Electronic Structure of Sulfur Studied by X-ray Absorption and

Anal. Chem. 2009, 81, 6516–6525

Electronic Structure of Sulfur Studied by X-ray Absorption and Emission Spectroscopy ˇ itnik,§ K. Bucˇar,§ R. Alonso Mori,*,†,‡ E. Paris,‡ G. Giuli,‡ S. G. Eeckhout,† M. Kavcˇicˇ,§ M. Z | ,† L. G. M. Pettersson, and P. Glatzel* European Synchrotron Radiation Facility (ESRF), BP 220, 38043 Grenoble Cedex 9, France, Dipartamento di Scienze della Terra, Universita´ di Camerino, I-62032 Camerino, Italy, J. Stefan Institute, P.O. Box 3000, SI-1001, Ljubljana, Slovenia, and FYSIKUM, AlbaNova University Center, Stockholm University S-10691 Stockholm, Sweden An X-ray spectroscopy and theoretical study of the chemical state of several sulfur bearing minerals and a synthetic sodium sulfite sample was performed. X-ray absorption and high-resolution Kr X-ray emission spectra were recorded and compared to ab initio quantum chemical calculations. A consistent interpretation of the chemical shift in the Kr emission spectra is obtained based on three different theoretical approaches (density functional theory, multiple scattering theory, and atomic multiplet theory). An analysis of the theoretical sulfur orbital population and valence bond is in agreement with the fluorescence energy position of the Kr lines even within the sulfide (S2-) series. It is shown that the Kr energy shifts can be used for a quantitative determination of the proportion of different sulfur species in heterogeneous samples. The metal sulfide group is a major source of the world’s metals and is extensively studied in earth sciences and in mineral physics,1-5 whereas disulfide minerals have interesting solid state properties and are studied in solid-state chemistry.6,7 On the other hand, gaseous sulfur compounds in nature include H2S and SO2, both highly toxic, which together with the sulfates (having a direct effect on scattering of light, effectively increasing the Earth’s albedo), represent some of the most important pollutants emitted in the atmosphere both by volcanic and anthropogenic activity.8-10 Understanding in detail the chemistry of sulfur provides the key to determining fundamental mechanisms * To whom correspondence should be addressed. E-mail: [email protected] (P.G.); [email protected] (R.A.M.). † European Synchrotron Radiation Facility (ESRF). ‡ Camerino University. § J. Stefan Institute. | Albanova University Center, Stockholm University. (1) Fleet, M. E. Can. Miner. 2005, 43, 1811–1838. (2) Farrell, S. P.; Fleet, M. E. Phys. Chem. Miner. 2001, 28, 17–27. (3) Li, D.; Bancroft, G. M.; Kasrai, M.; Fleet, M. E.; Feng, X. H.; Tan, K. Can. Miner. 1995, 33, 949–960. (4) Sugiura, C.; Gohshi, Y.; Suzuki, I. Phys. Rev. B 1974, 10, 338–343. (5) Oertzen, G. U.; Jones, R. T.; Gerson, A. R. Phys. Chem. Miner. 2005, 32, 255–268. (6) Mosselmans, J. F. W.; Pattrick, R. A. D.; Vanderlaan, G.; Charnock, J. M.; Vaughan, D. J.; Henderson, C. M. B.; Garner, C. D. Phys. Chem. Miner. 1995, 22, 311–317. (7) Sugiura, C.; Suzuki, I.; Kashiwakura, J.; Gohshi, Y. J. Phys. Soc. Jpn. 1976, 40, 1720–1724. (8) Paris, E.; Giuli, G.; Carroll, M. R.; Davoli, I. Can. Miner. 2001, 39, 331– 339. (9) Torres Deluigi, M.; Riveros, J. A. Chem. Phys. 2006, 325, 472–476.

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ranging from volcano-climatic interactions to the genesis of ore deposits and is furthermore of great economic importance to catalytic11 and glass-forming industrial processes and to the treatment of vitreous waste material from refuse incineration activities.1,8 Moreover, various forms of organically bound sulfur are important in petroleum and coal hydrocarbons and have thus been widely studied in these systems.12-16 Because of its wide range of oxidation states (from 2- to 6+), sulfur forms chemical bonds with atoms with very different electronegativity values, resulting in large effects on the local electronic structure involving the sulfur atoms. Spectroscopic methods provide the most direct means for experimentally obtaining information on the resulting electronic structure. Synchrotron radiation-based inner-shell spectroscopies are element-specific techniques that are sensitive to changes in the electronic structure and local coordination of a selected element. X-ray absorption spectroscopy (XAS) studies transitions of an electron from a core state to an empty state above the Fermi energy. The X-ray absorption near edge structure (XANES) arises from transitions close to the Fermi level that may include bound states (resonant excitations). The core hole resulting from the absorption process is subsequently filled upon emission of a photon or an electron. X-ray emission spectroscopy (XES) can thus be considered a secondary process that studies filled electron orbitals. The chemical behavior of sulfur has been studied by means of XANES17-21 and has been interpreted with the aid of band-structure2,5,22 and multiple scattering calculations23-27 as well (10) Kavcic, M.; Karydas, A. G.; Zarkadas, C. Nucl. Instrum. Meth., Phys. Res., Sect. B: Beam Interact. Mater. Atoms 2004, 222, 601–608. (11) Niemantsverdriet, J. W. Spectroscopy in Catalysis, 3rd ed.; Wiley-VCH: Weinheim, Germany, 2007. (12) Gorbaty, M. L.; George, G. N.; Kelemen, S. R. ACS Symp. Ser. 1991, 461, 127–136. (13) Kelemen, S. R.; George, G. N.; Gorbaty, M. L. Fuel 1990, 69, 939–944. (14) Waldo, G. S.; Mullins, O. C.; Pennerhahn, J. E.; Cramer, S. P. Fuel 1992, 71, 53–57. (15) Huffman, G. P.; Mitra, S.; Huggins, F. E.; Shah, N.; Vaidya, S.; Lu, F. L. Energy Fuels 1991, 5, 574–581. (16) Huffman, G. P.; Shah, N.; Huggins, F. E.; Lu, F.; Zhao, J. In Processing and Utilization of High-Sulfur Coals; Parekh, B. K., Groppe, J. G., Eds.; Elsevier Science Publishers: New York, 1993. (17) Szilagyi, R. K.; Frank, P.; George, S. D.; Hedman, B.; Hodgson, K. O. Inorg. Chem. 2004, 43, 8318–8329. (18) Glaser, T.; Hedman, B.; Hodgson, K. O.; Solomon, E. I. Acc. Chem. Res. 2000, 33, 859–868. (19) Solomon, E. I.; Hedman, B.; Hodgson, K. O.; Dey, A.; Szilagyi, R. K. Coord. Chem. Rev. 2005, 249, 97–129. 10.1021/ac900970z CCC: $40.75  2009 American Chemical Society Published on Web 07/02/2009

as based on calculations using the transition potential28 approach.29-33 However, difficulties may arise in the interpretation of the XANES spectra. Self-absorption effects in the X-ray absorption measurements can cause uncertainties in the spectral intensities making a detailed analysis difficult. Furthermore, the XANES spectral shape reflects a complex interplay between charge screening and orbital hybridization effects.19 X-ray emission spectroscopy is largely free of experimental artifacts, and the chemical dependence is considerably simpler than in XANES. This technique can thus provide important complementary information. While X-ray absorption probes the density of unoccupied electronic states, X-ray emission reflects the occupied electron levels and provides more direct information on the charge density. Several authors have presented measurements and interpretations of KR10,34,35 and Kβ9,36-41 emission spectra. In this work we report a comprehensive experimental and theoretical study of the KR fluorescence lines in a variety of minerals and sulfur compounds from sulfides (S2-) to sulfates (S6+) with a critical comparison to the corresponding X-ray absorption spectra. A wide range of sulfur minerals and compounds was selected in order to include different sulfur chemical states, degrees of coordination, and structures. Quantum chemical calculations were performed using the StoBe-deMon code,42 which is based on density functional theory (DFT), to obtain spectra and electron densities around (20) Solomon, D.; Lehmann, J.; Lobe, I.; Martinez, C. E.; Tveitnes, S.; Du Preez, C. C.; Amelung, W. Eur. J. Soil Sci. 2005, 56, 621–634. (21) Ray, K.; George, S. D.; Solomon, E. I.; Wieghardt, K.; Neese, F. Chem.sEur. J. 2007, 13, 2783–2797. (22) Hamajima, T.; Kambara, T.; Gondaira, K. I.; Oguchi, T. Phys. Rev. B 1981, 24, 3349–3353. (23) Kitamura, M.; Sugiura, C.; Muramatsu, S. Solid State Commun. 1988, 67, 313–316. (24) Gilbert, B.; Frazer, B. H.; Zhang, H.; Huang, F.; Banfield, J. F.; Haskel, D.; Lang, J. C.; Srajer, G.; Stasio, G. D. Phys. Rev. B 2002, 66, 245205. (25) Kravtsova, A. N.; Stekhin, I. E.; Soldatov, A. V.; Liu, X.; Fleet, M. E. Phys. Rev. B 2004, 69, 134109. (26) Lavrentyev, A. A.; Gabrelian, B. V.; Nikiforov, I. Y.; Rehr, J. J. J. Phys. Chem. Solids 1999, 60, 787–790. (27) Soldatov, A. V.; Kravtsova, A. N.; Fleet, M. E.; Harmer, S. L. J. Phys.: Condens. Matter 2004, 16, 7545–7556. (28) Triguero, L.; Pettersson, L. G. M.; Agren, H. Phys. Rev. B 1998, 58, 8097– 8110. (29) Damian, E.; Jalilehvand, F.; Abbasi, A.; Pettersson, L. G. M.; Sandstrom, M. Phys. Scr. 2005, T115, 1077–1079. (30) Risberg, E. D.; Eriksson, L.; Mink, J.; Pettersson, L. G. M.; Skripkin, M. Y.; Sandstrom, M. Inorg. Chem. 2007, 46, 8332–8348. (31) Mijovilovich, A.; Pettersson, L. G. M.; Mangold, S.; Janousch, M.; Susini, J.; Salome, M.; de Groot, F. M. F.; Weckhuysen, B. M. J. Phys. Chem. A 2009, 113, 2750–2756. (32) Risberg, E. D.; Jalilehvand, F.; Leung, B.; Pettersson, L. G. M.; Sandstrom, M. Dalton Trans. 2009, DOI: 10.1039/b819257j. (33) Sarangi, R.; George, S. D.; Rudd, D. J.; Szilagyi, R. K.; Ribas, X.; Rovira, C.; Almeida, M.; Hodgson, K. O.; Hedman, B.; Solomon, E. I. J. Am. Chem. Soc. 2007, 129, 2316–2326. (34) Sato, T.; Takahash, Y; Yabe, K. Bull. Chem. Soc. Jpn. 1967, 40, 298–&. (35) Coulson, C. A.; Zauli, C. Mol. Phys. 1963, 6, 525–533. (36) Sugiura, C. J. Phys. Soc. Jpn. 1995, 64, 3840–3852. (37) Adachi, H.; Taniguchi, K. J. Phys. Soc. Jpn. 1980, 49, 1944–1953. (38) Uda, E.; Kawai, J.; Uda, M. Nucl. Instrum. Meth., Phys. Res., Sect. B: Beam Interact. Mater. Atoms 1993, 75, 24–27. (39) Kavcic, M.; Dousse, J. C.; Szachetko, J.; Cao, W. Nucl. Instrum. Meth., Phys. Res., Sect. B: Beam Interact. Mater. Atoms 2007, 260, 642–646. (40) Karlsson, G.; Manne, R. Phys. Scr. 1971, 4, 119. (41) Sugiura, C. Jpn. J. Appl. Phys., Part 1: Regul. Pap. Short Notes Rev. Pap. 1993, 32, 3509–3514. (42) StoBe-deMon. (Stockholm-Berlin version of deMon, a Density Functional Theory (DFT) molecule/cluster package), version 3.0; June 2006, StoBe2005; http://w3.rz-berlin.mpg.de/∼hermann/StoBe/.

sulfur. Multiple-scattering calculations by means of the FEFF 8.4 code43 were performed in order to compare the electron population analysis with the results obtained in the framework of DFT theory. Finally, atomic multiplet calculations of electronic states, based on the code by Cowan,44 were performed to accurately simulate the spin-orbit effect in the KR lines and assesses the degree of interaction between the core hole and the valence electrons. EXPERIMENT The measurements were carried out at beamline ID26 of the European Synchrotron Radiation Facility (ESRF). The theoretical resolution of the beamline monochromator with a pair of cryogenically cooled Si crystals in (111) reflection is 0.36 eV at the S K edge energy (2472.0 eV). The incoming flux is 5 × 1012 photons/ s. Higher harmonics are rejected by two Si mirrors operating in total reflection. Instrumental errors due to temperature variations or other instabilities in the optic elements of the beamline are within the precision limit of 0.01 eV. All spectra were normalized to the incident flux as monitored by the scattering from a 1 µm silicon nitride foil. XANES (X-ray Absorption Near-Edge Structure). Spectra were recorded in fluorescence mode (total fluorescence yield, TFY) using a Si diode mounted horizontally at a 90° scattering angle to the incident X-ray beam. The TFY spectra are obtained by monitoring the diode current while the incident energy is scanned across the sulfur edge. The total acquisition time for each XANES spectrum is 5 min. The penetration depth into the sample of the incident beam varies with energy, in particular as the incident energy is tuned through an absorption edge. This may give rise to self-absorption effects.45 At low energies such as the S K-edge preparing sufficiently thin samples (103 counts/s in the maximum of the KR1 line, and sufficient statistics were thus obtained already after a few seconds. The position spectra recorded by the CCD detector were converted into an energy scale. In order to determine the energies of the emission lines, the measured spectra were fitted to Pearson VII functions, and the fit maximum at the KR lines is used to describe the energy positions. The reference energy was set equal to 2307.89 eV for the KR1 line of pure sulfur.49 Materials. A variety of sulfur mineral and crystalline compounds was selected in order to include different sulfur chemical states, coordinations, and local structures. The mineral name and formula for the 5 sulfates, 1 sulfite, and 10 sulfides that were used in this study are given in Table 1. The bond distances, angles, and symmetry parameters necessary to construct the cluster models for calculations were extracted from crystallographic databases.50,51 The sulfur compounds were provided by the “Dipartimento di Scienze della Terra” at the “Universita´ di Camerino”. The samples were prepared by finely grinding crystal chips to powder and mounting them on a sulfur free Al plate (over an area of several squared millimeters). All samples were characterized by X-ray powder diffraction. (48) Fuggle, J. C.; Inglesfield, J. E. Unoccupied Electronic States, Topics in Applied Physics; Springer: Berlin, Germany, 1992. (49) Deslattes, R. D.; Kessler, E. G.; Indelicato, P.; de Billy, L.; Lindroth, E.; Anton, J. Rev. Mod. Phys. 2003, 75, 35–99. (50) Inorganic Crystal Structure Database, I. http://icsdweb.fiz-karlsruhe.de/. (51) Crystallographic and Crystallochemical Database for Mineral and their Structural Analogues, M. http://database.iem.ac.ru/mincryst/search.php?.

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Table 1. Energy Edge Position of XANES Spectra and Energy Position and Intensity Ratio ((4%) of Kr1 and Kr2 Emission Lines of Some Sulfur-Bearing Compounds

compound

formula

Na sulfite chalcopyrite cinnabar bornite orpiment pyrite hawleyite tetrahedrite sphalerite pyrrhotite galena molybdenite oldhamite thenardite gypsum celestine barite anhydrite anglesite pure sulfur

Na2SO3 CuFeS2 HgS Cu5FeS4 As2S3 FeS2 CdS (Cu,Fe)12Sb4S13 ZnS Fe1-xS PbS MoS2 CaS Na2SO4 CaSO4 · 2H2O SrSO4 BaSO4 CaSO4 PbSO4 S8

formal oxidation XAS state (OS) edge (eV) 4+ 2222112222226+ 6+ 6+ 6+ 6+ 6+ 0

2478.62 2470.41 2471.67 2470.65 2471.7 2472.29 2472.55 2471.8 2473.80 2471.02 2473.22 2482.85 2482.75 2482.56 2482.46 2482.59 2482.46 2472.86

KR1 (eV)

KR1/KR2 ratio

2308.88 2307.74 2307.73 2307.80 2307.73 2307.86 2307.72 2307.77 2307.69 2307.77 2307.69 2307.82 2307.72 2309.12 2309.14 2309.13 2309.13 2309.14 2309.12 2307.89

1.70 2.06 2.04 2.21 2.05 2.24 1.95 2.26 2.00 2.31 2.09 2.18 1.93 1.59 1.78 1.86 1.90 1.76 1.94 1.87

THEORY Theoretical calculations of XANES were performed by means of the StoBe-deMon DFT program system.42 The electronic transitions were described by the transition potential (TP) method,28,52 where the orbitals for the molecular species are determined using a high-quality molecular basis set with a halfoccupied core orbital at the excitation site, i.e., the potential used for the excited states is derived by removing half an electron from the sulfur atom 1s orbital. The transition moments were calculated as the dipole matrix element between the initial and final state using the same set of orbitals to describe both states. A double basis set technique28,53 was applied in which a large set of diffuse functions was added to the molecular basis set to improve the description of Rydberg and continuum states in the spectrum calculation. The excitation energies and their corresponding transition moments were used to generate a theoretical spectrum by convoluting the discrete spectral transitions with a Gaussian function. An overall shift of the energy scale of each spectrum was applied to coincide with experiment. The calculated XANES spectrum, with transition energies and moments modified in this way, could then be directly compared with the experimental spectral features. For further details on the calculations see Kolczewski et al.54 and Risberg et al.,30,32 where, in the latter, sulfur edges were calculated by means of this code. The StoBedeMon code uses cluster models to represent extended systems, i.e., including a limited number of atoms surrounding the center of interest. However, in many cases it proved impossible to derive a computationally stable model sufficiently small to be tractable. This is particularly the case for ionic systems including larger (52) Slater, J. C.; Johnson, K. H. Phys. Rev. B 1972, 5, 844. (53) Agren, H.; Carravetta, V.; Vahtras, O.; Pettersson, L. G. M. Theor. Chem. Acc. 1997, 97, 14–40. (54) Kolczewski, C.; Puttner, R.; Plashkevych, O.; Agren, H.; Staemmler, V.; Martins, M.; Snell, G.; Schlachter, A. S.; Sant’Anna, M.; Kaindl, G.; Pettersson, L. G. M. J. Chem. Phys. 2001, 115, 6426–6437.

Figure 1. S K absorption edges: (left panel) sulfides, (right panel) pure sulfur, sulfite, and sulfates.

ions with counterions where it is difficult to build a balanced neutral model and when the effects of the environment are more long-range. In order to confirm the DFT results, we also performed full multiple scattering (FMS) calculations using FEFF 8.4.43 This code expresses Fermi’s Golden Rule by means of a Green’s function formulation. One does not obtain molecular wave functions like in DFT, but a comparison can be made at the level of the ground state electron density with a subsequent projection of the density of states (DOS) on the angular orbital momenta (l ) 1,2,3) with respect to the central S atom. FEFF uses the muffin-tin approximation, and the final potential is obtained by adding the Hedin-Lundqvistand exchange and correlation potentials.55 All FEFF 8.4 calculations include the effect of the 1s core hole. Spectroscopies with a core hole in the final state can often be successfully modeled using atomic multiplet theory.44,56,57 We used the code by Cowan as implemented in the MISSING interface to calculate the S 2p to 1s transitions (KR lines).58 The 2p spin-orbit interaction is determined, and electron-electron interactions are expressed as Slater integrals. Their values can be scaled to account for electron delocalization effects. RESULTS AND DISCUSSION A-XANES. The sulfur K-edge absorption arises from transitions of S 1s core electrons to unoccupied orbitals above the Fermi level. The transitions are governed by the dipole selection rule (55) Hedin, L. Phys. Rev. 1965, 139, A796. (56) de Groot, F.; Kotani, A. Core Level Spectroscopy of Solids; Taylor and Francis: New York, 2008; Vol. 6. (57) Glatzel, P.; Bergmann, U. Coord. Chem. Rev. 2005, 249, 65–95. (58) Gusmeroli, R.; Dallera, C. Missing (Multiplet Inner-Shell Spectroscopy INterective GUI); http://www.esrf.eu/UsersAndScience/Experiments/TBS/ SciSoft/OurSoftware/MISSING.

and only orbitals with symmetries T1u (in octahedral), T2 (in tetrahedral coordination), or A1 + E (in cubic C3v coordination) are probed. The number, position, and intensity of the spectral peaks depend primarily on the number and kind of first neighbors around the scattering element but in some cases also on effects due to next nearest-neighbor atoms (vide infra). Shifts in the position of the absorption-edge between different oxidation states of S are mainly due to screening effects, and XANES is thus used as a chemical ruler for the valence electron occupation. Here, we separate the analysis into systems that contain oxyanions, including sulfates (S6+) and sulfites (S4+), and fully reduced sulfur (S2-) in sulfides. We discuss the general spectral features for the different sulfur compounds and then compare one example for each oxidation state with DFT calculations. Oxy-Anions. The first coordination shell of sulfur in sulfates and sulfites is composed of four and three oxygen atoms, respectively. The S-O interatomic distance ranges from 1.47 to 1.49 Å, and the O-S-O angle from 106.3° to 112.2° in the different sulfate compounds. The sulfate ion (SO4)2- has tetrahedral symmetry. The three pyramidal oxygen atoms in the sulfite ion (SO3)2- form a trigonal C3v symmetry with a S-O interatomic distance of 1.505 Å and all O-S-O angles at 105.68°. Figure 1 shows the sulfur K absorption spectra of sodium sulfite, Na2SO3, and some sulfate compounds. The sulfate spectra (Figure 1) are quite similar to each other, with a strong peak, A, around 2483.3 eV and a shoulder, B, around 2486.5 eV of variable intensity. Other differences are visible at higher energy, between 2490-2505. The sodium sulfite spectrum (Figure 1) is similar to those of the sulfates, although the edges are at different energies. The sulfite main peak is at 2479.2 eV (I), with a shoulder Analytical Chemistry, Vol. 81, No. 15, August 1, 2009

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Figure 2. Experimental (top) S K-edge spectra of Na2SO4, Na2SO3, and ZnS along with DFT calculations performed including the first coordination shell (middle) and a larger cluster (bottom). For the calculations, the final states (sticks) and the convoluted spectra (lines) are shown. The insets show the cluster of atoms that was included in the calculations (sulfur, yellow; oxygen, red; cation, blue).

(II) and a third peak present at 2482.6 eV (III). In the following we investigate the origin of these features. Calculated spectra for Na2SO4 and Na2SO3 are compared to experiment in parts A and B of Figure 2, respectively. The overall shape of the sulfate spectra is already reproduced by considering only the (SO4)2- molecule indicating that the cations have little influence the XANES spectral shape. However, the shoulder B in the higher part of the main peak is not observed in the tetrahedral (SO4)2- calculation. Intensity in this spectral region is only obtained when including a larger cluster in the calculation. The (SO3)2- calculation also reproduces the edge and the feature II of the sodium sulfite XANES spectrum, while the peak III cannot be modeled. The main edge in the sulfates and sulfite XANES spectra is attributed to the transition from a S 1s core electron to the 3p like (σ* type)37 lowest unoccupied level. On the basis of the (SO4)2- and (SO3)2- simulations, this feature is composed of various molecular orbitals that are mainly formed by O 2p and S 3p atomic orbitals and to a lesser extent by S 3d. In the bottom part of parts A and B of Figure 2, we show calculations of the sodium sulfate and sodium sulfite using larger clusters. We observe that the cations somewhat influence the spectral shape with some Na 2s contribution in the main edge. Feature B in the sulfate series gains intensity when the alkali metal ion Na+ is replaced by an alkaline earth metal Ca, Sr, or Ba with a charge of 2+. 6520


According to the (SO3)2- calculation, peak II of sodium sulfite arises from transitions to empty molecular orbitals consisting of S 3s and 3p and to a small degree of O 2p, indicating hybridization between the 3s and 3p atomic orbitals of the central sulfur ion. This hybridization is forbidden in Td and allowed in C3v symmetry, and peak II thus manifests the local symmetry which is nicely demonstrated in the comparison between sodium sulfite and sulfate. This is confirmed by the 7 Å cluster calculation of the sodium sulfite, where including the cations does not significantly change the overall spectral shape. Peak III is not reproduced in the calculations. Its origin could be assigned to sulfate contamination. However, on the basis of the XES measurements (vide infra), we believe that the compound is pure sulfite and assign the feature to band structure (i.e., long-range order) effects that are not accounted for in the computational model. Sulfides. S K-edge XANES spectra of sulfides are shown in Figure 1. In contrast to sulfites and sulfates where the first coordination shell is composed of oxygens, sulfides include the metal cation in the first coordination sphere of sulfur. The samples represent a large variety of compounds with different metal cations (Zn, Hg, Cd. . .) and a group of sulfide minerals with variable Cu and Fe contents. The different geometries and cation valence shell configurations give rise to pronounced differences in the XANES spectral shapes. A detailed study of the Cu/Fe sulfide spectra shows that they are characterized by a prominent edge peak

around 2472 eV and a broad feature toward higher energy. Several authors have suggested that orbital hybridization between the S 3p and the metal 3d orbitals can explain the edge peak.2,18,25,27 According to the initial state rule in XANES,59 the integrated intensity in this peak should reflect the number of empty S 3p states in the ground state. Formally, the 3p shell is fully occupied in the case of sulfides (S2-). Orbital hybridization with metal 3d orbitals in a partially filled d-shell will transfer some S 3p electron density to the cation, thus creating unoccupied states of S 3p character. This mechanism will yield spectral intensity in the S 1s to 3p transitions, i.e., the XANES feature at lowest energy. A methodology has been developed by Solomon et al. that relates the S pre-edge to ligand-metal covalency in coordination complexes.19 The transfer of electron density furthermore results in a shift of the edge position to higher energies because of reduced screening. Copper has an almost filled 3d shell, and this mechanism is less available. Thus, upon an increase in the Cu content in the series of Cu/Fe sulfides, the sulfur edge intensity will decrease (Figure 3) and the edge will move to lower energy (cf. Figure 1). Consequently, within an ionic picture, the spectral feature should be absent in the filled 3d shell of ZnS. The edge position does not only follow the screening effects but also depends on the energy of the cation 3d shell as well as the local symmetry and thus the type of orbital hybridization.19 We show below that the sensitivity of XES to the local charge density provides an important means to disentangle the effects. Along the group 12 elements (Zn, Cd, Hg), the d-shell becomes increasingly delocalized. Following the above arguments, this may transfer electron density back to the sulfur ion via the S p- and cation d-hybridized orbitals. As a result, the edge moves to lower energies again consistent with an interpretation of the edge shift as a result of screening effects. We do not observe a pre-edge in ZnS, CdS and HgS, neither in As2S3 whose edge position coincides with HgS. We were not able to achieve convergence in the theoretical modeling for these systems, which prevents a more detailed analysis of the electronic structure.

Figure 2C shows a comparison of the ZnS experimental spectrum with theoretical calculation of S K-edge XANES. Density of states (DOS) calculations by Oertzen et al.5 show a considerable mixing between p-like S and Zn states suggesting that the postedge features are due to transitions to mixed S p/Zn p orbitals.60 A calculation was performed including only the first coordination shell with 4 Zn atoms. This calculation does not reproduce the overall shape of the experimental spectrum. This is in contrast to the sulfates and sulfite where including the oxyanions already satisfactorily simulated the spectral shape. A calculation of ZnS performed with a larger 5.5 Å cluster consisting of 35 atoms presents a better modeling of the overall experimental XANES features (cf. Figure 2). The calculation indicates some hybridization between S p/Zn s and p, which gives rise to the main postedge feature located around 2475.3 eV. The calculations for a larger cluster predict a pre-edge feature that is not observed in experiment. Unlike sulfates and sulfite, the sulfides evidently pose considerable more challenges for theoretical modeling and in most cases only approximate correspondence with experiment can be achieved. This is due to the delocalized character of the nearest neighbor 3d wave functions and possible band formation in the minerals. B-Kr XES. The previous section showed that the XANES is influenced by various effects, namely, the local symmetry, the type of ligands up to high coordination spheres (in sulfides), and the valence shell electron population. The excited states that give rise to an absorption spectrum subsequently decay. The radiative decay channels result in the fluorescence lines. The KR lines are emitted upon an intra-atomic S 2p to 1s transition. They are expected to be mostly free from chemical bond effects except from small energy shifts that reflect the valence orbital electron population via screening effects. This screening is due to the finite probability of finding a sulfur valence electron close to the nucleus thus reducing the effective nuclear potential experienced by the S 2p electrons. When XES spectra are recorded with high energy resolution, the energy position of the KR lines can be used as a measure of the valence electron population, i.e., the redox state of sulfur. We show in this section that screening is the dominant effect on the KR fluorescence rendering the high-resolution X-ray emission considerably more sensitive to the local charge density state than the X-ray absorption. The energy position of the KR lines can be measured with high accuracy, and the relative peak intensity is barely influenced by self-absorption in the sample. Thus, even though the spectral changes on an absolute scale are smaller in XES than in XAS, a very detailed analysis of the energy position is possible. S KR spectra of different sulfur compounds are shown in Figure 4. The 2p orbital is split into two levels due to the spin-orbit interaction resulting in the two spectral peaks KR1 and KR2. The overall spectral shape is similar for all compounds. The CaS XES spectrum shows a shoulder at around 2309 eV. This feature indicates a change in the sulfur oxidation state upon irradiation with the intense X-ray beam (radiation damage). This spurious contribution, less than 10% of the total sulfur

(59) Nilsson, A.; Ma˚rtensson, N. Phys. B: Condens. Matter 1995, 208-209, 19– 22.

(60) Li, D.; Bancroft, G. M.; Kasrai, M.; Fleet, M. E.; Feng, X. H.; Tan, K. H.; Yang, B. X. J. Phys. Chem. Solids 1994, 55, 535–543.

Figure 3. Integrated intensity of peak a (cf. Figure 1) in Cu/Fe sulfides versus the ratio Cu/Fe/S atoms.


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Figure 4. High-resolution S KR X-ray spectra of some sulfur-bearing minerals: (right panel) sulfides, (left panel) pure sulfur, sulfite, and sulfates.

Figure 5. Atomic multiplet calculations of the KR lines with different charges on the sulfur ion.

signal, does not significantly affect the energy position of the KR1 emission line. The example of CaS shows that the simple KR line shape allows for a quick and straightforward identification of X-ray induced damage in the sample. This is in contrast to XANES spectroscopy where the complex spectral features make it necessary to record the development of the line shape with increasing damage in subsequent scans, i.e., possible damage can often not be identified in just one scan. The energy position of the experimental KR spectra show the same trend as observed in the XANES: a higher oxidation state results in a shift to higher energies (cf. Figures 4 and 6). In Figure 5 we report atomic multiplet calculations of the KR emission spectra for the sulfur ion. The calculations are performed in spherical symmetry, and the electron configurations are chosen to generate ions with charges that correspond to the oxidation 6522


state. The transitions are convoluted with Lorentzian functions to match the S KR lifetime broadening (0.59 eV). The experimentally observed shift of the KR1,2 lines is qualitatively reproduced in the calculations. This confirms that screening effects cause the chemical sensitivity of the KR lines. We note that this is in contrast to the fluorescence in 3d transition metals where the chemical shift is dominated by intra-atomic electron-electron interactions.56 We observe that the atomic multiplet calculations are only able to reproduce the spectral shape if all electron-electron interactions between the 2p hole and the valence electrons are removed. Electron-electron interactions are expressed by the Slater integrals in atomic multiplet theory.61 Scaling, i.e., reducing the magnitude of the Slater integrals, is commonly used to account for electron delocalization.56 The absence of visible interactions between the 2p hole and the valence electrons for sulfur thus confirms the strongly delocalized character of the valence electrons. Electron delocalization, i.e., orbital hybridization, also explains why the experimentally observed energy shifts are considerably smaller than predicted by atomic theory. The effective nuclear charge experienced by a S 2p electron changes more if an electron is removed from a localized atomic wave function. C-Analysis of the Chemical Shift in XANES and Kr XES. The chemical state of an ion is usually described by the oxidation state. In a quantum chemical picture this translates into the electron population of the atomic orbitals. Absorption spectra probe the unoccupied density of states which relate to the oxidation state via charge screening and a shift of the absorption energy. However, the XANES contains considerable more information than just the oxidation state. This gives the opportunity for a detailed analysis but also raises the need for a more selective probe. The KR emission spectra reflect the chemical state by a similar screening effect that changes the core level binding energy but has little sensitivity to the fine structure of the occupied density of electronic states. In the following, an analysis of the chemical shifts in both techniques is presented. Numerous studies have shown that XANES spectroscopy is a sensitive probe of the chemical state of sulfur in minerals and chemical compounds.20,45,62 The energy of the K absorption edge is given in Figure 6A for the different sulfur compounds analyzed in this work. We observe a strong shift of the edge position with the formal oxidation state. This energy shift spans ∼12 eV, from 2471.14 for sulfides (S2-) to 2483.58 eV for sulfates (S6+). The relationship between chemical shift and the sulfur oxidation state is very precise in oxy-compounds, for which the edge positions differ by at most 0.4 eV. In the oxy-compounds, the nearest neighbors of the absorbing atom are O2-, and the metal cations are restricted to the second or more distant coordination spheres. However in sulfides, where the sulfur atom is bonded directly to the metal cation, the nature of the metal and the resulting bonding character of the sulfide have a considerable influence on the position of the S K edge. The (61) Slater, J. C. Quantum Theory of Atomic Structure; McGraw-Hill: New York, 1960. (62) Bare, S. R. http://cars9.uchicago.edu/xafs/NSLS_EDCA/July2003/Bare. pdf, 2003.

Figure 6. S K-edge position (a) and sulfur KR1 peak (b) versus the formal oxidation state of sulfur for a series of sulfur compounds. Identical colors in the two plots indicate the same compounds. The series of sulfide compounds is magnified in the insets.

edge energies in sulfides differ by 2.08 eV ranging from 2471.14 eV for chalcopyrite (CuFeS2) to 2473.22 eV for oldhamite (CaS) (cf. Figure 6). The sulfur KR1 position shows an energy shift with the change in the formal number of valence orbital electrons. The energy shift for the different sulfur species ranges from 2307.29 for sphalerite (2-) to 2308.70 for anglesite (6+). This only spans 1.5 eV and is thus almost an order of magnitude less than the XAS edge shift. The S KR1 energy position within the sulfides changes by 0.13 eV ranging from sphalerite (ZnS) at 2307.69 eV to molybdenite (MoS) at 2307.82 eV. The observed energy shift between the sulfates is 0.02 eV and thus within the experimental error. The group of sulfides is well separated from pure sulfur and (S2)2- in FeS2 in XES but not in XANES. We furthermore observe shifts within the series of sulfides. This holds for XAS and XES but with the two techniques giving different ordering within the series of sulfides. In the case of XES, the shift between the sulfides is larger than the experimental uncertainty and any systematic error due to data treatment. The strong orbital hybridization as discussed before suggests that the KR chemical shifts can be explained by small changes in the orbital populations. In order to better understand this shift, we compare in the following the charge density as extracted from the quantum chemical calculations with the experimental results. The sulfur electronic configuration was obtained by calculating the effective charge around the sulfur atom based on the Mulliken population analysis from calculations of the electron density. Calculations were not performed for the whole set of compounds since we did not achieve convergence for all systems. The correlation between the number of 3p and 3s electrons, calculated by means of DFT, and the shift of the KR1 emission line is given in Figure 7B. We do not include the S d orbitals in this analysis assuming that they do not considerably contribute to the screening because of their large radius as compared to s and p orbitals and

their strongly delocalized character. To verify these results, we also performed full multiple-scattering calculations by means of the FEFF 8.4 code (Figure 7C). We find that the mean number of valence electrons using the multiple-scattering approach is consistent with the DFT results. A summary of the outer-shell electronic configuration of several sulfur compounds, obtained by the two different approaches, is given in Table 2. Further analysis of the redox state of sulfur was performed by calculating the valence of the sulfur atom in some compounds based on a Mayer bond analysis63,64 following the DFT calculations. We did not, however, obtain physically reasonable valence bond numbers for FeS2, which may be due to the S-S bond present in this compound and thus FeS2 is not included in the Mayer analysis. We report in Table 2 the sulfur diagonal element of the bond-order matrix, which corresponds to the effective valence of the selected sulfur compounds in the Mayer method. A comparison with the experimental XANES and KR results is given in Figure 7A. The three approaches to quantify the electron density that is localized on the sulfur ion all show a monotonic relation between the KR1 line position and the sulfur charge. In particular, this relation also holds within the series of sulfides. The ordering FeS2 > Fe1-xS > CuFeS2 > ZnS that we previously obtained using qualitative arguments based on the metal d-shell population and number of metal cations (vide supra) is confirmed in the calculations and the XES results. The monotonic relation is not observed for the XAS edge position. The absence of significant electron-electron interactions in the KR emission makes the screening effect the dominant source of the chemical sensitivity. We find that XES can serve as a probe of the local charge density with considerably higher sensitivity than XANES. X-ray emission thus provides important information to disentangle the various mechanisms that influence the XANES spectral shape. The techniques are complementary. (63) Mayer, I. J. Comput. Chem. 2007, 28, 204–221. (64) Mayer, I. Chem. Phys. Lett. 1983, 97, 270–274.


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Figure 7. S KR1 energy peak position and S K-edge versus charge density: (A) sulfur valence calculated by DFT; (B) number of valence 3p and 3s electrons calculated by DFT; and (C) number of valence 3p and 3s electrons calculated by FMS. Table 2. Electron Configuration Based on DFT and FMS Calculations As Well As Theoretical and Formal Valence of Selected Sulfur Compounds

compound sphalerite (ZnS) chalcopyrite (CuFeS2) pyrite (FeS2) Na sulfite (Na2SO3) thenardite (Na2SO4) anhydrite (CaSO4)

formal valence OS (DFT) 2224+ 6+ 6+

electron configuration (DFT)

2.14- 3s1.43 3p4.48 3d0.96 1.68- 3s1.5 3p4.30 3d0.64 3s1.81 3p3.76 3d0.43 4.11+ 3s1.5 3p2.68 3d0.76 5.57+ 3s0.82 3p2.33 3d1.09 5.68+ 3s0.87 3p2.33 3d1.13

electron configuration (FMS) 3s1.84 3p4.05 3d0.18 3s1.82 3p3.80 3d0.36 3s1.78 3p3.43 3d0.59 3s1.53 3p2.76 3d0.96 3s1.36 3p2.49 3d1.14 3s1.35 3p2.49 3d1.14

An analysis of the 2p binding energy in S containing compounds with comparison between experiment and theory has been presented by Gerson et al.65 The rather large experimental uncertainty in the cited 2p XPS spectra makes a comparison between the present KR XES work for the sulfide series difficult. (65) Gerson, A. R.; Bredow, T. Surf. Interface Anal. 2000, 29, 145–150.

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Figure 8. S KR spectrum of a mixture composed of CuFeS2 (66.67%) and CaSO4 + H2O (33.32%) fitted with a linear combination of the isolated sulfur species.

The selectivity of XES can be used to quantify the amount of sulfur species in heterogeneous systems. We show in Figure 8 a mixture with equal molar quantities of CuFeS2 and CaSO4 · 2H2O. The corresponding percentage of sulfur present in the chemical state S2- is therefore 66.67%. Fitting of the experimental spectrum gives a contribution of 66.3% from the S2- spectrum. The simple KR spectral shape renders such a quantitative analysis considerably more robust than a similar approach in XANES. Furthermore, for sulfate and sulfite contributions, the exact composition (i.e., geometry and ligand environment) does not need to be known since the spectral shape and the energy position are mainly influenced by the local charge density apart from small changes in the KR1/KR2 intensity ratio (cf. Table 1). We note, however, that this analysis may lead to inaccurate results in mixtures of powders where the grain size exceeds the absorption length of sulfur of a few micrometers due to different self-absorption effects for the different species. SUMMARY AND CONCLUSIONS We measured the K-edge XANES and KR fluorescence lines for a wide range of sulfur containing compounds and compared the results to quantum chemical calculations using density functional, multiple-scattering, and atomic multiplet theory. The XANES spectral shape is mainly determined by the geometry of

the first coordination sphere in case of the sulfates and sulfite while strong orbital hybridization in the case of sulfides results in a considerably more complex analysis. The spectral shape of the KR fluorescence lines shows little influence of the chemical environment. Comparison with calculations shows that its energy position can be correlated to high accuracy with the valence-shell electron population. A considerably better agreement was achieved for the KR lines than for XANES. X-ray absorption spectroscopy provides a wealth of information on the electronic structure, but the selectivity and sensitivity of XES to the electronic charge makes it an important tool for chemical characterization. Furthermore, the simple KR spectral shape allows for a robust spectral deconvolution in mixed-valence systems. Unlike for XAS measurements, no monochromatic tunable incident energy is required, and an efficient XES spectrometer can push the detection limit in the range of a few hundreds or even tens of part per million. ACKNOWLEDGMENT The help of the ESRF support groups for installing the emission spectrometer is gratefully acknowledged. Received for review May 5, 2009. Accepted June 17, 2009. AC900970Z


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Electronic Structure of Sulfur Studied by X-ray Absorption and

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