American Mineralogist, Volume 85, pages 732–738, 2000
Bonding in alpha-quartz (SiO2): A view of the unoccupied states LAURENCE A.J. GARVIE,1,* PETER REZ,2 JOSE R. ALVAREZ,2 PETER R. BUSECK,1,3 ALAN J. CRAVEN,4 AND RIK BRYDSON5 1
Department of Geology, Arizona State University, Tempe 85287, U.S.A. Department of Physics, Arizona State University, Tempe 85287, U.S.A. 3 Department of Chemistry/Biochemistry, Arizona State University, Tempe 85287, U.S.A. 4 Department of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, U.K. 5 Department of Materials, School of Process, Environmental and Materials Engineering, University of Leeds, Leeds LS2 9JT, U.K. 2
ABSTRACT High-resolution core-loss and low-loss spectra of α-quartz were acquired by electron energyloss spectroscopy (EELS) with a transmission electron microscope (TEM). Spectra contain the Si L1, L2,3, K, and O K core-loss edges, and the surface and bulk low-loss spectra. The core-loss edges represent the atom-projected partial densities of states of the excited atoms and provide information on the unoccupied s, p, and d states as a function of energy above the edge onset. The band structure and total density of states were calculated for α-quartz using a self-consistent pseudopotential method. Projected local densities of Si and O s, p, and d states (LDOS) were calculated and compared with the EELS core-loss edges. These LDOS successfully reproduce the dominant Si and O core-loss edge shapes up to ca. 15 eV above the conduction-band onset. In addition, the calculations provide evidence for considerable charge transfer from Si to O and suggest a marked ionicity of the Si-O bond. The experimental and calculated data indicate that O 2p-Si d π-type bonding is minimal. The low-loss spectra exhibit four peaks that are assigned to transitions from maxima in the valence-band density of states to the conduction band. A band gap of 9.65 eV is measured from the low-loss spectrum. The structures of the surface low-loss spectrum are reproduced by the joint density of states derived from the band-structure calculation. This study provides a detailed description of the unoccupied DOS of α-quartz by comparing the core-loss edges and low-loss spectrum, on a relative energy scale and relating the spectral features to the atom- and angular-momentum-resolved components of a pseudopotential band-structure calculation.
INTRODUCTION Silica is an important material from both the geological and the materials science points of view. Amorphous SiO2 is vital to the electronics and glass industries, and crystalline varieties are important as precision oscillators and dielectric materials. Hence, considerable effort has been devoted to the study of this material. The bonding and valence bands of α-quartz are well understood from band-structure (Chelikowsky and Schlüter 1977; Xu and Ching 1991; Simunek et al. 1993; Di Pomponio et al. 1995) and molecular-orbital (Tossell 1973, 1975) calculations. These calculations were used to interpret X-ray photoelectron and emission spectra (XPS and XES) from α-quartz (e.g., Tossell 1975; Simunek et al. 1993). The conduction-band structure is not nearly as well understood. This lack of understanding is in part caused by the theoretical limitations in modeling the higher-lying conduction-band states and, up to now, experimental difficulties in probing these states at high-energy resolution.
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[email protected] 0003-004X/00/0506–732$05.00
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Electron energy-loss (EELS) spectroscopy is efficient for studying unoccupied states because inner-shell electrons are excited into unoccupied states in the conduction band. Because the inner-shell states have well-defined energy and angular momentum, EELS probes the variation in the angular-momentum-resolved density of conduction-band states at a particular atomic site weighted by an appropriate squared matrix element. The matrix element represents the probability of a transition from the initial state in the inner-shell level to a final state in the conduction band. When the dipole approximation is used for the evaluation of the matrix elements, dipole selection rules apply, and the angular and energy dependence of scattering for cubic materials is described by the double differential cross section (Weng et al. 1989)
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d 2σ 4γ 2 2 2 = 2 2 m l + 1 ρl + 1 ( E ) + m l − 1 ρ l − 1 ( E ) dE dΩ a 0 q
where ρl±1(E) is the localized density of states, with angular momentum quantum number l at energy E, γ = (1–v2/c2)1/2 is the relativistic correction, ml±1 are the matrix elements to states of angular momentum l ± 1, a0 = 0.529 × 10–10 m is the Bohr radius, and q is the momentum transfer.
GARVIE ET AL.: EELS OF QUARTZ
All core-loss edges of SiO2 are accessible by EELS, i.e., the Si L1, L2,3, and K edges and the O L1 and K edges. These edges represent transitions from core states to unoccupied states above the band gap. Close to the edge onset and for small scattering vectors, the transitions that give rise to the core-loss edge are governed by the atomic-dipole selection rules for electronic transitions Δl = ±1, and Δj = 0, ±1, where l and j are the orbital and total angular momentum quantum numbers of the excited electron’s subshell. The K and L1 edges probe unoccupied plike states whereas the L2,3 edge probes unoccupied s- and dlike states. In addition, the plasmon region is accessible and provides information regarding the bulk electron density, valence- to conduction-band transitions, and on the magnitude of the band gap. Interpretation of the core-loss, near-edge structures can be undertaken via a number of methods at differing levels of approximation (Brydson 1991; Rez 1992; Rez et al. 1995; Egerton 1996). The simplest is to relate changes among spectra with a knowledge of the local coordination symmetry and valency, the ‘fingerprint’ technique (Brydson et al. 1992; Garvie et al. 1994, 1995a, 1995b; Garvie and Buseck 1998, 1999; Poe et al. 1997; van Aken et al. 1998). Another method of interpretation is from theoretical calculations such as molecular orbital (MO), multiple scattering (MS) (Wu et al. 1998), or band-structure methods (Brydson 1991; Rez 1992, Rez et al. 1995). The occupied states of α-quartz were calculated many times using a range of methods, [e.g., see review by Cohen (1994)], although these studies mainly concentrate on the valence states. Previous investigations of the unoccupied states have almost exclusively dealt with selected spectra only, (e.g., Nithianandam and Schnatterly 1988; McComb et al. 1991; Lagarde et al. 1992; Bart et al. 1993; Li et al. 1993, 1994a; Garvie and Buseck 1999), and only the study of Wu et al. (1998) considers the Si L2,3, K, and O K edges together. In no studies have all edges been shown together so as to provide a complete description of the unoccupied states. A further difficulty is that previous theoretical studies do not show the complete sets of data required to interpret the EELS data. The unoccupied states of SiO2 were interpreted with the results of MO (Hansen et al. 1992; Li et al. 1993; Tanaka et al. 1995), band-structure (Gupta 1985; Xu and Ching 1991; Jollet and Noguera 1993), and multiple-scattering (Davoli et al. 1992; Jollet and Noguera 1993; Hansen et al. 1992; Wu and Seifert 1996; Wu et al. 1996, 1998) calculations. Using the MO method, ELNES features are assigned transitions between occupied and unoccupied states in a MO diagram for that species. The antibonding MOs for the SiO4– 4 tetrahedron are 6t2 (plike), 6a1 (s-like), 2e (d-like), 7t2 (d-like), and 7a1 (s-like) (Tossell 1975, 1976). McComb et al. (1991) reversed the positions of 6t2 (p-like) and 6a1 (s-like) and assigned peak A to states with 6a1 and peak B to states with 6t2 character, respectively. The MS method and self-consistent, embedded-cluster calculation successfully reproduces the main Si K ELNES (Jollet and Noguera 1993). Molecular-orbital methods, using small cluster sizes, are not usually sufficient for interpreting core-loss ELNES because these calculations do not usually include long-range effects. For example, a cluster comprising 109 atoms was required to simulate the Si K edge of quartz using the MS method (Wu et al. 1998). In addition, comparison of
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the Al and Si L2,3 and Al, Si, O, and F K core-loss edges of topaz illustrates the influence of neighbor effects and mixing of unoccupied states (Garvie and Buseck 1999). This mixing illustrates the limitations of ab initio methods that model coreloss edges and neglect non-nearest-neighbor interactions. Therefore, we present and compare high-resolution coreloss and low-loss EELS spectra of α-quartz with local densities of states (LDOS) calculated by the pseudoatomic orbital method. By comparing different spectra from the same material, we infer information on the unoccupied states and on the nature of the Si-O bond.
MATERIALS AND METHODS The O K and Si L2,3 spectra were acquired with a Gatan 666 parallel electron energy-loss spectrometer (PEELS) attached to a VG HB5 scanning transmission electron microscope (STEM) equipped with a cold field-emission gun (FEG). The normal working current was 0.2 nA, energy resolution of 0.4 eV, probe semiangle of 8 mrad, and collection semi-angle of 12 mrad (which is well within the region for dipole-allowed transitions). The experimental setup is described in more detail in Garvie et al. (1994). The low-loss data and Si L1 edge were acquired using a Philips 400ST-FEG TEM with a Gatan 666 PEELS spectrometer. The TEM was operated with a cold FEG, at 100 keV, probe current of ca. 10 nA, a probe semiangle of 6 mrad, a collection semiangle of 5.5 mrad, and a resolution of 0.7 eV. Spectra were acquired in diffraction mode (spectrometer is image coupled), with a camera length of 92 mm. The experimental setup is described in more detail in Garvie and Buseck (1999). Alpha-quartz is beam sensitive so we took particular care to acquire data free of beam-damage artifacts. Initial changes in the energy-loss near-edge structure (ELNES) of the coreloss edges of α-quartz were observable after doses of > 5 × 103 e/Å2 for a thickness of ca. 0.4 × mean free path (MFP). Several spectra were acquired from separate areas on the same thin area, and these spectra were subsequently summed to provide data with a good signal-to-noise ratio. Channel-to-channel gain variations were minimized by acquiring a series of spectra with each spectrum shifted prior to acquisition by ca. 0.5 eV relative to the previous spectrum. Before processing, the shifted spectra were realigned. Bulk low-loss spectra were acquired from thin regions of sample, typically
