% of the water molecules, and reoptimizing the structure. This procedure can lead to location of local minima only, but the results should capture general trends as discussed in subsequent sections. The energetics of the hydrated surfaces were analyzed with two metrics, the adsorption energy and the surface free energy. We utilized the adsorption energy as a measure of the exothermicity of the adsorption reaction. The adsorption energy, ΔEads, is defined as H 2O clean ΔEads = (Eslab − Eslab − NH2OE Hgas2O)/NH2O

γ (T , p) =

1 {Gslab(T , p , Ni) − 2A

∑ Niμi (T , p)} i

(2)

where A is the surface area, Gslab is the Gibbs free energy of the slab, and Ni and μi denote the number and chemical potential, respectively, of atom type i. The Gibbs free energy of the slab is obtained from the DFT total energy of the slab at 0 K (Eslab) and enthalpic and entropic contributions to the energy at finite temperature. These contributions derive from the vibrational energy (including the zero point energy) of the slab and were calculated using the fundamental relationships of statistical mechanics as follows: ⎛1 1 ΔGvib = kB ∑ Θυi⎜ + Θ / T υi ⎝ 2 e − i

⎞ ⎟ 1⎠

⎤ ⎡ Θυ /T − ln(1 − e Θυi / T )⎥ − kBT ∑ ⎢ Θ / Ti υi ⎦ −1 i ⎣e

(3)

where ΔGvib is the change in Gibbs free energy due to vibrational energy, kB is the Boltzmann constant, the sum is over all vibrational frequencies υi, and Θυi is the vibrational temperature. The vibrational temperature is defined as hυi/kB, where h is Planck’s constant. Because of the chemical equilibrium, μi is the same in each phase and can therefore be calculated for any one phase. We utilized the Gibbs free energy of the bulk oxide per formula unit, Ebulk MnO2, to determine μMn, and μO was computed using the Gibbs free energy of gas-phase oxygen, Ggas O2 . bulk μMn + 2μO = G MnO 2

μO =

1 gas GO 2 2

(4)

(5)

For μH, the relevant gas-phase species depends on the oxygen content in the reservoir. At low μO, μH is independent of μO and is equal to half of the Gibbs free energy of molecular hydrogen, Ggas H2 .

μH =

1 gas GH 2 2

(6)

When the partial pressure of oxygen increases beyond a certain threshold, hydrogen desorbing from the surface reacts with

(1) 11590



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thermodynamics over most of the range of μO. In agreement with earlier studies,30,49 the absolute errors in H2 and H2O atomization energies are small (0.13 and 0.042 eV, respectively). Therefore, uncorrected energies were used for these species.

oxygen to form water. Then the Gibbs free energy of water vapor, GHgas2O, is the relevant quantity for calculating μH. 2μH + μO = G Hgas2O

(7)

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The Gibbs free energy of bulk MnO2 was computed using the DFT energy and contributions from the vibrational energy. Because of the lack of experimental data for MnO2, the vibrational energy was estimated with eq 3. Data from the NIST-JANAF tables50 that encompass enthalpic and entropic contributions to the Gibbs free energy at finite temperature were used for the gas-phase species. Pressure effects on the Gibbs free energy of the gas-phase species were calculated with a simple thermodynamic relationship for ideal gases. μi (T , p) = μi (T , p°) +

⎛ p⎞ 1 kBT ln⎜ ⎟ 2 ⎝ p° ⎠

RESULTS (110) Surface. The β-MnO2 (110) stoichiometric surface was shown to be the most stable surface of the three surfaces under consideration and was discussed in detail in earlier work.26 Structural details are summarized here for comparison with those of the hydrated surface models. Figure 1a depicts the stoichiometric surface and the layer spacing sequence used to calculate vertical relaxations. At the stoichiometric surface, 5‑fold coordinated and 6-fold coordinated manganese (Mn5 and Mn6, respectively) form alternating rows along the [110̅ ] direction (see Figure 1a). The Mn6 atoms are bridged by 2-fold coordinated Obr atoms along [001]. Surface oxygen atoms in the second atomic layer, Os, are 3-fold coordinated to two Mn5 and one Mn6. The vertical layer spacings, d, are given in Table 1, and Table 2 lists the lateral relaxations. The Obr and Mn5 atoms are predicted to undergo modest inward relaxations, while the Os and Mn6 atoms relax out of the surface. The Os atoms move away from Mn6 along [110̅ ] by 0.03 Å. Adsorption of water at the surface occurs via coordination of the oxygen (Ow) to Mn5, which completes the coordination sphere of Mn5. For the (110) surface, nine initial water geometries in the 1 ML coverage regime were optimized to give only four unique adsorption geometries: one molecular, two dissociative (one with H+ adsorbing on Obr and one with H+ adsorbing on Os), and one containing both associatively and dissociatively adsorbed water [optimized using a (2 × 1) surface cell], hereafter referred to as a mixed adsorption mode. These structures are shown in Figure 2. Table 3 contains relevant bond lengths as well as ΔEads and γ at maximum μO and minimum μH, excluding vibrational energy. With the exception of dissociative adsorption with H+ coordinating to Os, hydrogen-bonding networks form along the [001] direction between adsorbed H2O or OH− groups at 1 ML coverage (Figure 2). The strong hydrogen bond of 1.88 Å between the adsorbed hydroxyl group and Obr is preferable to the formation of a hydrogen-bonding network along [001] for dissociation on Os as no stable structure was found with the hydrogen-bonding network. Molecular adsorption and dissociative adsorption on Obr (Figure 2a,b, respectively) appear to have similar geometries except that hydrogen is transferred from the adsorbed water to Obr in the latter case. Another notable dissimilarity between these two surface reconstructions is the Mn−Ow bond length. As expected, water is more loosely bound to Mn5 than the hydroxyl group (Mn−Ow of 2.11 Å vs 1.90 Å). Mn5 therefore experiences relaxation into the surface during associative adsorption, as on the stoichiometric surface, while it undergoes outward relaxation during dissociative adsorption to facilitate the formation of a strong bond with the OH− group (Table 1). Dissociative adsorption on Obr also pulls Obr out of the surface, in contrast to what is observed for the stoichiometric surface and for molecular adsorption. These differences in relaxations can be used to identify surface reconstructions observed in experiments. Mixed adsorption shows a combination of the geometric characteristics and relaxations of association and dissociation (Tables 1−3). As shown in Tables 1 and 2, similarities exist for the vertical and lateral relaxations corresponding to the surface recon-

(8)

where p° is the reference pressure (101 kPa). In ab initio thermodynamics, the range of μO studied is defined based on physical constraints on the system. At the oxygen-rich limit, condensation of O2 on the surface occurs, and the maximum μO is therefore given by eq 5. Oxygen-poor conditions have the effect of removing oxygen from the oxide, leaving behind manganese metal. The minimum μO possible is then obtained from eq 4 when the Gibbs free energy of manganese metal, Gbulk Mn , is at a maximum. The range of μO employed is rescaled so that the maximum occurs at 0 eV and is given by the following relationship: 1 bulk 1 bulk (G MnO2 − GMn − GOgas2 ) < μO − GOgas2 < 0 2 2

(9)

was computed for α-Mn using GGA-optimized lattice constants,51 a (4 × 4 × 4) Monkhorst−Pack grid, and a collinear spin arrangement, which has been shown to be nearly degenerate with the complex, noncollinear spin arrangement at the optimized lattice constants.51 As is common practice in ab initio thermodynamics,26,35,47,49 the energy of the O2 molecule was corrected with the experimental atomization energy because of the large error (0.90 eV) in the GGA atomization energy. The heat of formation of β-MnO2 at 0 K (left-hand side of eq 9 in parentheses) is therefore calculated to be −5.88 eV, giving a lower limit of −2.94 eV for μO. Because of the uncertainty in the α-Mn and bulk MnO2 energies due to treating their complex spin arrangements as collinear, the percent error in the heat of formation is 10.2%, as found in previous work.26 While modeling noncollinear magnetism is possible,51 the common practice in calculations on these compounds is to use simplified collinear models of magnetism.3,4,26,51−54 Advances in simulating magnetism and increased availability of experimental data for method validation will be needed to improve the accuracy of calculations on manganese compounds. The strength of the chemical interactions between the surfaces and water, however, is much larger than the differences in energy between magnetic states of the oxide, and we therefore expect water−surface interactions to dominate the behavior of the surfaces. Finally, we address issues related to the H2 and H2O species. Over the range of possible μO values, μH is assumed to be at a minimum. The crossover from equilibrium with H2 to equilibrium with H 2 O was determined based on the intersection of eqs 6 and 7 for μH as a function of μO. When the O2 energy correction is applied, the crossover occurs at −2.88 eV, and equilibrium with H2O thus controls the Gbulk Mn

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surface by −14% relative to the bulk, while the other half of the Os atoms experience significant outward relaxation of +21% (Table 1). The most substantial lateral relaxations are observed for atoms in the second and third layers (Table 2). The greater relaxation of the second-layer atoms relative to that of Obr brings Obr closer to the adsorbed water or hydroxyl group. The layer 3 oxygen moves even further along [11̅0] to maintain the planarity of the equatorial oxygens in the coordination sphere of Mn6. Lindan and Zhang55 described these vertical and lateral movements of the Os atoms in terms of rotation of the linked octahedra at the (110) surface of rutile TiO2 to relieve the stress associated with hydrogen bonding between the adsorbed water and Obr. Figure 2 illustrates that all hydrogen bonds along the [110̅ ] direction are on the same side of Obr for the stable surfaces found in this study. This geometry is in contrast to several studies of hydrated rutile TiO255−58 and rutile-type SnO257,59 (110) surfaces, in which reconstructions obtained from optimization of a (2 × 1) surface cell had the hydrogen bonds involving Obr alternating in direction along [11̅0] (see Figure 4 for an example). Lindan and Zhang55 calculated adsorption to be slightly more favorable (by 0.03 eV/H2O) for alternating hydrogen-bonding direction on the rutile TiO2 (110) surface, while Kowalski et al.58 found a slight preference for all hydrogen bonds on the same side of Obr on the same surface (adsorption energies differed by no more than 0.02 eV/H2O). These energetic differences are small enough for the surfaces to be considered equivalent and are likely a factor of variations in the model used, which is known to have a significant impact on the relative stability of the adsorption modes for that system. We have investigated the alternation of the hydrogen bonds along [11̅0] for all three adsorption modes and found that for β-MnO2, this geometric variation is higher in adsorption energy by 0.05 eV/H2O than that shown in Figure 2. The surface reconstructions such as the one in Figure 4 experience less relaxation, and the hydrogen bonds involving Obr are longer and thus weaker than those pictured in Figure 2. These results demonstrate that less stress is released after hydrogen-bond formation when hydrogen bonds alternate in direction along [11̅0] (the octahedra cannot rotate as far because octahedra next to each other along [001] rotate in opposite directions). In fact, the energy of distortion is significantly higher for reconstructions involving alternating hydrogen-bonding direction than for those with all hydrogen bonds aligned in the same direction. A comparison of the energetics for the reconstructions in Figure 2 show that association, dissociation on Obr, and mixed adsorption are nearly degenerate at 1 ML coverage (Figure 5; Table 3), suggesting that a mixture of associated and dissociated water is likely to be observed in the real system. Dissociation on Os is significantly higher in energy because no hydrogen-bonding network forms and Os is already coordinatively saturated compared to Obr. Mixed adsorption is more favorable than dissociation on Obr and molecular adsorption by 0.06 eV/H2O and 0.08 eV/H2O, respectively. The fact that 75% of the hydrogen bonds formed by mixed adsorption are less than 1.80 Å in comparison to only 50% for molecular and dissociative adsorption modes may contribute to the small preference for mixed adsorption (Table 3). The comparable adsorption energies for association and dissociation on Obr are in contrast to calculated adsorption energies on the γ-MnOOH (010) surface. On this surface, molecular adsorption was found to be significantly more favorable than dissociation,49 and the

Figure 1. β-MnO2 stoichiometric surfaces showing surface atom types and layer stacking sequence. (a) (110) surface viewed along the [001] direction; (b) (100) surface viewed along the [001] direction; (c) (101) surface viewed along the [101̅] direction (O, red/dark sphere; Mn, purple/light sphere).

structions in Figure 2. Generally, the vertical relaxations for the hydrated surfaces tend to be more modest than those for the stoichiometric surface (Table 1) because completion of the Mn5 coordination sphere renders Mn5 more similar to manganese in the bulk oxide. The formation of hydrogen bonds along the [11̅0] direction, however, causes considerable buckling of the surface as the adsorbed H2O or OH− group and Obr (with or without adsorbed hydrogen) lean toward each other (see Figure 3). The effects of the buckling are observed in the vertical relaxations of the Os atoms and layer 5 oxygens and in the lateral relaxations of all atoms in the slab along [11̅0]. On average, the Os atoms below the hydrogen bonds relax into the 11592



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Table 1. Calculated Vertical Layer Spacings, d (Å), and Percent Relaxations with Respect to Theoretical Bulk Spacings for the β‑MnO2 (110) Stoichiometric Surface and Most Stable Hydrated Surface Models stoichiometrica d

layers

%Δ

x−1

dissociative (Obr)b

molecular d

d

%Δ

0.747

3−4 4−5 5−6

d

mix (Obr)c d

%Δ

0.761d 0.675 1.205d 1.290 1.194d 1.240 1.248 1.095 1.428 0.663 1.239 1.225 1.239 1.105 1.349

−2 +5 −3 +1 +1 −11 +16 −4 +1 −1 +1 −10 +9

%Δ

0.614

1.130

−8

1.194

−3

1.302

+6

1.179

−4

Mn5

1.121

−9

1.182

−4

1.251

+2

1.240

+1

Mn6 Os

1.315 1.378

+7 +12

Mn Mn O

0.669 1.274 1.199 1.269 1.235

−3 +3 −3 +3 0

1.280 1.083 1.475 0.650 1.251 1.215 1.251 1.090 1.356

+4 −12 +20 −5 +2 −1 +1 −12 +10

1.215 1.060 1.417 0.681 1.226 1.237 1.227 1.115 1.350

−1 −14 +15 −1 0 0 0 −10 +10

1.270 0.995 1.630 0.633 1.252 1.225 1.238 1.085 1.359

+3 −19 +32 −8 +2 −1 0 −12 +10

1−2 2−3

%Δ

0.584

dissociative (Os)b

a

Reference 26. bH+ is adsorbed on the oxygen indicated in parentheses. cMix denotes the case where half of the water is molecularly adsorbed and the other half is dissociatively adsorbed with H+ adsorbing on the oxygen indicated in parentheses. dFirst value is for H2O or atoms below it; second value is for OH− or atoms below it.

Table 2. Calculated Lateral Relaxations (Å) with Respect to Theoretical Bulk Positions for the β-MnO2 (110) Stoichiometric Surface and Most Stable Hydrated Surface Models stoichiometrica layers 1 2

3 4 5

6 7

Mn5 Mn6 Os

Mn Mn O

dissociative (Obr)b

molecular

dissociative (Os)b

mix (Obr)c

[11̅0]

[11̅0]

[001]

[11̅0]

[11̅0]

[001]

[11̅0]

+0.01 +0.01 +0.01 −0.02 +0.05 +0.01 0.00 +0.01 +0.01 0.00 +0.02 +0.01 0.00

+0.16 +0.30 +0.30 +0.31

0.00 0.00 0.00 ±0.01

+0.14 +0.28 +0.27 +0.28

+0.18 +0.43 +0.26 +0.33

0.00 0.00 ±0.04 ±0.01

+0.17 +0.28 +0.28 +0.29

+0.40 +0.05 +0.15 +0.16 +0.15

0.00 0.00 0.00 0.00 0.00

+0.37 +0.06 +0.14 +0.14 +0.14

+0.43 +0.05 +0.14 +0.16 +0.15

0.00 ±0.01 ±0.01 0.00 0.00

+0.37 +0.06 +0.14 +0.15 +0.14

+0.21 −0.06

0.00 0.00

+0.20 −0.06

+0.21 −0.06

0.00 0.00

+0.20 −0.06

a

Reference 26. bH+ is adsorbed on the oxygen indicated in parentheses. cMix denotes the case where half of the water is molecularly adsorbed and the other half is dissociatively adsorbed with H+ adsorbing on the oxygen indicated in parentheses.

reports of water adsorption on TiO2 and SnO2.57,59 First, the covalency of Mn−O bonds can be expected to fall between those of Ti−O and Sn−O bonds with Ti−O being least covalent and Sn−O most covalent based on electronegativity arguments (electronegativities are 1.32, 1.60, and 1.72 for Ti, Mn, and Sn, respectively).67 Therefore, the ability of hydrated manganese to act as a proton donor should be intermediate to those of hydrated titanium and hydrated tin. The second explanation relies on the basicity of Obr. On the SnO2 (110) surface, Obr was calculated to have electronic energy levels higher than oxygen in the bulk, whereas the oxygen electronic energy levels at the surface and in the bulk were similar on the TiO2 surface.57 Dissociative adsorption of water on the SnO2 surface led to the lowering of the Obr electronic energy levels. A similar shift in energy levels was not observed for dissociation of water on TiO2. In the present work, PDOS calculations shown in Figures 6b and 7a reveal similar results for the Obr electronic energy levels as found for the SnO2 (110) surface.

Mn−Ow bond lengths were much longer, revealing weak interactions between Mn3+ and adsorbed water.49,60 The degeneracy of molecular and dissociative adsorption on β‑MnO2 also differs from calculated water adsorption energies for rutile TiO2 and rutile-type SnO2. In most studies on rutile TiO2, associative adsorption is preferred to dissociative adsorption by a considerable energetic margin.55−58,61−64 The rutile-type SnO2 literature has indicated the opposite trend, namely, that water will dissociate on the SnO2 (110) surface.57,59,65,66 These results have been rationalized in terms of the larger unit cell parameters of SnO2, which do not allow for hydrogen bonding along the [001] direction during molecular adsorption.57,59,65 This explanation, however, does not capture the intermediate character for water adsorption on MnO2 as MnO2 has smaller unit cell parameters than TiO2 and SnO2. Instead, two possible reasons that may elucidate why the extent of water dissociation on MnO2 is predicted to be intermediate to that on TiO2 and SnO2 have been proposed in 11593



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Figure 2. Top-view of β-MnO2 (110) hydrated surfaces with oxygen and hydrogen atoms of adsorbed H2O, OH−, and H+ species pictured as blue/ black spheres and hydrogen bonds shown as dashed lines: (a) molecular adsorption; (b) dissociative adsorption on Obr; (c) dissociative adsorption on Os; (d) mixed adsorption with dissociation on Obr (structural O, red/dark sphere; Mn, purple/light sphere).

approach the stability of the hydrated surfaces. Therefore, the hydrated surfaces should be observed in experiments. To verify this prediction, γ was calculated as a function of temperature at the state point defined by ambient partial pressures of oxygen and water (pO2 = 20 kPa and pH2O = 3.2 kPa; Figure 5b). The hydrated surfaces are more stable than the stoichiometric surface up to 673 K. Because molecular, dissociative, and mixed adsorption modes are within 4.5 meV/Å2 in γ between 0 and 800 K, any combination of the modes may occur under ambient conditions. For surface science studies that are typically carried out in UHV, we have modeled an additional state point at pO2 = pH2O = 10−8 kPa. The results (not shown) indicate that the transition temperature from the hydrated surfaces to the stoichiometric surface simply shifts to a lower temperature of 468 K. In a real system containing water vapor, it is thus expected that water readily adsorbs on the β-MnO2 (110) surface associatively and/or dissociatively. (100) Surface. In previous work,26 the redox behavior of the β-MnO2 (100) stoichiometric surface, which is less stable than the (110) surface, was considered. Here, we examine hydration of the surface and briefly summarize appropriate details for the stoichiometric surface. As shown in Figure 1b, this surface consists of rows of 5-fold coordinated manganese (Mn5) along the [001] direction, which are bridged by 2-fold coordinated oxygen atoms (Obr). The Obr and layer 3 oxygen atoms relax out of the surface, while Mn5 undergoes inward relaxation (Table 4; see Figure 1b for layer sequencing). Small lateral movements along the [010] direction are experienced throughout the slab (Table 5). Hydration of the (100) surface was examined starting with a total of ten initial geometries, which resulted in the location of three unique molecular, two dissociative [with H+ adsorbing on Obr in one case and on layer 3 oxygen (L3−O) in the other], and one mixed adsorption mode. Table 3 lists ΔEads, γ, and bond lengths involving adsorbed water for these surfaces. Depictions of the lowest-energy surface reconstructions obtained for each adsorption mode are given in Figure 8, and the corresponding vertical and lateral relaxations appear in

The bare Obr atom exhibits energy levels above those of oxygen in the bulk (Figure 6a,b), and they shift to lower energies within the bulk valence band upon hydroxylation (Figure 7a). These findings demonstrate the energetic advantage of dissociation on the β-MnO2 (110) surface. The impact of hydrogen bonding on the energetics was explored by considering 0.25 ML coverage as well as a second hydration layer at the surface for associative and dissociative water adsorption. The adsorption energies and surface energies at low coverage are given in Table 3. The adsorption energies become slightly less favorable with decreasing coverage, while γ increases significantly. The large difference in γ between the low and high coverage regimes (0.25 and 1 ML, respectively) results from the difference in hydrogen bonding at the surface. The hydrogen-bonding networks along the [001] direction, which are absent at 0.25 ML, confer considerable stabilization to the surface. For example, distortion energies of the slabs with molecularly adsorbed water are comparable in both regimes, but the water−water interactions are stronger by 0.16 eV/H2O at 1 ML. Adding a second layer of water to the fully hydrated surface also shows the impact of hydrogen bonding on surface energies. Whereas surface energies are lowered by an average of 33.7 meV/Å2, interactions between the first and second hydration layers lead to an unfavorable increase in ΔEads by an average of 0.33 eV/H2O. It should be cautioned that additional water layers above the surface conceal the intrinsic surface physics (while dissociated water is predicted to be more stable than associated water at low and high coverage, the addition of the second hydration layer results in a preference for molecular adsorption). Finally, we discuss the ab initio thermodynamics results in the context of previous work and predict the relevant surface structure under environmental conditions. The calculated γ values as a function of μO at minimum μH, excluding vibrational contributions to the energy, are presented in Figure 5a. All of the fully hydrated surfaces are significantly lower in γ than the stoichiometric surface. Comparison to an earlier study26 shows that only at the lower limit of μO does any reduced surface 11594



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Table 3. Calculated Properties for Water Adsorbed on β-MnO2 Surfaces surface (110)

ML

ΔEads (eV/H2O)

γa (meV/Å2)

RMn−Ow (Å)

RO−H (Å)

0.25 1.0 0.25 1.0 1.0 1.0

−1.19 −1.26 −1.23 −1.28 −0.54 −1.34

35.8 −17.4 35.1 −18.2 22.2 −21.6

molecular

0.25 1.0 1.0

−1.13 −1.14 −1.08

42.5 −24.3 −19.8

2.08 2.11 1.86 1.90 1.84 1.93 2.06 2.08 2.11 2.11

molecular

1.0

−1.03

−15.6

1.71 1.57 1.82 1.64 1.88 1.74 1.78 1.76 1.71 1.81 2.30 1.68

dissociative (Obr)b

0.25 1.0

−0.91 −1.03

46.9 −15.4

dissociative (L3−O)b mix (Obr)c

1.0 1.0

−0.79 −1.07

3.38 −18.9

1.82 1.90 2.09

molecular

0.25 1.0 1.0

−1.25 −1.28 −1.20

53.4 −28.7 −21.5

2.06 2.08 2.13

0.25 1.0 1.0 1.0

−1.23 −1.32 −0.57 −0.95

53.7 −31.6 31.5 −0.764

1.0

−1.30

−30.3

1.88 1.90 1.82 1.82 1.92 1.94 2.07

1.0

−0.98

−2.78

type of adsorption molecular dissociative (Obr)b dissociative (Os)b mix (Obr)c

(100)

(101)

molecular

molecular dissociative (O2)b dissociative (L3−O)b dissociative (O2/L3−O)b mix (O2)c

mix (L3−O)c

2.06 2.18 1.88 1.86

1.90 2.00

1.63 1.92 2.15 2.43 1.57 1.64 1.84 2.45 1.59 1.46 1.63 2.29 1.57 1.55 1.68 1.48 2.05 1.53 1.56 2.44 1.65 1.86

ROw−H (Å) in hydrogen-bonding network 2.05 2.06 1.71 2.47 2.22 2.01 2.42

2.33

2.04 2.04d

1.92 1.88

1.94 1.83 1.75 2.06 1.64 1.94 1.51d

Surface free energies are given at maximum μO and minimum μH, excluding vibrational energy. bH+ is adsorbed on the oxygen indicated in parentheses. cMix denotes the case where half of the water is molecularly adsorbed and the other half is dissociatively adsorbed with H+ adsorbing on the oxygen indicated in parentheses. dThe hydrogen-bonding network is not fully formed because only half of the bonds in the usual direction of the network are present. a

Tables 4 and 5, respectively. Unlike on the (110) surface, the lowest-energy molecular and dissociative adsorption geometries involve more than just hydrogen transfer between Ow and Obr. Instead of the hydrogen bond remaining nearly linear as in the

Figure 3. Illustration of significant lateral relaxations upon water adsorption on the β-MnO2 (110) surface viewed along the [001] direction. Oxygen and hydrogen atoms of adsorbed H2O molecules are pictured as blue/black spheres, and hydrogen bonds are shown as dashed lines (structural O, red/dark sphere; Mn, purple/light sphere).

Figure 4. Illustration of the alternating direction of the hydrogen bonds with Obr upon water adsorption on the β-MnO2 (110) surface. Oxygen and hydrogen atoms of adsorbed H2O molecules are pictured as blue/black spheres, and hydrogen bonds are shown as dashed lines (structural O, red/dark sphere; Mn, purple/light sphere). 11595



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Figure 5. Surface free energies of the β-MnO2 (110) stoichiometric surface and most stable hydrated surface models as determined by ab initio thermodynamics (a) as a function of μO at minimum μH, excluding vibrational energy, and (b) as a function of temperature at pO2 = 20 kPa and pH2O = 3.2 kPa, including vibrational energy. In panel a, the vertical solid black lines bracket the range of accessible μO values as defined in the text. The vertical dashed black line indicates the crossover between equilibrium with H2 and equilibrium with H2O.

molecular adsorption mode, the transferred hydrogen moves along the [011] direction to form weak hydrogen bonds of 1.92 Å and 2.15 Å with adjacent Ow (see Figure 8a,b). This conformation is more favorable than one with a linear Obr− H···Ow configuration and one short Ow−H hydrogen bond because it leads to a shift of the Ow 2p orbitals to lower energies as determined by PDOS analysis (Figure 9). This rotation of the hydrogen bond also causes a lengthening of the hydrogen bonds in the network formed along the [001] direction compared to those at the surface with molecularly adsorbed water (Table 3). The different adsorption modes can be identified by measuring the vertical and lateral relaxations. As expected, the water overlayer is significantly closer to the surface when water dissociates on the (100) surface than when it adsorbs associatively (0.454 Å vs 0.730 Å above the Obr atoms). The weaker Mn5−Ow interaction observed for molecular adsorption leads to vertical and lateral relaxations similar to those for the stoichiometric surface, except that they are considerably smaller for the first several atomic layers (see Tables 4 and 5). The decrease in the magnitude of the surface relaxations results from the completion of the coordination sphere of Mn5 by Ow, which makes Mn5 more bulk-like. Dissociation of water at the

Figure 6. Oxygen 2p PDOS of (a) oxygen in the bulk and 2-fold coordinated oxygen on the β-MnO2 (b) (110), (c) (100), and (d) (101) stoichiometric surfaces. The curves are shifted so that the Fermi level is the Fermi energy of the bulk. The Fermi levels of the surfaces relative to that of the bulk are indicated with black vertical lines in panels b−d.

surface produces a MnO6 octahedron closely resembling that in the bulk, and therefore, the surface hardly relaxes relative to the bulk. Only Obr and L3−O undergo significant relaxations of +8% and +5%, respectively. A mixture of association and dissociation generates a surface reconstruction that shares characteristic surface relaxations of both adsorption modes (see Tables 4 and 5). It should be noted that the hydrogen bond between the adsorbed proton and hydroxyl group is shorter (more linear) than for the pure dissociative mode and that the 11596



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adsorbed proton and bringing Obr and L3−O closer by 0.65 Å relative to the bulk. Because of these large variations in relaxations compared to those for dissociation on Obr, the distortion energy of dissociation on L3−O is 0.97 eV higher than that for dissociation on Obr. This difference in distortion energies together with the fact that Obr is coordinatively undersaturated compared to L3−O on the stoichiometric surface leads to less favorable adsorption of H+ on L3−O than on Obr by 0.24 eV/H2O despite the significantly stronger hydrogen bonds formed when H+ adsorbs on L3−O. The energetics for the other adsorption modes (molecular, dissociative on Obr, and mixed) do not follow the same trends as observed for water adsorption on the (110) surface. Associative adsorption is calculated to be more stable than dissociative adsorption by 0.11 eV/H2O at 1 ML (Table 3). In contrast, water dissociation on the (100) surface of rutile TiO262,68 and rutile-type SnO259 was found to be more favorable than molecular adsorption. On the β-MnO2 (100) surface, molecular adsorption may be preferred over dissociation because Obr is not as basic as it is on the (110) surface [it has less density of states above the bulk valence band on the (100) surface than on the (110) surface (see Figure 6)]. No synergistic effect of mixing the two binding modes is observed on the β-MnO2 (100) surface with the adsorption and surface energies for mixed adsorption falling between those of associative and dissociative adsorption (Table 3). At low coverage (0.25 ML), the preference for molecular adsorption increases (ΔEads is −1.13 eV/H2O for association vs −0.91 eV/ H2O for dissociation). Kamisaka et al.69 also calculated greater stability for molecularly adsorbed water than for dissociatively adsorbed water at 0.25 ML on the rutile TiO2 (100) surface. Although the difference in adsorption energies doubles at low coverages, the difference in γ is halved, showing that the loss in hydrogen bonding along [001] affects surface energies more for molecular adsorption because the network involves shorter bonds. These results again reveal the sensitivity of surface energies to hydrogen bonding as does the fact that γ increases significantly (by approximately 65 meV/Å2) at low coverages. Ab initio thermodynamics results demonstrate the stability of the fully hydrated surfaces and are shown in Figure 10 for the four adsorption modes illustrated in Figure 8. As with the (110) surface, water adsorption stabilizes the (100) surface. Even dissociation on L3−O, which is accompanied by significant structural distortion, lies 61.2 meV/Å2 lower in γ than the clean stoichiometric surface when vibrational energy is neglected (Figure 10a). All other adsorption modes fall between 18.8 meV/Å2 and 27.7 meV/Å2 in γ below that. Calculated surface energies of (100) reduced and oxidized surfaces26 are substantially higher than those of any of the hydrated surfaces. At ambient conditions modeled as pO2 = 20 kPa and pH2O = 3.2 kPa (Figure 10b), the surface with 1 ML of associated water is predicted to be the most favorable surface up to 652 K. Above that temperature, entropic effects drive water from the surface, making the stoichiometric surface the most thermodynamically stable. Association, dissociation on Obr, and mixed adsorption are calculated to be within approximately 9 meV/Å2 to 12 meV/Å2 between 0 and 800 K under these conditions, and it is therefore possible that a combination of the binding modes may be observed experimentally. (101) Surface. The redox behavior of the β-MnO2 (101) surface was previously examined along with those of the (110) and (100) surfaces, and the stoichiometric surface was found to

Figure 7. Oxygen 2p PDOS of the 2-fold coordinated oxygen on the β-MnO2 (a) (110), (b) (100), and (c) (101) stoichiometric surfaces and stable hydrated surface models. For dissociative adsorption, H+ is adsorbed on the oxygen indicated in parentheses.

hydrogen-bonding network along [001] is not formed with only every other hydrogen bond being present (Figure 8d). L3−O is accessible for H+ adsorption as can be seen in Figure 8c. The hydrogen-bonding network and the hydrogen bond donated to Obr along [01̅0] for this adsorption mode are shorter and thus stronger than those on other (100) surfaces (Table 3). To accommodate the adsorbed proton, however, considerable structural rearrangement of the surface occurs. The largest differences in relaxations compared to the stoichiometric surface involve Obr and L3−O (Tables 4 and 5). Obr undergoes inward relaxation of −35% relative to the bulk, while L3−O experiences outward relaxation of +85%. Along with these translations along the surface normal, Obr and L3−O also move toward each other along [010], facilitating the formation of the 1.57 Å hydrogen bond between Obr and the 11597



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Table 4. Calculated Vertical Layer Spacings, d (Å), and Percent Relaxations with Respect to Theoretical Bulk Spacings for the β‑MnO2 (100) Stoichiometric Surface and Most Stable Hydrated Surface Models stoichiometrica layers

d

dissociative (Obr)b

molecular d

%Δ

x−1

d

%Δ

0.730

dissociative (L3−O)b d

%Δ

0.454

mix (Obr)c d

%Δ

0.715d 0.655 0.868d 0.984 0.775d 0.849 0.570 0.842 0.846 0.536 0.850 0.852

0 +13 −11 −3 +17 −3 −3 +10 −2 −2

%Δ

0.935

1−2

0.969

+11

0.888

+2

0.937

+8

0.569

−35

2−3

0.735

−16

0.795

−9

0.850

−2

0.764

−12

3−4 4−5 5−6 6−7 7−8 8−9

0.591 0.843 0.827 0.567 0.849 0.840

+22 −3 −5 +17 −3 −4

0.564 0.840 0.847 0.543 0.850 0.849

+16 −4 −3 +12 −2 −3

0.508 0.877 0.866 0.481 0.873 0.874

+5 +1 −1 −1 0 0

0.897 0.794 0.753 0.662 0.793 0.816

+85 −9 −14 +36 −9 −6

a


Table 5. Calculated Lateral Relaxations (Å) with Respect to Theoretical Bulk Positions for the β-MnO2 (100) Stoichiometric Surface and Most Stable Hydrated Surface Models stoichiometrica

dissociative (Obr)b

molecular

dissociative (L3−O)b

mix (Obr)c

layers

[010]

[010]

[001]

[010]

[001]

[010]

[001]

[010]

[001]

1 2

−0.21 +0.07

−0.02 +0.04

−0.01 +0.01

0.00 −0.02

−0.04 −0.02

+0.29 +0.17

−0.01 0.00

3 4 5 6 7 8 9 10

−0.13 −0.06 +0.02 +0.03 +0.02 +0.01 −0.03 −0.02

−0.08 −0.04 +0.01 +0.02 +0.02 +0.01 −0.02 −0.02

+0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00

−0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

−0.21 −0.09 −0.03 +0.10 +0.08 0.00 −0.06 −0.05

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

+0.01 +0.04d −0.02 −0.07 −0.04 ±0.01 +0.02 +0.02 0.00 −0.02 −0.02

−0.03 +0.04d −0.03 +0.01 0.00 ±0.01 0.00 0.00 0.00 0.00 0.00

a


be the least stable of the three.26 This surface is composed of 2‑fold coordinated oxygen atoms (O2) that bridge 5-fold coordinated manganese (Mn5) in different rows (Figure 1c). The undersaturated Mn5 relaxes into the surface by −9% relative to the bulk, while O2 experiences outward relaxation of +6% (Table 6; see Figure 1c for layer sequencing). Small vertical and lateral movements are observed throughout the rest of the slab (Tables 6 and 7, respectively). Atoms in the same layer translate toward each other along the [010] direction, which can be seen particularly clearly for Mn5 in Figure 1c. Initially, eight configurations of adsorbed water were optimized. The unique minima located included two molecular, three dissociative, and two mixed adsorption modes. Dissociation with H+ adsorption on O2, on L3−O, and on both O2 and L3−O constitute the three unique dissociative adsorption geometries. Figure 11 shows the lowest-energy surface reconstructions for association, dissociation on O2, dissociation on L3−O, and mixed adsorption, and Table 3 lists calculated properties for all unique minima. At 1 ML coverage, a hydrogen-bonding network forms along [101̅]. These hydrogen bonds tend to be stronger than those in the networks on the (110) and (100) surfaces (see Table 3) because the water

molecules can pack closer together along the [101̅] direction than they can along the [001] direction (Ow−Ow distances of 2.66 Å vs 2.88 Å). The lowest-energy associative and dissociative modes have similar structures (Figure 11a,b) as is the case on the (110) surface. The transfer of hydrogen to O2 results in a longer hydrogen bond along [010] and tighter binding of the hydroxyl group compared to water as demonstrated by a shorter Mn5−Ow bond (Table 3). The latter difference leads to variations in vertical relaxations that can be used to identify molecular vs dissociative adsorption. Mn5 is pulled out of the surface relative to its bulk position when OH− adsorbs, whereas it experiences slight relaxation into the surface for associative adsorption (Table 6). The height of the adsorbed oxygen atom above the surface is also a useful metric to discriminate between the two adsorption modes with associated water at a distance of 0.946 Å and dissociated water at 0.834 Å above O2. Other than these differences, the vertical and lateral relaxations for association and dissociation on O2 are similar (see Tables 6 and 7). Mixed adsorption (Figure 11d) results in a geometry that exhibits characteristics of both association and dissociation on O2 as indicated in Tables 3, 6, and 7. 11598



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Figure 8. Top-view of β-MnO2 (100) hydrated surfaces with oxygen and hydrogen atoms of adsorbed H2O, OH−, and H+ species pictured as blue/black spheres and hydrogen bonds shown as dashed lines: (a) molecular adsorption; (b) dissociative adsorption on Obr; (c) dissociative adsorption on L3−O; (d) mixed adsorption with dissociation on Obr (structural O, red/dark sphere; Mn, purple/light sphere).

Figure 10. Surface free energies of the β-MnO2 (100) stoichiometric surface and most stable hydrated surface models as determined by ab initio thermodynamics (a) as a function of μO at minimum μH, excluding vibrational energy, and (b) as a function of temperature at pO2 = 20 kPa and pH2O = 3.2 kPa, including vibrational energy. In panel a, the vertical solid black lines bracket the range of accessible μO values as defined in the text. The vertical dashed black line indicates the crossover between equilibrium with H2 and equilibrium with H2O.

leads to ΔEads and γ being an average of the two separate modes, even though the hydrogen bonding at the surface is not simply an amalgamation of the two. This averaging effect of combining different adsorption sites in a 1:1 ratio is also observed for the mixed adsorption modes. The adsorption energetics parallel those for the (110) surface in a number of ways. The lowest-energy structures for molecular, dissociative, and mixed adsorption have adsorption energies within 0.04 eV/H2O of each other and surface energies within 2.9 meV/Å2 [ΔEads and γ span 0.06 eV/H2O and 4.2 meV/Å2 for the equivalent geometries on the (110) surface]. Therefore, any combination of these modes may be observed experimentally. Similar to the (110) surface, dissociative adsorption is slightly more stable than molecular adsorption (Table 3). Batzill et al.70 calculated a significant preference for dissociation over association on the rutile-type SnO2 (101) surface, however, and confirmed that the water dissociates on this surface with photoemission spectroscopy. As discussed previously, dissociation on the SnO2 surface may be aided by the greater covalency of the Sn−O bond and by possibly greater basicity of O2. On the β-MnO2 (110) surface, a synergistic effect is revealed for mixed adsorption as it is the most favorable adsorption mode, but this effect is absent on the

Figure 9. Oxygen 2p PDOS of the adsorbed oxygen (Ow) on the β‑MnO2 (100) surface when dissociated water is present comparing a nonlinear Obr−H···Ow arrangement to a linear one. H+ is adsorbed on the oxygen indicated in parentheses.

L3−O may also act as an adsorption site for H+. Figure 11c shows the surface reconstruction for all dissociated hydrogen adsorbing on L3−O. The hydrogen-bonding network along [101̅] still forms between adsorbed OH− groups. Strong hydrogen bonds of 1.68 Å are donated from L3−O to O2. These interactions give rise to considerable vertical relaxations as O2 is pulled into the surface by −45% relative to the bulk and layer 3 expands outward by +23%, bringing O2 and L3−O closer together by 0.54 Å compared to the bulk. The distortion energy of the slab for this adsorption mode is nearly twice that for dissociation on O2. This result along with the fact that O2 is undersaturated explains the large difference in adsorption energies between dissociation on O2 and dissociation on L3−O with H+ adsorption on O2 being more favorable by 0.75 eV/ H2O (Table 3). Interestingly, adsorption of half of the protons on each site [the dissociative (O2/L3−O) entry in Table 3] 11599



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Table 6. Calculated Vertical Layer Spacings, d (Å), and Percent Relaxations with Respect to Theoretical Bulk Spacings for the β‑MnO2 (101) Stoichiometric Surface and Most Stable Hydrated Surface Models stoichiometrica d

layers

%Δ

x−1

dissociative (O2)b

molecular d

d

%Δ

0.946

%Δ

0.834

dissociative (L3−O)b d

%Δ

1.203

1−2

0.781

+6

0.766

+4

0.776

+5

0.405

−45

2−3

0.669

−9

0.730

−1

0.753

+2

0.764

+4

3−4 4−5 5−6 6−7 7−8 8−9

0.958 0.710 0.773 0.906 0.769 0.753

+1 −4 +5 −4 +4 +2

0.922 0.741 0.764 0.908 0.762 0.757

−3 +1 +4 −4 +3 +3

0.926 0.757 0.749 0.916 0.754 0.759

−2 +3 +2 −3 +2 +3

1.165 0.708 0.669 1.015 0.693 0.718

+23 −4 −9 +7 −6 −3

mix (O2)c d

%Δ

0.982d 0.926 0.741d 0.804 0.729d 0.769 0.913 0.752 0.762 0.905 0.761 0.760

+1 +9 −1 +4 −3 +2 +3 −4 +3 +3

a


Table 7. Calculated Lateral Relaxations (Å) with Respect to Theoretical Bulk Positions for the β-MnO2 (101) Stoichiometric Surface and Most Stable Hydrated Surface Models stoichiometrica

dissociative (O2)b

molecular

dissociative (L3−O)b

mix (O2)c

layers

[101̅]

[010]

[101̅]

[010]

[101̅]

[010]

[101̅]

[010]

[101̅]

[010]

1 2

+0.05 −0.08

±0.08 ±0.18

+0.03 −0.02

±0.06 ±0.08

+0.02 −0.01

±0.07 ±0.03

−0.21 −0.11

±0.13 ±0.10

±0.07 ±0.03

3 4 5 6 7 8 9 10

−0.04 +0.02 0 −0.04 +0.02 −0.01 −0.03 +0.03

±0.04 ±0.05 ±0.06 ±0.04 ±0.03 ±0.02 ±0.03 ±0.04

−0.03 +0.01 −0.01 −0.04 +0.02 −0.01 −0.04 +0.03

±0.02 ±0.04 ±0.03 ±0.04 ±0.03 ±0.01 ±0.04 ±0.04

−0.03 +0.01 −0.02 −0.04 +0.02 −0.01 −0.04 +0.03

±0.02 ±0.03 ±0.02 ±0.03 ±0.03 ±0.01 ±0.04 ±0.04

+0.12 −0.14 −0.09 −0.01 −0.08 −0.03 0.00 −0.03

±0.17 ±0.08 ±0.06 ±0.05 ±0.04 ±0.02 ±0.03 ±0.03

+0.05 +0.04d −0.04 −0.03 +0.01 −0.01 −0.04 +0.03 0.00 −0.04 +0.03

±0.03 ±0.03 ±0.01 ±0.04 ±0.04 0.00 ±0.04 ±0.04

a


(101) surface. Instead, ΔEads for mixed adsorption is simply an average of ΔEads values for association and dissociation on O2. Hydration of the (101) surface also differs from that of the (110) surface in that the preferred adsorption mode changes with coverage. At 0.25 ML coverage, molecular adsorption becomes slightly lower in energy than dissociation on O2. As shown in Figure 12, the ab initio thermodynamics results for the hydrated (101) surfaces are similar to those pictured in Figure 5 for the hydrated (110) surfaces. A large separation of 48.3 meV/Å2 in γ is observed between the stoichiometric surface and the surface with dissociation on L3−O, and the surface with associated water falls 60.1 meV/Å2 lower in γ than that (Figure 12a). Surfaces with dissociation on O2 and mixed adsorption are essentially degenerate with the one with molecularly adsorbed water. All three of these surfaces are significantly lower in γ than any reduced or oxidized surface found in previous work.26 At ambient conditions of pO2 =

surface is therefore likely to be observed under environmental conditions, as is noted for the (110) and (100) surfaces as well. Surface Reactivity. The 3d DOS of Mn5 on different surface slabs are shown in Figure 13 to demonstrate changes in the 3d states when Mn5 interacts with water. The Lewis acidity of Mn5 on the (110) and (100) surfaces decreases upon water adsorption as evidenced by the reduction in the number of 3d states directly above the Fermi energy EF (Figure 13a,b). While the acidity of Mn5 on the (101) surface does not appear to diminish appreciably, a downward shift in the 3d DOS below the Fermi level is observed when water adsorbs, indicating that the stability of the surface is enhanced (Figure 13c). Because of an increased hybridization between the Mn5 3d states and Ow 2p states, dissociative adsorption lowers the energy of the Mn5 3d states more than associative adsorption. This trend in the energy of the Mn5 3d states is also observed for water adsorption on the (100) surface. Because of good orbital overlap between Mn5 and the Os atoms on the (110) stoichiometric surface (not shown), the Mn5 3d states are already lower in energy relative to EF than those on the (100) and (101) stoichiometric surfaces, and their energies are not reduced when water adsorbs at the Mn5 sites.

20 kPa and pH2O = 3.2 kPa (Figure 12b), adsorbed water is predicted to be driven off the surface by entropic effects at a temperature of 727 K. The fully hydrated form of the (101) 11600



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Figure 11. Top-view of β-MnO2 (101) hydrated surfaces with oxygen and hydrogen atoms of adsorbed H2O, OH−, and H+ species pictured as blue/black spheres and hydrogen bonds shown as dashed lines: (a) molecular adsorption; (b) dissociative adsorption on O2; (c) dissociative adsorption on L3−O; (d) mixed adsorption with dissociation on O2 (structural O, red/dark sphere; Mn, purple/light sphere). Figure 12. Surface free energies of the β-MnO2 (101) stoichiometric surface and most stable hydrated surface models as determined by ab initio thermodynamics (a) as a function of μO at minimum μH, excluding vibrational energy, and (b) as a function of temperature at pO2 = 20 kPa and pH2O = 3.2 kPa, including vibrational energy. In panel a, the vertical solid black lines bracket the range of accessible μO values as defined in the text. The vertical dashed black line indicates the crossover between equilibrium with H2 and equilibrium with H2O.

We also note interesting trends in reactivity of surface oxygen atoms based on PDOS analysis. Figure 7 illustrates the decrease in reactivity of the 2-fold coordinated oxygen on all surfaces upon water adsorption as the 2p bands of these oxygen atoms shift to lower energies below their respective Fermi levels. These energy shifts reflect the increasing saturation of Obr or O2 through interactions with adsorbed water or adsorbed protons. When water associatively adsorbs, these oxygen atoms benefit from hydrogen-bonding interactions with the adsorbed water. Covalent bonding with adsorbed H+ upon water dissociation leads to even greater energetic gains because of hybridization of the H 1s and O 2p orbitals leading to new DOS below −6 eV (see Figure 7). These oxygen atoms are therefore less basic after donating electron density to protons. The reactivities of different oxygen types on the same surface are compared in Figure 14. The left-hand panel shows the results for associative adsorption, and results for dissociative adsorption are given in the right-hand panel. As expected, Ow of adsorbed water is significantly less reactive than Obr or O2 in the case of molecular adsorption. Most of the 2p DOS of Ow is lower than −3 eV, while Obr and O2 still exhibit substantial basicity with greater than 70% of their 2p DOS above −3 eV. The relative reactivities of the 2-fold coordinated oxygen and Ow become reversed upon water dissociation on the (110) and (100) surfaces (see Figure 14b,d, respectively). On the (101) surface with dissociated water, the O2 and Ow 2p bands are similar because of the stronger hydrogen-bonding network on this surface (Figure 14f). These results indicate that they should have approximately the same basicity. An analysis of the energetics also leads to general observations about the surface reactivity. First, hydration of the surfaces decreases their surface energies to a greater degree

as the thermodynamic stability of the clean surface decreases. The surface energies of the (110), (100), and (101) stoichiometric surfaces at maximum μO and minimum μH, excluding vibrational energy, are 52.1 meV/Å2, 64.6 meV/Å2, and 79.7 meV/Å2, respectively. Upon adsorption of 1 ML of water, the lowest-energy surface becomes the (101) surface with dissociated water at γ = −31.6 meV/Å2, followed by the (100) surface with associated water at γ = −24.3 meV/Å2 and the (110) surface with mixed adsorption at γ = −21.6 meV/Å2. These results are expected because stronger and/or greater proportions of bonds are broken to create the less stable stoichiometric surfaces, leaving more reactive atoms at the surface. Reformation of the broken bonds via hydration therefore leads to greater stabilization for the more reactive high-energy surfaces. The trends in stability for the different surface planes as calculated with ab initio thermodynamics do not correspond to the adsorption energies. Water adsorption energies on the (110) and (101) surfaces are essentially degenerate at both low and high coverages. Adsorption on the (100) surface is, however, less favorable by approximately 0.20 eV/H2O at 1 ML. This difference in adsorption energetics likely arises from variations in the basicity of the terminal oxygen on the surface [Obr on the (110) and (100) surfaces; 11601



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vibrational modes that may aid the interpretation of future experimental results. Water bending modes are computed to occur in the range of 1598 cm−1 to 1644 cm−1 and support the presence of associated water, although they do not definitively rule out dissociation as in a mixed adsorption mode. Shifts in the water bending mode may, however, suggest the presence of dissociated water. For the (110) and (101) surfaces, molecularly adsorbed water exhibits a bending mode at 1598 cm−1 that shifts to 1644 cm−1 and 1626 cm−1, respectively, for mixed adsorption. In contrast, the water bending mode undergoes a small red shift from 1621 cm−1 for molecular adsorption to 1615 cm−1 for mixed adsorption on the (100) surface. Differences in O−H stretching modes can also be used to distinguish between molecular and mixed adsorption. Both the (110) and (100) surfaces have twice as many O−H stretching modes on surfaces with a mix of adsorption modes as on surfaces with associatively adsorbed water only. This doubling in vibrational modes accounts for the fact that there are twice as many different O−H bonds at the surface with mixed adsorption. Calculated O−H stretching frequencies are given in Table 8 and show that these modes are distinct for molecular and mixed adsorption on all surfaces studied.

■

CONCLUSIONS Hydration of the β-MnO2 (110), (100), and (101) surfaces has been studied using periodic DFT and ab initio thermodynamics calculations. Generally, fully hydrated surfaces are significantly lower in surface free energy than the stoichiometric surfaces and are likely to be observed under environmental conditions when water vapor is present. On the (110) surface, a mixed adsorption mode is the most stable, but surfaces with only dissociated or associated water are close in energy. The nearly degenerate surface energies for the three modes demonstrate the intermediate ability of the β-MnO2 (110) surface to dissociate water compared to those of the rutile TiO2 and rutile-type SnO2 (110) surfaces, resulting from the intermediate covalency of Mn−O bonds and basicity of Obr in this system. The three adsorption modes are essentially degenerate on the (101) surface as well, although dissociated water is predicted to be somewhat more favorable than mixed or molecular adsorption. In contrast, the (100) surface shows a marked preference for molecularly adsorbed water, likely due to the decreased basicity of Obr on this surface compared to 2-fold coordinated oxygen on the (110) and (101) surfaces. On all three surfaces, the adsorption on H+ on exposed 3-fold coordinated oxygen atoms leads to considerable geometric distortion of the slab and thus unfavorable energetics compared to adsorption on 2-fold coordinated surface oxygen. In the low coverage regime (0.25 ML), the results for the three surfaces are generally unchanged with molecular and dissociative adsorption being degenerate on the (110) and (101) surfaces and association being more favorable on the (100) surface. The loss of the hydrogen-bonding networks at low coverage causes considerable increases in γ for all surfaces (between 53 meV/Å2 and 85 meV/Å2), although the energies are still lower than those of the stoichiometric surfaces. The sensitivity of γ to the presence of hydrogen bonds is also revealed by adding a second hydration layer, which conceals the true physics of the water− surface interactions as shown in the case of the (110) surface. PDOS analysis has been performed to explore changes in surface reactivity upon water adsorption. As expected, adsorption of water or hydroxyl groups on Mn5 generally shifts the Mn5 3d states to lower energies, indicating that the

Figure 13. Manganese 3d PDOS of Mn5 on the β-MnO2 (a) (110), (b) (100), and (c) (101) stoichiometric surfaces and stable hydrated surface models. For dissociative adsorption, H+ is adsorbed on the oxygen indicated in parentheses.

O2 on the (101) surface] and in the aciditiy of Mn5. On the (100) stoichiometric surface, Obr has less DOS above the bulk oxygen 2p valence band (see Figure 6), and Mn5 has less DOS within 0.5 eV above EF (see Figure 13). The reactivity of these atoms should therefore be reduced compared to the corresponding atoms on the (110) and (101) surfaces. Interestingly, these results are consistent with the relative ease of manganese oxidation on the (110) and (101) surfaces compared to that on the (100) surface as discussed in previous work.26 Calculated Vibrational Frequencies. As stated previously, comparisons of measured and calculated surface relaxations can be utilized to identify the type of adsorption at all three surfaces, and measured and calculated vibrational spectra are also useful for this purpose. Here, we list calculated 11602



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Figure 14. Oxygen 2p PDOS of surface oxygen on β-MnO2 hydrated surfaces: (a) molecular adsorption on (110); (b) dissociative adsorption on Obr on (110); (c) molecular adsorption on (100); (d) dissociative adsorption on Obr on (100); (e) molecular adsorption on (101); (f) dissociative adsorption on O2 on (101).

Table 8. Calculated O−H Stretching Frequencies (cm−1) for Various Water Adsorption Modes on β-MnO2 Surfaces (110)

(100)

(101)

molecular

dissociative (Obr)a

mix (Obr)b

molecular

dissociative (Obr)a

mix (Obr)b

molecular

dissociative (O2)a

mix (O2)b

2504 3515

2680 3494

2975 3039 3102 3677

3024 3577

3340 3632

2924 3147 3461 3656

2113 2203 3509 3556

2575 2589 3507 3532

2586 2665 3021 3610

a

H+ is adsorbed on the oxygen indicated in parentheses. bMix denotes the case where half of the water is molecularly adsorbed and the other half is dissociatively adsorbed with H+ adsorbing on the oxygen indicated in parentheses.

β‑MnO2 surfaces also decreases upon water adsorption as these oxygen atoms donate electron density to adsorbing water via hydrogen bonds or to adsorbing protons via covalent interactions. These oxygen atoms become less basic than

Mn5 atoms become less reactive as Mn5 becomes coordinatively saturated. This shift in electronic energy levels is not observed for Mn5 on the (110) surface because the energy levels are already low relative to EF on the stoichiometric surface. The basicity of undersaturated oxygen atoms at 11603



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adsorbed hydroxyls on surfaces with dissociated water present and are therefore less likely to adsorb additional protons. Also presented in this work are metrics that would be useful to experimentalists studying hydration of β-MnO2 surfaces. Calculated vertical relaxations can be employed to identify molecularly and dissociatively adsorbed water, which have different effects on the layer spacings. Most notably, hydroxyl groups are more tightly bound to the surface than adsorbed water molecules and therefore affect the layer spacings in a number of ways. First, the oxygens of the OH− groups are closer to the surface layer by 0.11 Å to 0.28 Å compared to those of adsorbed H2O. The OH− groups also pull Mn5 out of the surface relative to the stoichiometric surface to a greater degree than the H2O molecules do. Furthermore, calculated vibrational spectra show distinct modes associated with each type of adsorption, which can be compared to measured spectra and aid classification of experimentally observed adsorption. The presence of associated water is easily detected with the water bending mode. This mode tends to shift if water dissociation and association occur simultaneously at the surface. The O−H stretching modes similarly show characteristic frequencies for each type of adsorption. The validation of the predicted stable surfaces through experimental means will help to elucidate environmentally relevant surface terminations that participate in important geochemical and technological processes.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Pacific Northwest National Laboratory, Richland, Washington 99352, United States. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.A.E.O. was supported by the National Research Council. This work utilized high-performance computing resources of the Raritan cluster at the National Institute of Standards and Technology and of the Arctic Region Supercomputing Center at the University of Alaska Fairbanks. We would like to thank Professors Sara Mason and Tom Trainor and Drs. Peter Eng and Joanne Stubbs for useful discussions.

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Structure and Stability of Hydrated Î²-MnO2 Surfaces - American

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