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Ge Solid-State NMR of Germanium Oxide Materials: Experimental and Theoretical Studies Vladimir K. Michaelis and Scott Kroeker* Department of Chemistry, UniVersity of Manitoba, Winnipeg, Manitoba, R3T 2N2 Canada ReceiVed: July 29, 2010; ReVised Manuscript ReceiVed: October 7, 2010
A comprehensive series of crystalline germanates has been studied by ultrahigh-field 73Ge NMR and quantum chemical calculations. Despite its low gyromagnetic ratio, low natural abundance and large quadrupole moment, interpretable spectra were obtained in almost all cases, demonstrating that 73Ge is an accessible NMR nucleus. The spectra yield a wide range of quadrupole coupling constants (CQ ) 9 to 35 MHz), with calculations indicating a range twice that, which are rationalized principally in terms of the variation in Ge-O bond lengths. The isotropic chemical shifts appear to fall into distinct regions for four-, five-, and six-coordinate Ge, with increasing coordination number corresponding to lower frequencies. Both CASTEP and WIEN2k consistently underestimate the CQs, suggesting that the exchange-correlation functional is poorly optimized for these systems. 73Ge NMR spectra of alkali germanate glasses are broad and featureless, rendering them difficult to interpret in terms of specific structural elements, even with the well understood NMR parameters from the crystalline systems. This study represents the first systematic 73Ge NMR investigation of solids, and shows that valuable structural information can be obtained in favorable cases. 1. Introduction Germanium is used in many materials applications including optical fibers and lenses, catalysts, mesoporous materials, and nanocrystalline semiconductors,1-4 where the lack of periodic longrange order limits diffraction-based structural methods. The characterization of germanium in these systems is far from routine, despite the fact that their physical properties are often determined by local structure.2,5 In principle, germanium nuclear magnetic resonance (NMR) spectroscopy is ideal for studying such effects, as it is sensitive to the local environment of the nucleus of interest. However, the only NMR active isotope (73Ge), suffers from unfavorable NMR properties, and has traditionally been considered an “impossible” nucleus to study in the solid state.6 The nuclear properties of 73Ge include a nuclear spin, I ) 9/2, a low resonance frequency (Ξ ) 3.498, relative to 1H in TMS at 100 MHz), large quadrupole moment (-19.6 fm2) and low natural abundance (7.73%), giving it a receptivity of 1.09 × 10-4 relative to 1H. The quadrupolar interaction in particular can complicate the spectrum, causing significant anisotropic broadening of the line shape and effectively reducing sensitivity. When the Ge nucleus is at a site of cubic symmetry or undergoes rapid isotropic tumbling, sharper peaks may be observed.7,8 However, this is rare in solids, and only a handful of solid-state 73Ge NMR studies have appeared in the literature.9-12 Recently, we demonstrated that the employment of the QCPMG pulse sequence in an ultrahigh magnetic field (21.1 T) enables this nucleus to be studied,9 effectively yielding valuable structural information (e.g., coordination environment, isotropic shift and quadrupolar interaction). Here, we extend our study of germanate phases by investigating a comprehensive series of oxides containing different local structures, coordination environments, and a variety of countercations (with varying charges). This is required to establish trends in NMR properties and lay the groundwork for application of 73Ge NMR to oxide materials. This work is complemented by density functional theory (DFT) calculations of the structural effects and provides benchmarks to add to the growing body of theoretical data on 73Ge NMR.13,14 * Corresponding author. Tel: (204) 474-9335. E-mail: Scott_Kroeker@ umanitoba.ca.
Terminology and Definitions. Central transition (1/2 T -1/2) peak shapes subject to a second-order quadrupolar interaction can be described by the quadrupolar coupling constant, CQ, and the quadrupolar asymmetry parameter, η
CQ ) eVzzQ/h
(1)
η ) (Vxx - Vyy)/Vzz
(2)
where e is the charge of an electron, Q is the quadrupolar moment intrinsic to the nucleus of interest, h is Planck’s constant, and Vnn are eigenvalues of the electric field gradient (EFG), with Vzz being the largest component (Vzz > Vyy > Vxx). A more comprehensive explanation of the quadrupolar interaction in solids can be found elsewhere.15-17 Chemical shielding anisotropy can also influence the spectral appearance. Although its magnitude is negligible compared to that of the quadrupolar interaction in the germanates studied here, these parameters have been calculated and are reported here for completeness. The chemical shift tensor components (δ11 g δ22 g δ33) are calculated from the corresponding calculated shielding constant by
δii ) 106(σref - σii)/(1 - σref)
(3)
where σref represents the calculated shielding of crystalline GeCl4. The isotropic shift is given by
δiso ) (δ11 + δ22 + δ33)/3
(4)
The overall breadth of the tensor is given by the span, Ω, and the relative magnitude of the components by the skew, κ
Ω ) δ11 - δ33
10.1021/jp1071082 2010 American Chemical Society Published on Web 11/10/2010
(5)
NMR of Germanium Oxide Materials
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TABLE 1: Experimental and Calculated 73Ge NMR Parameters for Germanium Oxides experimental material
CN
Bi4Ge3O12 Zr3GeO8 Ca2GeO4 Mg2GeO4 Li4GeO4 PbGeO3 Bi2Ge3O9 GeO2 (quartz) K2Ge8O17
Ga4GeO8 Na4Ge9O20 GeO2 (rutile) GeO2 9 mol% Li2O · GeO2 14 mol% Na2O · GeO2
CQ (MHz)
11.5 ( 0.5 24 ( 1 22 ( 1 26.5 ( 1 12 ( 1 29 ( 1 32 ( 2 9.2 ( 0.5e 8-10d 5 n.d. 4 n.d. 4 n.d. 4 n.d. 6 35 ( 2 4 n.d. 6 n.d. 4 n.d. 6 19.3 ( 0.5e glass e10.5e 8-10d glass
