Electronic and structural properties of bulk arsenopyrite and its cleavage surfaces – a DFT study

Abstract

Arsenopyrite is the most abundant arsenic containing mineral on Earth and it is normally associated with many other minerals of economic importance. Therefore, it is involved in the environmental impacts of mining activities. The bonding nature of arsenopyrite and its preferential cleavage surface are still controversial. In the present work we have investigated the structural and electronic properties of arsenopyrite and its cleavage surface formation using a density functional/plane waves method. The quantum theory of atoms in molecules (QTAIM) and electron localization function (ELF) were applied for investigating the nature of the bonding in arsenopyrite. No evidence was found for Fe–Fe bonding in the bulk structure. The As–S bond has large covalent character and it is unexpected to be broken in the surface formation. The cleavage and surface energies have been calculated indicating that the (001) surface is the most favored.

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1. Introduction

Arsenopyrite is a mineral sulfide commonly found in nature and is associated with noble metals such as gold, copper and silver. This mineral has little economic value¹ and the mining process generates a huge quantity of tailings which are disposed in dams.² The exposition of sulfide minerals, such as arsenopyrite, to the environment normally leads to acid rock drainage (ARD).

During ARD, the mineral sulfides present in the mining tailings oxidize producing sulfuric acid. The generated solution acts as a leaching agent, i.e., as a mixture that solubilizes the solid mineral constituents, producing an acidic solution containing dissolved metals, which can contaminate soil and underground water. ARD is a spontaneous process that arises where the rock is exposed to air and moisture. A classic example occurs in Río Tinto in Spain.³ Along this river there is a large deposit of pyrite and the process of ARD has occurred for centuries, leading to a pH of about 2 with a high concentration of heavy metals. However, ARD normally occurs due to anthropogenic activities, such as mining, which expose large amounts of sulfide minerals to the atmosphere.⁴

Although arsenopyrite is stable under reducing conditions, its oxidation due to weathering effects releases sulfate, arsenite (As(III)) and arsenate (As(V)) species¹ to the environment. The arsenic released due to arsenopyrite oxidation is an environmental hazard and may become a health problem.⁵ The understanding of the kinetics and the mechanism of dissolution of this material in different conditions is essential for assessing the stability of the arsenic containing tailings and the development of more efficient processes to control its remobilization with great environmental, social and economic consequences.

There are several studies in the literature concerning the products formed in arsenopyrite oxidation in different media.^1,2,6–11 However, in many of them the results diverge and there is no consensus concerning the reaction mechanism at a molecular level. In this context, first-principles calculations emerge as a tool for providing information about the surface reactivity of arsenopyrite and insights about its oxidation mechanism. For pyrite there are many theoretical studies concerning its cleavage surfaces,^12,13 water adsorption^14,15 and mechanism of oxidation,¹⁶ as well as about chalcopyrite’s surfaces and adsorption of leaching agents.^17–20 Nevertheless, to the best of our knowledge, there is only one theoretical study about the electronic and geometric characteristics of the (110) surface of arsenopyrite²¹ and two studies about arsenic incorporation into pyrite.^22,23 More information about arsenopyrite and its chemical reactivity is therefore necessary.

Arsenopyrite (ideal formula FeAsS) is the most common arsenic containing mineral on Earth and may be found in many ore deposits. It is a diamagnetic semiconductor.²⁴ Its unit cell is monoclinic and has a space group P2₁/c derived from marcasite (orthorhombic FeS₂)²⁵ with 4 FeAsS per unit cell, as shown in Fig. 1a and b. However, a refinement of the arsenopyrite structure was also accomplished in space group C2₁/d,²⁶ in a pseudo-orthorhombic unit cell, as shown in Fig. 1c. Its structure contains arsenic and sulfur dianions (As–S) coordinated to the iron atom in an octahedral shape (Fig. 2a). The Fe atoms are coordinated to three As and three S atoms and each anion is coordinated to three iron atoms and another anion in a tetrahedral shape. The FeAs₃S₃ octahedrons are asymmetric and share two opposite edges to form single strips parallel to the (10̄1) surface (Fig. 2b). The adjacent octahedral coordinations in a row are related to each other by an inversion operation, leading to distances between Fe cations alternating between short and long. In the direction of the Fe–Fe contact, the short Fe–Fe bond cuts the long S–S edge, whereas the long Fe–Fe bond cuts the short As–As edge. Natural arsenopyrite has a composition ranging from FeAs_0.9S_1.1 to FeAs_1.1S_0.9 ²⁷ and there may be metal impurities such as Co replacing Fe²⁶ in the structure. Mössbauer spectroscopy indicates that the Fe atom is divalent in the low-spin state, in an octahedral environment.^28,29

Fig. 1 Arsenopyrite structure. (a) View of the monoclinic cell along the a axis; (b) view of the monoclinic cell along the b axis; (c) view of the pseudo-orthorhombic cell along the c axis.

Fig. 2 (a) As–S dianions octahedrally coordinated to Fe. (b) Neighboring octahedrons sharing one edge. Yellow atoms are sulfur, purple are arsenic and red are iron.

Concerning the favorable cleavage plane, there is no consensus regarding which is the favored plane among the (100),¹¹ (001),³⁰ (101)^25,31 and (110)^21,32 planes. Many of the reported works did not define clearly which is the unit cell used as the reference, leading to some ambiguity in defining the favored cleavage.

In the present work, the structural and electronic properties of the arsenopyrite bulk and different cleavage surfaces have been investigated aiming to fulfil the lack of information about this system.

2. Methodology

The calculations have been performed based on the density functional theory (DFT)/plane waves methodology with periodic boundary conditions as implemented in the Quantum Espresso package.³³ The PW91³⁴ exchange/correlation (XC) functional and ultrasoft pseudopotentials proposed by Vanderbilt³⁵ with the following valence configurations: Fe (3s² 3p⁶ 3d^6.5 4s¹ 4p⁰), As (4s² 4p³) and S (3s² 3p⁴) were used. For the bulk, a cutoff energy of 60 Ry was used and a 4 × 4 × 4 K-point mesh sampling based on the Monkhorst-Pack scheme³⁶ was chosen, besides Marzari–Vanderbilt³⁷ 0.02 Ry smearing. For the surface, 30 Ry energy cutoff and a 2 × 2 × 1 K-point mesh was used. The energy was converged to 10⁻⁹ Ry. All surfaces were set using a (2 × 2 × 2) slab model with 15 Å of vacuum.

All calculations were spin compensated. Geometry optimization was carried out using a damped dynamics method³⁸ with a Parrinello-Rahman extended Lagrangian,³⁹ keeping a force tolerance criterion of 10⁻³ Ry Bohr⁻¹. The atomic positions, as well as the cell parameters, were fully optimized for the bulk. For the slab calculations only the atomic positions were fully optimized.

Bader’s QTAIM (Quantum Theory of Atoms In Molecules) method⁴⁰ was used to investigate the electronic structure of the solid using the program Critic2.⁴¹ For the bulk modulus calculation, the program Gibbs2 ⁴² was used. Band structure, density of states (DOS), electron localization function (ELF) and electron density plots were built using the Quantum Espresso code and a 8 × 8 × 8 mesh of K-points and for the QTAIM analysis the electron density was built using a 12 × 12 × 12 mesh of K-points.

3. Results and discussion

Bulk

The calculated interatomic distances of arsenopyrite bulk are shown in Table 1 and compared with available experimental values. The theoretical estimates are closer to the experimental results of Bindi et al.²⁹ with a maximum of 2% difference, which are more recent and refer to a sample rich in As. The average Fe–S distance is 2.203 Å, 0.028 Å less than the experimental value²⁹ and also less than the values calculated using similar methodologies for marcasite (orthorhombic FeS₂, 2.23 Å)⁴³ and chalcopyrite (CuFeS₂, 2.241 Å),¹⁷ as expected. The average Fe–As distance of 2.402 Å is 0.005 Å larger than the experimental value,²⁹ and the As–S distance of 2.405 Å is 0.031 Å larger. The As–S bond length is also larger than the S–S distance calculated by Gudelli et al.⁴³ for marcasite (2.20 Å), which is expected due to the larger atomic radius of As. Gudelli et al.⁴³ also found only one Fe–Fe distance for marcasite (3.38 Å), an intermediate value between both distances found in the present work.

Table 1 Interatomic distances for bulk arsenopyrite. All values are in angstroms

Reference	Short Fe–Fe	Long Fe–Fe	Fe–S	Fe–As	As–S
This work	2.668	3.765	2.190	2.380
			2.198	2.410	2.405
			2.222	2.415
Experimental (1961)^27	2.82	3.62	2.22, 2.24	2.30, 2.32
			2.25, 2.26	2.32, 2.38	2.33
			2.26, 2.29	2.39, 2.41
Experimental (1987)^26	2.922	3.627	2.239	2.336
			2.250	2.371	2.346
			2.257	2.375
Experimental (2012)^29	2.734	3.741	2.229	2.370
			2.230	2.409	2.374
			2.233	2.412

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The cell parameter results after optimization are shown in Table 2. They are in agreement with the experimental data and are closer to these data than the DFT/PBE/plane waves results of Corkhill et al.²¹ The differences between lattice parameters did not exceed 0.022 Å, 0.33 degrees in β and 1.72 ų in volume, compared to Bindi et al.²⁹

Table 2 Crystallographic data of arsenopyrite bulk

	a/Å	b/Å	c/Å	β/°	Volume/Å^3
This work	5.739	5.668	5.763	112.05	173.74
DFT/PBE^21	5.61	5.56	5.63	111.67	164.20
Experimental (1961)^27	5.744	5.675	5.785	112.17	174.50
Experimental (1987)^26	5.741	5.649	5.756	110.59	174.73
Experimental (2012)^29	5.761	5.684	5.767	111.72	175.46

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Several studies tried to explain the differences in pyrite (cubic FeS₂), marcasite (orthorhombic FeS₂), arsenopyrite (FeAsS) and lollingite (FeAs₂) structures. Hulliger and Mooser,⁴⁴ Pearson⁴⁵ and Nickel^46,47 used ligand field theory to explain the stabilities of each structure. In pyrite, neighboring octahedrons share common corners, while in the other three sulfides, they share edges. In lollingite, the Fe–Fe distance is shorter than in marcasite, and in arsenopyrite there are alternating short and long distances. In these works, as well as in the works of Brostigen and Kjekshus,⁴⁸ and Goodenough,⁴⁹ the iron atom in arsenopyrite was considered to be in the trivalent oxidation state. These authors, except Goodenough,⁴⁹ considered that there should be an Fe–Fe bond in arsenopyrite to explain the fact that iron is trivalent, but in a low spin state in this mineral, since arsenopyrite is diamagnetic. In fact Pauling⁵⁰ has found complexes with an Fe–Fe bond up to 2.78 Å long. Vaughan and Craig,²⁸ and Bindi et al.²⁹ showed through Mössbauer spectroscopy that iron is actually in a divalent state for all of these sulfides. Tossell et al.⁵¹ considered this result and calculated the ionization energy of orbitals in a MA₆ model for sulfides through the SCF-X_α-SW method. They concluded that these structures are defined by a metal–dianion interaction and proposed an explanation for the different structures based on molecular orbital occupation. Schmokel and coworkers⁵² made a detailed analysis of the experimental and theoretical electron density of pyrite and marcasite. They found that S–S bonds are more covalent and Fe–S bonds are weaker in pyrite when compared to marcasite. This is explained based on the distribution of the d-orbital-like density difference between the two polymorphs.

XPS experiments performed by Nesbitt et al.^1,53 checked that in bulk arsenopyrite and lollingite, the iron is divalent because the main peak on the spectra is very close in bonding energy to pyrite’s spectra. They also suggested that As and S atoms are in the (−1) oxidation state in arsenopyrite. Then, it is accepted that the oxidation states in arsenopyrite are Fe²⁺As⁻S⁻.

In order to better understand the electronic properties of arsenopyrite and also validate the bulk model, the band structure was calculated using the K-points path suggested by Setyawan et al.⁵⁴ for a monoclinic cell, see Fig. S1.† It can be seen by the band structure shown in Fig. 3 that arsenopyrite is a semiconductor, according to the literature.⁵⁵ The indirect band gap of 0.75 eV from the D to Γ point is shown with the red vector. This value is 0.07 eV lower than the experimental value of 0.82 eV,⁹ as expected, since it is well known that the GGA XC functional underestimates the band gap.⁵⁶ The band gap values for pyrite vary from 0.7 to 2.62 eV, but the most reliable ones are between 0.9 and 0.95 eV, measured in photoconductivity experiments.^57,58 Opahle et al.⁵⁹ found a value of 0.85 eV in a DFT/LDA-PZ calculation for pyrite, the same difference from experimental values was found for arsenopyrite in the present work. Gudelli et al.⁴³ calculated a band gap of 1.186 eV for pyrite and 1.603 eV for marcasite using the TBmBJ potential,⁵⁶ which are overestimated.

Fig. 3 Band structure calculated for arsenopyrite.

The total and projected density of states (DOS) are shown in Fig. 4. The iron atom is the one that most contributes to the states around the Fermi level, in both the valence and conduction bands, especially the d orbitals of iron (Fig. S2†). According to the discussion made by De Oliveira and Duarte,¹⁷ this characteristic is coherent with an Fe atom in the oxidation state (II) since this atom can be oxidized as well as reduced.

Fig. 4 Total and projected DOS over the atoms of arsenopyrite plotted using a Gaussian width of 0.005 Ry.

The electron density map of the (010) plane is shown on Fig. 5, indicating that the electron density between neighboring Fe atoms is very small.

Fig. 5 Electronic density map of the arsenopyrite (010) plane. Red balls are iron atoms.

QTAIM analysis was performed for arsenopyrite in order to characterize the chemical bonding in the structure. A total of 90 critical points were found, with 24 of them being nonequivalent: 3 nuclei critical points (NCP), 7 bond critical points (BCP), 9 ring critical points (RCP) and 5 cage critical points (CCP). Their positions are shown in Fig. 6 and the respective data are shown on Table 3 (a complete table is shown as Table S2†). The Morse relationship ensures that n − b + r − c = 0, with n, c ≥ 1, and b, r ≥ 3 which holds for the nonequivalent points.

Fig. 6 Bond critical points (BCP) in green, ring critical points (RCP) in blue, and cage critical points (CCP) in pink for arsenopyrite QTAIM analysis. Atoms in red are iron, in yellow are sulfur and in purple are arsenic.

Table 3 Critical points in QTAIM analysis

Critical points	ρ(rc)^a	∇^2ρ(rc)^a	Chemical meaning
a In atomic units.
Fe	6.2235	−73.0292
As	0.5412	−18.0058
S	0.3588	−10.8180
b1	0.0721	0.0492	Fe–As
b2	0.0961	0.1501	Fe–S
b3	0.0733	0.0730	Fe–As
b4	0.0924	0.1996	Fe–S
b5	0.0725	0.0475	Fe–As
b6	0.0828	−0.0075	As–S
b7	0.0881	0.2232	Fe–S
r1	0.0326	0.0546	Fe⋯Fe long
r2	0.0430	0.0539	Fe⋯Fe short

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Concerning the BCPs, three are Fe–S bonds, three are Fe–As bonds and one is an As–S bond, as shown in Fig. 7a. The critical points involving Fe–S bonds have a positive Laplacian indicating a larger ionic character. Schmokel et al.⁵² have proposed that the Fe–S bond in pyrite and marcasite has some covalent character due to Fe d orbitals mixing involved in this bond. The Fe–S BCP shows values of density and Laplacian (see Table 3) close to those of Gibbs et al.⁶⁰ calculated using DFT/LDA and localized basis sets, and also close to the values published by Schmokel et al.⁵² in a DFT/PBE study using multipole refinement. Aray et al.⁶¹ found a value of 0.079 a.u. of density for the Fe–S BCP in pyrite and 0.13251 a.u. for the S–S BCP in DFT/PBE (FP-LAPW, full-potential linearized augmented plane-wave + local orbitals) calculations. The Fe–As BCP has a density and positive Laplacian smaller than the Fe–S BCP indicating that Fe–S has larger ionic character and is stronger than the Fe–As bonding. The As–S BCP has a density of 0.0828 a.u. and Laplacian of −0.0075, which means it has covalent character. Schmokel et al.⁵² found similar results for density and Laplacian of S–S BCP in pyrite and marcasite. The electron density and Laplacian of the S–S BCP in marcasite is 0.115 a.u. and −0.015 a.u., respectively, compared to the values of the same bond in pyrite of 0.126 a.u. and −0.043 a.u., respectively, indicating that this bond is stronger in pyrite than in marcasite. This result is similar to the density of S–S BCP in covellite (0.135 a.u.) and its Laplacian (−0.079 a.u.) found by Morales-García et al.⁶² using a similar computational method. Comparing with our results for As–S BCP in arsenopyrite of 0.083 and −0.007 a.u. for density and Laplacian, respectively, it is expected that the As–S bond in arsenopyrite is weaker than the S–S bond in pyrite, marcasite and covellite. However, analyzing the values shown in Table 3, the As–S bond is strongest in arsenopyrite and, therefore, unlikely to break in surface cleavage.

Fig. 7 (a) Bond critical points and (b) ring critical points in detail. Yellow atoms are sulfur, purple are arsenic and red are iron.

The ELF (electron localization function) map was generated (Fig. 8) for the As–S bond. In the region where the ELF value is close to 1, the electrons are localized, and in the regions where they are delocalized, like a homogeneous electron gas, as in metallic bonding, it has a value of 0.5. In Fig. 8, it is possible to see the shared cloud between As and S atoms, indicating a covalent bond.

Fig. 8 ELF of the arsenopyrite As–S bond. Red is iron, purple is arsenic and yellow is sulfur.

In the QTAIM analysis no evidence of the Fe–Fe bond has been found in arsenopyrite. A ring critical point (RCP) between two neighboring iron atoms was found as expected, see Fig. 7b. From our QTAIM analysis, the hypothesis of the Fe–Fe bond is completely discharged. The values of density and Laplacian for the r1 and r2 RCPs corresponding to the Fe⋯Fe distances of 3.765 and 2.668 Å are very similar and the interaction of these atoms must have the same nature. The ELF map was generated (Fig. 9) for the Fe–Fe region. The ELF value between two Fe atoms is estimated to be 0.25, which is not characteristic of chemical bonding.

Fig. 9 ELF of the arsenopyrite (010) plane. Red balls are iron.

The calculated atomic charges and volumes in QTAIM are reported in Table 4. The estimated positive atomic charge for As is reasonable since sulfur is more electronegative. The integration of the AsS basins leads to −0.41e and 0.41e for the iron basin. This is in agreement with Fe²⁺(AsS)²⁻. The As and S atoms have the largest volumes, which means that these atoms dominate the crystal compressibility.

Table 4 Atomic charges in AIM analysis

Atoms	Charge	Volume (a.u.)	Pauling’s electronegativity
Fe	0.41	69.9	1.83
As	0.18	112.9	2.18
S	−0.59	111.8	2.58
Total		1178.5

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The c parameter⁶³ can be used to evaluate the difference between topological charge, Q(Ω), and nominal oxidation state, OS(Ω), according to eqn (1) and it indicates the ionicity of the crystal.

The closer to 1 c is, the more ionic the crystal, and the closer to 0, the more covalent it is. The value of c for arsenopyrite is 0.205 taking Fe²⁺As¹⁻S¹⁻ oxidation numbers as reference, which indicates a solid that presents large covalent character.

The bulk modulus of arsenopyrite was calculated and compared with experimental and theoretical values of other compounds, as shown in Table 5. Our value of 147.5 GPa is 15 GPa greater than the experimental value obtained by Fan et al.⁶⁴ in X-ray diffraction in the pressure range from 0 to 9.6 GPa. The calculated and experimental values for marcasite and pyrite are in the same level of magnitude as our results. This shows that the method used in this work describes well not just each atom individually, but also the whole crystal structure.

Table 5 Calculated and experimental bulk moduli for arsenopyrite, marcasite and pyrite

Compound	Bulk modulus (GPa)	Reference
Arsenopyrite	147.5	This work
Arsenopyrite	133	X-ray diffraction^64
Marcasite	150.1	PBE/plane waves^43
Marcasite	146.5	X-ray diffraction^65
Pyrite	150	PAW/plane waves^66
Pyrite	143	X-ray diffraction^67

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Surface

To the best of our knowledge, there is no consensus in the literature concerning the favored arsenopyrite cleavage. The (100),¹¹ (001),³⁰ (101)^25,31 and (110)^21,32 surfaces have been indicated by different references as most favorable to be cleaved. It is important to highlight that in some of these works the unit cell used to define the Miller indices was not clearly indicated explaining part of this divergence. Table S1† shows the correspondence between the C2₁/d and P2₁/c unit cells which are normally used to describe arsenopyrite. We stress that it is important to clearly define the unit cell used to define the surfaces.

Several surfaces were created based on the P2₁/c optimized bulk cell to compare their energies and the planes are shown in Fig. S3.† The non-optimized structures are presented in Fig. S4.† All the different terminations were calculated. All of them are type II from Tasker,⁶⁸ namely, they had charged layers formed by cations and anions symmetrically arranged in a way that the charges cancel on the surface and they do not have a resultant dipole perpendicular to the surface. Usually, this means that there is no reconstruction of these surfaces, only relaxation. The surface energy was calculated according to eqn (2):⁶⁹

where Eⁿ is the energy of a n-layer slab, E_bulk is the energy of the unit cell which corresponds to a single layer, and A is the surface area. The cleavage energy (E_cleav) was calculated before the relaxation, in a single point calculation, and the surface energy (E_surf) was calculated after the relaxation. The results are shown in Table 6 together with the coordination of each surface atom in the different cleavages. Fig. 10 shows the structures after relaxation.

Table 6 Surface energies and coordination of surface atoms of different arsenopyrite surfaces

Surface	Surface energy/J m^−2	Cleavage energy/J m^−2	Coordination
			Fe	As	S
Bulk	—	—	6	4	4
001	1.05	1.23	5	3	3
010	1.06	1.28	5	3	3
100 As-terminal	1.07	1.21	5	3	4
100 S-terminal	1.09	1.35	5	4	4
011	1.30	1.50	5, 4	2	3
101	1.47	1.65	4	3	3
110 S-terminal	1.52	1.91	4	3	3, 2
110 As-terminal	1.57	1.93	4	3, 2	3
111	1.51	1.78	5	2	2
210 (1)	1.44	1.59	4, 3	3, 2	4, 3
210 (2)	1.78	2.29	4, 3	3, 1	2

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Fig. 10 Optimized arsenopyrite surfaces. Iron is in red, sulfur in yellow and arsenic in purple. Miller indices are based on the P2₁/c symmetry.

As one can see in Table 6, the surface and cleavage energies are related to the number of bonds broken. The (001), (010), and (100) planes are the most favored cleavage surfaces with E_surf between 1.05 and 1.09 J m⁻² and E_cleav between 1.21 and 1.35 J m⁻². The (100) plane is more likely to cleave on the As-terminal surface. The top view of these planes is presented in Fig. 11, which shows that the (001) and (100) surfaces expose a similar terminal structure. In these planes no As–S bond is broken, as expected. The other ones have higher energies and are unlikely to be cleaved. Nevertheless, they may be exposed when fractured due to twinning along the high cleavage energy planes. According to Klein et al.,²⁵ twinning appears on surfaces (100) and (001) of the P2₁/c cell, whereas according to Dana and Ford³² it appears on surfaces (110) and (101).

Fig. 11 Top view of surfaces: (a) (001); (b) (100); (c) (010). Red is iron, purple is arsenic and yellow is sulfur.

Pyrite has a cubic unit cell, so the (100), (010), and (001) surfaces are equivalent and have been used in adsorption or oxidation studies of pyrite.^14,16 Hung et al.^12,13 have studied pyrite’s (100), (110), (111), and (210) surfaces through PBE/plane waves calculations. Their results follow the same tendency of arsenopyrite, except for the high value in (100) cleavage energy of 4.25 J m⁻². Table 7 shows a comparison between the surface and cleavage energies for arsenopyrite and pyrite. However, it is important to note that pyrite and arsenopyrite present different unit cells, therefore the bond breaking in the surface formation is different.

Table 7 Comparison of arsenopyrite and pyrite’s surface energies

Surface	Arsenopyrite		Pyrite^12,13
	Surface energy/J m^−2	Cleavage energy/J m^−2	Surface energy/J m^−2	Cleavage energy/J m^−2
a Microfacetted (110) pyrite surface.b Corkhill et al.^21c The (001), (010) and (100) pyrite surfaces are equivalent.
001	1.05	1.23	1.06^c	4.25^c
010	1.06	1.28
100	1.07	1.21
110 (S-terminal)	1.52	1.91	1.68	1.85
110 (As-terminal)	1.57	1.93	1.54^a	1.74^a
110 (1)^b	1.76	2.08	—	—
110 (2)^b	2.08	2.40	—	—
111	1.51	1.78	1.40	1.61
210	1.44	1.59	1.50	1.74

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Corkhill et al.²¹ also calculated the E_surf and E_cleav of (110) arsenopyrite surfaces in two different terminations using PBE/plane waves. The models used by them (24 atoms, 5.65 Å × 7.91 Å × 16.9 Å cell) are four times smaller than the ones considered in the present work and do not have equal terminations on the top and bottom surfaces. Their estimated values of E_surf (1.76 and 2.08 J m⁻²), and E_cleav (2.08 and 2.40 J m⁻²) are higher than our results, with both presented in Table 7.

The largest change in the relaxed slab model was observed for the surface atoms with values of 0.12 Å for Fe–As bond on the (100) surface, 0.14 Å for Fe–As bond on the (001) surface, and 0.14 Å for Fe–Fe distance on the (010) surface.

The projected DOS over the surface atoms of the (001), (010), and (100) planes are shown in Fig. 12. Similarly to the bulk, the Fe 3d orbitals are dominant around the Fermi level, which means that nucleophilic or electrophilic interactions with adsorbents are most likely to occur on this atom. For all surfaces, the band gap that was present in the bulk almost disappeared.

Fig. 12 Projected DOS over the atoms of the surfaces: (a) (001); (b) (010); (c) (100) plotted using a Gaussian width of 0.005 Ry.

4. Conclusion

The structural and electronic properties of the arsenopyrite and its different cleavage surfaces have been investigated by a DFT/plane waves method. For the arsenopyrite bulk, the structural parameters are in good agreement with the experimental data and previously reported calculated values. The Bader’s QTAIM analysis indicates that there is no Fe–Fe bond in arsenopyrite. Only a ring critical bond was found between the two Fe atoms. The As–S bond has covalent character and the Fe–As and Fe–S bonds have ionic character. In agreement to the previously reported calculations of covellite, pyrite and marcasite, which concluded that the S–S bond is unlikely to be broken, the As–S bond is also unlikely to be broken in the cleavage. The surface and cleavage energies have been estimated for different surfaces. The (001), (010) and (100) planes are considered the most favored cleavage planes, with surface energies close to 1.07 J m⁻². In these three surfaces the As–S bond is not broken and the Fe, As and S atoms are exposed on the surface. The (001), (010) and (100) surfaces are adequate models for investigating the surface reactivity of arsenopyrite. The projected DOS on the surface show that the valence and conduction bands close to the Fermi level are mostly due to the d-orbitals of iron atoms indicating that this atom is the preferred site for adsorption and, hence, must be involved in the initial steps of the arsenopyrite oxidation. The surface oxidation of arsenopyrite is presently being investigated in our laboratory.

Acknowledgements

We would like to thank Prof. Renata Diniz, Prof. Claudio de Oliveira and Dr Angel Morales-García for the fruitful discussions. The support of the Brazilian agencies Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG), Conselho Nacional para o Desenvolvimento Científico e Tecnológico (CNPq) and Coordenação de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES) are also gratefully acknowledged. The National Institute of Science and Technology for Mineral Resources, Water and Biodiversity has also supported this work – INCT-ACQUA (http://www.acqua-inct.org).

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Footnote

† Electronic supplementary information (ESI) available: Table with the surfaces corresponding to the C2₁/d and P2₁/c unit cells, QTAIM critical points, the K-points used for band calculations, project DOS over the arsenopyrite atoms and the cleavage surfaces are available. See DOI: 10.1039/c4ra13807d

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