J. Chem. SOC., Faraday Trans. I, 1988, 84(6), 1779-1794 Investigation of the Coordination of Lead in PbO-PbF, Glasses using XANES Kalya J. Rao and B. Govinda Rao Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India Joe Wong General Electric Corporate Research and Development, Schenectady, New York 12301, U.S.A. The Ledge spectra of lead in PbO-PbF, glasses have been investigated. Since PbO-PbF, glasses contain [PbO,F,] units throughout the glass- forming compositions and since PbF,-rich glasss are considerably more ionic than PbO-rich glasses, the symmetry of the [PbO,F,] units increases from C, through C,, to D,, and possibly to 0,. The changes in symmetry have been ascertained from XANES using appropriate molecular-orbital diagrams.We have shown that the splitting of the L, and L, edges, the variation of the half-widths of all three edges and the Ledge intensities are indeed consistent with symmetry changes in the [PbO,F,] units and the suggested molecular-orbital diagrams. While the extent of ionicity of bonding undergoes a continuous increase as the PbF, content in the glass is increased, the white-line intensities at the edges decrease in the same manner. This has been shown to be a consequence of the deshielding of final states responsible for the Ledge spectra by evaluating the dipole-matrix elements using Slater orbitals. The evolution of the symmetry of the [PbO,F,] units, the variation of Ledge absorption intensities and the variation of ionicity have thus been shown to be directly related.X-Ray absorption near-edge structure (XANES) arises from the excitation of electrons from core levels such as ls(K), 2s(L1), 2p,,,(L,), 2p3,,(L3) etc. to the lowest allowed unoccupied electronic states in the atom.lv2 The high-energy side of the absorption edge consists of an undulatory continuum of absorption which exponentially decreases in intensity. Absorption undulations above 30-50 eV from the edge constitute the extended X-ray absorption fine structure (EXAFS), which contains direct structural information. 3-5 Both EXAFS and XANES are finding increasing applications in investigations of structure and bonding in both crystalline and amorphous The L-absorption edge of an element is often very sharp and well defined, and is referred to as a white line.1*2.7 White lines appear when the final state is a discrete allowed atomic level or a band state with a high amplitude of an orbital of allowed symmetry on the absorber atom.'-1° Since the Ledge transitions are associated with p and d final states,l' they reflect the extent to which p and d final states are affected by the nature of bonding1, and by the symmetry of the coordination polyhedronf3 around the atom.Hence the analysis of the XANES can give rise to vital chemical information, namely local structure and bonding. Glasses can be formed in the PbO-PbF, system over a wide range of c~mpositions.~~ We have ~ h o w n l ~ * ~ ~ that the PbO-PbF, glass structure is built up of [PbO,F,]-type octahedral units throughout the glass-forming compositions. The nature of bonding in the components of this glass system, namely PbO and PbF,, is widely different16 (highly covalent in PbO and highly ionic in PbF,).Hence the ionicity of Pb-0 and Pb-F 5 9 59 1779 F A R 11780 XANES Spectra of Pb in PbO-PbF, Glasses bonds in [PbO,F,] units can be expected to exhibit a continuous variation as a function of composition. Since increased ionicity decreases the rigidity and directionality of bonds we may expect the more ionic PbF,-rich region to consist of more symmetrical [PbO,F,] units. Such a change of symmetry and bonding may be expected to affect the Ledge spectra which involve 1s -+ 6 p and 2p -+ 6d transitions of lead as a function of composition; hence the relevance of XANES of Pb in these investigations. Bonding in [PbO,F,] units requires hybridization of the 6s, 6p and 6d states on lead in order to accommodate in them a significant degree of covalency of bonding.In fact such hybridization of valence orbitals has been invoked in the bonding models of pure Pb0.l' An important consequence of hybridization in XANES studies is the incidence of new features in Ledge spectra arising from otherwise forbidden transitions. This aspect of bonding is therefore particularly well suited to examination using XANES.1S-20 The Ledge absorption intensity itself can be used to infer the nature of bonding because electrons involved in covalent bonding screen the final states relevant to Ledge transition~.~l-~~ Hence variation of Ledge absorption intensities in the binary series of PbO-PbF, glasses can reflect the trend in the nature of bonding.explain the near-edge feature of X-ray absorption spectra. Further, no band-structure calculations are available for any of these glasses. Hence an MO approach has been assumed to be quite adequate for our discussions. We may, however, note that these approaches do not adequately take care of the effect of core hole^.^^.^^ Also, lead atoms are separated by intervening oxygen and fluoride atoms, which limit the overlap of p and d orbitals of Pb while forming bands. An atomic description of the spectroscopic phenomena may not therefore be unrealistic. With this background we have examined the consequences upon the XANES spectra of the evolution of symmetry in [PbO,F,] units as a function of PbF, concentration, because with increasing PbF, content the glasses become more ionic and the [PbO,F,] units tend to become more symmetrical. In our analysis we have considered excitations up to 30 eV above the edge as the upper limit of XANES, though recent reports suggest even higher energy limits.,, Other features such as the L,/L, intensity ratio and variations of half-widths and energies of the various peaks in the XANES spectra are also informative about the structure of these glasses, and we have discussed these aspects using the same MO description.Symmetry-based molecular-orbital (MO) theory has been widely invoked''. 24-33 to Experimental The PbO-PbF, .glasses used in this study were prepared by melting together appropriately weighed quantities of Pb,O, (AR) and PbF, (AR) in quartz tubes and quenching drops of melt between polished steel plates (Pb,O, decomposes quantitatively to PbO at ca.840 K). The details of the method of preparation have been reported ea~1ier.l~ Samples for recording XANES were prepared by mulling fine powders (400 mesh) ground from transparent thin discs of the glass with Duco cement and casting the mull into thin films between microscope slides. Details of these casting procedures have been given el~ewhere.,~ The concentrations of glass powders in the mull and the thickness of the films were manipulated so as to provide two absorption lengths of the material at energies just above the L,, L, and L, edges of lead with the use of one or two such films. Only pinhole-free films (by visual examination over a light box) were used.Uniformity of thickness was better than 5 O h over a 2 in length,? and no radiation damage was detected after beam exposure. Room-temperature spectra were obtained with the C-2 spectrometer at CHESS (the Cornell High Energy Synchrotron Source) with CESR (the Cornell Electron Storage Ring) running at 5.3 GeV and an injection current of 12 mA. The synchrotron X-ray t 1 in = 2.54 x lo-' m.K. J. Rao, B. G. Rao and J . Wong 3.60 s: p 2.80 E - 2.00 E .r. Y 0.80 8 2 a, s 3 0.40 I I 1 I I I 15800 16200 16600 17000 1: 60 - 20 20 60 EIeV EIeV 1781 I Fig. 1. (a) Room-temperature Pb L, absorption spectrum of lead foil, schematically showing the edge normalization procedure (see the text). (b) Normalized edge spectrum in the range f 60 eV. The zero of energy is taken with respect to the L, edge of Pb at 15860.8 eV.beam from CESR was monochromatized with a channel-cut Si(220) crystal and a 1 mm entrance slit. The incident beam was detuned 50 % to minimize harmonic contents at the Pb L,, L, and L, energies.,* This yielded a resolution of 5 eV at the lead L, edge at 13035.0 eV, which is comparable to the estimated life time broadening of the Pb L, edge of 4.6 eV. Spectra were recorded in three energy regions about the respective L, (13035.0 eV), L, (15200.0 eV) and L, (15860.8 eV) edges: -200 to -50 eV in 10 eV steps; - 50 to 50 eV in 1 eV steps; and above 50 eV in 3 eV steps. This scanning procedure yielded quality data of both pre-edge and post-edge backgrounds for subsequent normalization of the XANES spectra.The spectrometer was calibrated with a Pb foil before, between and after scanning the lead compounds and glasses. No spectrometer drifts were detected over a period of two days of continuous scanning. The procedure for obtaining normalized XANES spectra is similar to that used in an earlier study of lead compounds and PbO-PbC1, gla~ses.~’ This is briefly described here for the L, spectra of Pb metal. Fig. 1 (a) is a plot of In (Z,,/Z) us. energy around the Pb L , edge energy at 15 860.8 eV. The pre-edge region XY (- 200 to - 50 eV) is linearly fitted and extrapolated above the edge(E = 0) to Z. The post-edge (EXAFS) background AB to 500 eV above the edge was determined by using a cubic spline fit procedure with equal segments (usually three) and extrapolating below the edge to C.The absorption jump is given by PQ at E = 0. The near-edge spectrum is then normalized by subtracting the line XZ from all points in the region & 60 eV and dividing the difference by the edge jump PQ to yield the normalized spectrum shown in fig. 1 (b). In the case of L,, L, and L,. edges the zeros of energy were taken with respect to the corresponding threshold of photoelectron ejection at 13 035.0, 15 200.0 and 15 860.8 eV, re~pectively.,~ These threshold energies were calibrated with the first peak in the corresponding derivative spectra. The derivative spectra in the range -20 to 40 eV were obtained by drawing through points given by dA/dE = [A(E+A)-A(E)]/A (1) where A is the energy step size in the absorption spectra. Thus various inflection points in the normalized XANES spectra show up as peaks in the derivative spectra, and the absorption maxima of the XANES spectra correspond to zero on the decreasing parts of the derivative spectra.The half-widths at half-maximum (h.w.h.m.) of the main 59-21782 XANES Spectra of Pb in PbO-PbF, Glasses absorption peaks in normalized XANES spectra were determined as the difference between the energies of the peak and the zero on the high-energy side of the peak in the derivative spectrum (extrapolated wherever necessary). Areas under the absorption peaks were determined by deconvoluting the XANES peaks into Gaussians by a non- linear fitting program. In the case of the L, edge the spectra were fitted to one Gaussian, while two Gaussians were necessary for the L, and L, edges.The pre-edge absorptions were ignored in these fits (see later). Reasons for, and limitations of, using Gaussian fit instead of Lorentzian fit are discussed later. Results and Discussion Results Normalized XANES spectra of crystalline PbO, PbF, and four PbO-PbF, glasses containing different percentages of PbO are presented in fig. 2 for the L, (a), L, (b) and L, (c) edges. The differentiated spectra are presented in fig. 3(a), (b) and (c), in the same order. The h.w.h.m. is indicated for one spectrum in each case, for illustration. As pointed out earlier, the peaks corresponding to allowed transitions 2s + 6p (for the L, edge) and 2p -+ 6d (for the L, and L, edges) have been identified with reference to the L edges of a Pb foil. The energies of other absorptions in the near-edge spectra are also listed in table 1 for all three edges and are again referred uniformly to the appropriate L edges of a Pb foil. Variations of the energies of the pre-edge and post-edge peaks associated with the L, and L, edge are shown in fig.4. The L, edge does not appear to be associated with the subsidiary peaks. The variation of the h.w.h.m. of the principal absorptions is shown in fig. 5, and the variation of the area under the principal peak, as a function of composition (for all the three edges), is presented in fig. 6. General Features of XANES Pb is formally in its divalent state in PbO and in all the glasses. The 6p and 6d states of Pb are therefore completely vacant, and one should expect reasonably intense white lines for the three Ledge transitions since they involve vacant final states.The L, transition in PbF, is associated with typically well-defined white-line characteristics. Contrary to their appearance on cursory examination, the differentiated spectra of fig. 3 suggest that the h.w.h.m. of PbO and the PbO-PbF, glasses are also similar to the h.w.h.m. of the &-edge absorption of PbF,. Values of the h.w.h.m. of the various L-edge absorptions are listed in table 1 along with the peak energies. Since the absorption peaks at the edges are sufficiently well defined it appears that the transitions occur to discrete final states. From table 1 and fig. 2 and 3 we note that there are two additional transitions, which may be described as pre-edge and post-edge absorptions, respectively, associated with L, and L, spectra, while L, spectra have no such features.These additional features can arise from crystal-field splitting of the 6d levels on Pb in a low-symmetry coordination polyhedron. However, such low symmetries would also split the 6 p levels, whereas the &-edge spectra, being free of shoulders, do not support this possibility; hence, considering lead to the present as simple Pb2+ ions in a crystal field is not adequate. We may note in this context that Pb-0 bonding is quite covalent in pure PbO, and also the Pb-F bond can be quite covalent in the glassy state, as suggested in several investigations of PbF,-based glasses. l4> 37,38 Hence, we consider that MO description of bonding in [Pb0,F4] octahedra is appropriate.The origin of the observed XANES spectra may then be discussed in the light of an MO model. In the crystal structure of yellow PbO it is found16 that Pb is coordinated to four oxygens at two unequal distances and that all oxygens are present on the same side ofK. J. Rao, B. G. Rao and J. Wong 1783 -60.00 -20.00 20.00 60.00 EIeV 1.20 0.80 0.40 0 -60.00 -20.00 20.00 60.00 I c E/eV 0 EIeV Fig. 2. Normalized spectra of the L, (A), L, (B) and L, (C) edges of Pb in PbO, PbO-PbF, glasses and PbF,. The ordinate scale corresponds to the PbO spectrum. Other spectra are systematically displaced for clarity. %PbO = (a) 0, (b) 40, (c) 50, ( d ) 60, (e) 80 and (f) 100. the lead atom. This gives rise to a pyramidal [PbO,] unit with C, symmetry. When PbF, is added in order to form glasses, Pb atoms acquire mixed oxygen-fluorine coordination.This results in a decrease of the oxygen coordination of an average Pb atom. The novel feature of these glasses, as revealed by X-ray diffraction is that in the entire glass-formation range lead is coordinated to two oxygens and four fluorines.0.12 0.08 0.04 0.00 -0.04 -24.00 -8.00 8.00 24.00 EIeV -0.04 40.00 l o \ 0.12 0.08 0.04 0.0c K C - EIeV Fig. 3. Derivative spectra of the L, (A), L, (B) and L, (C) edges of Pb in PbO, PbO-PbF, glasses and PbF,. The ordinate scale corresponds to the PbO spectrum. Other spectra are systematically displaced for clarity. The half-width at half maximum (h.w.h.m.) is indicated for PbO spectrum in each case. The energies (in eV) of the peak shoulders are also indicated.K .J. Rao, B. G. Rao and J. Wong 12.0 0 I I I I I 1 1785 Fig. 4. Variation of the energies of pre-edge and post-edge peaks associated with L, and L, edges with composition. These energies for PbO and PbF, are also marked in the figures. A, L, pre- edge; a, L, pre-edge; A, L, post-edge and 0, L, post-edge. l x b I I I I I 0 20 40 60 80 100 Pb5 PbFz (mol%) Fig. 5. Variation of the h.w.h.m. of the principal absorption of all the three edges with composition. The h.w.h.m. for PbO and PbF, is also marked in the figure. x , L, edge; A, L, edge and 0, L, edge. PbO Further, the analysis of the EXAFS associated with the Pb L, edge of these glasses shows that Pb atoms are in coordination polyhedra of the type [PbO,F,]. The results of the EXAFS analysis are reported e1~ewhere.l~ Such a structure helps retention of Pb-0-Pb linkages which, as we suggested earlier, is important for the stability of lead oxyhalide glasses.Further, the glass structure requires fluoride ions to possess variable coordination.1786 XANES Spectra of Pb in PbO-PbF, Glasses 9.5 n .; 9.0 d a g 8.5 a 3 v 8.0 X 0 20 40 60 80 100 PbO PbFz (mol%) Pb5 Fig. 6. Variation of the normalized area under the principal absorption of all the three edges with composition. These areas for PbO and PbF, are also marked in the figure. x , L, edge; A, L, edge and 0, L, edge. As the PbF, concentration increases we should expect an increase in ionicity of bonding, and the structure of [PbO,F,] units should undergo a continuous shape modification.The evolution of symmetry of [PbO,F,] units may be visualized as follows. Initially the two longer (weaker) Pb-0 bonds" in PbO are broken to accommodate the newly introduced Pb atoms from added PbF,. Fluoride ions from the added PbF, would now surround the Pb atoms generating the [PbO,F,] octahedra. Such octahedra in the PbF,-poor compositions can possess only C, symmetry because the initial 0-Pb-0 bond angle is close to a right angle. At high concentrations of PbF,, however, an average Pb-0 bond becomes more ionic, the 0-Pb-0 angle opens up into a large obtuse angle, the fluoride ions readjust their position and the symmetry around the lead atom increases to CZv. At much higher concentrations of PbF,, the ionicity of the Pb-0 bond becomes even higher, and the 0-Pb-0 units can become almost linear.This allows a rearrangement of the octahedra into considerably more symmetrical, more tightly packed [PbO,F,] units of D,, symmetry. Since oxygen and fluorine ions possess similar nephelauxetic character,39 and also since their sizes are nearly equal (0,- and F- ions may be treated as indistinguishable in the ionic limit), the [PbO,F,] unit may be considered as an octahedral unit of Oh symmetry. The evolution of the geometry of the [PbO,F,] units suggested in this work is indicated in fig. 7. The assertion that the geometry of high-PbF, glasses becomes highly packed is supported by our EXAFS investigations. l5 Molecular-orbital Approach and XANES Tentative MO diagrams relevant to bonding in [PbO,F,] units in different geometries are presented in fig.8. It has been assumed in drawing the MO schematics that only the 2p orbitals on the fluorine and oxygen atoms are important for ligand bonding and that they are of similar energies. The 6s, 6p and 6d orbitals of Pb are all assumed to be required in bonding. Note that the 6d orbitals of Pb must be utilized in order to account for bonding to six ligands and in order to conform to the symmetry requirements in the various geometries. Further, 6p and 6d levels of Pb atoms are ca. 8 and 1 1 eV above itsTable 1. Absorption peak energies a and their widths for the absorption features in the L,, L, and L, edges absorption absorption absorption compound or glass half-width/eV energy/eV half-width/eV energy /eV half-width/eV energy/eV PbO 5.56 0 6.0 -8.8, 0, 8.8 8.6 -7.1, 0.0, 11.5 80 PbO : 20 PbF, 6.18 0 7.7 -8.8, 0, 8.8 8.2 -7.7, -0.6, 10.3 60 PbO : 40 PbF, 6.14 0 6.4 -8.8, 0, 8.8 8.4 - 10.3, - 1.3, 9.0 50 PbO : 50 PbF, 6.00 0 6.5 -8.8, 0, 8.8 9.1 -8.8, - 1.9, 8.9 40 PbO : 60 PbF, 5.96 0 6.5 -8.8, 0, 8.8 8.3 - 10.3, - 1.9, 7.7 PbF, 5.66 0 6.4 0, 10.5 5.6 2.6, 10.9 a See experimental section, paragraph 3 for the calibration and scaling procedure used.Table 2. Symmetry species of ligand and metal orbitals and of Pb-0 bonds in the four point groups ligand orbitals metal orbitals 2 4 , +A,, +B1, + E u 6s A’(s) A&) A&) 6P A’&, P,) + A”@,) A,@,) + Bl@J + B,@J Eu@, +PJ + A,,@,) 6d A’(+) + A”(dzz) 4 ( d z z ) + B,(d,,) A,,(4+ + 4,(dz2-y2> two Pb-0 bonds A’ + A” A1 +Bl Al, + A,, (2p of 0 and F) 4A’ + 2A“ 3A1 + 2B1 + B, Table 3.The final states for the L,, L, and L, absorptions of Pb in the different point groups L2 L3 point pre-edge principal edge post-edge pre-edge principal edge post-edge group Ll 4a’* 2b: 1 e,* 5a’ (or 6a’, 3a’) 2a’* 4a‘* 3a” (or 6a’, 5a’) a”* 4a1 (or 1 a,, 2b,) 1 b: 26: 2b, (or la,, 4a1) 2a: 4 1 e* lb,,(or le,) a,*, 4 leg (or 1b2,) t 2 , n 00 t 2 , - W U -1788 XANES Spectra of Pb in PbO-PbF, Glasses (C) ( d ) Fig. 7. Geometry of six-coordinated Pb in PbO-PbF, glasses in various symmetries. The symmetry evolves as a function of composition (see text). (a) C,, (b) CZv, (c) D,, and (6) 0,. 0 , Pb; 0, R@' 0 and@, O/F. 6s levels, re~pectively,~' which is not prohibitive for hybridization. Since [PbO,F,]'- units carry 10 valence electrons they are accommodated in the first five molecular orbitals of lowest energy.In table 2 the symmetry species of the metal orbitals in the four point groups are indicated, along with the species designation of the Pb-0 bonds. The metal 6s orbital is assumed to be involved in the formation of the lowest-energy MO. In the C, point group, metal-oxygen bonds which form only a slightly obtuse 0-Pb-0 angle make use of the two p-orbitals hybridized with the 6s orbitals. In C,, symmetry the 0-Pb-0 angle becomes more obtuse and requires the use of hybridized (dxz-pz) orbitals for the formation of one Pb-0 bond and hybridized (s-p,) orbital for the other. In PbF,-rich compositions, where the symmetry of the [PbO,F,] unit becomes D,,, the 0-Pb-0 angle opens out to 180".The two Pb-0 bonds may now be formed using a hybridized (di-s) orbital and a p , orbital of the metal atom. Note also that the axis of symmetry is turned by 90" as we change from the C,, to D,, point group, which accounts for the sudden change of the p-orbital labelling in table 2. We have identified the fourth and fifth molecular orbitals in our bonding scheme as utilizing largely the d orbitals in C, and C,, symmetries. In D,, symmetry the fifth level is one of the degenerate e, orbitals which uses 6p orbitals of Pb. However, since the symmetries in glasses cannot be expected to be perfect, these levels may become non-degenerate, allowing one of the levels to become totally unoccupied, as indicated in fig. 8. In all three symmetries the lowest unoccupied MO is therefore formed from a metal 6p orbital and is energetically well separated from other higher vacant orbitals.The lowest unoccupied metal orbitals of d symmetry are non-bonding in character. In D,, symmetry they are made up of a doublet and a singlet level, whereas in C, and C,, symmetry the non-bonding levels are made up of singlets. It is reasonable to assume further that these non-bonding levels are affected by the ligand field in a higher order of perturbation and to different extents by the coordinating ions. In these three symmetries the non-bonding d levels are separated from the bonding orbitals on the low-energy side of antibonding p orbitals which have the same effective symmetry as d orbitals. Similar antibonding p orbitals are present on the higher-energy side of non-bonding d orbitals in these symmetries.In 0, symmetry the splitting of the levels is quite simple and is generated by a 'bunching up' of several levels of the D,, MO diagram of fig. 8.K. J . Rao, B. G. Rao and J . Wong 1789 6d 3 6P 6s la1 I a** A ---l&J a' Pb 0, F4 Pb 02 5 Fig. 8. Molecular-orbital diagrams of ebO,F,] units in various symmetries: (a) C,, (b) C,,,, (c) D,, and ( d ) 0,. (See text for definition of the symbols.) It is evident that the lowest unoccupied MO level not only has metal p-character, but also is present in the lower three symmetries and is moreover separated from filled orbitals on the low-energy side and from the unfilled orbitals on the higher-energy side. This feature of MO diagrams accounts for the well defined single-peak character of the L, absorption edge of fig.2. The L2,3 edges are due to the transitions to empty orbitals which are of uniformly non-bonding character. Below these non-bonding d orbitals empty antibonding pa orbitals are present in these cases. Since transitions to antibonding pa levels are not forbidden, prominent lower-energy shoulders appear with L2,-edge absorptions. The absorption peak on the higher-energy side of the L2,3 spectra may possibly arise from transitions to antibonding p-type orbitals on the higher-energy side of non-bonding d orbitals. These levels are indicated in table 3 for these symmetries. Thus all the principal features of the L-edge spectra are qualitatively consistent with the MO description. Note also that in the MO diagrams of fig.9 the retention of two Pb-0 bonds and the opening up of 0-Pb-0 bond angle from near 90" in the pyramidal [PbO,] units present in parent PbO to 180" in [PbO,F,] units of D,, symmetry in PbF,-rich glasses appears quite consistent and natural.1790 XANES Spectra of Pb in PbO-PbF, Glasses g Fig. 9. Variation of calculated adsorption coefficient, p, as a function of g , the number of electrons transferred from the metal p orbital to the ligand orbital (in the MO picture shown in fig. 8). The dashed line corresponds to the L, edge and the solid line to the L2,3 edges. The L, absorption is due to the transition 2p,/, --* 6d,/,, while the L, absorption arises from the transition 2p,,, + 6d,,,. Since any of these transitions results in less than half- filled shells, the higher-energy orbitals may be assumed to constitute the d5,, (higher-j] statesg and hence the levels indicated in table 3.We further assume that the non-bonding higher-j orbitals are spatially so directed that they are always more perturbed (the perturbation is, however, only of a higher order). In comparison, the d3/, (lower-I] states are less perturbed by the symmetry changes of the octahedron. We should like to stress that the magnitude of these perturbations is low, and indeed for the L, edge it is insignificant; however, the L, edge is stabilized (see table 1). The energy of the post-edge absorption peak associated with the L, edge decreases as a function of PbF, concentration (fig. 4). This is equivalent to a decrease in the energy gap as a function of the evolution of the symmetry of [PbO,F,] units.Note from fig. 8 that as the symmetry changes from C, to C,, to D,, the energy of one of the p a orbitals increases, crosses that of the da orbitals and rises to the top of the bonding orbitals. The energy of the corresponding antibonding p a orbital is lowered. Since the particular antibonding p a orbital has been identified as the final state responsible for the post-edge absorption, a lowering of its energy is reflected in fig. 4. Since the other p a orbital retains its relative energy with respect to the other bonding orbitals (always being associated with the lower-energy p , orbital in table 2), the corresponding antibonding orbital is essentially unaffected in energy. Since this is the antibonding level responsible for the post-edge peak associated with the L, edge, its energy remains unaffected (fig.4). The pre-peaks also behave roughly similarly. Their origin is attributed to the excitations to antibonding levels formed from metal p orbitals. Corresponding bonding orbitals are unoccupied, as pointed out earlier. While the L, pre-edge behaviour is understandable in the sense that these final states are essentially unaffected, the behaviour of L, pre-edge is difficult to rationalize. At this point we feel that this may be a specific final-state effect which is more stable for higher effective-. states (for electrons excited from 2p,,, levels). The variation of the h.w.h.m. as a function of composition is shown in fig. 5 , which is again consistent with the MO diagrams of fig.8. The L, edge arises from a transitionK. J. Rao, B. G. Rao and J. Wong 1791 to a single discrete p level in all glasses, and the h.w.h.m. values are therefore generally low. L, and L, edges are associated with considerably high values of the h.w.h.m., since the final states possess a spread of energy. When the symmetry evolves to there is a noticeable decrease in the h.w.h.m. values of the L, edge absorption, and this is consistent with the occurrence of a lower-energy (lower--) non-bonding doublet of d levels. The h.w.h.m. values of the L, edges are the largest. Perhaps this is due to the larger spatial extension of the corresponding higher-j orbitals which overlap with similar orbitals of neighbouring [PbO,F,] units and give rise to band-type character.Absorption Intensities and Covalency The absorption intensities have been calculated from areas under the L-edge absorption peaks treating the peaks as Gaussians rather than as Lorentzians. The error introduced by this procedure is likely to be both systematic and low. Since we intend to evaluate only the systematic changes as a function of composition, this procedure is adequate. The variation of the areas is shown in fig. 6 as a function of PbF, content in the glass. The areas decrease systematically as the PbF, content increases, or equivalently as the ionicity of the glass increases, because an average Pb-0 bond can be expected to become more ionic as PbF, content increases. This general feature of a larger white-line intensity in a more covalently bonded situation (such as in a glass) has been noted by us in the studies of Ledges of Nd3+ and Th4+ in the glasses and crystals.21y22 It is gratifying to note that in the present instance a correlation of white-line intensities with ionicity is evidenced in the glassy phase itself, in which the bond ionicity has been varied by varying the composition.Referring to the MO diagrams of fig. 8, an increase in the ionicity amounts to a flow of electrons from the bonding orbitals to the ligands, creating vacancies or decreased density of electrons in the participating metal orbitals. Removal of electrons from the s or p orbitals of Pb unshields the metal p and d orbitals which are the final states for the L-edge transitions. The reduction in shielding affects the final state orbitals, thereby affecting the transition-dipole matrix elements, ( ~ y , ~ 1 ra 1 v 6 d ) and ( vZs I ra I f y 6 p ) ' In general the magnitudes of the matrix elements decrease with a reduction in shielding (see later), and hence the absorption intensity, which is determined by the square of the matrix element, decreases.Therefore, as the PbF, content increases in the glass, the Ledge absorption intensities decrease. We wish to make a semi-quantitative evaluation of this effect by calculating the matrix elements using Slater functions for the I,Y,~, yZp, ~y~~ and ysd orbitals. Assuming that in a perfectly covalent situation, 10 electrons of the first five occupied bonding orbitals (of fig. 8) are equally shared between the metal atom and the ligands, Pb atoms may be formally associated with five electrons; two 6s and three 6p electrons. We can set out to evaluate the absorption coefficient for this situation using the one-electron approxi- mation and with Koopman's theorem.The absorption coefficient, p, is given by4' p = (47~/n) (e2/hc) holMij12 6(Ei - Ej -hm) (2) where Mij = (il ra l j ) is the dipole matrix element connecting the two states (il and lj), S is the Kronecker delta, Ei and Ej are the initial and final state energies, n is the refractive index, o is the frequency of absorption and c is the velocity of light. The states (il and ( j ) correspond to the 2s and 6p levels, respectively, in the case of the L, edge, and to the 2p and 6d levels, respectively, in the case of the L,,, edge of Pb.With Slater functions the j states are not distinguished, and the functions themselves are nodeless. Mij for the L, and L2,, edges are given by1792 Slater functions have the form4, XANES Spectra of Pb in PbO-PbF, Glasses Un,, s Un = rn*-l exp [-(Z-S)r/n*] ( 5 ) where Z is the atomic number and S is the screening constant, which is calculated using Slater's rules.42 For the above (fully covalent) situation, the values of S relevant to 2s/2p, 6p and 6d are 4.15, 77.05 and 79.75, respectively, and the n* values corresponding to the principal quantum numbers 2 and 6 are 2.0 and 4.2, respectively. As the ionicity increases we assume that g electrons are transferred to the ligands. When g = 3 it would leave Pb in the divalent Pb2+ state, and this situation is assumed to be completely ionic. Since the electrons are transferred from the p levels of Pb, the screening constants relevant to the 6p and 6d wavefunctions decrease.The reduction of the screening constant is found to be 0.35g and l.Og, respectively, for the 6p and 6d wavefunctions. Using relatively simple algebra one can show that the transition-dipole matrix elements are given by M i = y(6.2)/(40.472 + 0. log)", (6) and M i = y(6.2)/(39.622 + 0.3 1 3g)6.2 (7) pL1 = (KmLla2)/(bl + c1g)12.4 (8) pL,., = (Ko,2,,a2)/(b2 + c2d12.4 (9) where y(x) are the gamma functions. Therefore p L l and p L , , , can be written as where K , a, b,, b,, c, and c, are constants ( K = 4ne2/nc, a = r(6.2) = 169.41, b, = 40.472, c1 = 0.109, b, = 39.622 and c, = 0.313).p L , and pL, have been evaluated for various values of g and are shown in fig. 9 as a function of g. Note that the nature of the variation of p as a function of g is similar to that of the absorption intensity as a function of the PbF, content in the glass. Thus an increase in the bond ionicity of g causes a decrease of the white-line intensity. It is difficult to make an absolute comparison between the absorption coefficients obtained for various degrees of electron transfer (fig. 9) with absorption intensities shown in fig. 6 obtained as a function of the PbF, content. However, it is instructive to compare the fractional changes occurring in the absorption coefficients of fig. 9 with the fractional variation of absorption intensities of fig. 6. In fig. 9 p changes by ca.10 and 30% for the L, and L, edges, respectively, when bonding becomes completely ionic. In fig. 6 there is a variation of ca. 3.2 and 6.4%, respectively, in the intensities for the L, and L, peaks when the PbF, concentration is changed from 20 to 60 mol% in the the glassy range. If we further make the approximation that the relative changes in the total absorption intensities at the L, and L, edges are directly related to relative changes in p of fig. 9, then the change in the ionicity of the glasses is in the range of 22-32 O/O. Such a change appears to be plausible. The semiquantitative approach made here is admittedly inadequate for at least two important reasons. The first is that Slater functions are nodeless and make no distinction between j states, since they are independent of both 1 and s.Secondly, the 2s and 2p electrons of Pb should be treated in a relativistic framew~rk,~, and no account has been made of this effect. However, it provides a basically sound qualitative explanation of the trend in the variation of absorption intensities as a function of ionicity. Also, the relative magnitudes of the L, and L, absorption intensities from these calculations are quite satisfactory (cf. fig. 6 and 9). L,/L, Absorption Intensity Ratios Another aspect of the XANES spectra which has been discussed in the literature at considerable length is related to the ratio of the L, to L, absorption intensities. We haveK. J . Rao, B. G. Rao and J . Wong 1793 Table 4. Experimental amplitude ratio, L,/L,, and calculated free volume per Pb atom, 5 experimental calculated" amplitude free volume ratio, per Pb atom, glass composition L J L , Y 80 PbO : 20 PbF, 1.304 29.06 60 PbO : 40 PbF, 1.467 30.19 50 PbO : 50 PbF, 1.429 30.48 40 PbO : 60 PbF, 1.492 30.69 a = (M/p-4/3, Nx,r:) 1024/N, where A4 is the experimental molar volume, xi and ri are the mole fraction and the radius of the ion, respectively, and N is the Avogadro number.[See ref. (44) for details.] computed this simply from the ratios of the absorption peak heights in the raw spectra for the various glass samples, and give these data in table 4. These ratios are typically < 1.5 and are higher for more ionic samples. Since they appear to be affected by the ionicity of bonding in the glass, which is a chemical effect, it suggests that the j character at the non-bonded d orbitals varies as a function of ionicity.The larger j states may be considered as having a slightly higher spatial extension (j being considered in place of E in the corresponding spherical harmonics). Conversely, slightly higher volumes are preferred by the high-j non-bonding d orbitals of Pb. In fact the available free volume44 per Pb atom increases with increasing PbF, in the glass (see table 4), which suggests that the 6d states of Pb are perhaps characterized to a greater extent by j = states in PbF,-rich compositions. This accounts for the general increase of the L3/L2 absorption intensity ratio as a function of increasing ionicity . Nevertheless, the ratio is itself considerably lower than the theoretical value of 2.0.It is therefore possible that the initial 2p,,, and 2p,,, populations are effected by the relativistic behaviour of the electrons in the Pb atoms. Conclusions XANES has been employed to study the changes in the nature of bonding in PbO-PbF, glasses. Since the two important features of these glasses are that (a) Pb is present in coordination polyhedra of the type [PbO,F,] in the entire glass-forming range and (b) the nature of bonding changes as a function of composition; the symmetry of [PbO,F,] units changes with the composition, or equivalenty as a function of ionicity from C, to CZv to D,, symmetry. This results from a change from directionally rigid covalent Pb-0 bonds to relatively loose, non-directional ionic bonds, as discussed using plausible MO diagrams.The variation of XANES features, such as pre-edge and post-edge positions etc. is consistent with such an evolution in geometry. The intensities of the L, and absorption peaks (given by areas under the peaks) also vary in a manner consistent with the increasing ionicity of PbF,-rich glasses. The absorption coefficients have been calculated from transition4ipole matrix elements in the one- electron approximation and with Slater orbitals, and have been used to justify the L,3/L2 intensity ratios in the experimental Ledge absorptions. Additionally, these calculations yield an estimate of ca. 22-32 % change in ionicity in the composition range 2MO% PbF,.1794 XANES Spectra of Pb in PbO-PbF, Glasses We are grateful for the experimental opportunity at CHESS which is supported by N.S.F., U.S.A.K.J.R. and B.G.R. thank Prof. C . N. R. Rao for this kind encouragement and D.S.T. India for financial support. Our grateful thanks are also due to a referee for helpful suggestions for improving the manuscript. 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