Interaction of Oxygen and Water with the (100) Surface of Pyrite

Aug 16, 2012 - Ab initio Studies of O2 Adsorption on (110) Nickel-Rich Pentlandite (Fe4Ni5S8) Mineral Surface. Peace Mkhonto , Hasani Chauke , Phuti ...
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Interaction of Oxygen and Water with the (100) Surface of Pyrite: Mechanism of Sulfur Oxidation Patrick H.-L. Sit,*,† Morrel H. Cohen,†,‡ and Annabella Selloni† †

Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, United States

‡

S Supporting Information *

ABSTRACT: We present a density-functional study of the adsorption and reactions of oxygen and water with the (100) surface of pyrite. We find that dissociative adsorption is energetically favorable for oxygen, forming ferryl-oxo, Fe4+O2−, species. These transform easily to ferric-hydroxy, Fe3+−OH−, in the presence of coadsorbed water, and the latter fully covers the surface under room conditions. A mechanism for surface oxidation is identified, which involves successive reactions with molecular oxygen and water, and leads to the complete oxidation of a surface sulfur to SO42−. The crucial recurring process is the surface O2− and OH− species acting as proton acceptors for incoming water molecules. Using a recently proposed method, we examine the oxidation state changes of the surface ions and the electron flow during the adsorption and oxidation processes. The oxidation mechanism is consistent with isotopic labeling experiments, suggesting that the oxygens in SO42− from gas-phase oxidation are derived from water. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis

P

molecular and dissociative adsorption configurations are examined, and the structure of the surface exposed to water vapor and gaseous oxygen at finite temperature is determined. We then study a possible mechanism for the oxidation of the pyrite surface by water and O2 in gaseous phase. We identify several important reaction intermediates and analyze in detail the oxidation state (OS) changes of the surface ions during the reaction. Oxygen and Water Adsorption on the FeS2(100) Surface. Computed molecular adsorption and coadsorption structures of O2 and water on FeS2(100) are shown in Figure 1. Binding to surface sulfurs is found to be unstable for both O2 and H2O. O2 binds stably to a single surface undercoordinated Fe ion in an end-on configuration (Figure 1a) and to two neighboring Fe’s connected by a subsurface S in a side-on configuration (Figure 1b). In the former, the distance between the Fe and the O bound to it is 1.83 Å, and the O−O distance is 1.29 Å, compared to 1.23 Å for gas phase O2. This theoretical end-on binding configuration has been reported previously.6,25,26 However, the side-on binding configuration is new and slightly more stable. In it, the two Fe−O distances and the O−O distance are 1.97, 1.99, and 1.38 Å, respectively. We shall show below that this stretched binding configuration is a key reaction intermediate in pyrite surface oxidation. The adsorption geometry of water on FeS2(100) is shown in Figure 1c. H2O binds to an undercoordinated Fe with an

yrite (FeS2), the most abundant sulfide mineral on the earth’s surface,1,2 has been extensively studied for its important and often detrimental effects on the environment. For instance, the oxidative decomposition of pyrite at coal and metal mining sites leads to acid mine drainage, a very serious environmental problem.3,4 More recently, pyrite has attracted significant interest5−9 as a potentially promising material for photovoltaic applications and photoelectrochemical cells10−12 due to its suitable bandgap, its strong photoabsorption, and its practically unlimited supply on earth. Still, the facile oxidation of pyrite by water and oxygen3,5,13−16 remains a major problem that severely limits the potential applications of this material. Protection of pyrite against unwanted oxidation demands detailed understanding of the underlying reaction mechanisms. Experimental surface science studies of the reaction of pyrite with water vapor and oxygen have focused on hydration,15−21 oxidation,14−16 and desulfurization.20,22 A model of surface oxidation23,24 based on X-ray photoelectron spectroscopy (XPS), UV photoelectron spectroscopy (UPS), and scanning tunneling microscopy (STM) experiments was proposed, which involved the cycling of Fe2+/Fe3+ on the surface to explain the propagation of oxidized patches on the surface. Ab initio studies have been also performed to gain insight into the chemistry of different stoichiometric and defective pyrite surfaces.8,9,15,21,22,25 However, a full atomistic understanding of the mechanism of pyrite oxidation has not yet been established. The aim of this work is to contribute microscopic insight into the mechanisms of pyrite oxidation by comprehensive firstprinciples density-functional theory (DFT) calculations of the reactions of O2 and water with the FeS2(100) surface. Various © 2012 American Chemical Society

Received: July 20, 2012 Accepted: August 16, 2012 Published: August 16, 2012 2409

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occupancy (i.e., occupation number = 1), and the OS can therefore be inferred. A brief description of the method is also found in the Supporting Information (SI). The occupation numbers on which the OS assignments are based are shown in Table SI1. As expected, both the bulk Fe and the undercoordinated surface Fe have +2 OS with zero net spin. The binding of an H2O does not change the OS of the Fe to which it binds. This agrees with previous studies, which suggested that water only physisorbs on the pyrite surface.17,29 An Fe ion bound to an end-on O2, on the other hand, has a +3 OS and is in the S = 1/2 spin state, indicating that an electron is transferred from the Fe to the dioxygen upon binding, which then becomes a superoxide. This is consistent with the elongated O−O bond of 1.29 Å compared to 1.23 Å of an isolated O2 molecule, although this bond length is still slightly shorter than that of the typical superoxide bond, ∼ 1.33 Å. The formation of a superoxide via electron transfer from a surface Fe was also suggested previously.23 For the two Fe bound to a side-on O2, the determination of OS by the method of ref 28 is less straightforward: the smallest occupation numbers that indicate “full” occupation differ from the largest partial occupation numbers of the same spin by only 0.11 (see Table SI1). However, from the O−O distance of 1.38 Å suggestive of a O22− peroxide species, we infer that the OS of each Fe ion is +3. Since the slab has a total spin of S = 1, a net spin of 1/2 was assigned to each Fe3+. The O−O bond of the side-on O2 readily breaks. The energy barrier is 6.1 kcal/mol (Figure 1e), and the process is exoenergetic by 26.2 kcal/mol. The OS analysis shows unambiguously that the two O-bound Fe ions are +4 (Table 1). The O2 binding and the subsequent O−O bond cleavage thus oxidize the two surface Fe ions from +2 to +4, leading to the formation of ferryl-oxo, Fe4+ = O2−, surface species. The FeO bond length is 1.67 Å. An adsorbed H2O molecule is stabilized by the presence of a neighboring O2− adatom by the formation of an H-bond between them; the H2O binding energy increases from 15.7 to 23.1 kcal/mol. However, an H-bond can form only when the H2O is bound to an Fe connected to the O2−-bound Fe by a subsurface sulfur (Figure 2a left panel). H2O and O2− bound to two Fe connected by a surface sulfur do not form an H-bond (Figure 2b). No significant change in the H2O binding energy occurs in this case. When there is an H-bond between an adsorbed H2O and an O2− adatom, proton transfer from water to O2− can occur. This process is slightly endoenergetic, by 0.6 kcal/mol, and has an energy barrier of 2.9 kcal/mol (Figure 2a). After the proton transfer, the surface Fe originally bound to the water is oxidized from +2 to +3, while the Fe originally bound to the O2− is reduced from +4 to +3, resulting in the formation of two ferrichydroxy species, Fe3+−OH−, with an Fe−OH bond length of 1.84 Å. This transformation is an example of a proton-coupled electron-transfer process in which a proton is transferred from a surface-bound water to a surface O2−, and an electron is concurrently transferred along the pyrite surface between two Fe. Structure of FeS2(100) in Contact with Gaseous Water and O2. Phase stability diagrams for the pyrite (100) surface in contact with water vapor and O2 were determined using an ab initio thermodynamic approach30,31 (see the SI for details). Figure 3a shows the surface free energies as a function of water vapor pressure at 298.15 K, where γ0, γ1, and γ8 denotes the free energy for the surface with zero, 1/8 monolayer (ML), and 1

Figure 1. Adsorption structures and energies of oxygen and water on FeS2(100). (a) Oxygen end-on configuration. (b) Oxygen side-on configuration. (c) Water. (d) Water/oxygen coabsorption with the oxygen in the side-on configuration. (e) O−O bond cleavage from the side-on O2 configuration. The Fe ions bound to the O are oxidized to +4 (see Table 1). ΔE is the energy of reaction and Ea is the barrier, both in kcal/mol. The top three pyrite layers (surface S, surface Fem and subsurface S) are shown in the stick format. The rest of the atoms of the pyrite are not shown. The spheres represent atoms of the absorbed molecules: Fe atoms are brown, S yellow, O red, and H white. This color code is used in all the following figures.

energy of 15.7 kcal/mol and an Fe−O distance of 2.13 Å. In a previous DFT study, Stirling et al.21 found a similar adsorption energy, 12.9 kcal/mol, using DFT calculations with the BLYP functional. Other theoretical studies predicted an energy of 50.8 kcal/mol from Hartree−Fock cluster calculations,25 or 11.2 kcal/mol using empirical potentials.27 Temperature-programmed desorption (TPD) experiments,20 on the other hand, provided an estimate of the water adsorption energy of ∼10.0 kcal/mol, which is 5.7 kcal/mol smaller than our computed value. Such a difference can be considered within the expected errors of DFT calculations for systems as complex as the one under investigation. When water is coadsorbed with O2 (Figure 1d), the total adsorption energy is 32.3 kcal/mol, and does not depend on the relative positions of the two adsorbates. In fact, this value is very close to the sum of the individual adsorption energies, suggesting minimal interaction between the two adsorbates. Useful insight into the adsorption and reaction mechanisms can be obtained from an analysis of OS of the surface ions. Table 1 shows the OS of relevant bulk and surface Fe ions with Table 1. Spin States and OS of the Relevant Fe Ions in the Presence of Water and Oxygen Surface Adsorption representative bulk Fe representative surface Fe Fe bound to the end-on oxygen, Figure 1a 1st Fe bound to a side-on oxygen, Figure 1b 2nd Fe bound to a side-on oxygen, Figure 1b Fe bound to the O of H2O, Figure 1c Fe bound to an O adatom, Figure 1e (right panel)

spin of Fe

OS

0 0 −1/2 1/2 1/2 0 1

+2 +2 +3 +3 +3 +2 +4

and without adsorbed water and O2 obtained using the method of ref 28. In this method, a 5 × 5 d-orbital occupation matrix is constructed by projecting the Kohn−Sham orbitals onto the atomic d-orbitals of the transitional metal ion. The occupation numbers are then computed as the eigenvalues of this occupation matrix. We assign the number of d electrons to the transition metal ion as the number of d-orbitals with full 2410

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and the black dashed lines in Figure 3a cross), all surface waters desorb. Experiments18−20,32 performed in ultrahigh vacuum (UHV) conditions (p ∼ 10−10 mbar = 10−13 atm) also suggested that all surface waters desorb at room temperature. Our results thus appear consistent with experiment despite our slightly overestimated water adsorption energy. Figure 3b shows the surface free energies in the presence of adsorbed O2 at 298.15 K. We focus here on the most stable dissociated configuration, and consider 1, 2, 3, and 4 adsorbed O2 per unit cell, which correspond to O surface coverages of 25%, 50%, 75% and 100%, respectively. The total adsorption energies are 42.8, 83.1, 114.7, and 143.7 kcal/mol, respectively, indicating that the adsorption energy per molecule decreases with increasing coverage as in the case of water. From Figure 3b, we see that full O-coverage is favored at the O2 partial pressure in air (∼ 0.21 atm). A somewhat smaller 75% coverage becomes more favorable only when the partial pressure is below ∼10−12 atm (not shown in Figure 3b; see Figure 4).

Figure 2. Water coadsorbed with two O2− formed from an O2. (a) An H-bond between the water and the O2− stabilizes the binding of water. The water binding energy is 23.1 kcal/mol compared to 15.7 kcal/mol without the O2−. The H-bond can only form when the two Fe bound to the water and to the O2− are connected by a subsurface sulfur. The formation of the H-bond also allows a proton transfer from the water to the O2− to occur readily. This proton transfer is coupled to an electron transfer between the two Fe bound to the water and to the O2−. ΔE is the energy of reaction, and Ea is the barrier, both in kcal/ mol. (b) No H-bond between the water and the O2− when the two Fe are connected by a surface sulfur.

Figure 4. Surface phase diagram for water/oxygen coadsorption at 298.15 K.

In order to determine the surface structure in the presence of coadsorbed O2 and water, we examined numerous configurations and searched for the energetically most favorable one in different conditions. Figure 4 shows the coadsorption phase diagram at different water and O2 partial pressures and a temperature of 298.15 K. The inset figures show the corresponding geometries. At high O2 partial pressure and low H2O partial pressure, a surface with 100% O-adatom coverage is the most stable phase (lower right corner of Figure 4). As the water partial pressure increases, the system favors an intermediate phase with coadsorbed oxygen (75%) and water (25%). However, the region corresponding to this phase on the phase diagram is so narrow that its existence cannot be unambiguously confirmed due to errors in DFT. As the water partial pressure further increases, the system reaches another phase in which all surface Fe are bound to hydroxyls. This is the most stable phase in normal conditions. This adsorption configuration starts with 50% of the surface Fe atoms bound to O2 and the other 50% bound to H2O molecules. After O−O bond breaking, the system is further stabilized when one proton of each adsorbed water is transferred to a neighboring O2− adatom. The OS of all the surface Fe are +3 in this phase. Finally, there is a fourth phase at low O2 and water partial pressures that consists of 75% O2 coverage (lower left corner of Figure 4).

Figure 3. Surface free energy in the presence of adsorbed (a) water and (b) O2, as a function of water vapor and O2 pressure, respectively, at 298.15 K.

ML of water molecules bound to the surface Fe ions, respectively. The computed total adsorption energy at full coverage is 112.0 kcal/mol, which amounts to 14.0 kcal/mol per water molecule, a value slightly smaller than that found at 1/8 ML (15.7 kcal/mol). A similar reduction in the adsorption energy per water molecule at full coverage compared to low coverage was also reported by Stirling et al.21 At room temperature, the vapor pressure of water in air is around 0.023 atm. The configuration with lowest free energy at this vapor pressure corresponds to the fully hydrated surface, as indicated by the green line in Figure 3a. On the other hand, when the vapor pressure is below 6 × 10−4 atm (the point where the red 2411

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Oxidation of FeS2(100) in Contact with Gaseous O2 and H2O. Experimental studies of the oxidation mechanism15,18,20,33 have been performed by exposing a clean pyrite surface prepared by ion bombardment and acid rinsing19,20 to a mixture of H2O and O2 or to the individual gases for finite periods of time. The surface oxidation was then studied in UHV by STM, photoelectron spectroscopy, or electron diffraction. A pyrite surface exposed to water vapor alone was found to result in no surface oxidation, whereas exposure to pure O2 gas oxidizes both surface Fe and S.15,34 For exposure to a mixture of H2O and O 2 , however, the oxidation is significantly more pronounced than in the case of exposure to O2 alone, with iron oxyhydroxide, FeO(OH), and different sulfur oxides as products. Isotopic labeling experiments suggested35 that the oxygens from the sulfur oxide products are derived from H2O, and those of iron oxyhydroxide are from O2. On the basis of this experimental information and our results for oxygen and water adsorption in Figures 1−4, we have identified a possible oxidation mechanism that involves a sequence of reaction steps leading to the full oxidation of a surface S to an SO42− ion (see Figure 5). The Fe and S ions that exhibit OS changes during the reaction are the surface and subsurface sulfurs (S1 and S2), and the four Fe ions surrounding them (Fe1 to Fe4). The oxidation process starts with a dissociatively adsorbed O2 and a water molecule forming an Hbond with one of the O adatoms (Figure 5a). Two protons are

transferred from an incoming H2O to the two FeO species to form two surface Fe−OH, while the resulting bare water oxygen forms an S−O bond with the surface S (S1) close to the two Fe (Figure 5b). Nudged-elastic band (NEB) calculations36 show that this process has a barrier of 21.3 kcal/mol and is exoenergetic by 23.7 kcal/mol. Next, a second water molecule is added; by forming H-bonds with the other adsorbates, this water molecule is stabilized by 5.6 kcal/mol (Figure 5c). Two protons are transferred from the second water to the two Fe−OH, resulting in the formation of two surface-bound waters. The remaining O from the second added water molecule forms another S−O bond with S1 (Figure 5d). The S1−S2 bond is found to break in this step. Altogether, this step is endoenergetic by 0.5 kcal/mol and has an energy barrier of 22.7 kcal/mol. To proceed further, another O2 is added, which causes the displacement of the two adsorbed waters. After dissociation of the added O2 to form two FeO, a third water molecule is added, which forms H-bonds with the two FeO species (Figure 5e). The energy barrier for O−O bond cleavage in this case is expected to be smaller than that of the first O−O cleavage of 6.1 kcal/mol. In this case, the O−O bond length after side-on adsorption is in fact 1.43 Å, longer than the O−O bond length of 1.38 Å before the first cleavage. Compared to the intermediate in 5d, this reaction intermediate is more stable by 8.4 kcal/mol. Two protons are again transferred from the third water molecule to the O-adatoms, and a third S1−O bond is formed (Figure 5f). The process is exoenergetic by 32.1 kcal/ mol with a barrier of 20.5 kcal/mol. Finally, a fourth water is added, and H-bonds between this molecule and the surface species are formed (Figure 5g). Proton transfers from the fourth water to Fe−OH lead to the formation of two waters on Fe1 and Fe2. The resulting O of water forms a covalent bond with S1, and a surface SO42− is formed (Figure 5h). The final step is exoenergetic with a large energy gain of 48.6 kcal/mol. However, there is also a barrier of 25.0 kcal/mol. This and the other barriers are likely to be significantly lower at defect sites, e.g., steps, which may thus represent preferential or initial sites for the oxidation process. In any case, it is noteworthy that each reaction step in the mechanism of Figure 5 is exothermic except for the step from 5c to 5d, which is only slightly endoenergetic by 0.5 kcal/mol. The energy changes along the oxidation pathway, and the energy barriers of the key steps are summarized in the lower panel of Figure 5. The OS of the relevant surface Fe and S ions in each step of the oxidation reaction are given in Table 2. The OS of the Fe Table 2. OS of Fe and S in Each Step of the Oxidation Reactiona

Figure 5. Possible mechanism of the oxidation of a surface S to SO42−. Structures (upper panel) are shown as top views with the same color code as in Figure 1. ΔE and Ea are, respectively, the energy changes and energy barriers in kcal/mol. The adsorbates and the surface Fe and S having OS changes during the reaction are represented as spheres. The rest of the surface ions are represented as sticks. The step from (d) to (e) includes the following substeps: addition of one O2 which displaces the two adsorbed waters; the added O2 dissociates to form O adatoms; addition of a water molecule, which forms H-bonds with the two O adatoms. The total spin state for (a) is S = 2. The steps from (b) to (g) all have spin states S = 1, while the spin state for (h) is S = 0. Energy changes along the reaction pathway and energy barriers of some of the key steps are summarized in the lower panel.

5a 5b 5c 5d 5e 5f 5g 5h

Fe1

Fe2

Fe3

Fe4

S1

S2

+4 +3 +3 +3 +4 +4 +4 ?

+4 +3 +3 +2 +4 +3 +3 +2

+2 +2 +2 +3 +3 +2 +2 +2

+2 +2 +2 +2 +3 +3 +3 ?

−1 +1 +1 +2 +2 +4 +4 +6

−1 −1 −1 −2 −2 −2 −2 −2

a

In cases where the OS cannot be unambiguously determined, question marks (?) are used.

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these results, we propose that the crucial recurring process of pyrite oxidation involves the surface O2− and OH− species acting as proton acceptors for incoming water molecules. The mechanism consists of a sequence of steps that lead to the formation of a surface SO42− as the final product and is consistent with isotopic labeling experiments suggesting that the O in SO42− from gas-phase oxidation is primarily derived from water and the O in the Fe-containing products from gaseous oxygen. The activation energies for the various steps are all in the range 20−25 kcal/mol, suggesting that the process is slow but still accessible at room temperature. Finally, it should be noted that the mechanism we have investigated in this work is not the only possible pathway in the reaction of pyrite with oxygen and water. Other plausible pathways may exist for this complex reaction, and our results also represent a reference for future studies aimed at exploring such pathways.

were determined using the method for transition metal ions in ref 28, while the OS of the S are inferred from those of Fe assuming standard OS of O and H. The occupation numbers that lead to the Fe OS assignments in each step are shown in Tables SI2 and SI3. In Figure 5a, the two Fe bound to the O2− adatoms have OS of +4. After the two proton transfer processes (Figure 5b), Fe1 and Fe2 are both reduced to +3. The two electrons on these Fe atoms originate from S1, which is then oxidized from −1 to +1. This assignment is supported by the computed Löwdin charge of S1 which is +0.81, compared to −0.10 for the other surface S atoms. In Figure 5c, the OS of the surface Fe and S ions remain unchanged. In Figure 5d, Fe2 is reduced back to +2, whereas the OS of Fe1 remains +3. At the same time, Fe3 is found to be oxidized to +3. These OS changes can be understood as a sequence of electron transfer processes. Fe2 is reduced by an electron transfer from Fe3 via their common neighbor S1. The S1−S2 breaks heterolytically in such a way that the OS of the subsurface S (S2) becomes −2, while that of S1 is +2. These OS assignments for S1 and S2 are supported by their computed Löwdin charges. The Löwdin charge of S1 increases from +0.81 to +1.15, while the Löwdin charge of S2 is reduced from −0.11, before S−S bond cleavage, to −0.22, after cleavage. In Figure 5e, Fe1 and Fe2 are both oxidized to +4. Since Fe1 is +3 in the previous step, one more electron is needed to reduce the Fe1-bound O-adatom to O2−. This extra electron is found to originate from Fe4, which is oxidized to +3. Proton transfers from the water to the two O2− leads to the reaction intermediate in Figure 5f. The OS of Fe2 and Fe3 are each reduced by 1 in this step, while those of other surface Fe remain the same. S1 is therefore expected to be oxidized from +2 to +4, which is also consistent with the increase of its Löwdin charge from +1.15 to +1.81. Upon addition of the fourth water molecule (Figure 5g), the OS of the surface ions are unchanged. In Figure 5h, an SO42− is formed. The OS of S1 in the sulfate ion is expected to be +6, consistent with its Löwdin charge increase from +1.81 to +2.37. The OS of Fe2 and Fe3 were determined to both be +2, whereas those of Fe1 and Fe4 are ambiguous from the OS determination method. The oxidation of S1 from +4 to +6 implies that two electrons are transferred out of it. One of them goes to Fe2, leading to the reduction from +3 to +2. If the remaining electron had gone to Fe1, the OS of Fe1 and Fe4 would have both been +3. OS of +3 implies net spins on both Fe1 and Fe4. However, the ground state was found to be spin-unpolarized, possibly due to the stabilization from electron delocalization. The OS determination method is based on counting the number of d-orbitals with full occupancy, and such electron delocalization leads to ambiguous results in this case. In conclusion, our DFT study of the adsorption and reactions of water and O2 with the FeS2(100) surface provides detailed mechanistic insight into pyrite oxidation and the complex electron flow accompanying this process. Oxidation of the pyrite surface occurs through successive reactions of the surface with adsorbed O2 and water molecules. Water and oxygen are found to adsorb at undercoordinated surface Fe atoms, and it is energetically favorable for adsorbed O2 to dissociate, which leads to the formation of ferryl-oxo, Fe4+= O2− species. Water can form H-bonds with these species, and proton-coupled electron transfer through the H-bond leads to the formation of ferric-hydroxo, Fe3+−OH−, groups. These groups are predicted to fully cover the FeS2(100) surface when this is exposed to air under normal conditions. On the basis of

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METHODS AND MODELS Spin-polarized DFT calculations were carried out using the gradient-corrected PBE functional37 within the plane wavepseudopotential scheme as implemented in the QuantumESPRESSO38 package. We used ultrasoft pseudopotentials, with plane-wave cutoff energies of 30 and 240 Ryd for the wave functions and the augmented charge density, respectively. Reciprocal space was sampled at the Γ point. All the results reported in this work correspond to the most stable spin state of each configuration. The NEB36 technique was used to calculate the energy barriers for the reaction steps with the climbing image (CI) option. The pyrite (100) surface was modeled using a slab geometry with periodic boundary conditions at the experimental lattice parameter, 5.428 Å.39 (The computed lattice constant is 5.404 Å, i.e., only 0.4% shorter than the experimental one.) We considered a 2 × 2 supercell having the ideal termination of the bulk (Figure SI1 in the SI) exposing eight undercoordinated Fe sites. The slab was 12 atomic layers thick with 32 FeS2 units. The pyrite surface was situated in a tetragonal simulation box with a = 10.856 Å and c = 21.712 Å.

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ASSOCIATED CONTENT

S Supporting Information *

Brief descriptions of the OS determination method and of the ab initio thermodynamics methodology, tables with the occupation numbers that lead to the Fe OS assignments, and a figure of the model pyrite surface used in this study are available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-06ER-46344. We used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231. We also acknowledge computational resources 2413

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The Journal of Physical Chemistry Letters

Letter

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from the PICSciE-OIT High Performance Computing Center and Visualization Laboratory at Princeton University.

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dx.doi.org/10.1021/jz300996c | J. Phys. Chem. Lett. 2012, 3, 2409−2414