Stability, Structure, and Electronic Properties of the Pyrite

Article pubs.acs.org/JPCC

Stability, Structure, and Electronic Properties of the Pyrite/ Arsenopyrite Solid−Solid Interface−A DFT Study Egon C. Dos Santos,† Maicon P. Lourenço,† Lars G. M. Pettersson,‡ and Hélio A. Duarte*,† †

GPQIT, Departamento de Química, ICEx, Universidade Federal de Minas Gerais, Belo Horizonte, 31.270-901 Minas Gerais, Brazil Department of Physics, AlbaNova University Center, Stockholm University, S-10691 Stockholm, Sweden

‡

S Supporting Information *

ABSTRACT: Pyrite is the most common sulfide in the Earth. In the presence of arsenopyrite its oxidation is delayed, and instead, the arsenopyrite increases its oxidation rate, releasing As(III) and As(V) species in the medium. DFT/plane waves calculations were performed on pyrite/arsenopyrite interface models to understand the stability, structure, and electronic properties of the interface. This is the first step to understand the influence of the inlaid arsenopyrite in the pyrite oxidation mechanism. The interface is slightly stressed with minor changes in the bond lengths and lattice parameters with respect to the pure phases. The work of adhesion and the formation energy indicate that the miscibility of the two phases is not favorable, explaining the presence of large domains of either pyrite or arsenopyrite forming bulk granular regions. The valence band of the pyrite/arsenopyrite interface has large contributions from the pyrite phase, while the conduction band has large contributions from the arsenopyrite. This is consistent with the pyrite as cathode and arsenopyrite as anode in a galvanic contact. Furthermore, the interface formation shifts the valence states upward and decreases the band gap, facilitating interfacial electron transfer.

1. INTRODUCTION In nature, sulfide ores are complex solid mixtures, and consequently, their structural, mechanical, and electrochemical properties are difficult to assess. Hydrometallurgical routes rather than pyrometallurgical processes are always considered for treating low-grade ores. However, hydrometallurgical recovery of noble metals has to deal with the secondary reactions provoked by the galvanic interactions between associated minerals within the concentrates. In aqueous leaching or bioleaching processes the galvanic interaction substantially increases the oxidative dissolution of one or both of the minerals constituting the galvanic cell.1−5 The outcome will depend on the electrochemical characteristics of the minerals and on the occurrence of the distinct sulfides contained in the soils, sediments, substrates, and ore concentrates. Pyrite (FeS2) is the most abundant and widespread sulfide mineral and commonly found associated with other minerals that have economic interest, such as marcasite,1 galena,6 sphalerite,7 covellite,7 chalcopyrite,8 and arsenopyrite.9−13 Furthermore, it is mostly responsible for acid rock drainage (ARD) due to its oxidation when exposed to air, releasing acid and heavy metals. ARD is hazardous for the environment and is a major concern in the mineral industry. Since sulfide minerals are semiconductor materials that can participate in redox reactions, the contact between the distinct minerals may lead to galvanic effects. One mineral will act as anode by promoting the © XXXX American Chemical Society

oxidation reaction and the other as cathode, in which the reduction reaction occurs.14,15 Abraitis et al.7 showed that, in the presence of pyrite, the dissolution of sulfide mixed-mineral systems can be dramatically affected by galvanic effects, and the rates can increase by a factor greater than 30 if compared with the isolated phases under the same experimental conditions. Therefore, it is important to consider how other sulfide minerals inlaid in pyrite affect its chemical reactivity toward oxidation. Arsenopyrite (FeAsS) is also an important mineral because it is primarily associated with other sulfide minerals and valuable metals (e.g., copper, silver, and gold). In certain ores, extracting the arsenopyrite contribution has considerable economic significance since it carries the major portion of the gold in the ore. When mined and exposed to the environment, its oxidation also leads to ARD releasing arsenite [As(III)] and arsenate [As(V)] in addition to acid and heavy metals. Natural arsenopyrite samples are always associated with pyrite and are generally found with large domains of pyrite randomly inlaid in its structure.16−21 In several studies the galvanic effect between arsenopyrite and pyrite minerals has been found to lead to an increase in the dissolution oxidation process.9−13,22−24 More recently, Urbano et al.13 carried out a voltammetric study of arsenopyrite containing 11.84% of pyrite mineralogical impurity Received: March 20, 2017 Published: March 22, 2017 A

DOI: 10.1021/acs.jpcc.7b02642 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

as U = [1.0, 1.5, 2.0, 2.5, and 3.0 eV]. The Hubbard value of 1.5 eV reproduces the band gap of pyrite and arsenopyrite with an absolute difference of approximately 0.2 eV for both systems (see Figure 1). For this reason, in the PDOS, band structure

and compared the results to the oxidation of a natural pyrite mineral of 98.96% purity. The authors concluded that the reactivity in the presence of galvanic effects is electrochemically modified, and the pyrite oxidation is delayed when it is associated with the arsenopyrite. Consequently, the oxidation process of arsenopyrite is enhanced with larger release of arsenic into the medium. Pyrite has the highest rest potential among the sulfides.1,3 Therefore, in a mixture of sulfides, pyrite acts as cathode in the oxidative process and the more reactive sulfides as anode. The available data suggest that the rest potential of pyrite is more affected by the galvanic processes due to associated minerals than by its elemental composition. However, the knowledge about the interface between pyrite and other sulfide minerals is scarce and has not received attention commensurate with its importance. In the present work, several pyrite/arsenopyrite interfaces are investigated aiming to provide a better understanding of the structure, stability, electronic, and mechanical properties of the interface as an initial step to understand the oxidation mechanism of pyrite associated with arsenopyrite.

Figure 1. Pyrite and arsenopyrite calculated band gaps as a function of the Hubbard (U−J) parameter. Black and red dashed lines represent the experimental band gap for pyrite38 (0.90 eV) and arsenopyrite27 (0.82 eV), respectively.

2. METHODOLOGY 2.1. Computational Details. All calculations were performed using the QUANTUM-Espresso software,25 which has been extensively used in several other works, including studies of sulfide minerals.26−29 All DFT calculations were performed using the GGA functional developed by Perdew, Burke, and Ernzerhof (PBE).30 Different total spin polarizations were evaluated, and the reported results are for the most stable spin state of each structure (see SI for more information). Geometry optimizations were carried out using the damped dynamics method31 in the Parrinello−Rahman extended Lagrangian formulation,32 and the forces on the ions were converged to within 10−3Ry/Bohr. For all calculations, the Kohn−Sham orbitals were expanded in a plane-wave basis set using a kinetic energy cutoff of 50 Ry (or 680 eV). A Gaussian smearing of 0.02 eV for the Fermi−Dirac distribution function was used for all systems. Norm-conserving pseudopotentials with Fe (3s23p64s23d64p0), S (3s23p43d0), and As (4s24p34d0) valence electron configurations were used. Following the Monkhorst−Pack scheme, different k-point meshes were used in order to obtain a good description of the electronic structure of the systems. For bulk calculations, we used a Γ-centered 4 × 4 × 4 grid in optimizations, and a single-point calculation was performed at the equilibrium geometry using 10 × 10 × 10 kpoints to get a better description of the KS wave function. We also tested the convergence of the cutoff and k-point meshes for bulk pyrite and arsenopyrite (see Figure S1−S3), and for both systems the total energy was converged to 1 mRy/atom. For the surface and interface models we used 4 × 4 × 2 k-point meshes for the optimizations and 10 × 10 × 6 for single-point calculations. From the obtained KS wave function the projected density of states (PDOS), electronic band structure, and electron localization function (ELF) were evaluated and analyzed. The definition of ELF29,33 is given in the Supporting Information. The Hubbard parameter (U−J) has been shown to be crucial to study sulfide minerals34,35 and particularly for interfaces.36,37 Since for the bulk and interface structures the iron electronic states dominate both the valence and the conduction band, we tested the influence of the (U−J) parameter in all iron atoms. The J parameter was set to 0.0 eV, and the U value was varied

and ELF investigations a (U−J) value equal to 1.5 eV was used. Inclusion of the (U−J) parameter for geometry and formation energies gave no improvement (see Tables S1−S4 for comparison); hence, it was not considered in the structural optimizations. The unit cell used to start the pyrite bulk calculations was obtained from Brostigen and Kjekshus, who used crystallographic refinement data.39 At room temperature, pyrite crystallizes in a face-centered cubic system (space group Pa3) and includes four FeS2 units in the primitive unit cell. The lattice parameter was determined experimentally to be 5.418 Å, and the Fe−S and S−S chemical bond lengths are 2.262 and 2.177 Å, respectively. The calculated lattice parameter is a = 5.381 Å, with a relative error of 0.5% compared to experiment. Arsenopyrite exhibits a monoclinic cell with P21/c space group and four FeAsS units per unit cell. Its cell parameters were recently determined by Bindi et al.,40 being a = 5.761 Å, b = 5.684 Å, c = 5.767 Å, β = 111.72°, and α = γ = 90.00°. The calculated lattice parameters of a = 5.714 Å, b = 5.648 Å, c = 5.737 Å, and β = 112.1° and bond lengths are in good agreement with the experimental data, with relative errors not exceeding 2%. From the optimized bulk structures, the pyrite and arsenopyrite surfaces and the interfaces were built. From each surface the atomic-layer thickness was chosen such that the two interface distances were greater than 11 Å, which eliminates nonphysical interactions between the two interfacial regions and preserves bulk properties in the inner layer. 2.2. Pyrite/Arsenopyrite Coherent Interface Construction. The construction of the interface models followed the same protocol as described elsewhere.37,41 The coherent model was applied, where a (1 × 1) bulk base unit cell is used and the lattice parameters are tuned in order to find the best match that maximizes the overlap area, SA/B, between surfaces A and B in contact. Then the A(1 × 1)/B(1 × 1) interface is formed, see Figure 2. This approach is widely used for ab initio calculations of interface models and can be used for stacked surfaces with a relatively small mismatch.42 More realistic models which use A(nxn) and B(mxm) supercells have been proposed. However, these large supercells are normally intractable at the ab initio level with the current computing facilities. They are normally used in classical approaches using force fields.43 B


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The interface plane between the phases was chosen to determine the stacking direction by evaluating the mismatch parameter, ξ. Experimentally, it has been shown that a low value for ξ is related to a stable interface formation.47 As one can see in Table 1, the mismatch between the pyrite (100) surface and the arsenopyrite surfaces varies significantly for the 12 arsenopyrite surfaces considered in this work. The (011), (101), (110)−S, (110)−As, (111), (210)-1, and (210)-2 surfaces present large values for ξ (from 21.1% to 42.9%), which clearly shows that these surfaces do not match with the pyrite to form a stable interface. The (010) surface could interact favorably with the pyrite surface, but as it is a triclinic cell and as the pyrite surface is orthorhombic, it is necessary to perform a crystallographic transformation from the arsenopyrite(010) triclinic surface to an equivalent orthorhombic cell in order to evaluate the commensurability. This transformation, illustrated in Supporting Information Figure S17, was done by maintaining the magnitude of the a lattice parameter while increasing the b lattice parameter. This difference is sizable and makes the ξ parameter change to 41.2%, which is too large to form a coherent interface. Finally, the (001) and (100) surfaces presented a relatively small mismatch, 5.5%, and these surfaces were used to prepare the three most stable interfaces formed from pyrite and arsenopyrite surfaces: FeS2(100)/FeAsS(001), FeS2(100)/FeAsS(100)−As, and FeS2(100)/FeAsS(100)−S. Figure 3 shows the interfaces formed by a sequence of atomic layers composed of iron, sulfur, and arsenic, leading to 24

Figure 2. Scheme showing how to construct a coherent interface model that maximizes the overlapping area, SA/B, between phases A and B.

Generally, the lattice parameters of two heterogeneous phases cannot be perfectly matched; thus, it is necessary to evaluate the commensurability of the phases. Only in some cases it is conceivable to build interfaces with the same crystalline phase and surface area via a unit-cell transformation;37 however this is not the case of pyrite/arsenopyrite interfaces. Since a new lattice parameter is necessary in the calculations for coherent solid−solid interface models, stress regions are naturally formed along the interface region. The mismatch parameter, ξ, between pyrite (A) and arsenopyrite (B) is defined as ξ=1−

2SA/B SA + SB

(4)

where SA and SB are the surface areas and SA/B is the overlapping surface area shown in Figure 2. The pyrite (100) cleavage plane was used due to its highest occurrence in nature, in all pyritic soils, sediments, and substrates. Also, it has been largely investigated by experimental and theoretical techniques.44 The choice of the arsenopyrite mineral cleavage planes is, however, not straightforward.27,45 Recently, Silva et al.27 reported a detailed investigation of arsenopyrite cleavage planes by means of GGA/DFT calculations. They investigated 12 possible cleavage surfaces, and their surface energy estimates were very close in energy and are reproduced in Table 1. The differences are no larger than 0.73 J/m2. Furthermore, no preferential cleavage planes are observed in nature, and X-ray diffractogram data identify different cleavage planes depending on the sample. Table 1. Mismatch Parameter, ξ, for Different Arsenopyrite Surfaces in Combination with the (100) Pyrite Surfacea arsenopyrite surfaces (001) (100)−As (100)−S (010)-triclinic (010)-orthorhombic (011) (101) (110)−S (110)−As (111) (210)-1 (210)-2 pyrite (100)

surface energy,b J/m2 c

1.05 [0.96] 1.07c [1.04] 1.09c [1.00] 1.06c 1.30c 1.47c 1.52c 1.57c 1.51c 1.44c 1.78c 1.06d [1.03]

ξ, %

Figure 3. Interface structures. (a) Interface layered structure along the c axis. (b) Pyrite and arsenopyrite bulk, where the two Fe−Fe distances (short and long) are highlighted in the structure of arsenopyrite. (c) Interfacial Fe−Fe distances and the interface types. From left to right the interfaces in c are FeS2(100)/FeAsS(001), FeS2(100)/FeAsS(100)−As, and FeS2(100)/FeAsS(100)−S. Red, yellow, and green spheres represent, respectively, the Fe, S, and As atoms. Red dotted lines represent the normal interfacial plane formed by the contact of the two phases.

5.5 5.5 5.5 6.2 41.2 22.8 29.8 21.1 21.1 38.2 42.9 42.9

atomic layers for each structure in the z direction. Along the pyrite side (also labeled in this work as “pyrite region” or “pyrite phase”), the interface is formed by consecutive sulfur and iron layers and the sequence of sulfur−iron−sulfur has the same FeS2 stoichiometry as the pyrite bulk structure. In the arsenopyrite side (also called in this work “arsenopyrite region” or “arsenopyrite phase”), a sequence of sulfur−iron−arsenic−

a

The arsenopyrite surface energy for three terminations is shown for comparison. bThe values in brackets are from the present work. c Values from ref 27. dValues from ref 46. C


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distances presented deviations less than 0.5% in the pyrite region when compared to pyrite bulk, and in the arsenopyrite region bond differences were found in the range of 0.2−2.8%. These geometrical differences may be considered negligible and would not be expected to involve strong modifications of the electronic properties compared to the bulk. Somewhat larger structural deviations were found for the X− S (As−S and S−S) bond distances placed in the equatorial position, Table S5. In the arsenopyrite phase, the As−S bond distance decreased by 2−3%. Otherwise, in the pyrite region, formation of interfacial bonds led to an increase in the sulfur− sulfur distances by 3.1−3.8% for the three interfaces. It was reported earlier, based on DFT/plane-wave calculations for bulk and slab structures of pyrite26,51,52 and arsenopyrite,27,45,53 that the X−S bonds are stronger than Fe−X and that the X−S bonds have a covalent character. Larger structural differences between the pure minerals and the interfaces were found mainly for the Fe−Xax bond distances, see Supporting Information Table S6. The most favorable formation of interfaces occurs through the interaction of the pyrite(100) surface with the arsenopyrite (001), (100)− As, and (100)−S surfaces. For all of them the exposed Fe(II) ions are 5-fold coordinated, which enables the surfaces to interact by forming new Fe−X bonds and thus restoring the 6fold octahedral structures of the bulk pure minerals. Due to the presence of the arsenic atom in the arsenopyrite structure, the Fe−S bond distances have different magnitudes in the two different interface regions. Moreover, the S−S in pyrite and the As−S bonds in arsenopyrite have different bond lengths and generate distorted octahedral sites, Figure 3, and the axial distances were thus found to be distinct from those of either the pyrite or the arsenopyrite bulk. Another important point is related to the composition of the arsenopyrite surfaces at the interface, where the atoms present in the first atomic layer vary according to the target surface. Consequently, octahedral sites with different atomic configurations are formed. In the case of the FeS2(100)/FeAsS(001) interface, sulfur and arsenic atoms are present in the first interfacial layer and Fe(As)3(S)3, Fe(As)2(S)4, Fe(As)1(S)5, and Fe(S)6 sites are formed. In FeS2(100)/FeAsS(100)−As only arsenic atoms are exposed in the arsenopyrite region to form the interfacial bonds; hence, the Fe(As)2(S)4, Fe(As)1(S)5, and Fe(S)6 sites are formed. Finally, for FeS2(100)/FeAsS(100)−S only arsenopyrite sulfur atoms are able to interact with pyrite Fe(II) sites, forming Fe(As)2(S)4 and Fe(S)6 sites. 3.2. Mechanical Properties. Since the hard phase in a mixture presents more resistance under stretching than the soft phase, the resultant cell parameters along the interface plane are typically found to be closer to the harder phase when an interface is formed. Comparing pyrite and arsenopyrite, pyrite (6.5 on Mohs scale) is, however, only slightly harder than arsenopyrite (around 5.5−6.0 on Mohs scale), and thus, the difference between the initial bulk and the interface cell parameters is insignificant, as expected since they are close to aaverage and baverage. We also calculated the bulk modulus (BM) for the FeS2 and FeAsS minerals and compared with the experimental results obtained by X-ray diffraction data for different pressures.54,55 At our theoretical level the BM was estimated to be 150 GPa (experimental value is 143 GPa) for pyrite and 147 GPa (experimental value of 137 GPa) for arsenopyrite, in reasonable agreement with the experimental data. Comparing the values for the two solid phases we find only a minor difference

arsenic−iron−sulfur forms two FeAsS stoichiometric units of arsenopyrite. As discussed by Wang and Smith,43 it is a good strategy to first optimize the interfacial unit cell to reduce the mismatch strain. To find the best cell parameters for the interfaces we thus optimized the systems in two steps. First, all interfaces were optimized, maintaining the relation between the structural lattice parameters and keeping the angles fixed. In other words, we first optimize the systems changing the cell volume while maintaining the cell shape. From the obtained structures, we performed a full optimization procedure, and then we estimated the structural parameters of the cell. As shown in Figure 3, we classified the structure of the interfaces in three types according to the contained Fe−Fe distances: I1 for an interface containing both short and long distances, I2 for the interface containing only long distances, and I3 for the interface containing only short Fe−Fe distances. To understand this classification, it is instructive to compare the atomic structure in the interface region with the arsenopyrite and pyrite bulk Fe−Fe distances.48−50 As discussed in detail by Nickel et al.,50 in pyrite the neighboring octahedrons in the structure share common corners, while in arsenopyrite they share edges. Consequently, in arsenopyrite two distinct Fe−Fe distances are present in the structure, which we obtain as 2.732 Å (short) and 3.741 Å (long); these are not present in the pyrite structure where all Fe−Fe distances are equal, see Figure 3.

3. RESULTS AND DISCUSSION 3.1. Structural Parameters of the Interface. Each structure shown in Figure 3 is formed by four FeS2 layers in the pyrite region and four FeAsS layers on the arsenopyrite side, and the average of the total eight interlayer nearestneighbor distances was predicted by our calculations to be 2.688 Å for FeS2(100)/FeAsS(001), 2.693 Å for FeS2(100)/ FeAsS(100)−As, and 2.684 Å for FeS2(100)/FeAsS(100)−S. This range is comparable to the layer distances in the pyrite and arsenopyrite in the same crystalline direction which for the FeS2(100), FeAsS(001), and FeAsS(100) plane directions are 2.690, 2.656, and 2.625 Å, respectively. All structures had angles close to 90°, and the angular mismatch has not exceeded 1% for any of the solid−solid interface models. The structural lattice parameters along the interface were found to be close to the average values of the pyrite and arsenopyrite crystalline phases [aaverage= (apyrite + aarsenopyrite)/2 = 5.548 Å and baverage= (bpyrite + barsenopyrite)/2 = 5.515 Å], and the structural parameters calculated were a = 5.557 Å; b = 5.525 Å for FeS2(100)/ FeAsS(001), a = 5.560 Å; b = 5.523 Å for FeS2(100)/ FeAsS(100)−As, and a = 5.560 Å; b = 5.524 Å for FeS2(100)/ FeAsS(100)−S. All values are comparable, and the structural cell parameters do not change significantly among the interfaces. The interfacial Fe−Fe distances of the FeS2(100)/FeAsS(001) interface (I1) were obtained as 2.738 and 3.463 Å, respectively. At the interface alternating long and short Fe−Fe distances are found in a 1:1 ratio. The FeS2(100)/FeAsS(100)−As system (I2) is composed by Fe−Fe long (4.090 Å) distances. The FeS2(100)/FeAsS(100)−S interface (I3) is formed by Fe−Fe short (2.822 Å) distances. In the present work the Fe−X (where X = As or S) chemical bonds in the interface plane are denoted equatorial (eq), while bonds crossing the interfacial plane directed along the z axis are denoted axial (ax). The Fe−Xeq (Fe−Aseq and Fe−Seq) bond D


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The Journal of Physical Chemistry C between the pyrite and the arsenopyrite BM. Fan et al.54 compared the BM values for the two minerals taking into account the crystalline phase present in the two structures. The authors suggested that the difference in the ionic radius of the As−1 (1.59 Å) and S−1 (1.44 Å) species in arsenopyrite distorts the crystal structure, changing its elastic behavior. 3.3. Bonding Analysis. 3.3.1. Pyrite and Arsenopyrite Phases. In pyrite, the S2−2 dimer is formed by two sulfur atoms with filled p-orbital states, which is consistent with the spin compensation observed for pyrite bulk26,56 and for the interfaces. For arsenopyrite, the different valences of As and S may suggest the formation of the AsS−3 trivalent anion. However, XPS experiments performed by Nesbitt et al.57 and Jones and Nesbitt58 on arsenopyrite bulk led to assignment of iron as divalent because the main peak in the spectra was found very close in binding energy to that of iron in pyrite. According to these authors it is not possible to distinguish the Fe(II)−(S− S) and Fe(II)−(As−S) bond environments by XPS. They also suggested that the As and S atoms are in the −1 oxidation state in the arsenopyrite structure and that the formal charges in arsenopyrite are Fe2+As−S−. Supporting these arguments, a Mössbauer analysis provided by Bind et al.59 indicated the presence of Fe(II) sites in arsenopyrite, where the doublets present in the spectrum suggest a low-spin configuration for the iron sites. The bonding in arsenopyrite has been discussed to explain how the AsS−2 with an odd number of electrons can lead to spin compensation in the arsenopyrite. Hulliger and Mooser first suggested a chemical bond behind the short Fe−Fe distances which could lead to spin compensation.48,50 However, recently, Silva et al.27 argued, based on a Bader decomposition of the computed charge density, that there is no bonding behind the short Fe−Fe distances since only a ring critical point was found. In order to understand the chemical bonding in the arsenopyrite it is necessary to remember that arsenic and sulfur centers are tetrahedral, leading to hybrid sp3 orbitals. At the arsenic center there is one hybrid orbital doubly occupied, and the other three are singly occupied. In the valence band the contribution of the arsenic is larger than that from the sulfur, see Figure 5b, around −2.5 eV below the Fermi level. The bonding is rationalized as follows: the doubly occupied hybrid orbitals donate charge to the Fe center to form the Fe−As bond along the z direction. The As−Fe−As bonding shown in Figure 4 is a 4c-2e bond due to the Fe d orbitals and the singly occupied hybrid orbitals of As. The last singly occupied hybrid orbital interacts with the singly occupied hybrid sulfur orbital to form the As−S orbital. This explains why the Fe−As−Fe distances (2.403 Å) are longer than the Fe−AsS (2.178 Å) bond distances.

3.3.2. Pyrite/Arsenopyrite Interface. One could argue that the stress at the interface could modify the electronic properties and, consequently, the chemical bonding strength. We evaluated the stress influence on the electronic structure by calculating the density of states for pyrite and arsenopyrite minerals with strained bulk with the average of the calculated lattice parameters for the three interface models, i.e., a = 5.559 Å and b = 5.524 Å. We observed that the shape and intensity of the DOS features remain the same; only minor changes were observed (see Figure 5). In addition, the position of the band

Figure 5. Strain influence on the electronic structure of pyrite (a) and arsenopyrite (b) minerals.

gap is not modified by the deformation through the changed lattice parameters. The last result suggests that the electronic structure of the interface will not be changed by the strained structure. A Bader topological analysis has been performed for the separate systems earlier27 and the pyrite and arsenopyrite bond critical points (BCP) determined permitting one to assess the bonding nature in the respective bulk structure. The Fe−S BCP has a higher value in arsenopyrite [ρBCP(rc) = 0.090 e/ao3] than in pyrite [ρBCP(rc) = 0.079 e/ao3], which means that this bond is somewhat stronger in arsenopyrite than in pyrite. Furthermore, the Fe−As bonds are slightly weaker than Fe− S, but the ρBCP(rc) value difference is less than 0.006 e/ao3. The major difference is in the S−S and As−S bonds. For arsenopyrite, the As−S [ρBCP(rc) = 0.0828 e/ao3] BCP density value is only a little more than one-half of that in S−S [ρBCP(rc) = 0.1325 e/ao3] BCP in pyrite. The ELF contour distribution along the S−S and As−S bonds shown in Figure 6 clearly shows high electron-pair localization around the bond region, suggesting that S22− and AsS2− anionic dimers are present in the pyrite/arsenopyrite interface region. This is consistent with the presence of Fe2+, as expected. One could argue that the interface could lead to spin polarization of the system. In order to test this hypothesis, we investigated different initial spin polarization guesses for the three different atoms (Fe, As, and S) located in the interfacial region of the three systems. We tested (i) the ferromagnetic,

Figure 4. (Left) Illustration of the structure of arsenopyrite and (right) isosurface and section of the 4c-2e electron state at −2.5 eV below the Fermi level, calculated at the Γ point. Color code: yellow, sulfur; green, arsenic; red, iron. E


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Figure 6. Electron localization function (ELF) for (a) FeS2(100)/ FeAsS(001), (b) FeS2(100)/FeAsS(100)−As, and (c) FeS2(100)/ FeAsS(100)−S interface planes located in the pyrite region (left side) and arsenopyrite region (right side). ELF plots for the axial Fe−X bonds are shown in Figure S18.

(ii) antiferromagnetic, and (iii) the spin-compensated systems. These results are shown in Supporting Information Tables S7− S9, and for all interfaces the results indicated no spin polarization, leading to total and absolute magnetization equal to zero. This is also in agreement with the presence of Fe(II) at the interface. 3.4. Electronic Properties. For all interface systems iron states dominate both the valence and the conduction bands, see Figure 7. Only a small contribution to the valence band is observed from sulfur and arsenic p orbitals. This is similar to the pyrite60−62 and arsenopyrite27,49,59 bulk, where Fe 3d states dominate the valence states, with a small contribution from S and As. Many works have discussed the electronic structure of pyrite and arsenopyrite, and there is a consensus that in both minerals the electronic structure can be described based on ligand-field theory. The similarities of the density of states projected on the interfaces, Figure 7, and the two individual phases, Figure 5, permit one to describe the Fe−X and X−S bonds as follows. The Fe d orbitals split to form the t2g and eg states in a pseudo-octahedral field, where the eg orbitals are empty while the t2g orbitals are completely filled with 6 electrons. The empty eg states interact with the sp3 hybrid orbitals of the AsS2− to form σ bonds, since the As (or S) atoms are bridging the two iron centers (see Figure 6). It is in agreement with the formal oxidation state of +2 for iron suggested by the absence of spin polarization in the Fe(II) sites and with the structural analysis for the interfacial bonds. For the three interfaces the band gap corresponds mainly to a charge transfer excitation from the filled t2g orbitals of Fe states to eg* antibonding states (formed by the hybridization of iron 3d and S and As p states). However, despite the interfaces having similar electronic structure, we find that the contact at the interface changes the density of states around the Fermi level. The interface FeS2(100)/FeAsS(001) has metallic behavior, while the other two interfaces have small band gaps. The applied Kohn−Sham method without contribution

Figure 7. Density of states (DOS) projected on the interface atoms in the range from −8 to 4 eV: (a) FeS2(100)/FeAsS(001) system, (b) FeS2(100)/FeAsS(100)−As, and (c) FeS2(100)/FeAsS(100)−S system. Band gap (BG) was calculated from the band structures depicted in Figure S19.

from exact exchange is known to underestimate band gaps, and the estimated values of 0.25 and 0.78 eV for the FeS2(100)/ FeAsS(100)−S and FeS2(100)/FeAsS(100)−As interfaces, respectively, must thus be taken as lower bounds to the respective band gap (see Figure 7). The trends in the estimated band gaps for the similar systems pyrite, arsenopyrite, and the three interface models should, however, still be relevant. The projected density of states for the FeS2 and FeAsS stoichiometric layers placed in the interface region (Int) and in the bulk region (Bulk) are shown in Figure 8. The PDOS for FeS2(100)/FeAsS(001) shows that the states in the range from −1.2 to 1.2 eV are dominated by contributions from the interface atoms and that the interface DOS is mainly responsible for modulating the band gap of the system. For the FeS2(100)/FeAsS(100)−As and FeS2(100)/FeAsS(100)−S interfaces, the density of states in the range from −0.3 to 0.3 eV is the same as in the bulk of the respective system. The Hubbard correction used in the electronic structure calculations improves the estimates of band gaps (Figure 1) in comparison with experiment for the bulk. Including this correction also for the interfaces we find smaller band gaps than for the bulk pyrite and arsenopyrite minerals which can be expected to favor electron transport during oxidation of arsenopyrite in the presence of pyrite. This finding is consistent with the trend discussed above in connection with Figure 7. F


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For the three most favorable interfaces the work of adhesion is predicted to be less than one-half the work of self-adhesion (following case ii). Thus, we conclude that thermodynamically the interface area will be minimized and lead to large domains of pyrite or arsenopyrite. In fact, in nature the combined mineral is normally found as pyrite encrusted in arsenopyrite. The domains are relatively large (microns), which can be understood as the interface not being favored compared to selfadhesion in agreement with the present results. The formation energies, Eform, of the three different interfaces have been estimated. Eform represents the energy required to dissociate the material into its individual components and is given by Eform = E bulk −

Figure 8. Projected density of states. “Bulk” and “Int” label the density of states for the atoms in the bulk and interface regions, respectively.

(6)

j

where Ebulk is the bulk energy per unit formula, xj is the number of atoms of type j in the unit cell, and μj* is the chemical potential for species j in the standard state. To calculate μFe * the iron BCC unit cell was used, for μAs * the gray arsenic rhombohedral cell, and for μ*S the S8 orthorhombic cell (see optimized geometries in the SI). The results are presented in Table 2, and the values were found to be in the range from −2.44 to −2.53 eV. These values must be compared to the sum of the pyrite (−1.51 eV/(formula unit)) and arsenopyrite (−1.31 eV/(formula unit)) formation energies (Table S4) of −2.82 eV/(formula unit). The formation of pyrite and arsenopyrite pure phases is thus at least 0.3 eV/(formula unit) more favored than the pyrite/arsenopyrite interface. The nonmiscibility and adhesion properties of pyrite and arsenopyrite have been discussed previously.17,18,20,21 As a result of the structural differences between pyrite and arsenopyrite in As-rich ore soils and sediments, pyrite and arsenopyrite are generally found mixed but in two distinct phases.1,20 In contrast, HRTEM and XAS data for arsenian pyrites with lower arsenic concentrations suggest that the As atoms are in a one-phase solid solution system. This shows how the concentration of arsenic can modify the structure and the grain distribution present in the structure of pyrite and arsenopyrite. However, large arsenopyrite domains are only found in As-rich regions. Palenik et al.17 documented a complex matrix for arsenian pyrite in auriferous soils. The heterogeneous nature of the matrix in these samples was described as a polycrystalline mixture of pyrite and arsenopyrite nanodomains of about 20 nm2 in size. In addition, high-resolution transmission electron microscopy (HRTEM) observations of As-rich arsenian pyrite from natural ore deposits by Fleet et al.16 and Simon et al.21 suggested the presence of stacking faults separating alternating pyrite and arsenopyrite thin (10−12 Å) lamellae. These HRTEM observations suggest that high As contents in arsenian pyrite might be related to the presence of nanoscale aggregates of sulfides, with As residing in arsenopyrite domains. As a conclusion, the compiled data show clearly that pyrite and

3.5. Interface Adhesion and Stability. Our strategy is to compare the ideal work of adhesion, Wad, between the pyrite and the arsenopyrite phases with the ideal work of self-adhesion of the two individual phases. The ideal work of adhesion is the energy required to reversibly separate a material into two nonbonded surfaces.36 This property can be estimated by a DFT approach using the difference between the two surfaces DFT (EDFT and EDFT A B ) and the interface energies (EAB ), as shown in eq 5. It is very important to calculate the interface energy using surfaces with the same lattice parameter as the interface, as then part of the mismatch strain is avoided. Since dissipative plastic effects and/or defects in the structure are not involved in theoretical calculations, the real work needed to create an interface is greater than the estimated ideal work of adhesion, Wad. Hence, our calculations must be considered a lower bound to the experiment. The ideal work of self-adhesion, labeled Wpyrite for pyrite and Warsenopyrite for arsenopyrite, can be calculated as the energy necessary to cleave the bulk along a specific plane direction to form two identical slabs. As for the work of adhesion, a greater self-adhesion corresponds to stronger bonding along the selected plane in the bulk. DFT Wad = (EADFT + E BDFT − EAB )/2S

∑ xjμj*

(5)

Table 2 shows the work of adhesion and the work of selfadhesion for the three most stable interfaces. As discussed by Martin et al.,36 three different situations might occur in this analysis: (i) the self-adhesion of the two phases is lower than the work of adhesion, such that the growth of one phase on top of the other is favored, and as a consequence, the system will maximize the interfacial area; (ii) the work of self-adhesion of the phases is greater than Wad, and the system will tend to minimize the area of the interface region and instead grow bulk granular regions; (iii) Wad has a value intermediate between the two surface energies, which makes predicting the interface growth ambiguous by only theoretical calculations.

Table 2. Work of Adhesion, Wad, and Formation Energy, Eform, for the Most Stable Interfacesa

a

interface

Wpyrite, J/m2

Warsenopyrite, J/m2

Wad, J/m2

Eform, eV/(formula unit)

FeS2(100)/FeAsS(001) FeS2(100)/FeAsS(100)−As FeS2(100)/FeAsS(100)−S

4.12 4.12 4.12

3.84 4.16 4.00

1.63 1.47 1.70

−2.497 −2.533 −2.441

Wpyrite and Warsenopyrite denote the work of self-adhesion for pyrite and arsenopyrite, respectively. G


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two minerals they must have a common Fermi level, making the pyrite an electron donor relative to arsenopyrite. Consistent with this, the empty conduction band of arsenopyrite is lower than the conduction band of pyrite, making arsenopyrite the acceptor of electrons. It is clear that in a junction of these two phases the pyrite has cathodic character and arsenopyrite anodic character, as observed in electrochemical experiments.9,13 Furthermore, Blanchard et al.63 showed that the mechanism of arsenic incorporation into pyrite occurs through the formation of AsS anions, which is consistent with the cathodic character of the pyrite found in the present study. The decrease in the band gap thus facilitates electron transfer at the pyrite/arsenopyrite interface, which can result in a galvanic effect which would enhance the process of oxidation of these minerals in nature.

arsenopyrite surfaces do not present strong preferential adhesion. The low nucleation rate in synthesizing mixed arsenopyrite and pyrite minerals is consistent with the low adhesion estimated in our calculations.

4. CONCLUDING REMARKS The adhesion, bonding structure, and electronic properties of several pyrite/arsenopyrite interfaces were investigated by a DFT/PBE/plane wave method. The mismatch, ξ, between the pyrite(100) surface and the arsenopyrite (001), (100)−As, (100)−S, (010), (011), (101), (110)−S, (110)−As, (111), (210)-1, and (210)-2 surfaces was evaluated. Only the arsenopyrite (001), (100)−As, and (100)−S presented ξ values suitable to form stable interfaces with the pyrite(100) surface. From the selected surface planes, FeS2(100)/FeAsS(001), FeS2(100)/FeAsS(100)−As, and FeS2(100)/FeAsS(100)−S were built and investigated. The bond lengths and lattice parameters are slightly changed due to the interface formation. The structural lattice parameters along the interface are close to the average values of the pyrite and arsenopyrite crystalline phases and the angles close to 90°, as expected. Both phases have similar hardness and bulk modulus, explaining why the structural parameters at the interface are very close to those of the respective pure phases. The adhesion at the pyrite/arsenopyrite interface is less favorable than the self-adhesion for pyrite/pyrite or arsenopyrite/arsenopyrite. Thus, in the genesis of the mineral the interfacial area would tend to be minimized, and possibly its formation would occur due to kinetic effects in the formation of the two minerals when they were associated. These results are consistent with the low miscibility between the two phases, which is observed experimentally. The ELF and PDOS calculations for the interfaces compared with results reported previously for the pyrite and arsenopyrite bulk show that the electronic structure at the interfaces exhibits similarities to that of the pyrite and arsenopyrite bulk. However, even with the similarities, the band gaps (t2g → eg transition) of the pyrite/arsenopyrite interfaces are small (or metallic) and the atoms present in the interface region dominate the density of states at the Fermi level. Figure 9 shows the DOS of the pure phases of pyrite and arsenopyrite but taking both curves with respect to the arsenopyrite Fermi energy. This puts the valence band of the pyrite in a region above the valence band of arsenopyrite and formally above the Fermi level of the arsenopyrite. Clearly, when forming an interface between the

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet link. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b02642. Convergence test for pyrite and arsenopyrite bulk; structural parameters of pyrite and arsenopyrite bulk versus Hubbard parameter; electronic band structures used to calculate the band gap values depicted in Figure 1; crystallographic transformation of the arsenopyrite (010) surface from triclinic to an orthorhombic cell; structural parameters and spin test for the three most stable interfacesl ELF description and plots for the Fe− Xax bonds in the interface region; electronic band structure for the three interfaces; structures used to calculate μ*Fe, μ*As, and μ*S in eq 6 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The support of the Brazilian agencies, Fundaçaõ de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Conselho ́ Nacional para o Desenvolvimento Cientifico e Tecnológico (CNPq), and Coordenaçaõ de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES), is gratefully acknowledged. The National Institute of Science and Technology for Mineral Resources Water and Biodiversity also supported this work− ACQUA-INCT (http://www.acqua-inct.org). Additional support was provided by the Swedish Research Links program under project number 348-2013-6723. Computational resources provided by the Swedish National Infrastructure for Computing (SNIC) at the HP2CN center are gratefully acknowledged.

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REFERENCES

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Figure 9. Density of states of arsenopyrite and pyrite. The Fermi level was set with respect to that of arsenopyrite. H


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Stability, Structure, and Electronic Properties of the Pyrite

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