research papers
Electronic structure and Kedges
of CaS by means of Xray absorption spectroscopy at Ca and S^{a}Insitute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People's Republic of China, ^{b}Canadian Light Source, University of Saskatchewan, Saskatoon, Canada, ^{c}Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy, and ^{d}National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, People's Republic of China
^{*}Correspondence email: xuw@mail.ihep.ac.cn, wuzy@ustc.edu.cn
The cubic calcium sulfide (CaS) is a well known system and an attractive building block material for many luminescence technological applications. However, it is essential to achieve an accurate understanding of its electronic structure in order to engineer its band structure for optimized applications. Here a study of the electronic structure of CaS by means of Xray absorption spectroscopy performed at both Ca and S Kedges, and calculations performed in the framework of the multiplescattering theory and of the finite difference method are presented. At the Ca Kedge the presence of an anomalous d states feature is discussed while in the S Kedge spectrum the presence of a preedge shoulder owing to the among Ca d states and S p states is pointed out. Although the lprojected of CaS is in good agreement with previous firstprinciples calculations, the standard muffintin potential is inadequate to reproduce nearedge structures at both Ca and S Kedges in this system. Indeed, with its highly symmetric and less compact structure, CaS is characterized by a large set of collinear atomic configurations that pose severe constraints on the construction of the atomic potential. On the contrary, the finitedifference method with no muffintin approximation is more suitable for Xray absorption calculations in this system.
Keywords: CaS; Xray absorption spectroscopy; Ca Kedge; S Kedge.
1. Introduction
Calcium sulfide (CaS) (Fig. 1) has a typical cubic with (No. 225) and large of 5.68 Å. Owing to the wide bandgap (∼5.38 eV), CaS is technologically important as a host material in luminescence technology (Rao, 1986; Versluys et al., 2001; Hakamata et al., 2005; Barrett et al., 2005). Meanwhile, it also exhibits unique structural behavior under high pressure. At room temperature and ambient pressure CaS has the NaCltype (B1) structure but at high pressure, above 40 GPa, the transforms into the CsCltype (B2) (Luo et al., 1994). B2–B4 (wurtzite) and B2–B3 (zinc blende) phase transitions have also been predicted (Chen et al., 2007) to occur at low pressure, around 0.829 GPa and 0.679 GPa, respectively. Theoretical calculations based on density functional theory have been successfully employed to calculate the electronic structure, optical properties and thermodynamic parameters (Chen et al., 2007; Shaukat et al., 2008; Guo et al., 2008). The electronic structure varies with the type of exchangecorrelation potential functional (Shaukat et al., 2008).
Furthermore, Xray absorption spectroscopy is a recognized local structure and elementselective probe to study electronic structures, widely used in different fields. Absorption spectroscopy at intermediate energies is experiencing continuously increasing interest, not only for the easy availability now offered by modern Xray beamlines but also because the elements with edges falling in this energy regime are nontoxic light elements such as calcium, potassium, sulfur, etc. For instance, the including CaS were investigated extensively by Xray absorption spectroscopy at the sulfur Kedge and L_{2,3}edge, respectively (Farrell et al., 2002; Kravtsova et al., 2004). Owing to the improvement of energy resolution, the experimental spectrum can be measured with detailed features (Alonso Mori et al., 2009). On the other hand, theoretical simulation of XANES spectra is improved by either using the muffintin (MT) method with a constant potential in the interstitial region among atoms, or with a full potential with no boundaries. To justify the electronic structure, it is essential to investigate the potential effects that may exist in some open structure (Xu et al., 2011). The combination of advanced analytical tools and the improved experiment allows us to improve the interpretation of the electronic structure of CaS. Therefore, the major motivation of this research is the optimization at midenergy of Xray absorption spectroscopy calculations by comparing conventional MT and nonMT potentials within the framework of the multiplescattering theory (MST). We will explore the system at two different edges, i.e. the Ca Kedge and S Kedge, which may provide a more comprehensive overview of the electronic structure. To the best of our knowledge, this is the first attempt to perform an accurate comparison of simulations at intermediate energy, though a previous work at the potassium Kedge has already partially faced up the potential issue in micas (Xu et al., 2011). It is worth mentioning here that the CaS system is highly symmetric with a cubic symmetry and a small containing only two atoms. This configuration is extremely different from micas, a system characterized by a low symmetry and a much larger (>20 inequivalent atoms). An additional goal of this work is then identifying limitations of the MT potential at different absorption edges, in order to provide evidence for of theory.
2. Experiment
The CaS powder with a purity of 99.9% was purchased from Alfa Aesar. Xray absorption spectra at both Ca and S Kedges were collected at the 06B11 (SRXMB) beamline at the Canadian Light Source. The incident energy was tuned by a Si (111) doublecrystal monochromator characterized by a theoretical energy resolution of 0.24 eV and 0.4 eV at the S and Ca Kedges, respectively. The totalelectronyield (TEY) mode was employed to collect spectra. For the following analysis a linear background was subtracted from the raw data and spectra were then normalized to the edge step by using the IFEFFIT package (Ravel & Newville, 2005).
3. Theoretical calculations
To interpret Xray nearedge absorption spectra, we performed theoretical calculations in the framework of the MST within the MT potential approximation and the finite difference method with a full potential. Both methods were implemented in the FDMNES(2012) code (Joly, 2001). The nonMT calculation was performed by constructing a grid of order 4, with an interpoint distance equal to 0.25 Å within a cluster radius of 0.65 Å. A discretization of the Schrödingerlike equation at finite points of this grid was considered. For MT calculations, two types of clusters with radii of 8 Å and 12 Å were adopted to calculate the selfconsistent potential as well as XANES spectra. Clusters with radii of 7 Å and 12 Å were employed for nonMT calculations. The starting unitcell parameter for the cubic CaS B1 (, No. 225) structure is 5.68 Å. The final converging cluster size was 12 Å wide and contained 305 atoms around the central absorber for both S and Ca atoms. Meanwhile, we compared the FEFF9.0 code (Rehr et al., 2009) that employs the realspace Green's function method in the framework of the MST but with a selfconsistent MT potential. The Hedin–Lundqvist (Hedin & Lundqvist, 1970) exchangecorrelation potential was used and a cluster radius of 5 Å was adopted to construct the selfconsistent potential. The radius of the full multiplescattering cluster was also 12 Å and the projected was obtained using the FEFF9.0 code. Note that all calculations (FEFF and FDMNES) employed selfconsistent potential.
4. Results and discussions
Both FEFF and FDMNES codes employ Green's function to construct the transition matrix and the absorption cross sections within the MT potential approximation in the framework of the full multiplescattering theory (FMST). In order to illustrate the universality of these calculations, we performed MT FMST calculations with the same cluster size using both FEFF and Green's function mode of the FDMNES code. As shown in Figs. S1 and S2^{1}, calculations for a cluster with a radius of ∼12 Å made with FEFF and FDMNES are quite similar at both Ca and S Kedges. However, a difference occurs in the nearedge region at the Ca Kedge, which is due to the different convolution function that accounts for the corehole lifetime and the inelastic losses during the scattering process of electrons. The spectra also show that in this case the MT approach cannot reproduce experimental XANES spectra, especially in the nearedge region. In a previous MT calculation (Kravtsova et al., 2004) the experimental spectrum was less resolved and not all features were reproduced. Owing to the low energy resolution at least one shoulder was smeared (Kravtsova et al., 2004). Working at high spectral resolution, the recent measured XANES spectra (e.g. Ca Kedge) are characterized by a structured preedge not reproduced by MT potential methods. With a nearestneighbor bond length of 2.84 Å, MT potentials are not able to properly reproduce the potential experienced by photoelectrons and a full potential approach is required. In the following sections we will discuss MT versus nonMT calculations at both Ca and S Kedges.
4.1. MT radius and potential effects
The nearestneighbor interatomic distance in CaS is 2.84 Å and the lattice structure is not closely packed. It has already been pointed out that a MT potential is not optimized for an open structure (Rehr & Albers, 2000). As we will show next, by performing calculations with varying MT potentials and MT radii, this also holds true for the cubic CaS structure. Regarding the MT potential, the conventional way to construct the potential is by imposing a constant interstitial potential with either overlapping or nonoverlapping MTs (Rehr & Albers, 2000). We analysed potential effects by changing the overlap value and determining the MT radius for the different procedures. In Table 1 we list the corresponding MT radii for each atom in the XANES calculations at the Ca and S Kedges. In the Norman procedure (Norman, 1974) the MT radius is determined so as to guarantee that the integral charge within the MT sphere is equal to the total atomic charge. An extra 10% overlap is introduced (Natoli et al., 2003). In the Raydem approach the MT radius is arbitrarily defined as half of the interatomic distance. A third procedure optimizes the MT radii in order to minimize discontinuities at the boundaries. The overlap factor we considered (10%, 12% and 15%) will compensate for discontinuities between adjacent MT spheres (Joly, 2001).
Spectral difference among models with different MT radius determined from the aforementioned procedures and a model with a 10% overlap factor are compared for both Ca and S Kedges. In Figs. 2 and 3, spectral differences as well as spectra calculated with different MT radii are shown. Clearly the nearedge region shows differences for different MT radii; and the intensity of the preedge peak is much higher in the case of the Raydem and Norman procedures. In Table 1 the MT radii of atoms corresponding to different procedures are listed. Apparently, the MT radius of calcium as determined by the Norman procedure is larger than others while the MT radius of sulfur is slightly smaller. Remarkably, spectral variations with respect to different MT radii are distinctive of both Ca and S Kedges. At the Ca Kedge the 12% and 15% overlaps show similar spectral trends while the Raydem and Norman results belong to a different group with similar variation. As shown in Table 1, the MT radius of the S atom in the first overlap set (12% and 15%) is larger than that of the second set (Raydem and Norman). Since the firstshell atoms around calcium are S atoms, their MT radii directly determine how much charge is contained in the small atomic cluster. The smaller sulfur MT radius and the larger one of Ca lead to an increased dispersion of sulfur p orbitals towards Ca d orbitals, in agreement with the observed intensity enhancement of the preedge feature at the Ca Kedge. Indeed, preedge features at the Ca Kedge originate from empty states of d character hybridized with p orbitals, as confirmed by calculations presented in the following sections. The interpretation of spectral variations at the S Kedge is, on the contrary, not straightforward. S Kedge XANES changes dramatically versus the MT radius as determined by different procedures: (i) most of the spectral variations concentrate at the nearedge region from 2470 to 2480 eV, except for the case of the 12% overlap whose spectral variation extends over a larger energy range up to 30–40 eV above the edge; (ii) the Raydem case also shows significant spectral differences around 2476 eV, corresponding to the second peak of the structured edge; (iii) the spectral difference for 15% overlap is less relevant than the Norman one and of the 12% overlap, pointing out that the choice of the MT radius is much more critical at the S Kedge.
To achieve semiqualitative information, we compared the MT radius (Table 1) from different procedures simulating S Kedge XANES. For the excited sulfur, the Norman procedure generates the smallest MT radius (1.40908 Å) while the Raydem procedure produces the largest one (1.44891 Å). For S atoms in the ground state, the MT radius for 12% overlap is 0.02 Å shorter than that for 10% overlap. It implies that charged states penetrate into the Ca MT regions. Consequently, the MT radius of Ca is larger with 12% overlap than that with 10% overlap (Table 1). Moreover, the 12% overlap also induces a shift of the level that determines a threshold of empty and occupied states; therefore, there is a significant spectral difference between the 12% overlap and 10% overlap. It is already known that the determined from the MT potential approximation has an uncertainty of about 1 eV (Moreno et al., 2007). In this case we point out that the is significantly affected by the selected MT radius for light elements such as sulfur. Although the MT approximation is trustworthy as tested in many different systems, the CaS system poses severe constraints to potential boundary conditions and the determination of the is not straightforward. We ought to consider a nonMT potential to better understand the origin of the observed spectral variations that is probably induced by potential boundary effects.
4.2. Calcium Kedge: MT versus nonMT potential
In Fig. 4 (left), experimental and theoretical Ca Kedge XANES spectra of CaS are compared. Four types of theoretical spectra have been calculated to compare size effects induced by different cluster sizes and potential effects owing to MT versus nonMT approximations. The collinear alignment of atoms in the rocksalt cubic lattice generates longrangeorder effects in CaS in both the Ca and S Kedge spectra. Actually, a longrange atomic arrangement (cluster of radius ∼12 Å) has to be considered as in a previous report (Kravtsova et al., 2004). To study the potential effects we performed nonMT potential calculations using the same cluster size. It shall be underlined here that the nonMT method, i.e. the finitedifference method, is extremely timeconsuming and computationally challenging. In this case, only two cluster sizes were attempted for the FDM method because of practical limitations.
Size effects at the Ca Kedge are evident for both MT and nonMT approaches. Specifically, the features d and e in Fig. 4 are more evident as the cluster radius increases from 8 Å to 12 Å. Therefore, the highenergy feature e originates from multiplescattering contributions occurring in an outer sphere extending over the smaller radius. As mentioned above, preedge features at the Ca Kedge are closely related to the among Ca d states and S p states. Moreover, the level is also slightly affected by the size of the MT radii of each atom. Apparently the nonMT approach reproduces very well the and also the position of both the preedge feature a and the whiteline b. Size effects also determine unique behaviors in the XANES spectra of CaS: (i) the preedge peak (feature a), regardless of its position, appears in large clusters while it disappears in the smaller one, no matter whether MT or nonMT potentials are employed; (ii) the intensity of the white line (feature c) reduces in larger clusters, a behavior present in both MT and nonMT simulations. The feature a probes the among electron orbitals as well as longrangorder scattering effects, while the feature c mainly mirrors the interference between different scattering waves from different atomic shells.
Neglecting the anomalous feature b′, in between the b and the c features, the nonMT approach reproduces experimental spectra quite well both in terms of peak positions and intensity. As for the feature b′, it probably probes an additional transition channel opened to electron transition. It may be a multiple electron excitation or an extra charge transfer from sulfur to calcium owing to radiation damage. In silicate glasses it has been observed that a fraction of S^{2−} changes to S^{4+} owing to radiation damage (Wilke et al., 2008). Independently, data confirm that the MT approach is inadequate to describe the at the Ca Kedge in CaS. Calculations could be improved by introducing a nonMT treatment of the potential, and using a large cluster to better reduce size effects.
4.3. Sulfur Kedge: MT versus nonMT potential
In this section we will describe potential and size effects at the S Kedge. The spectra we measured at the Kedge shown in Fig. 4 (right) are actually different from those available in the literature. The preedge peak a is not present in Kravtsova's spectrum (Kravtsova et al., 2004) while it is probably present in a more recent contribution (Alonso Mori et al., 2009). We point out here that the origin of the differences is the experimental resolution, which is significantly improved in the recent years.
Unlike the size effects observed at the Ca Kedge, the S Kedge spectra shows clear features in the larger clusters: (i) the longrange multiple scattering peaks d, e and f increase as the cluster size increases and become more pronounced in the nonMT approach; (ii) the whiteline peaks, namely the features b and c, are enhanced in the large cluster within the nonMT approach; (iii) opposite to the Ca Kedge, the preedge peak (feature a) appears also in a relatively small cluster (e.g. 8 Å). However, the peak position agrees well with experimental spectra only when a large cluster and a nonMT potential is employed.
We have to mention here also that S atoms may exhibit several valences and easily react with Xray radiation (Wilke et al., 2008; Hackett et al., 2012). As a consequence, the anomalous feature f cannot be explained without taking into account the complex valence state possibly owing to a charge transfer induced by radiation damage. This mechanism hampers the experimental determination of the sulfur valence and also poses a great challenge to the theoretical description. This work is mainly a comparison between MT and nonMT potentials and a further investigation of the sulfur valence states is left to a further work.
In this section we discussed potential effects and size effects in CaS. We have yet another tool to probe the system and better understand the CaS electronic structure. This tool is the orbitalprojected
that reflects the population of atomic states available from different orbitals and atoms. It is a useful and important tool to recognize peaks and reconstruct details of the system electronic structure.4.4. Projected the calcium Kedge
As discussed above, the preedge at the Ca Kedge in the CaS is complex and interesting owing to the possible interplay between electron and longdistance atomic scattering contributions. In Fig. 5 (left) we show the projected and compare it with the theoretical spectrum at the Ca Kedge. From the comparison we may claim that the preedge feature a mainly originates from Ca d states hybridized with S p states, similarly to transition metal oxides where the of transition metal d states and oxygen p states drives the preedge behavior. Moreover, the also occurs between Ca p and d. The origin of features b, c and d can be assigned to the strong between Ca p, d states and S p states. Recently, Chen et al. (2007) calculated the band structure and the projected using density functional theory. In their calculation the band structure shows a wide direct bandgap about 4.47 eV wide at the Γ point and the indicated that Ca d states dominate at the Our calculation shows a similar trend: (i) calcium d states are present at the giving rise to the preedge feature; (ii) the sulfur p states dominate at energies about 5 eV below the The extracted from XANES calculations is then in agreement with firstprinciples calculations.
4.5. Projected the sulfur Kedge
In Fig. 5 (right) the projected at the S Kedge is presented and compared with the theoretical XANES spectrum. Also in this case, it is evident that the edge structure (features b and c) originates from S empty p states. Furthermore, the features d, e and f also resemble p states of S atoms, pointing out the presence of strong electronic effects at the S Kedge. The preedge feature a is due to a strong between S p states and Ca d states, evident also at the Ca Kedge spectrum. The s states of sulfur partially contribute to the preedge feature of the S Kedge XANES spectrum. For the p states of sulfur, the largest is around −10 eV on our energy scale, i.e. far away from the as confirmed also by firstprinciples calculations (Chen et al., 2007). These states are fully occupied and not available for electron transitions; as a consequence, no other features below the feature a can be observed.
As listed in Table 2, electronic parameters (the absolute charge transfer and charge counts for different atomic orbitals) have been compared at both Ca and S Kedges. The charge transfer is about 0.21–0.25 electrons while Ca d states have a large charge count (∼0.86 electrons), close to the value (0.855) of the CaO system (Modrow et al., 2003), indicating similarity of the charge distribution in the two systems.

5. Conclusions
We have presented here the electronic structure of CaS, a simple system with a cubic structure but large interatomic distances. Xray absorption spectra at the Ca and S Kedges have been measured and interpreted within the framework of the MST using both the MT potential and the finitedifference method without the MT approximation.
We found that, owing to the less compact structure of the CaS, both potential and size effects dominate either at both the Ca and the S Kedges. The between calcium d states and sulfur p states drives the structure of the preedge at both edges. Finally, the of the system mainly depends on Ca d electrons, implying that a strong is present in this system. It is interesting to note that a similar behavior can be observed in transition metal oxides, in particular in terms of similar of states between cation d states and anion p states. Thinking about applications, CaS is a well known material in the luminescence technology. The between doped rareearth metals and the element in the matrix compound influences the band structure near the gap, and thus the performance of devices that employ the hybridized materials. It is therefore interesting and promising to investigate in situ operation of the CaSbased luminescent devices, using the approach outlined in this contribution.
Supporting information
Supporting information file. DOI: https://doi.org//10.1107/S0909049512040617/hf5217sup1.pdf
Acknowledgements
The project has been supported by the National Natural Science Foundation of China (grant No. 11105172). We thank Professor Y. Joly for many fruitful discussions.
References
Alonso Mori, R., Paris, E., Giuli, G., Eeckhout, S. G., Kavčič, M., Zitnik, M., Bučar, K., Pettersson, L. G. M. & Glatzel, P. (2009). Anal. Chem. 81, 6516–6525. Web of Science CrossRef CAS Google Scholar
Barrett, E., Fern, G. R., Ray, B., Withnall, R. & Silver, J. (2005). J. Opt. A, 7, S265. Web of Science CrossRef Google Scholar
Chen, Z. J., Xiao, H. Y. & Zu, X. T. (2007). Physica B, 391, 193–198. Web of Science CrossRef CAS Google Scholar
Farrell, S. P., Fleet, M. E., Stekhin, I. E., Kravtsova, A., Soldatov, A. V. & Liu, X. (2002). Am. Mineral. 87, 1321–1332. CAS Google Scholar
Guo, Y. D., Yang, Z. J., Gao, Q. H., Liu, Z. J. & Dai, W. (2008). J. Phys. Condens. Matter, 20, 115203. Web of Science CrossRef PubMed Google Scholar
Hackett, M. J., Smith, S. E., Paterson, P. G., Nichol, H., Pickering, I. J. & George, G. N. (2012). ACS Chem. Neurosci. 3, 178–185. Web of Science CrossRef CAS PubMed Google Scholar
Hakamata, S., Ehara, M., Kominami, H., Nakanishi, Y. & Hatanaka, Y. (2005). Appl. Surf. Sci. 244, 469–472. Web of Science CrossRef CAS Google Scholar
Hedin, L. & Lundqvist, S. (1970). Solid State Physics, Vol. 23, edited by D. T. Frederick Seiz and E. Henry, pp. 1–181. New York: Academic Press. Google Scholar
Joly, Y. (2001). Phys. Rev. B, 63, 125120. Web of Science CrossRef Google Scholar
Kravtsova, A., Stekhin, I., Soldatov, A., Liu, X. & Fleet, M. (2004). Phys. Rev. B, 69, 134109. Web of Science CrossRef Google Scholar
Luo, H., Greene, R. G., Ghandehari, K., Li, T. & Ruoff, A. L. (1994). Phys. Rev. B, 50, 16232. CrossRef Web of Science Google Scholar
Modrow, H., Bucher, S., Rehr, J. J. & Ankudinov, A. L. (2003). Phys. Rev. B, 67, 035123. Web of Science CrossRef Google Scholar
Moreno, M. S., Jorissen, K. & Rehr, J. J. (2007). Micron, 38, 1–11. Web of Science CrossRef PubMed CAS Google Scholar
Natoli, C. R., Benfatto, M., Della Longa, S. & Hatada, K. (2003). J. Synchrotron Rad. 10, 26–42. Web of Science CrossRef CAS IUCr Journals Google Scholar
Norman, J. G. (1974). Mol. Phys. 81, 1191–1198. Google Scholar
Rao, R. (1986). J. Mater. Sci. 21, 3357–3386. CrossRef CAS Google Scholar
Ravel, B. & Newville, M. (2005). J. Synchrotron Rad. 12, 537–541. Web of Science CrossRef CAS IUCr Journals Google Scholar
Rehr, J. J. & Albers, R. C. (2000). Rev. Mod. Phys. 72, 621–654. Web of Science CrossRef CAS Google Scholar
Rehr, J. J., Kas, J. J., Prange, M. P., Sorini, A. P., Takimoto, Y. & Vila, F. (2009). C. R. Phys. 10, 548–559. Web of Science CrossRef CAS Google Scholar
Shaukat, A., Saeed, Y., Ikram, N. & Akbarzadeh, H. (2008). Eur. Phys. J. B, 62, 439–446. Web of Science CrossRef CAS Google Scholar
Versluys, J., Poelman, D., Wauters, D. & Meirhaeghe, R. L. V. (2001). J. Phys. Condens. Matter, 13, 5709. Web of Science CrossRef Google Scholar
Wilke, M., Jugo, P. J., Klimm, K., Susini, J., Botcharnikov, R., Kohn, S. C. & Janousch, M. (2008). Am. Mineral. 93, 235–240. Web of Science CrossRef CAS Google Scholar
Xu, W., Chen, D., Chu, W., Wu, Z., Marcelli, A., Mottana, A., Soldatov, A. & Brigatti, M. F. (2011). J. Synchrotron Rad. 18, 418–426. Web of Science CrossRef CAS IUCr Journals Google Scholar
© International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.