16499
J. Phys. Chem. 1995, 99, 16499
Symmetry and Cluster Size Effects in XANES Spectra A. Muiioz-Phez*
TABLE 1: Models for Crystalline Ti02 Rutile no. of atoms model Ti 0 no. of shells radius (A). 1
Departamento de Quimica Inorghnica, ICMSE, CSIC, Facultad de Quimica Universidad de Sevilla, P.O.Box 553, 41012 Sevilla, Spain
2 3 4 5
1 11 15 31 31
6 14
36 44 68
1 3 5
1.983 3.569 4.615
I
5.500
9
6.495
" Distance from the absorbing Ti atom to the most distant atom.
M. F. Ruiz-L6pez Laboratoire de Chimie Thtorique, URA CNRS 510 Universiti Henry Poincart Nancy 1 BP 239, 54506 Vandoeuvre-les-Nancy Ctdex, France Received: October 31, 1994; In Final Form: July 19, I995
In a recently published paper presenting a structural study of Ti-silicalite,' X-ray absorption spectroscopies (EXAFS and XANES) are used to identify Ti centers presenting tetrahedral environments. This assignment is made on the basis of qualitative analysis of the XANES region, by comparing it with that of compounds of known structure, and confirmed with the results of the EXAFS data analysis. This analysis, being very cautious, includes only one shell, but the information obtained from it is relevant for the purpose of the article. We agree, in general, with the main conclusions of the article, based upon the use of the XANES spectrum as a fingerprint of structure around Ti atoms. Nevertheless, the explanation given by the authors for the origin of the pre-edge features observed in titanium compounds appears to be rather oversimplified and could lead to misleading conclusions for other systems. Moreover, recent results obtained with elaborate theoretical methods have not been considered in the discussion presented in the Introduction. For instance, using multiple-scattering calculations,2we have analyzed the pre-edge features of anatase and rutile XANES spectra, and we have attributed the extreme sensitivity of the results to long-range order and symmetry. In fact, the pre-edge intensity can be only explained if the true symmetry groups ( D zand ~ D2h for anatase and rutile, respectively) and large cluster size are taken into account. First, one should note that whereas Is 3d transitions are forbidden in centrosymmetric systems, like rutile, some of them are allowed in anatase (to b2 and e 3d orbitals). Hence, one can hardly analyze the experimental data for these systems by assuming an octahedral symmetry, as suggested by Bordiga et al.' In addition, the pre-edge features in the XANES spectra of anatase and rutile have been shown to be connected to longrange effects.2 The interaction of the p orbitals of the central Ti atom with d orbitals of neighboring Ti atoms is at the origin of the transitions observed. It depends, among other factors, on the Ti-Ti distances, so that the intensity of the pre-edge can be roughly related to the value of these distances. The dependence of the XANES on long-range effects is illustrated in ref 2, Figure 1, where the results of the analysis of the cluster size on the computations of the Ti-K edge of
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* To whom correspondence ADELA @CICA.ES.
should
be
addressed.
E-mail:
0022-3654/95/2099-16499$09.0010
TiO2-rutile are shown. To carry out these computations, the cluster has been defined as formed by one Ti atom (the absorbing atom) surrounded by a given number of neighboring atoms for which the distance to the central Ti atom is shorter than a given value. The basic unit is a deformed octahedron with two different Ti-0 distances, four Ti-0 at 1.946 A and two Ti-0 at 1.984 A. The symmetry group is D2h. The computations of models 1-4 (described in Table 1) have been carried out using simple X u potential. Once the minimum number of atoms to be included in this cluster has been determined, the more elaborate Dirac-Hara potential is used. The spectrum calculated with this new potential and the experimental one are included in Figure 3 of ref 2. In the computations using the X u potential, it has been observed that 5 1 atoms (model 3) should be included in the cluster model to reproduce all the spectral features, whose intensity, however, may still be modified by further shells. A good convergence is obtained for 75 atoms, a model that includes all atoms lying within a radius of 5.5 A. Thus, one can consider that scattering paths of total length greater than about 11 A contribute little to the absorption. Small pre-edge features are observed for model 2, but these features appear clearly only in model 3 and above, and their intensities are quite sensitive to the number of atoms considered. No trace of them appears in model 1, which considers the absorbing Ti atom and six neighboring oxygen atoms at 1.983 A. Moreover, other excitation mechanisms could lead to 1s 3d allowed transitions (see ref 2 and references cited therein) although their intensity is expected to be small. Finally, one should note that although in the analysis of the XANES region the maxima can be associated with electronic transitions of the absorbing atom, as well as with other atomic effects, the so-called AXAFS3multiple scattering phenomena substantially contribute to the total absorption ~oefficient.~ In general, the shape of these MS contributions depends on the radial distribution and on the symmetry of the whole system. Therefore, they should be taken into account to correctly describe the experimental spectra of Ti oxide compounds, which still deserve further theoretical investigations.
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References and Notes (1) Bordiga, S.; Colucia, S.; Lambed, C.; Marchese, L.; Zecchina, A,; Boscherini, F.; Buffa, F.; Genoni, F.; Leofanti. G.; Petrini, G.; Vlaic, G. J . Phys. Chem. 1994, 98, 4125. (2) Ruiz-Lboez. M. F.: Muiioz-PBez. A. J . Phvs.: Condens. Matter 1991.3. 9881. (3) Rehr. J. J.; Zabinskv, S. I.; Ankudinov, A.; Albers, R. C. Phvsica
B 1995, 208-209, 23. (4) Benfatto, M.; Natoli, R. C.; Bianconi, A,; Garcia, J.; Marcelli, A,; Fanfoni, M.; Davoli, I. Phys. Rev. B 1986,34, 5774. JP942927P
0 1995 American Chemical Society
