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Experimental and theoretical X-ray K-spectra of sulfur of zincblende-based compounds AgGaS2–CdGa2S4–InPS4
Journal of Physics and Chemistry of Solids 63 (2002) 227±231
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Experimental and theoretical X-ray K-spectra of sulfur of zincblende-based compounds AgGaS2 ±CdGa2S4 ±InPS4 A.A. Lavrentyev a, B.V. Gabrelian a, V.A. Dubeiko a, I.Ya. Nikiforov a, J.J. Rehr b,* a
Department of Physics, Don State Technical University, Gagarin Sq.1, Rostov-on-Don, Russia b Department of Physics, University of Washington, Seattle, WA 98195-1560, USA Received 9 March 2000; accepted 5 April 2001
Abstract The K-edge X-ray absorption spectrum of sulfur in AgGaS2, CdGa2S4, and InPS4 was investigated both experimentally and theoretically. The lattices of these compounds can be represented as chalcopyrite with various amounts of defectiveness. The spectra were obtained with an experimental resolution about 0.2 eV. To obtain the theoretical absorption spectrum, the FEFF7 high order multiple scattering code was used. The clusters considered contained 80±87 atoms; up to 624 multiple-scattering paths of the photoelectron were taken into account, with the highest order scattering equal to 6. A very good correspondence between the theoretical and experimental spectra was achieved when the energy dependent exchange energy was calculated according to the Dirac±Hara approximation. q 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction The complicated diamond-like semiconductor compounds of the row AgGaS2 ±CdGa2S4 ±InPS4 are applied in various devices of nonlinear optics as gyrotropic media in narrowband optical ®lters etc. [1,2]. In this paper, the K-edge X-ray absorption spectrum of sulfur of these materials is investigated both experimentally and theoretically. The structures of these compounds originate from the sphalerite structure, and are summarized in detail as follows. The compound AgGaS2 is defect free and exists in the chalcopyrite structure (Fig.1). For this case, the atoms of silver and gallium substitute one by one the atoms of zinc in sphalerite lattice winding along the by a double spiral around the reverse fourth axis 4, 2 D12 direction z of the lattice. The space group is I42d 2d . The parameters of the crystal lattice used in the present ab Ê, initio calculations of the X-ray spectra are: a 5.757 A Ê c 10.304 A; the number of the formula units in the elementary cell z 4, and the coordinates of atoms in it: 4Ag(a) 000; 4Ga(b) 00 12 ; 8S(d) x 14 18 (x 0.291) [3]. The structure is characterized by the closed packing of the sulfur atoms, with half of the tetrahedral interatomic spaces occupied regularly by * Corresponding author. Tel.: 11-206-543-8593; fax: 11-206685-0635. E-mail address: [email protected] (J.J. Rehr).
atoms of silver and gallium. Thus in the vicinity (i.e. the ®rst atomic shell) of the sulfur atom, there are two atoms of silver Ê and two gallium atoms at a at a distance RAg2S 2.557 A Ê. distance RGa2S 2.276 A The second of these compounds, CdGa2S4 belongs to a type of `defective chalcopyrite'. Here the gallium atoms of the ®rst type (Ga 1) are placed in half of gallium positions in AgGaS2 (Fig. 1), and the gallium atoms of the second type (Ga 2) are in half of the silver positions in AgGaS2 [4]. The remainder of these sites are occupied by cadmium atoms, where as the second half of the gallium sites of the AgGaS2 are vacant in CdGa2S4. Thus the coordination number (i.e. the number of neighboring atoms in the ®rst coordination shell) of the sulfur atom in this structure is equal to three. The spiral axis of gallium atoms in CdGa2S4 can be called `right', and contrarily in AgGaS2, `left'. The second spiral built of cadmium atoms along the z-axis is a broken one. The space group is I4 2 S24 ; Z 2 and the crystal lattice paraÊ , c 10.16 A Ê . The sets of the equivameters are a 5.536 A lent positions in CdGa2S4 are: 2Cd(a) 000; 2Ga 1(b) 00 12 ; 2Ga 2(c)0 12 14 ; 8S(g) xyz (x 0.27; y 0.26; z 0.14). It is worth noting that the last coordinates y and z in an ordinary chalcopyrite (for example in AgGaS2) are equal to 0.25 and 0.125. The atom of sulfur in CdGa2S4 has an umbrella coordination and the following interatomic distances: Ê ; RGa1 2S 2.33 A Ê ; RGa2 2S 2.25 A Ê. RCd2S 2.52 A
0022-3697/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(01)00134-2
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A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
The third compound in our study, InPS4 (Fig. 1) belongs to the structure of twice defected chalcopyrite with space 24 , Z 2, the lattice parameters being a group I4 S Ê Ê , and the coordinates of atoms in the 5.623 A, c 9.058 A elementary cell: 2In(a) 000; 2P(d) 0 12 34 ; 8S(g) xyz (x 0.3057; y 0.2389; z 0.1302) [5]. The sulfur atom has so called `angle-like' coordination (Fig. 1), with the Ê ; RP2S 2.04 A Ê. following bond lengths: RIn2S 2.48 A The crystal structure is a close-packed face-centered cubic lattice of sulfur atoms which form the layers of (112) orientation. A quarter of the tetrahedral hollows of this structure are occupied by indium and phosphorus atoms. Thus comparing the crystal structures in the row AgGaS2 ± CdGa2S4 ±InPS4 (Fig. 1), one can state that they are all derivatives of the sphalerite structure (doubled lattice), with a gradually growing de®ciency of metallic atoms from defectfree chalcopyrite AgI4 GaIII 4 S8 to the defective chalcopyrite AII2 CdII2 GaIII 4 S8 , and then further to the double-defective chalIII V V copyrite AIII 2 In2 A2 P2 S8 , where the symbol A denotes a vacancy as in the notation of crystallography. In these structures the coordination of metallic atom is tetrahedral, and the coordination number of sulfur atoms diminishes from four for AgGaS2, to three (CdGa2S4), and then to two (InPS4), as the defectiveness of the structure increases. This analysis of crystal structures of the compounds being investigated gives a precise prescription for building clusters properly, as input to the theoretical calculations of their X-ray spectra using the FEFF7 code, and to interpret the change in the form of the experimental K-edge sulfur spectra due to a decreasing sulfur coordination. 2. Experiment The sul®des are bene®cial objects, from the point of view of the abundance of information that their sulfur X-ray spectra can deliver, because of the `rich' ®ne structure they dispose. The latter is due to the comparatively narrow (0.57 eV) width of the inner K-level of sulfur, and hence, the smearing of the ®ne structure in the experimental Kspectra of sulfur in the near-edge region is negligible. The experimental sulfur K-edge X-ray spectra of AgGaS2, CdGa2S4, and InPS4 studied in this work are shown below (Figs. 2±4). These spectra have been obtained with the X-ray spectrograph DRS-2, with a resolution about 0.2 eV. As the dispersion element, a quartz crystal bent to a radius 50 cm was used. As a reference, the lines Bi Ma 1 and Bi Mb in the ®rst order of re¯ection, with energies 2422.5 and 2525.6 eV, correspondingly [6], were applied. The Xray tube was operated at a current of 80 mA and voltage 5 kV. Such a low voltage was chosen to exclude the X-ray radiation of higher orders of re¯ection, but it was high enough to excite the K-level of sulfur at about 2470 eV. The exposure time was about 8 h. The X-ray spectrogram recorded on the X-ray ®lm were photomeasured along ®ve runs. The resulting spectrum was the average of three different micro-photograms measured at 250 equidistant points.
3. Method of calculation The calculations of sulfur K-edge absorption spectra have been carried out with the ab initio FEFF7 code, as described in detail by its authors [7,8], and applied successfully in a previous paper to calculate the X-ray spectra of KCl and PbS [9]. The essence of the approach used in the FEFF7 code is that the calculations of the absorption coef®cient m(E) in the XANES region are carried out using the approximation of high order multiple scattering of limited multiplicity, according to Rehr±Albers algorithm. The X-ray crosssection calculation in FEFF7 is formally equivalent to the `golden rule' of Fermi, within the dipole approximation, X ^r u f lu2 d E 2 Ef ; m E 4pav ukcue~ 1 f
where a < 1=137 is the ®ne structure constant; v the energy of X-ray radiation in this paper, Hartree atomic units are being used (e m É 1), E v ÐEc is the energy of the ®nal state of the photoelectron; e^ the vector of X-ray polarization, and the sum is carried out over all unoccupied ®nal states u f l, with energies E Ef, in the presence a fully relaxed core hole. 4. Results and discussion In Figs. 2±4, the theoretical X-ray K-absorption spectra of sulfur calculated with FEFF7 for AgGaS2, CdGa2S4, and InPS4, are compared with experimental data. Clearly one observes good agreement between the forms of calculated spectra and their experimental analogues, except for some structure for the compound CdGa2S4. For AgGaS2 a cluster of 87 atoms has been used in the calculations, 80 atoms were used for CdGa2S4, and 83 for InPS4. In the center of such clusters was an atom of sulfur, and the scattering of the photoelectron by the other atoms of the cluster was calculated. For AgGaS2 624 multiplescattering paths were used, and the greatest multiplicity was six. Similarly, for CdGa2S4 62 paths were taken into account, and the maximum multiplicity was only three, because of the rather high critical value of the number of spherical waves taken into account. Lastly, for InPS4 443 multiple-scattering paths were considered, and the greatest multiplicity was not more than six. Recently [9] we have investigated the convergence of the calculation of K-spectra of the components of KCl due to the dimensions of the cluster considered, again using the FEFF7 code. It was found that the main features of XANES-spectra appeared for a cluster with only two atomic shells (AS), i.e. for a total number of atoms in the cluster equal to 19. An increase in the number of atoms in the cluster up to 81 (6 AS) did not change the energy positions of the main maximum and minimum, but does in¯uence their intensities. A further increase of the number of atoms in the cluster did not change the shape of the XANES-spectra. The analogous investigation
A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
229
Fig. 1. Crystal chalocpyrite structureÐAgGaS2, defective chalcopyriteÐCdGa2S4, and double defective chalcopyriteÐInPS4. To the right the environment of the sulfur atom in these structures is shown.
has been carried by us for the set of compounds AgGaS2 ± CdGa2S4 ±InPS4. We have found that the shape of the calculated spectra did not change when the number of atoms in the cluster was greater than that discussed above for the analogous compound. The best correspondence between the theoretical and experimental spectra was achieved when we used the energy dependent Dirac±Hara exchange energy. We tried to use other formulas for the exchange energy, in particular, the energy-independent exchange energy of the ground state or the energy-dependent exchange energy following Hedin and
Lundquist, but these attempts led to worse results not shown here. A possible reason for this is that the Dirac±Hara exchange energy is analogous to Hartree±Fock exchange and is more appropriate for insulating materials like those studied here, than the Hedin±Lundqvist model, which is usually more appropriate for metals. However, the calculated forms of the XANES are somewhat compressed compared to the experimental curves for AgGaS2 and InPS4, suggesting that the Dirac±Hara exchange model is still not optimal. If one performs a scaling of the theoretical curve, as has been carried out for other compounds in Ref.
230
A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
Fig. 2. Experimental and theoretical (FEFF7) K-absorption spectrum of sulfur in AgGaS2.
Fig. 3. Experimental and theoretical (FEFF7) K-absorption spectrum of sulfur in CdGa2S4.
[7], i.e. to change the energy values on the abscissa from E to aE, where a is a coef®cient that is close to unity (1.0 # a # 1.1), then it is possible to achieve a nearly perfect coincidence of the energy positions of all signi®cant peaks of the theoretical XANES with experimental ones. For AgGaS2 we have found that a 1.001. In the case of InPS4 this coef®cient can be taken with less difference to unity. However, for CdGa2S4 this scaling does not work everywhere, because there is a noticeable distinction between the theoretical and experimental XANES, i.e., the rather deep minimum in the theoretical curve is absent in the experiment. The scattering-multiplicity (or order) in these XANES was
not less than six to achieve reasonable convergence. Recently [9] we have stated that for the KCl and PbS with rock-salt crystal structure (where the number of the nearest neighbors was equal to six) single-scattering by itself `reproduces' all main features of the experimental spectra. However, the compounds investigated in the present work have lower symmetry than those with NaCl structure, and the number of the nearest neighbors to the absorbing atom decreases from four in AgGaS2 to three in CdGa2S4, and to two in InPS4. This lowering of the symmetry forces us to take into account more scattering events of the photoelectron to obtain for certain, all main features of the K-absorption spectrum of sulfur. That is also probably why the theoretically calculated spectrum of
A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
231
Fig. 4. Experimental and theorectical (FEFF7) K-absorption spectrum of sulfur in InPS4.
sulfur in CdGa2S4 does not so well correspond to the experimental spectrum everywhere, i.e. even more scattering paths appear to be necessary. However, overall these results do show that a high-order multiple scattering approach can account for the main features of the absorption spectrum in these complex materials. References [1] Yu.V. Voroshilov, V.Yu. Slivka, (In Russian), Unoxide Materials for Electronic Technique, Vysha Shkola, Lvov, 1989.
[2] Yu.A. Hazitarhanov, L.M. Suslikov, Z.P. Gadmashi, V.Yu. Slivka, Quantum Electronics (Kiev) 44 (1993) 24. [3] S.C. Abrahams, J.L. Bernstein, J. Chem. Phys. 59 (1973) 1625. [4] S.T. Kshirsagar, A.P.B. Sinha, J. Mater. Sci. 12 (1977) 2441. [5] R. Diehl, C.D. Carpentier, Acta Crystall. 334 (1978) 1097. [6] M.A. Blokhin, I.G. Scweizer, X-ray Handbook, Nauka, Moscow, 1982. [7] J. Mustre de Leon, J.J. Rehr, S.I. Zabinsky, R.C. Albers, Phys. Rev. B. 44 (1991) 4146. [8] S.I. Zabinsky, J.J. Rehr, A. Ankudinov, R.C. Albers, M.J. Eller, Phys. Rev. B. 52 (1995) 2995. [9] A.A. Lavrentyev, B.V. Gabrelian, I.Ya. Nikiforov, J.J. Rehr, J. Phys. Chem. Solids 60 (1999) 787.
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Experimental and theoretical X-ray K-spectra of sulfur of zincblende-based compounds AgGaS2 ±CdGa2S4 ±InPS4 A.A. Lavrentyev a, B.V. Gabrelian a, V.A. Dubeiko a, I.Ya. Nikiforov a, J.J. Rehr b,* a
Department of Physics, Don State Technical University, Gagarin Sq.1, Rostov-on-Don, Russia b Department of Physics, University of Washington, Seattle, WA 98195-1560, USA Received 9 March 2000; accepted 5 April 2001
Abstract The K-edge X-ray absorption spectrum of sulfur in AgGaS2, CdGa2S4, and InPS4 was investigated both experimentally and theoretically. The lattices of these compounds can be represented as chalcopyrite with various amounts of defectiveness. The spectra were obtained with an experimental resolution about 0.2 eV. To obtain the theoretical absorption spectrum, the FEFF7 high order multiple scattering code was used. The clusters considered contained 80±87 atoms; up to 624 multiple-scattering paths of the photoelectron were taken into account, with the highest order scattering equal to 6. A very good correspondence between the theoretical and experimental spectra was achieved when the energy dependent exchange energy was calculated according to the Dirac±Hara approximation. q 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction The complicated diamond-like semiconductor compounds of the row AgGaS2 ±CdGa2S4 ±InPS4 are applied in various devices of nonlinear optics as gyrotropic media in narrowband optical ®lters etc. [1,2]. In this paper, the K-edge X-ray absorption spectrum of sulfur of these materials is investigated both experimentally and theoretically. The structures of these compounds originate from the sphalerite structure, and are summarized in detail as follows. The compound AgGaS2 is defect free and exists in the chalcopyrite structure (Fig.1). For this case, the atoms of silver and gallium substitute one by one the atoms of zinc in sphalerite lattice winding along the by a double spiral around the reverse fourth axis 4, 2 D12 direction z of the lattice. The space group is I42d 2d . The parameters of the crystal lattice used in the present ab Ê, initio calculations of the X-ray spectra are: a 5.757 A Ê c 10.304 A; the number of the formula units in the elementary cell z 4, and the coordinates of atoms in it: 4Ag(a) 000; 4Ga(b) 00 12 ; 8S(d) x 14 18 (x 0.291) [3]. The structure is characterized by the closed packing of the sulfur atoms, with half of the tetrahedral interatomic spaces occupied regularly by * Corresponding author. Tel.: 11-206-543-8593; fax: 11-206685-0635. E-mail address: [email protected] (J.J. Rehr).
atoms of silver and gallium. Thus in the vicinity (i.e. the ®rst atomic shell) of the sulfur atom, there are two atoms of silver Ê and two gallium atoms at a at a distance RAg2S 2.557 A Ê. distance RGa2S 2.276 A The second of these compounds, CdGa2S4 belongs to a type of `defective chalcopyrite'. Here the gallium atoms of the ®rst type (Ga 1) are placed in half of gallium positions in AgGaS2 (Fig. 1), and the gallium atoms of the second type (Ga 2) are in half of the silver positions in AgGaS2 [4]. The remainder of these sites are occupied by cadmium atoms, where as the second half of the gallium sites of the AgGaS2 are vacant in CdGa2S4. Thus the coordination number (i.e. the number of neighboring atoms in the ®rst coordination shell) of the sulfur atom in this structure is equal to three. The spiral axis of gallium atoms in CdGa2S4 can be called `right', and contrarily in AgGaS2, `left'. The second spiral built of cadmium atoms along the z-axis is a broken one. The space group is I4 2 S24 ; Z 2 and the crystal lattice paraÊ , c 10.16 A Ê . The sets of the equivameters are a 5.536 A lent positions in CdGa2S4 are: 2Cd(a) 000; 2Ga 1(b) 00 12 ; 2Ga 2(c)0 12 14 ; 8S(g) xyz (x 0.27; y 0.26; z 0.14). It is worth noting that the last coordinates y and z in an ordinary chalcopyrite (for example in AgGaS2) are equal to 0.25 and 0.125. The atom of sulfur in CdGa2S4 has an umbrella coordination and the following interatomic distances: Ê ; RGa1 2S 2.33 A Ê ; RGa2 2S 2.25 A Ê. RCd2S 2.52 A
0022-3697/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(01)00134-2
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A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
The third compound in our study, InPS4 (Fig. 1) belongs to the structure of twice defected chalcopyrite with space 24 , Z 2, the lattice parameters being a group I4 S Ê Ê , and the coordinates of atoms in the 5.623 A, c 9.058 A elementary cell: 2In(a) 000; 2P(d) 0 12 34 ; 8S(g) xyz (x 0.3057; y 0.2389; z 0.1302) [5]. The sulfur atom has so called `angle-like' coordination (Fig. 1), with the Ê ; RP2S 2.04 A Ê. following bond lengths: RIn2S 2.48 A The crystal structure is a close-packed face-centered cubic lattice of sulfur atoms which form the layers of (112) orientation. A quarter of the tetrahedral hollows of this structure are occupied by indium and phosphorus atoms. Thus comparing the crystal structures in the row AgGaS2 ± CdGa2S4 ±InPS4 (Fig. 1), one can state that they are all derivatives of the sphalerite structure (doubled lattice), with a gradually growing de®ciency of metallic atoms from defectfree chalcopyrite AgI4 GaIII 4 S8 to the defective chalcopyrite AII2 CdII2 GaIII 4 S8 , and then further to the double-defective chalIII V V copyrite AIII 2 In2 A2 P2 S8 , where the symbol A denotes a vacancy as in the notation of crystallography. In these structures the coordination of metallic atom is tetrahedral, and the coordination number of sulfur atoms diminishes from four for AgGaS2, to three (CdGa2S4), and then to two (InPS4), as the defectiveness of the structure increases. This analysis of crystal structures of the compounds being investigated gives a precise prescription for building clusters properly, as input to the theoretical calculations of their X-ray spectra using the FEFF7 code, and to interpret the change in the form of the experimental K-edge sulfur spectra due to a decreasing sulfur coordination. 2. Experiment The sul®des are bene®cial objects, from the point of view of the abundance of information that their sulfur X-ray spectra can deliver, because of the `rich' ®ne structure they dispose. The latter is due to the comparatively narrow (0.57 eV) width of the inner K-level of sulfur, and hence, the smearing of the ®ne structure in the experimental Kspectra of sulfur in the near-edge region is negligible. The experimental sulfur K-edge X-ray spectra of AgGaS2, CdGa2S4, and InPS4 studied in this work are shown below (Figs. 2±4). These spectra have been obtained with the X-ray spectrograph DRS-2, with a resolution about 0.2 eV. As the dispersion element, a quartz crystal bent to a radius 50 cm was used. As a reference, the lines Bi Ma 1 and Bi Mb in the ®rst order of re¯ection, with energies 2422.5 and 2525.6 eV, correspondingly [6], were applied. The Xray tube was operated at a current of 80 mA and voltage 5 kV. Such a low voltage was chosen to exclude the X-ray radiation of higher orders of re¯ection, but it was high enough to excite the K-level of sulfur at about 2470 eV. The exposure time was about 8 h. The X-ray spectrogram recorded on the X-ray ®lm were photomeasured along ®ve runs. The resulting spectrum was the average of three different micro-photograms measured at 250 equidistant points.
3. Method of calculation The calculations of sulfur K-edge absorption spectra have been carried out with the ab initio FEFF7 code, as described in detail by its authors [7,8], and applied successfully in a previous paper to calculate the X-ray spectra of KCl and PbS [9]. The essence of the approach used in the FEFF7 code is that the calculations of the absorption coef®cient m(E) in the XANES region are carried out using the approximation of high order multiple scattering of limited multiplicity, according to Rehr±Albers algorithm. The X-ray crosssection calculation in FEFF7 is formally equivalent to the `golden rule' of Fermi, within the dipole approximation, X ^r u f lu2 d E 2 Ef ; m E 4pav ukcue~ 1 f
where a < 1=137 is the ®ne structure constant; v the energy of X-ray radiation in this paper, Hartree atomic units are being used (e m É 1), E v ÐEc is the energy of the ®nal state of the photoelectron; e^ the vector of X-ray polarization, and the sum is carried out over all unoccupied ®nal states u f l, with energies E Ef, in the presence a fully relaxed core hole. 4. Results and discussion In Figs. 2±4, the theoretical X-ray K-absorption spectra of sulfur calculated with FEFF7 for AgGaS2, CdGa2S4, and InPS4, are compared with experimental data. Clearly one observes good agreement between the forms of calculated spectra and their experimental analogues, except for some structure for the compound CdGa2S4. For AgGaS2 a cluster of 87 atoms has been used in the calculations, 80 atoms were used for CdGa2S4, and 83 for InPS4. In the center of such clusters was an atom of sulfur, and the scattering of the photoelectron by the other atoms of the cluster was calculated. For AgGaS2 624 multiplescattering paths were used, and the greatest multiplicity was six. Similarly, for CdGa2S4 62 paths were taken into account, and the maximum multiplicity was only three, because of the rather high critical value of the number of spherical waves taken into account. Lastly, for InPS4 443 multiple-scattering paths were considered, and the greatest multiplicity was not more than six. Recently [9] we have investigated the convergence of the calculation of K-spectra of the components of KCl due to the dimensions of the cluster considered, again using the FEFF7 code. It was found that the main features of XANES-spectra appeared for a cluster with only two atomic shells (AS), i.e. for a total number of atoms in the cluster equal to 19. An increase in the number of atoms in the cluster up to 81 (6 AS) did not change the energy positions of the main maximum and minimum, but does in¯uence their intensities. A further increase of the number of atoms in the cluster did not change the shape of the XANES-spectra. The analogous investigation
A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
229
Fig. 1. Crystal chalocpyrite structureÐAgGaS2, defective chalcopyriteÐCdGa2S4, and double defective chalcopyriteÐInPS4. To the right the environment of the sulfur atom in these structures is shown.
has been carried by us for the set of compounds AgGaS2 ± CdGa2S4 ±InPS4. We have found that the shape of the calculated spectra did not change when the number of atoms in the cluster was greater than that discussed above for the analogous compound. The best correspondence between the theoretical and experimental spectra was achieved when we used the energy dependent Dirac±Hara exchange energy. We tried to use other formulas for the exchange energy, in particular, the energy-independent exchange energy of the ground state or the energy-dependent exchange energy following Hedin and
Lundquist, but these attempts led to worse results not shown here. A possible reason for this is that the Dirac±Hara exchange energy is analogous to Hartree±Fock exchange and is more appropriate for insulating materials like those studied here, than the Hedin±Lundqvist model, which is usually more appropriate for metals. However, the calculated forms of the XANES are somewhat compressed compared to the experimental curves for AgGaS2 and InPS4, suggesting that the Dirac±Hara exchange model is still not optimal. If one performs a scaling of the theoretical curve, as has been carried out for other compounds in Ref.
230
A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
Fig. 2. Experimental and theoretical (FEFF7) K-absorption spectrum of sulfur in AgGaS2.
Fig. 3. Experimental and theoretical (FEFF7) K-absorption spectrum of sulfur in CdGa2S4.
[7], i.e. to change the energy values on the abscissa from E to aE, where a is a coef®cient that is close to unity (1.0 # a # 1.1), then it is possible to achieve a nearly perfect coincidence of the energy positions of all signi®cant peaks of the theoretical XANES with experimental ones. For AgGaS2 we have found that a 1.001. In the case of InPS4 this coef®cient can be taken with less difference to unity. However, for CdGa2S4 this scaling does not work everywhere, because there is a noticeable distinction between the theoretical and experimental XANES, i.e., the rather deep minimum in the theoretical curve is absent in the experiment. The scattering-multiplicity (or order) in these XANES was
not less than six to achieve reasonable convergence. Recently [9] we have stated that for the KCl and PbS with rock-salt crystal structure (where the number of the nearest neighbors was equal to six) single-scattering by itself `reproduces' all main features of the experimental spectra. However, the compounds investigated in the present work have lower symmetry than those with NaCl structure, and the number of the nearest neighbors to the absorbing atom decreases from four in AgGaS2 to three in CdGa2S4, and to two in InPS4. This lowering of the symmetry forces us to take into account more scattering events of the photoelectron to obtain for certain, all main features of the K-absorption spectrum of sulfur. That is also probably why the theoretically calculated spectrum of
A.A. Lavrentyev et al. / Journal of Physics and Chemistry of Solids 63 (2002) 227±231
231
Fig. 4. Experimental and theorectical (FEFF7) K-absorption spectrum of sulfur in InPS4.
sulfur in CdGa2S4 does not so well correspond to the experimental spectrum everywhere, i.e. even more scattering paths appear to be necessary. However, overall these results do show that a high-order multiple scattering approach can account for the main features of the absorption spectrum in these complex materials. References [1] Yu.V. Voroshilov, V.Yu. Slivka, (In Russian), Unoxide Materials for Electronic Technique, Vysha Shkola, Lvov, 1989.
[2] Yu.A. Hazitarhanov, L.M. Suslikov, Z.P. Gadmashi, V.Yu. Slivka, Quantum Electronics (Kiev) 44 (1993) 24. [3] S.C. Abrahams, J.L. Bernstein, J. Chem. Phys. 59 (1973) 1625. [4] S.T. Kshirsagar, A.P.B. Sinha, J. Mater. Sci. 12 (1977) 2441. [5] R. Diehl, C.D. Carpentier, Acta Crystall. 334 (1978) 1097. [6] M.A. Blokhin, I.G. Scweizer, X-ray Handbook, Nauka, Moscow, 1982. [7] J. Mustre de Leon, J.J. Rehr, S.I. Zabinsky, R.C. Albers, Phys. Rev. B. 44 (1991) 4146. [8] S.I. Zabinsky, J.J. Rehr, A. Ankudinov, R.C. Albers, M.J. Eller, Phys. Rev. B. 52 (1995) 2995. [9] A.A. Lavrentyev, B.V. Gabrelian, I.Ya. Nikiforov, J.J. Rehr, J. Phys. Chem. Solids 60 (1999) 787.