Computational Investigation of FeS2 Surfaces and Prediction of Effects

J. Phys. Chem. C 2010, 114, 8971–8980

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Computational Investigation of FeS2 Surfaces and Prediction of Effects of Sulfur Environment on Stabilities Dominic R. Alfonso* National Energy Technology Laboratory, U.S. Department of Energy Pittsburgh, PennsylVania 15236 ReceiVed: January 20, 2010; ReVised Manuscript ReceiVed: March 8, 2010

Density functional theory calculations were employed to investigate the (001), (210), (111), and (110) surfaces of FeS2. The surface free energies were calculated in equilibrium with a sulfur environment using firstprinciples based thermodynamics approach. Surfaces that feature metal atoms in their outermost layer are predicted to be higher in energy. Within the studied subset of (1 × 1) terminations, the stoichiometric (001) surface terminated by a layer of sulfur atoms is the most stable for sulfur-lean condition. For increasingly sulfur-rich environment, two structures were found to have notably lower surface energies compared to others. They have (210) and (111) orientation, both terminated by layers of sulfur. Interestingly, these surfaces are nonstoichiometric exhibiting an excess of sulfur atoms. 1. Introduction The current interest in FeS2 (pyrite) is attributed to a wide range of potential applications. Under extreme environment, it exhibits catalytic properties that are similar to metal and/or metal oxides. For example, FeS2 facilitates Fischer-Tropsch chemistry and catalyzes N2 conversion to NH3 at high pressure and temperature conditions.1-3 The reactivity of its surface to organic xanthates and metals such as Cu plays an important role in the extraction of sulfides from coal and also in the area of cycling and entrapment of precious metals.4 FeS2 is the most abundant sulfide mineral in nature and is thought to be important in geochemical processes. In the so-called iron-sulfur world scenario, its interaction with biologically relevant molecules was used as a benchmark system in the field of the origin and early evolution of life.5,6 Synthetic FeS2 thin films prepared via thermal sulfurization has a suitable band gap and a good photoabsorption character. In view of this, they can be utilized as base materials in solar cells and thermoelectric devices.7-10 Moreover, FeS2 structures may be involved in the high-pressure H2 dissociation reactions on metal-based membranes for gas separation application.11 A fundamental understanding of surfaces of FeS2 provides a crucial starting point for obtaining a microscopic insight of the role of this important material in such applications. FeS2 crystallizes in a rock salt NaCl structure and the vast majority of surface science investigations were performed on the (001) surface of the single crystal, which is the most common cleavage plane.4 This face is also the predominant growth surface of a natural FeS2 crystal.12 A variety of techniques such as X-ray photoemission spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), low-energy ions scattering spectroscopy (LEISS), low-energy electron diffraction (LEED), and scanning tunneling microscopy (STM) were utilized.13-17 First-principles quantum mechanical calculations were also carried out to interpret the experimental observations on the surface properties.18-20 On the basis of these efforts, a picture of the (001) surface that is essentially in unreconstructed, truncated bulklike state formed by the rupture of the Fe-S bonds * To whom correspondence should be addressed. E-mail: alfonso@ netl.doe.gov. Phone: (412) 386-4113. Fax: (412) 386-4542.

10.1021/jp100578n

has emerged. Periodic density functional theory (DFT) studies reveal that the surface is sulfur terminated and show an insignificant relaxation from the top layer into the bulk.18,19 Cleavage in FeS2 was previously examined by means of optical light figure technique on coarsely abraded single crystals.21 In addition to (001), the (210), (111), and (110) surfaces were observed as well. Experimentally, the structures of the (210), (111), and (110) surfaces have not been studied to the same extent as the (001) surface. Previous studies involving (111) and (110) surfaces were mainly devoted to elucidating the surface rate of oxidation under biotic conditions or in the presence of water.22-24 From the theoretical standpoint, investigations focusing on the structures of (210), (111), and (110) surfaces are also somewhat scarce, but some strides have nonetheless become to be made. Studies of (110) in comparison with the (001) surface were reported using DFT.18 These investigations were extended to (111) and (210) surfaces as well.25 Bulk-terminated stoichiometric slab models with either plane of broken Fe-S and S-S bonds were employed. The (210) and (111) faces were predicted to undergo significant geometric relaxations compared to the other faces. On the basis of the calculated surface energies, the preference follows the trend (001) > (111) > (210) > (110). A particular limitation of these studies is that only stoichiometric surfaces were examined. The present work was undertaken to further enhance our understanding of the surfaces of FeS2. We report here systematic investigations of the various terminations of the (001), (210), (111), and (110) surfaces using DFT technique. We looked at both stoichiometric and nonstoichiometric structures. Nonstoichiometric FeS2 surfaces exhibit either an excess of metal or sulfur atoms and to the best of our knowledge, systematic fundamental investigations of their atomic structures have never been undertaken. It should be noted that these nonstoichiometric structures represent the so-called polar terminations that are traditionally viewed as unstable on electrostatic grounds.26,27 It is not straightforward to report the surface energy of nonstoichiometric structures. In these cases, we must take into account the fact the sulfur chemical potential can vary. Thus, firstprinciples-based thermodynamic approach is mandatory. That is, the stability of the various surfaces in equilibrium with an arbitrary sulfur environment was examined using DFT in

This article not subject to U.S. Copyright. Published 2010 by the American Chemical Society Published on Web 04/21/2010

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combination with a thermodynamic description of the surfaces. The rest of the manuscript is organized as follows. The technical details of the calculations were outlined in Section 2. In Section 3, we describe and discuss the results and place them in a wider context. Our conclusions were drawn in the final section. 2. Computational Approach First-principles spin-polarized DFT total energy calculations were carried out as implemented in the Vienna Ab Initio Simulation Package (VASP) program.28,29 This code employs efficient, robust and fast interative matrix diagonalization scheme for evaluating the self-consistent solution of the Kohn-Sham functional. We used the generalized gradient approximation (GGA) formulation of Perdew, Burke, and Enzerhoff (PBE) to calculate the exchange-correlation energy.30 The electron-ion interaction was described by the projector-augmented wave (PAW) method.31 PAW potentials reconstruct the exact valence wave function with all nodes in the core region. The Kohn-Sham one electron valence eigenstates were expanded in terms of plane-wave basis sets with a cutoff energy of 280 eV. For the primitive tetragonal bulk cell of FeS2 (containing four formula units of FeS2), Brillouin-zone sampling was performed on a dense Monkhorst-Pack k-point mesh of 11 × 11 × 11 points.32 To simulate the various terminations of (001), (210), (111), and (110) FeS2 surfaces, we used slab technique with periodic boundary conditions imposed in the two directions parallel to the slab. To ensure the decoupling of the adjacent slabs, a 15 Å thick vacuum region along the surface normal is employed. The slab thickness ranges from 16-26 atomic layers (40-66 atoms). The slabs were set up such that the two exposed faces are symmetrically equivalent. That is, they can be mapped into each other by an inversion, mirror, or glide type of symmetry operation in the middle of the slab. All the atoms were relaxed with the three innermost center layers fixed to their bulk values. The lattice constants were fixed at bulk optimized conditions. Brillouin-zone sampling was performed on a Monkhorst-Pack k-point mesh of 6 × 6 × 1 points for both the (001) and (110) surfaces. For (111) and (210), we used 5 × 5 × 1 and 4 × 4 × 1 k-point mesh, respectively. A Methfessel-Paxton smearing of σ ) 0.1 eV was utilized to improve convergence and the corrected energy for σ f 0 was employed. We linked our DFT results with concepts from thermodynamics33-35 to investigate the stability of the various considered surfaces. The free energy of a surface in equilibrium with particle reservoirs at temperature T and pressure p is defined as

γ(T, p) )

1 surf [G 2A

∑ Niµi(T, p)]

(1)

i

Here, Gsurf denotes the Gibbs free energy of a periodic repeated slab, which exposes a surface with area A. For the determination of A, the bottom and the top side of the slab are taken into account resulting in a factor of 2. The terms Ni and µi are the number and the chemical potential of species i, respectively, present in the system. For FeS2 surface, i ) Fe and S. Because the surface is in equilibrium with the underlying bulk sulfide, the two chemical potentials, µFe and µS, are related via the Gibbs bulk bulk , where gFeS free energy of the bulk. That is, µFe + 2 µS ) gFeS 2 2 denotes the Gibbs free energy per formula unit. Inserting this constraint in eq 1 leads to a surface free energy as a function of the chemical potential of S

γ(T, p) )

1 surf bulk + (2NFe - NS)µS) (G - NFegFeS 2 2A

(2) The surface free energy consists of contributions from the difference in the corresponding total energies, pV term, the configurational entropy and from changes in the vibrational free energy. The pV term for solids is negligibly small and can be omitted. For the configurational entropy, a full evaluation of this term requires the use of statistical mechanics approaches, like Monte Carlo simulation, to completely sample the configurational space. However, the use of this approach in conjunction with DFT is computationally prohibitive. It should be noted that the approach adopted here was for comparison of the stability of structures with a defined periodicity. Thus, this particular contribution was not considered since for every included structure there is only one specific configuration. The vibrational contribution, ∆γvib, was obtained from the difference between the surface and bulk vibrational mode plus contribution due to excess or deficient atoms35,36 NSsurf

vib

∆γ

∑

1 surf bulkFeS2 ) [Fvib(T, {ωi,j }) - Fvib(T, {ωi,S })] + ( 2A j)1 surf NFe

∑ [F

vib

surf bulkFeS2 (T, {ωi,j }) - Fvib(T, {ωi,Fe })] +

j)1

bulkFeS2 bulkS }) + (2NFe - NS)Fvib(T, {ωi,S })) (NS - 2NFe)Fvib(T, {ωi,S

(3) surf where NSsurf and NFe are the number of S and Fe, respectively, vib term }) is defined as at the surface. F (T,{ωi,j

n

term Fvib(T, {ωi,j }) )

∑ 21 pωi,jterm + kBT ln(1 - e-βpω

term i,j

)

i)1

(4) bulk FeS2 }, with β ) 1/kBT. The vibrational modes {ωi,jsurf}, {ωi,Fe bulk FeS2 bulk S } and {ωi,S } are those of the surface atoms, Fe in {ωi,S bulk FeS2, S in bulk FeS2, and S in R phase of bulk sulfur, respectively, and the summation runs over all degrees of freedom. We adopted the approach in ref 37 to calculate {ωsurf i,j }. The number of Fe and S atoms at the surface of each selected surface termination was identified and frozen phonon calculations for these atoms were then carried out. An atom whose nearest neighbor coordination is changed with respect to the bulk structure is considered to be at the surface and those that do not meet this requirement are considered as bulk atoms.37 We adopted the approach analogous to ref 35 to calculate the bulk FeS2 bulk FeS2 bulk S }, {ωi,S } and {ωi,S }). bulk vibrational modes ({ωi,Fe Frozen phonon calculations of each atom type in the unit cell of bulk FeS2 and bulk R phase of sulfur were carried out. The vibrational modes due to Fe and S in FeS2, and S in the R phase of sulfur were then averaged to obtain the various characteristic frequencies for each degree of freedom. ∆γvib was calculated for selected low energy FeS2 surfaces and as shown in Section 3, the formal incorporation of this term would not affect the physical conclusions drawn. The Gibbs free energy of the surface and the bulk in eq 2 then reduce to the internal energies which were directly obtained from DFT calculations. As a spot check, the surface free energy of selected low-lying FeS2 surfaces was also calculated using a plane wave basis cutoff

FeS2 Surfaces Effects of S Environment on Stabilities

J. Phys. Chem. C, Vol. 114, No. 19, 2010 8973

Figure 1. The bulk unit cell of FeS2. Violet spheres indicate Fe atoms and yellow spheres indicate S atoms.

energy of 350 eV. It was found that using a higher cutoff parameter does not result in any significant changes (i.e., < 5 meV/Å2). The term µS is restricted by the following conditions: (i) FeS2 does not decompose into Fe metal and sulfur and (ii) bulk sulfur does not condense on the surface. Appropriate and well-defined estimates for the limits of µS indicated above are then given by bulk ∆Hf,FeS (T ) 0 K, p ) 0) < µS - ESbulk < 0 2

(5)

bulk (T ) 0 K, p ) 0) is the low-temperature The term ∆Hf,FeS 2 limit for the heat of formation of FeS2 while ESbulk is the total energy of S atom in the R phase of bulk sulfur. The chemical potential of sulfur was referenced to a prototypical S-containing molecule, S2, and for arbitrary T and p can be expressed as

[

1 1 µS ) µS2 ) ∆hS2(T, p0) + ESvib2 (T ) 0 K) + ES2 2 2 pS2 TsS2(T, p0) + kBT ln 0 (6) p

( )]

For standard pressure p0 ) 1 bar, the differences in enthalpy (∆hS2) and entropy (sS2) of a S2 molecule can be found in standard thermodynamics tables.38 Evib S2 represents the zero-point vibration energies for the molecule, which is estimated from the experimental values for the molecular vibration frequencies.38 3. Results and Discussion A. Bulk FeS2. FeS2 crystallizes in a rock salt type structure with space group symmetry of Pa3.39 There are four formula units of FeS2 in the face-centered cubic cell. The Fe atoms are situated at all corners and face center positions, and the S2 dimers are at the center and midpoints of the twelve edges of the unit cell (Figure 1). All Fe atoms have an equivalent distorted octahedral coordination to six S atoms, while the S atoms are tetrahedrally sorrounded by three Fe atoms and its dimer partner. The unit cell is specified by two lattice parameters: the lattice constant of the unit cell, a, and an internal coordinate, u, for the S atoms in the unit cell. The experimental lattice constant and internal coordinate are aexp ) 5.416 Å and uexp ) 0.385, respectively.40,41 Our calculations yield a low-spin state for bulk FeS2 in agreement with experiments.42 Within our DFT approach, the calculated lattice constant and internal coordinate

Figure 2. The total and partial DOS (Fermi level, EF ) 0) of bulk FeS2.

are aDFT ) 5.404 Å and uDFT ) 0.383, respectively, which are in very good agreement with the experimental values. The lattice constant and internal coordinate deviate from experimental values by 0.2-0.5%. Our calculated values were obtained by relaxation of the unit cell with respect to the lattice and internal parameters with the experimental bulk structure as the starting point in the energy minimization procedures. The predicted total and partial electronic density of states (DOS) are shown in Figure 2. The bands in the energy range from -17 to -11 eV are attributed exclusively to S 3s states. They consist of two groups with width of about 2.7 and 2.0 eV. The splitting of the S 3s in this region was attributed to the S-S interaction which gives rise to the formation of bonding and antibonding states.43 In the energy range from -7.5 eV to the Fermi level (EF ) 0), two groups of d bands are observed. From -7.5 to -1.6 eV, we found broad features of low intensity due to overlapping of lower valence Fe 3d bands and S 3p bands. Close to the Fermi level, bands appear which consist of upper valence Fe 3d plus minimal contribution from the S 3p states. The salient features of the bulk FeS2 electronic DOS obtained in this work are consistent with previous DFT calculations.18,43 B. Low-Index FeS2 Surfaces. We investigated the four lowindex (001), (110), (111), and (210) surfaces of FeS2, each with different number of terminations. The (001) face has a surface unit cell that is a square. It exposes the face of the face-centered cube of the bulk metal sulfide with each (001) plane occupied by atoms of the same type. This surface has three different terminations, one contains 3-fold Fe atoms only ((001)-Fe) in the topmost layer and the other two have either one ((001)-S) or two layers ((001)-2S) of S atoms on the top (Figure 3). The surface cut in the (001)-S and (001)-2S structures leaves directly exposed one-fold and 3-fold S atoms, respectively. The (110) face has a surface unit cell that is rectangular. There are again three types of terminations, one having mixed Fe-S atoms in a ratio 1:1 in the topmost layer while the other two are sulfur terminated, one with a layer of S atoms and the other one with two layers of S atoms ((110)-FeS, (110)-S, and (110)-2S, respectively, see Figure 4). The surface cut for (110)-FeS gives rise to 4-fold Fe, 3-fold Fe, and 3-fold S exposed on the surface. The surface cut for both (110)-S and (110)-2S gives rise to 2-fold and 3-fold S atoms exposed on the surface. The surface unit cell of the (111) face is hexagonal. There exist five different

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Figure 3. Different terminations of the FeS2(001) surface (a) (001)Fe, (b) (001)-2S, and (c) (001)-S. Color setting for S and Fe is the same as in Figure 1. Left and right panels correspond to side view and top view, respectively. The surface unit cell is indicated.

Figure 4. Same as in Figure 3 for the different terminations of the FeS2(110) surface (a) (110)-FeS, (b) (110)-S, and (c) (110)-2S.

terminations for this surface. One of them is Fe-terminated with the underlying four layers occupied by S while the other ones contain 1-4 layers of S atoms. ((111)-Fe, (111)-S, (111)-2S, (111)-3S, and (111)-4S, respectively, see Figure 5). For (111)4S, the formation of this surface involves the breaking of Fe-S bonds and the removal of S dimer units. The outermost S is onefold coordinated to an inner S. The S atoms in the layer below are 2-fold coordinated, each bonded to an inner S and

Alfonso Fe atoms. For (111)-3S, the formation of this surface consists of removal of the outermost S from (111)-4S. The outermost S are 2-fold coordinated, each bonded to Fe and S. The S atoms in the layer below are 3-fold coordinated with bonds to an outermost S atom and two inner metal atoms. For (111)-2S and (111)-S, they are formed by the removal of the top two and three S layers of (111)-4S, respectively. In the case of the (210), the surface unit cell is rectangular which consists of two trilayer vertical repeat unit. Each trilayer contains a Fe layer followed by double layers of S. Six inequivalent ideal bulk terminations can be obtained by cutting the (210) stacking sequence (Figure 6). They can expose S single ((210)-S and (210)-S′) and S double layers ((210)-2S and (210)-2S′). In the original unrelaxed (210)-S, the S in the outermost layer is 2-fold coordinated. The surface cut also leaves 3-fold S and 4-fold Fe exposed on the surface. For (210)-S′, the outermost S has a higher coordination (3-fold). The termination also exposed 3-fold S, 4-fold F, and 5-fold F on the surface. The S double layer in (210)-2S consists of outermost one-fold S and a 2-fold S in the layer below. In the original unrelaxed structure, the outermost S is coordinated to an inner metal atom while the S in the layer below is bonded to Fe in the third layer and an inner S. The S in the corresponding double layer in (210)-2S′ has a higher coordination. That is, the surface cut gives rise to 2-fold and 3-fold S exposed on the surface. A cleavage through the trilayer units can also generate metal terminated surfaces ((210)-Fe and (210)Fe′). For (210)-Fe, the surface cut leaves 3-fold Fe in the outermost layer. The termination also creates 4-fold Fe, 2-fold S, and 3-fold S exposed on the surface. For the (210)-Fe′, the surface cut gives rise to outermost 3-fold Fe together with 3-fold S and 5-fold Fe in the layers below. In the unrelaxed structure, the outermost Fe in (210)-Fe′ stick further out from the surface compared to those in (210)-Fe. Overall, we looked at 17 different surface structures. It should be noted that out of the17 different surface terminations that were investigated, 5 are stoichiometric, ((001)-S, (111)-2S, (210)-S, (210)-S′, and (011)-S) while the remaining ones are nonstoichiometric. The nonstoichiometric structures consist of either an excess sulfur or metal atoms and belong to the class of polar surfaces. Our investigations were restricted to ideal surface terminations, without considering defect formations on the studied surfaces. C. Surface-Free Energies. The calculated surface phase diagram derived from the variation of surface free energies with S chemical potential is displayed in Figure 7. The vertical lines show the limits indicated by eq 5. The lower limit that is labeled as S-lean is defined by the decomposition of the sulfide into Fe and S. The upper limit labeled as S-rich corresponds to a situation where gas phase is so rich in sulfur that they condensed on the substrate. For the stoichiometric surfaces considered here, the surface free energy is independent of µS as expected since the coefficient of the term containing µS in eq 2 vanishes. For the nonstoichiometric cases, the surface free energy is a linear function of µS as expected or equivalently, of ∆µS ) µS - Ebulk S . The lines with negative slope correspond to structures with excess sulfur atoms ((001)-2S, (210)-2S, (210)-2S′, (111)3S, (111)-4S, and (011)-2S) while those with positive slopes correspond to structures with excess metal atoms ((001)-Fe, (111)-S, (210)-Fe, (210)-Fe′, and (011)-FeS). Hence, the former terminations become more stable under S-rich conditions. Relaxed configurations were found for all considered surfaces with the exception of (111)-Fe for which our calculations yielded no stable structure due to structural instability. At low ∆µS, the stoichiometric (001)-S structure is the most thermodynamically stable phase. For higher ∆µS from -0.76



Figure 5. Same as in Figure 3 for the different terminations of the FeS2(111) surface (a) (111)-Fe, (b) (111)-4S, (c) (111)-3S, (d) (111)-2S, and (e) (111)-S.

to -0.50 eV, the (210)-2S′ structure is the most thermodynamically favored. With further increase in µS, the (111)-3S becomes the most energetically favored. Overall, those structures that feature Fe atoms in their outermost layer are higher in energy. As a spot check, we estimated the vibrational component of the surface free energy for the (001)-S, (210)-2S′, and (111)3S, including two other low lying surfaces ((011)-2S and (111)4S). Using eq 3, we plot in Figure 8 ∆γvib for temperatures in a range between 0 and 1000 K. We observed that the plotted values stay within a range of about -5 to -10 meV/Å2 for temperatures up to 1000 K and formal incorporation of this term does not change the stability rank of the surfaces. We are mainly interested in the relative stability of the various surface structures and the inclusion of vibrational contributions does not affect the conclusions in this paper. The theoretical Wulff shape for FeS2 for two considered limits, S-lean and S-rich conditions, are shown in Figure 9. They were constructed based on the Gibbs-Wulff theorem of equilibrium shape44,45 and utilizing the surface free energies in Figure 7. It is evident from the relative stability plot in Figure 7 that (001)-S and (210)-2S′ are the two low-energy structures at the

S-lean limit, and they appear as the dominating facets in Figure 9. The other minority triangular facets are built by (111)-3S termination which is the next most stable. Only 3 of the 17 surfaces that we studied appear in the construction as the corresponding planes of other terminations lie outside of this Wulff shape. At the S-rich limit, FeS2 appears as a truncated octahedron-like, dominated by (111) facets at the faces with the minority (210)-2S′ terminating the apexes of the octahedron. This is again, reflected in the relative stability plot in Figure 7. At the S-rich limit, the low energy structures are (111)-3S, (210)2S′, and (111)-4S with the (111)-3S termination having the lowest surface energy. The relative stability of stoichiometric (001)-S, (210)-S, (111)2S, and (110)-S surfaces of FeS2 was examined previously using DFT.18,25 Within this studied subset of stoichiometric structures examined as isolated systems in vacuum at T ) 0 K, the (001)-S surface was found to be the most stable with the surface energy increasing in the following sequence: (001)-S (1.06 J/m2) < (111)-2S (1.40 J/m2) < (210)-S (1.50 J/m2) < (110)-S (1.68 J/m2). The order of stability predicted here for the above surfaces is in line with their findings. That is, our calculated surface

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Figure 6. Same as in Figure 3 for the different terminations of the FeS2(210) surface (a) (210)-Fe, (b) (210)-2, (c) (210)-S, (d) (210)-Fe, (e) (210)-2S′, and (f) (210)-S′.

energy (Figure 7) for the aforementioned structures follow the trend (001)-S < (111)-2S < (210)-S < (011)-S. Our calculated surface energies are, however, larger ((001)-S (1.21 J/m2), (111)2S (1.49 J/m2), (210)-2S (1.61 J/m2), and (011)-S (1.79 J/m2)), which could be due to some differences between the calculational details underlying these two studies. Moreover, we identified another stoichiometric structure for (210) (i.e., (210)S′) that is more stable than the corresponding (210)-S structure. The above DFT investigations were confined to stoichiometric structures only.18,25 In the present studies, we found nonstoichiometric structures that are more stable that their stoichiometric counterparts. The very high stability of (210)-2S′, (111)-

3S, and (110)-2S compared to the stoichiometric (210)-S, (111)2S, and (110)-S, respectively, under any thermodynamical conditions is easily recognizable. Another significant finding is that the stoichiometric (001)-S surface is the most favorable only in S-lean environment. In increasingly S-rich condition, this is not the situation. At this condition, the nonstoichiometric (210)-2S′ and (111)-3S become more important. It should be noted that (210)-2S′ and (111)-3S belong to the so-called polarterminated surfaces and structures like these were previously dismissed as unstable18,25 using the electrostatic arguments of Tasker.26,27 However, earlier efforts46,47 show that this ionic model breaks down if structural and electronic relaxations at



Figure 7. Calculated surface free energies of various FeS2 surfaces as functions of the change in S chemical potential. Corresponding S2 pressure axes at T ) 300, 600, and 900 K are included.

Figure 8. Change in the vibrational contribution to the surface free energy of selected FeS2 surfaces.

the surface are taken into account. This was also confirmed in our recent work on Pd4S surfaces.36 Hence, (210)-2S′ and (111)3S can be stabilized as in this case and could be relevant as the environment becomes richer in S. To the very best of our knowledge, no experimental information on such nonstoichiometric surfaces is presently available for crystalline FeS2. We are unable to carry out a comparative analysis in the absence of such information. Our findings then provide a database against which future experimental based nonstoichiometric models may be compared. D. Structural and Electronic Properties. Noticeable displacements of surface and subsurface layers were generally observed for the various FeS2 surfaces investigated here. These relaxation effects give rise to surface bond lengths that are

generally different compared to the bulk values. We illustrate this point further for (001)-S, (210)-2S′, and (111)-3S. The relaxed geometries of these surfaces are shown in Figure 10. For (001)-S (Figure 10a), it remains essentially bulk terminated in line with previous DFT,18,48 LEED,13 and STM14 investigations. We found that the dominating relaxations are the inward displacements of the 3-fold S(1) in the first layer and 5-fold Fe(2) situated in the second layer. They relaxed toward the bulk by 0.26 and 0.27 Å, respectively. The change in the topmost interlayer spacing is marginal with respect to the bulk value. S(1) are 2-fold coordinated to Fe(2) and one-fold coordinated to an inner S. The length of the bond between S(1) and Fe(2) drops very slightly from 2.25 to 2.23 Å while the distance between S(1) and an inner S is increased by 0.05 Å with respect to the bulk value (2.19 Å). For (210)-2S′, 2-fold S(1) and 3-fold S(2) are exposed on the surface (Figure 10b). They remain nearly coplanar upon relaxation; the vertical separation is 0.08 Å compared to the bulk value of 0.12 Å. Because of reduced coordination, S(1) is drawn toward its nearest neighbor Fe atom Fe(3) so that the length of the S(1)-Fe(3) bond is 7% shorter than the bulk distance. The bond between S(1) and an inner Fe atom also contracts by 5% with respect to the bulk value. The second layer S(2) is drawn toward its nearest neighbor 3-fold S(4) by 3% while the S(2)-Fe(3) and S(2)-inner Fe atom distances marginally changed relative to the bulk value. For the relaxed (111)-3S (Figure 10c), the outermost S(1) are 2-fold coordinated, each bonded to second layer S and third layer Fe. The S(2) in the second layer are 3-fold coordinated to an outermost S(1) and two Fe in the third layer. These undercoordinated S atoms show small displacements. The surface normal and in-plane displacements are found to be below 0.1 Å. There is an expansion of the first interplanar spacing by about 8% relative to the bulk value. The S(1)-S(2)) distance at the surface is reduced by 5% compared to the bulk value. There is also a 3% contraction of

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Figure 9. Theoretical Wulff construction of the FeS2 crystal under S-lean and S-rich conditions.

Figure 10. Local atomic structure of (a) FeS2(001)-S, (b) FeS2(210)-2S′, and (c) FeS2(111)-3S. Color setting for S and Fe is the same as in Figure 1. The undercoordinated atoms are labeled. Values in parentheses correspond to bulk values.

the bond length between the topmost S and of the Fe atom in the third layer. The bond lengths between the second layer S and the third layer metal atoms, on the other hand, are essentially unchanged relative to the bulk value. The calculated total and partial electronic density of states (DOS) of undercoordinated surface atoms of (100)-S are shown in Figure 11. S(1) is 3-fold coordinated due to Fe vacancy and

Fe(2) is 5-fold coordinated due to S vacancy. Overall, we found a spin neutral state for this structure in agreement with previous DFT calculations.18,43 The reduced number of coordination in the surface layers gives rise to slight narrowing of the overlapping S 3p-lower Fe 3d valence bands. Similar to the bulk case, there is still an energy separation of the lower and upper Fe 3d valence bands though the latter is now less intense and exhibits



Figure 11. The total and partial electronic DOS (Fermi level, EF ) 0) of FeS2(001)-S. The first and second panels correspond to second layer Fe and first layer S PDOS, respectively.

Figure 12. Same as in Figure 11 for FeS2(210)-2S′. The first, second, and third panels correspond to the third layer Fe, first layer S, and second layer S PDOS, respectively.

small splitting. For the low lying S 3s douple peaks, they are shifted to higher energy by about 0.2 eV. A spin neutral state was also found for (210)-2S′ and the electronic structures of selected surface layers are displayed in Figure 12. Bands that derive from hybridized lower valence Fe 3d and S 3p states can also be observed. The clear energy separation between the upper and lower valence Fe 3d disappears. Moreover, for the 2-fold S(1), the low-lying 3s bands consist of a distinct peak plus minimal split off states instead of a double peak. This feature is consistent with the absence of S-S interaction in S(1). The distinct splitting of the 3s bands is observed for the 3-fold S(2) arising from the interaction with a nearest S neighbor. The splitting between these two peaks is found to be about 0.7 eV larger than those in the bulk FeS2 resulting from the S-S bond length being shorter by 0.16 Å relative to the bulk value. The (111)-3S, in turn, is predicted to be spin polarized. The spin population calculations show small magnetic moment of 0.18 and 0.16 µB on the first (S(1)) and third layer S (S(3)) atoms, respectively. The second layer S (S(2)) has a negligible moment

Figure 13. Same as in Figure 11 for FeS2(111)-3S. The first, second, third, and fourth panels correspond to second layer S, first layer S, fourth layer Fe and third layer S PDOS, respectively.

(0.02 µB). The Fe atoms in the fourth layer are found to be relatively more spin polarized (0.89 µB). The partial spin up and spin down density of states of these atoms are shown in Figure 13. For S(1), the diffuse spin up 3p bands are fully occupied. For the spin down 3p bands we observed a peak with its center of gravity above the Fermi level leaving some part of this band unoccupied. This resulting spin unbalance gives rise to a noticeable magnetic moment on S(1). The resulting spin unbalance in S(3) (Fe(4)) can also be attributed to spin down 3p bands (Fe 3d bands) that are not completely filled. For Fe(4), the spin up and spin down 3d bands are not symmetric with the latter shifted up relative to the former. The contributed DOS from S(2), on the other hand, is nearly symmetric with respect to the spin up and down states, consistent with the negligible magnetic moment for these atoms. Finally, in contrast to S(1) and S(2), a well separated double peak low lying S 3s for S(3) is not observed due to the absence of interaction with a nearest S neighbor in S(3). 4. Conclusion We presented in this work systematic investigations of the various terminations of the (001), (210), (111), and (110)

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surfaces using first-principles technique. The stability of the various surfaces in equilibrium with an arbitrary sulfur environment is examined using DFT in conjunction with a thermodynamic description of the surfaces. The stoichiometric (001)-S surface exhibits the lowest surface free energy under S-lean conditions. It was shown that for increasingly sulfur-rich environment, two surfaces ((210)-2S′ and (111)-3S), none of which are stoichiometric, are favored. Noticeable displacements of surface and subsurface layers were generally observed for these surfaces giving rise to surface bond lengths that are generally different compared to the bulk values. The (001)-S and (210)-2S′ surfaces were found to be spin neutral similar to the bulk material, while (111)-3S was predicted to be noticeably spin-polarized. Acknowledgment. We are grateful to Y. Duan and D. Sorescu for useful discussions. References and Notes (1) Cody, G. D. Annu. ReV. Earth Planet Sci. 2004, 32, 569. (2) Cody, G. D.; Boctor, N. Z.; Brandes, J. A.; Filley, T. R.; Hazen, R. M.; Yoder, H. S. Geochim. Cosmochim. Acta 2004, 68, 2185. (3) Schooner, M. A. A.; Xu, Y. Astrobiology 2001, 1, 133. (4) Murphy, R.; Strongin, D. Surf. Sci. Rep. 2009, 64, 1. (5) Mateo-Marti’, E.; Rogero, C.; Briones, C.; J, A., M.-G. Surf. Sci. 2007, 601, 4195. (6) Plekan, O.; Feyer, V.; Sutara, F.; Skala, T.; Svec, M.; Chab, V.; Matolin, V.; Prince, K. C. Surf. Sci. 2007, 601, 1973. (7) Ares, J. R.; Pascual, A.; Ferrer, I. J.; Sanchez, C. Thin Solid Films 2005, 480-481, 477. (8) Pascual, A.; Ares, J. R.; Ferrer, I. J.; Sanchez, C. Appl. Surf. Sci. 2004, 234, 355. (9) Ennaoui, A.; Fiechter, S.; Jaegermann, W.; Tributsch, J. J. Electrochem. Soc. 1986, 133, 97. (10) Wang, S. S.; Seefurth, R. N. J. Electrochem. Soc. 1987, 134, 530. (11) Morreale, B. D. Influence of H2S on the permeability of Pd and Pd-Cu alloys; University of Pittsburgh: Pittsburgh, PA, 2006. (12) Nesbitt, H. W.; Bancroft, G. M.; Pratt, A. R.; Scaini, M. J. Am. Mineral. 1998, 83, 1067. (13) Pettenkofer, C.; Jaegermann, W.; Bronold, M. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 560. (14) Siebert, D.; Stocker, W. Phys. Status Solidi A 1992, 134, K17. (15) Eggleston, C. M.; Hochella, M. F. Am. Mineral. 1992, 77, 221. (16) Eggleston, C. M.; Ehrhardt, J.; Stumm, W. Am. Mineral. 1996, 81, 1036.

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JP100578N

Computational Investigation of FeS2 Surfaces and Prediction of Effects

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