491
2007, 111, 491-495 Published on Web 01/03/2007
39K
NMR of Solid Potassium Salts at 21 T: Effect of Quadrupolar and Chemical Shift Tensors Igor L. Moudrakovski* and John A. Ripmeester Steacie Institute for Molecular Sciences, National Research Council, Ottawa, Ontario, Canada K1A 0R6 ReceiVed: October 16, 2006; In Final Form: NoVember 21, 2006
39K
Solid State NMR spectra (static and magic angle spinning (MAS)) on a set of potassium salts measured at 21.14 T show that the chemical shift range for K+ ions in diamagnetic salts is well in excess of 100 ppm contrary to previous assumptions that it was quite small. Inequivalent potassium sites in crystals can be resolved through differences in chemical shifts, with chemically similar sites showing differences of over 10 ppm. The quadrupolar coupling constants obtained from MAS and solid echo experiments on powders cover the range from zero for potassium in cubic environments in halides to over 3 MHz for the highly asymmetric sites in K2CO3. Although the quadrupolar effects generally dominate the 39K spectra, in several instances, we have observed subtle but significant contributions of chemical shift anisotropy with values up to 45 ppm, a first such observation. Careful analysis of static and MAS spectra allows the observation of the various chemical shift and quadrupole coupling tensor components as well as their relative orientations, thereby demonstrating that high-field 39K NMR spectroscopy in the solid state has a substantial sensitivity to the local environment with parameters that will be of considerable value in materials characterization and electronic structure studies.
Introduction Potassium is one of the most important light elements in inorganic and biological chemistry, and potassium ions play a crucial role in stabilization of biological assemblies and in life processes. Until very recently, 39K NMR has seen very few applications in the solid state because of difficulties in obtaining spectra, as both isotopes, 39K and 41K (natural abundance of 93.7 and 6.3%, respectively), are spin-3/2 quadrupolar nuclei with low magnetogyric ratios (absolute resonance frequencies of Ξ ) 4.6664 MHz for 39K and Ξ ) 2.5613 MHz for 41K). The total number of publications involving the more easily observed 39K nucleus is relatively small and involves results on potassium halides (cubic lattice ) zero quadrupole interactions), several studies of single crystals,1-5 and powders.6-10 Most of the studies were performed in magnetic fields of intermediate strengths of 7-11 T, with a single study reporting 39K NMR in some minerals at 21 T.11 Two recent high-field studies (19.6 T) were devoted to examination of potassium tetraphenylborates12 and the detection of potassium cations bound to G-quadruplex structures found in telomeric DNA.13 Several other publications have used 39K as a testing ground for sensitivity enhancement techniques.14,15 Depending on the local environment, the observed quadrupolar coupling constants for the potassium cation have values up to about 2 MHz.6-8 Larger quadrupole constants for 39K in a range of 2.5-4.7 MHz have been observed so far only in polymeric potassium metallocenes with very low symmetry of the K environment.16 The chemical shift range of potassium * Corresponding author. Fax:
[email protected].
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compounds is largely unknown, as only a few values have been reported and there are no reports at all on the chemical shift anisotropy. Generally, it was assumed that for a light alkali metal such as potassium the range of the chemical shifts is small and that the contribution of the chemical shift anisotropy (CSA), at least at moderate magnetic fields, is negligible.7,16 Difficulties in the accurate determination of the 39K CSA were discussed in ref 12. There are numerous examples of the use of alkali metals, especially potassium, as promoters of catalysts of all kinds;17-25 however, often, recourse is taken to substitute potassium with either sodium or rubidium in NMR studies, as the relevant properties of 39K as a useful nucleus remain unknown, or are known to be difficult to obtain at magnetic fields commonly available. For similar reasons, the use of 39K NMR spectroscopy in ion channel studies remains almost completely in the realm of solution studies. In this work, we report the results of a solid state 39K NMR study in a series of potassium compounds at a magnetic field of 21 T. At this very high magnetic field, the effects of quadrupolar interactions are reduced significantly and the sensitivity and accuracy in determining chemical shifts and quadrupolar coupling parameters improve dramatically.26,27,35 We demonstrate that the chemical shift range of potassium in diamagnetic compounds is rather large at over 100 ppm for K+ alone. The quadrupolar effects dominate the 39K spectra of potassium cations in noncubic environments, but in several instances, we have also observed a significant contribution of the chemical shift anisotropy. A complete analysis of the observed powder patterns has allowed the evaluation of the electric field gradient and the chemical shift tensors including their relative orientations. This is the first experimental observation of the CSA in potassium.
Published 2007 by the American Chemical Society
492 J. Phys. Chem. B, Vol. 111, No. 3, 2007 Experimental Section Materials. All materials used in this work were purchased from Aldrich, and with the exception of KOH, they were used as received. Commercially available potassium hydroxide normally contains up to 15-20% water and can be easily contaminated by carbon dioxide from the air. To reduce the risk of contamination and remove the water, KOH was prepared by heating semiconductor grade KOH from Aldrich in a Pt crucible under dry nitrogen gas to above the melting point (679 K). All moisture-sensitive samples were packed into spinners or sample tubes in a glovebox in an atmosphere of dry Ar. NMR Measurements. The 39K spectra were obtained at a resonance frequency of 42.01 MHz on a Bruker Avance-900 instrument (magnetic field of 21.14 T) at the National UltraHigh Field NMR Facility for Solids in Ottawa. The magic angle spinning (MAS) experiments were performed using Bruker single-channel 7 and 4 mm low-γ probes with dry nitrogen as a carrier gas. A simple single-pulse sequence was used to acquire the MAS spectra. The solution π/2 pulses were 12 µs (7 mm probe) and 6 µs (4 mm probe), and the corresponding solid π/2 pulses were 6 and 3 µs. The preacquisition delay prior to collection of the data was 5 µs. Static powder spectra were obtained on a home-built 5 mm solenoid probe. A spin-echo pulse sequence was used with the pulses optimized to reproduce the powder line shapes accurately.28 Between 24 and 600 scans were acquired with relaxation delays ranging from 1 to 40 s. The optimal relaxation delays for each compound were found from three to four short (eight scans) runs and are listed in Table 1. All spectra were referenced to a 1 M solution of KCl. Spectral Simulations. Spectral simulations were performed using the DMFit program.29 For multiple interactions such as chemical shift anisotropy and quadrupolar interactions, the program utilizes the QUASAR module.30 In all simulations, we first fitted the MAS spectra, which provided the isotropic chemical shifts, δi, quadrupolar coupling constants, CQ, and quadrupolar asymmetry parameter, ηQ. These parameters were subsequently used in simulations of static powder patterns. Special attention was given to reproducing the spectral discontinuities and shoulders in fitting the spectra. Results and Discussion Both MAS and static spin-echo spectra were recorded for all materials studied. Using MAS allows for a greater accuracy in determining the chemical shifts and quadrupolar parameters. At the same time, all of the chemical shift anisotropy information and/or dipole-dipole interactions is almost completely removed. The information on the anisotropy and the relative orientation of the CS and electric field gradient (EFG) tensors can be obtained by fitting the static spectra with a model accounting for both chemical shift anisotropy and quadrupolar interactions.31 Some representative spectra obtained in this work along with corresponding simulations are shown in Figures 1 and 2. The experimental results on electric field gradient and chemical shift tensors obtained from 39K solid state NMR are summarized in Table 1. Acquiring the spectra at such a high magnetic field reduces dramatically the effects of the quadrupole interactions on the spectra and provides a remarkable increase in the sensitivity. Most of the spectra can be acquired with very good signal-tonoise ratio in under half an hour. No sensitivity enhancement techniques such as QCPMG or DFS/RAPT were necessary, thus simplifying setup experiments significantly and providing
Letters accurate line shapes very well suited for simulation and fitting. Use of MAS gives appreciable line narrowing by averaging the dipole-dipole interactions and anisotropy of the chemical shifts. The second-order quadrupolar interactions, however, only partially averaged by MAS, and fitting the spectra allows the extraction of accurate isotropic chemical shifts, quadrupolar coupling constants, and quadrupolar asymmetry parameters. These then can be further used in the fitting of the static spectra, thus reducing the number of variables in the simulations of static spectra. On the basis of the magnitude of quadrupolar interaction, the potassium salts studied can be separated into two distinct groups. The first group has the potassium cation in a symmetrical cubic environment and includes four potassium halides and KCN. The static spectra for these salts demonstrate single symmetric peaks residing on the top of broader, less intense and featureless pedestals. The MAS spectra show up as very sharp symmetrical signals, with the narrowest being only 18 Hz for KCN. Relatively intense spinning sidebands in the MAS spectra are observed for every compound in this group, indicating incompletely averaged quadrupolar interactions. The intensities and the span of the sidebands provide an estimate of the residual CQ’s,26 which fall in the range 15-25 kHz. If originating from specific sites in the crystal structure, quadrupolar interactions on this scale would result in easily observable singularities from the 3/2 T 1/2 and -3/2 T -1/2 satellite transitions in the stationary spectra. Since no such singularities were observed, we attribute the observed spinning sidebands to the defects in the crystals inducing nonzero EFGs. In the stationary spectra, these defects appear as the aforementioned pedestals under the narrow signals. The quadrupolar constants for the potassium sites in nondefect sites for the discussed materials are all very close to zero. Dynamic processes in the crystals can also be responsible for partially averaged quadrupolar and chemical shift interactions, at least in some materials. In the case of KCN, a fast reorientation of rather anisotropic CN- ions, as suggested by some neutron studies,28 could result in an averaged EFG as in a cubic environment. Among all compounds studied, the most prominent spinning sidebands were observed for KNO2. For this compound, they arise from the satellite transitions detectable also in the static spectrum. High sensitivity of the spinning sidebands in KNO2 to the magic angle setting combined with a relatively short relaxation time and high intensity of the signal make this compound a good reference sample for magic angle setting on 39K. All of the salts in the second group have potassium in a nonsymmetrical environment with different degrees of asymmetry which results in prominent quadrupolar coupling with constants in the range from about 0.7 to over 3 MHz. For the series of compounds studied, the largest quadrupolar constant observed was 3.26 MHz, associated with one of the two sites in anhydrous K2CO3. So far, this is the largest quadrupole constant observed in inorganic potassium salts. The second potassium site in potassium carbonate has a quadrupole coupling constant of only 1.05 MHz. The quadrupolar parameters for K2CO3 reported earlier7 are markedly different from those reported here. The difference is likely because the previous study involved a hydrated rather than an anhydrous salt. For the quadrupolar parameters reported here, this is the only notable disagreement with previously reported data. Previously, 39K chemical shifts have been reported only in two diamagnetic potassium salts with nonzero quadrupolar interactions, namely, KVO3 and K2MoO4.14 The values were
Letters
J. Phys. Chem. B, Vol. 111, No. 3, 2007 493
TABLE 1: Electric Field Gradient and Chemical Shift Tensor Data for a Series of Potassium Salts Obtained from 39K Solid State NMR compound KF KCl KBr KI KCN KNO2 K2(CO2)2×H2O K2(CH2CO2)2×1/2H2O KCO2CH3 KClO3 KBrO3 KClO4 KIO4 N.D. KNO3 KAl(SO4)2×12H2O KSCN K2SO4
KHCO3 K2CO3
K2MoO4
K2CrO4 KMnO4 KH2PO4 KOH KVO3 K2S2O8
δia (ppm)
CQb (kHz)
22.4 22.6 47.7 47.8 55.4 55.1 59.4 59.3 35.1 -5 N.D. 0.8 SI 15.0 SII 0.0 18.7 12.2 N.D. -2.8 N.D. -20.2 4.9 300 -12.8 N.D. -18.3 16.7 N.D. SI -4.5 SII 9.5 SI N.D. SII N.D. 6.6 N.D. 29.2 8 N.D. N.D. -8.8 -13.7 -9 ( 5 10 ( 5 SI -13.6 SII -29.4 -63.5 6.2 N.D. 53 N.D. -19.1 -31 ( 5 -9.9 N.D.
∼0 N.D. ∼0 N.D. ∼0 N.D. ∼0 N.D. ∼0 66 56 1248 1710 1740 1790 966 980 962 952 (970) 718 295 ∼0 1328 1322 1916 636 690 950 866 950 866 1490 1490 1050 3260 1536 1546 2130 2168 2190 2320 815 1830 1190 1694 1694 1646 1680 2440 2440 1245 1270
ηQc
∆δd (ppm)
0.2 0.49 0.7 0.55 0.05 0.69 0.71 0 0 0.3 0.15 7 0.17 0.17 0 0.7 0.64 0 0.95 0 0.95 0.25 0.24 0.65 0.25 0.86 0.83 0.34 1 0.32 0.97 1 0.75 0.63 0 0 0.14 0.1 0.81 0.8 0.49 0.57
ηCSAe
Rf
βf
γf
d1g (s)
0
20
0
30
0
30
0
30
0 0
3 1
-13 23.4 20 ?e -8 N.D. 11 -8.2 0 0 N.D. 0 -12.6 N.D. 11 6.2 N.D. N.D. 0 N.D. 0 0 N.D. N.D. -37 52 N.D. N.D. -41 -17 -45 ?e ND 0 N.D. 0 N.D. 10 N.D.
0.8 1 1 ?e 1
71 -5 1 ?e 13
45 70 70 ?e 32
9 20 30 ?e -10
10 10 1.5 15
0
0
0
0
10
0.6
87
35
82
20 20
0 0.4
0 87
0 74
0 3
5 20
0.7 1
8 59
26 30
9 10
15
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0
0
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0
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0 0
0 0
0 0
0 0
20
this work 7 this work 7
0.1 0.5
53 75
22 31
66 0
10
this work 14
0.1 1.0 0.1 ?e
-25 0 90 ?e
15 70 90 ?e
40 0 70 ?e
10
this work
10 15
0
0
0
0
10
0
0
0
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this work this work 8 this work 7 this work 14 this work 8
5
a Isotropic chemical shifts from MAS experiments (this work) or from the static spectra simulations (cited works). The experimental errors for the MAS data are better than 0.2 ppm. b Quadrupolar coupling constants from MAS experiments. The accuracy in most cases is better than (25 kHz and is not more than (50 kHz for the largest quadrupolar coupling constants. c Quadrupolar asymmetry parameter from MAS experiments. The accuracy is better than (0.05. d Components of the chemical shift tensor are defined according to the Haeberlen-Mehring-Spiess convention.31-33 e No satisfactory fit can be obtained. The reason for this could be unaccounted in the fit dipole-dipole interaction. f R, β, γ: Euler angles defining the relative orientation of the CSA and EFG tensors.31,36 The accuracy is expected to be (10° or better. g Shortest relaxation delay when no saturation was observed.
obtained from fitting the QCPMG data and should not be expected to be very accurate. The error for the isotropic shifts was set at (5 ppm,14 which likely is an underestimate. In both instances, the values cited deviate substantially from our values obtained from the MAS measurements, yielding more precise isotropic chemical shifts. The total span of the isotropic chemical shifts observed in the materials studied is more than 120 ppm, ranging from nearly +60 to less than -60 ppm. Several of the materials are known to have more than one distinct crystallographic site for potas-
sium, which can be easily distinguished in the MAS spectra. Considering that all of the materials are salts and potassium in each case is in its cationic state and a diamagnetic environment, it is a rather large range of the chemical shift. One can clearly see that with the use of very high magnetic fields the chemical shift of 39K has good potential as an analytical tool. With such a broad range of isotropic chemical shifts, one may well expect that 39K shielding will also have an anisotropic component. So far, there have been no reports on the experimental observations of the CSA in 39K and it was generally
494 J. Phys. Chem. B, Vol. 111, No. 3, 2007
Letters
Figure 1. Static and MAS (5 kHz) 39K NMR spectra of KCN (a, a′), KNO3 (b, b′), and KAl(SO4)2×12H2O (c, c′). Traces b′′, c′′ and b′′′, c′′′ are the fits to the experimental static and MAS spectra.
Figure 2. Experimental and simulated solid state 39K NMR spectra of potassium salts with two potassium sites and one potassium site: anhydrous K2CO3 (left), K2S2O8 (middle), and K2(CO2)×H2O (potassium oxalate) (right plate). a, a′: experimental 39K MAS (16 kHz) spectrum of K2CO3 and its respective fit. b: experimental static 39K spectrum of K2CO3. b′: simulation for spectrum b accounting only for quadrupolar interactions (CQ and ηQ are from the fit of the MAS spectrum). c, c′: experimental 39K MAS (7 kHz) spectrum of K2S2O8 and its respective fit. d: experimental static 39K spectrum of K S O . d′′: simulation for spectrum d accounting only for quadrupolar interactions (C and η are from the fit of the MAS 2 2 8 Q Q spectrum). d′: fit to spectrum d accounting for the quadrupolar interactions and the chemical shift anisotropy. e, e′: experimental 39K MAS (7 kHz) spectrum of K2(CO2)×H2O (potassium oxalate) and its respective fit. f: experimental static 39K spectrum of K2(CO2)×H2O. f′′: simulation accounting only for quadrupolar interactions (CQ and ηQ are from the fit of the MAS spectrum). f′: fit to spectrum f accounting for the quadrupolar interactions and the chemical shift anisotropy. Dotted lines indicate singularities in the experimental spectra and their correspondence in the simulated spectra.
assumed that anisotropic shielding was negligible.7 These assumptions, however, were based on measurements in a field of only 9.4 T, where the quadrupolar interactions clearly dominated. The situation is drastically different in a field of 21.14 T, with the quadrupolar interactions scaled down and the chemical shifts scaled up by more than factor of 2. Indeed, static spectra of many of the materials studied plainly demonstrate some features that can be attributed to a significant CSA. Figure 2 shows examples of static spectra, demonstrating the effect of CSA, along with spectra taken with MAS and
simulated powder patterns. The magnitudes of the observed CSAs range from about 10 to over 50 ppm, with the largest anisotropies observed in the salts of transition metals, such as potassium chromate, molybdate, and permanganate. In a number of cases, it was possible to perform a complete analysis of the observed powder patterns, yielding the magnitudes of the electric field gradient and chemical shift tensor components and their relative orientations.31 As one can see from Table 1, only in one case (KBrO3) do the orientations of the CSA and EFG tensors coincide. Quantum chemical calculations of the chemical
Letters shift and EFG tensors in potassium salts are currently in progress, and the results will be the subject of forthcoming publications. One complication in recording 39K spectra of the studied materials is the relatively long transverse relaxation times. The estimated T1’s range from 0.5 to over 10 s, and the minimum required relaxation delays are summarized in Table 1. Although the quadrupolar relaxation mechanism, commonly resulting in short T1’s, is expected to dominate in the materials studied, motions with appropriate correlation times to give effective relaxation are absent. Nevertheless, even with these long relaxation delays, the increased sensitivity allows for very high quality spectra to be obtained in short time. Conclusions We have surveyed the 39K NMR properties of the potassium cation in a series of its diamagnetic salts at a very high magnetic field of 21.14 T. Acquiring the spectra at such a high magnetic field dramatically improves sensitivity and spectral resolution. In most cases, spectra with very good signal-to-noise ratio could be obtained under 1 h. The quadrupole coupling constants up to 3.28 MHz were observed. The range of the chemical shifts has been found to be substantially wider than it was previously assumed and spans between about -60 and +60 ppm. For the first time, the anisotropy of the chemical shift was experimentally observed for 39K. The magnitudes and the relative orientations of the electric field gradient and the chemical shift tensors were obtained from the fits of 39K spectra of powders. Acknowledgment. The authors thank Mr. James Bennett for expert technical assistance and Dr. Victor Terskikh for discussions. We also thank Dr. Werner Maas (Bruker BioSpin) for providing access to a prototype of a low-gamma 7 mm MAS probe. Access to the 900 MHz NMR spectrometer was provided by the National Ultrahigh Field NMR Facility for Solids (Ottawa, Canada), a national research facility funded by the Canada Foundation for Innovation, the Ontario Innovation Trust, Recherche Que´bec, the National Research Council Canada, and Bruker BioSpin and managed by the University of Ottawa (www.nmr900.ca). The Natural Sciences and Engineering Research Council of Canada (NSERC) is acknowledged for a Major Resources Support grant. References and Notes (1) Bastow, T. J.; Stuart, S. N. Z. Naturforsch., A 1989, 45, 459. (2) Lim, A. R.; Yun, I. H.; Yoon, C. S. Solid State Commun. 2005, 134, 183. (3) Lim, A. R.; Jeong, S. Y. J. Solid State Chem. 2006, 179, 1009. (4) Lim, A. R.; Jung, W. K.; Han, T. J. Solid State Commun. 2004, 130, 481.
J. Phys. Chem. B, Vol. 111, No. 3, 2007 495 (5) Lim, A. R.; Jeong, S. Y.; Park, H.-M. J. Phys.: Condens. Matter 2001, 13, 3511. (6) Kunwar, A. C.; Turner, G. L.; Oldfield, E. J. Magn. Reson. 1986, 69, 124. (7) Bastow, T. J. J. Chem. Soc., Faraday Trans. 1991, 87, 2453. (8) Herreros, B.; Metz, A. W.; Harbison, G. S. Solid State Nucl. Magn. Reson. 2000, 16, 141. (9) Lambert, J.-F.; Prost, R.; Smith, M. E. Clays Clay Miner. 1992, 40, 253. (10) Hayashi, S.; Hayamizu, K. Bull. Chem. Soc. Jpn. 1990, 63, 913. (11) Stebbins, J. F.; Du, L. S.; Kroeker, S.; Neuhoff, P.; Rice, D.; Frye, J.; Jakobsen, H. J. Solid State Nucl. Magn. Reson. 2002, 21, 105. (12) Wong, A.; Whitehead, R. D.; Gan, Z.; Wu, G. J. Phys. Chem. A 2004, 108, 10551. (13) Wu., G.; Wong, A.; Gan, Z.; Davis, J. T. J. Am. Chem. Soc. 2003, 125, 7182-7183. (14) Larsen, F. H.; Skibsted, J.; Jakobsen, H. J.; Nielsen, N. C. J. Am. Chem. Soc. 2000, 122, 7080. (15) Schurko, R. W.; Hung, I.; Widdifield, C. M. Chem. Phys. Lett. 2003, 379, 1. (16) Widdifield, C. M.; Schurko, R. W. J. Phys. Chem. A 2005, 109, 6865. (17) Liu, Z.; Zhou, R.; Zheng, Z. J. Mol. Catal. A 2006, 255, 103. (18) An, H.; McGinn, P. Appl. Catal., B 2006, 62, 46-56. (19) Xiang, M.; Li, D.; Li, W.; Zhong, B.; Sun, Y. Fuel 2006, 85, 2662. (20) Santiago, A. F. J.; Sousa, J. F.; Guedes, R. C.; Jeroˆnimo, C. E. M.; Benachour, M. J. Hazard. Mater. 2006, 138, 325. (21) Klisin´ska, A.; Samson, K.; Gressel, I.; Grzybowska, B. Appl. Catal., A 2006, 309, 10. (22) Zhang, Y.; Zou, X.; Sui, L. Catal. Commun. 2006, 7, 855. (23) Jime´nez, R.; Garcı´a, X.; Cellier, C.; Ruiz, P.; Gordon, A. L. Appl. Catal., A 2006, 314, 81. (24) Minemura, Y.; Kuriyama, M.; Ito, S.; Tomishige, K.; Kunimori, K. Catal. Commun. 2006, 7, 623. (25) Terskikh, V. V.; Lapina, O. B.; Bondareva, V. M. Phys. Chem. Chem. Phys. 2000, 2, 2441. (26) Freude, D.; Haase, J. Quadrupole effects in solid-state nuclear magnetic resonance. In NMR Basic Principles and Progress; Diehl, P., Fluck, E., Gu¨nther, H., Kasfeld, R., Seelig, J., Eds.; Springer-Verlag: Berlin, 1993; Vol. 29, pp 1-90. (27) Ashbrook, S. E.; Duer, M. J. Concepts Magn. Reson. 2006, A28, 183. (28) Bodart, P. R.; Amoureux, J. P.; Dumazy, Y.; Lefort, R. Mol. Phys. 2000, 98, 1545. (29) Massiot, D.; Fayon, F.; Capron, M.; King, I.; Le Calve´, S.; Alonso, B.; Durand, J.-O.; Bujoli, B.; Gan, Z.; Hoatson, G. Magn. Reson. Chem. 2002, 40, 70. (30) The QUASAR module for the DMFit simulation program was provided by Jean-Paul Amoureux; UCCS, CNRS-8181, Lille, France. (31) Power, W. P.; Wasylishen, R. E.; Mooibroek, S.; Pettitt, B. A.; Danchura, W. J. Phys. Chem. 1990, 94, 591. (32) Haeberlen, U. In AdVances in Magnetic Resonance; Waugh, J. S., Ed.; Academic Press: New York, 1976. (33) Mehring, M. Principles of High Resolution NMR in Solids, 2nd ed.; Springer-Verlag: Berlin, 1983. (34) Spiess, H. W. In NMR Basic Principles and Progress; Diehl, P., Fluck, E., Kosfeld, R., Eds.; Springer-Verlag: Berlin, 1978; Vol. 15. (35) MacKenzie, K. J. D.; Smith, M. E. Multinuclear Solid-state NMR of Inorganic Materials; Pergamon: New York, 2002. (36) Rose, M. E. Elementary Theory of Angular Momentum; Wiley: New York, 1957.
