Nearly three-quarters of all NMR-accessible nuclides are quadrupolar with half-integer spin quantum numbers (I = 3/2, 5/2, 7/2, etc.). Far from being of only minor interest, therefore, NMR studies of nuclei such as 7Li, 11B, 23Na, 71Ga and 87Rb (I = 3/2), 17O and 27Al (I = 5/2), 45Sc, 51V and 59Co (I = 7/2) and 93Nb (I = 9/2) are central to the characterisation and investigation of a wide range of microporous materials, synthetic and naturally-occurring minerals, glasses, and novel oxide materials. Although their quadrupolar coupling constants can be large (typically up to ~10 MHz, but occasionally much greater), NMR of these nuclei is facilitated by the presence of a mI = +1/2 - -1/2 "central" transition which, to a first-order approximation, is not broadened by the quadrupolar interaction. The success of magic angle spinning (MAS) as a line-narrowing technique for spin I = 1/2 nuclei has encouraged its application to spectra of this type and yet, despite achieving a significant narrowing of the central transition, MAS usually fails to resolve the crystallographically-distinct sites present.
The reason for the relative failure of MAS in this case is that the broadening of the central transition arises largely from the second-order quadrupolar interaction and this has second- and fourth-rank terms in its orientational dependence, with MAS capable of only fully averaging the former. Starting in 1988, two methods were proposed for removing both the second- and fourth-rank quadrupolar broadening, and hence achieving truly high-resolution spectra of the central transition. The double rotation (DOR) [1] and dynamic angle spinning (DAS) [2] experiments both involve rapidly spinning the sample about two angles with respect to the magnetic field, either simultaneously in the case of DOR or sequentially in the case of DAS. Although these two techniques have been used with considerable success by a small number of research groups, their use has not become either widespread or commonplace, largely due to the significant additional cost and mechanical complexity of the specialised NMR probe equipment that is required
In this context, it is not surprising that the demonstration in 1995 by Frydman and Harwood of their novel multiple-quantum (MQ) MAS technique for removing the second-order quadrupolar broadening [3] generated such instant and enormous interest. Unlike DOR or DAS, this experiment is purely MAS-based and can be performed on any NMR spectrometer that is equipped with a standard MAS probe. Since its introduction, Frydman's idea has become established as a "modern NMR classic" with the original publication now having been cited over 400 times
In spite of its remarkably rapid acceptance as an important technique for structural studies of a broad range of solid materials, by 2000 it was widely recognised that there were aspects of the MQMAS experiment that required further development. The sensitivity of the technique needed to be improved, particularly for nuclei with very large quadrupolar coupling constants. Equally, if quantitation of the technique were to be made easier, then the excitation and detection of multiple-quantum coherence as a function of the magnitude of the quadrupolar coupling needed to be made more uniform. Finally, there was still much to be understood about the theory of the MQMAS experiment and the interpretation of the resulting data, particularly concerning some of the more subtle effects of the second-order quadrupolar interaction.
This then was the background to our EPSRC application, "NMR of Quadrupolar Nuclei: New Techniques and Applications" in 2000. We had been the first UK research group to publish work on the MQMAS experiment [4] and, thanks in part to EPSRC's award of grant GR/M12209 in 1998 (research quality rating "internationally leading" and overall rating "outstanding"), had already established ourselves as one of the leading groups in this area. Our new application was made so that we could continue our international-quality research into new experimental NMR methods for quadrupolar nuclei. Our requirements were: (i) a two-year postdoctoral fellow (Dr Sharon Ashbrook) to replace Dr Kevin Pike who was funded by GR/M12209; (ii) a new PhD student (Mr Sasa Antonijevic); and (iii) an upgrading ("reconsoling" in the jargon) of our old Bruker MSL 400 and MSL 200 spectrometers, dating from 1989, with the very latest consoles and probes.
Key Advances
The aim of the proposed research was to build on the early promise of the MQMAS experiment and to develop even more powerful high-resolution techniques that could be used routinely by chemists, physicists and material scientists in both the industrial and academic communities. The research involved experimental NMR work, theoretical calculations, and computer simulations and was focused in several key problem areas.
I. Cross-polarization and MQMAS. We have demonstrated a new approach to combining cross-polarization with MQMAS in a two-dimensional NMR experiment, involving cross-polarization from 1H to the single-quantum coherences of a quadrupolar nucleus [5]. These coherences are then converted directly to multiple-quantum coherences rather than via a population state. In two separate methods, pure-absorption lineshapes are obtained using a z filter and a shifted echo, respectively, with the latter, a "reversed split-t1" method, demonstrated to be particularly effective. The efficiency of both sequences can be improved by incorporating "fast-amplitude-modulated" (FAM) pulses for both the conversion and, in another original development, excitation of triple-quantum coherences.
II. Relative orientation of quadrupole tensors. Although techniques such as DAS, DOR and MQMAS enable resolution of crystallographically-inequivalent nuclei and also yield the quadrupolar coupling constant, CQ, quadrupolar asymmetry, h, and isotropic chemical shift, dCS, of each crystallographic site, no information is obtained that relates one quadrupole tensor to another, such as internuclear distances or relative orientations. We have demonstrated a modification of the MQMAS NMR experiment that utilises two-dimensional correlation of second-order (rank l = 4) broadened MAS lineshapes to obtain the relative orientation of quadrupole tensors [6, 7]. This new method involves the insertion of a "mixing time", tm, into the MQMAS experiment such that magnetization transfer between two distinct nuclei within a crystallite during this period will result in a two-dimensional "cross peak" correlating the two lineshapes. The shapes of these cross peaks are characteristic of the three Euler angles, a', b' and g', that describe the relative orientation of the two quadrupole tensors. We have used the example of 23Na (I = 3/2) NMR of borax (Na2B4O7.10H2O) to discuss in detail the nature of the magnetization transfer. We have also derived an analytical expression for the rank l = 4 orientational dependence of the second-order quadrupolar interaction in terms of the relative orientation of two quadrupole tensors and simulated the effect upon the shape of the cross peak when the angles a', b' and g' are changed. Finally, the use of this novel technique has been demonstrated in a 23Na NMR study of sodium metasilicate pentahydrate (Na2SiO3.5H2O) and in a comparative 23Na NMR study of sodium tungstate dihydrate (Na2WO4.2H2O) and sodium molybdate dihydrate (Na2MoO4.2H2O).
III. Satellite-transition (ST) MAS. One of the big and, as usual, unforeseeable surprises after submission of our original proposal was the development in mid-2000 of the satellite-transition MAS (STMAS) experiment by Gan [8]. This experiment offers an alternative approach to established methods such as DAS, DOR and MQMAS for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the MQ experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences, satellite transitions in t1 (or F1) and the central transition in t2 (or F2), and as a result yields signal-to-noise ratios that are typically up to 10 times greater than those achievable with MQMAS in the same experiment time. We were the first to develop a "shifted-echo" version of the experiment [9] and were the first to discuss the application of STMAS to nuclei with spin quantum numbers from I = 5/2 to 9/2 [10], extending Gan's original work to include nuclei with higher spin quantum numbers and demonstrating 27Al, 45Sc, 59Co and 93Nb STMAS experiments on both crystalline and amorphous samples. We have also considered the possibility of experiments involving satellite transitions other than mI = ±1/2 - ±3/2 and, using 93Nb NMR, have demonstrated the correlation of all single-quantum satellite transitions up to and including mI = ±7/2 - ±9/2. We have also discussed the absolute chemical shift scaling factors in these experiments, as well as the implications for isotropic resolution.
IV. SCAM-STMAS: self-compensation for angle misset. The STMAS experiment offers an approach to high-resolution NMR of quadrupolar nuclei that employs only conventional MAS hardware and yields substantial signal enhancements over the widely-used MQMAS experiment. However, the presence of the first-order quadrupolar interaction in the satellite transitions imposes the requirement of a high degree of accuracy in the setting of the magic angle on the NMR probehead. The first-order quadrupolar interaction is only fully removed if the sample spinning angle, c, equals cos-1(1/√3) exactly and rotor synchronization is performed. The required level of accuracy is difficult to achieve experimentally, particularly when the quadrupolar interaction is large. If the magic angle is not set correctly, the first-order splitting is reintroduced and the spectral resolution is severely compromised. We have demonstrated a novel STMAS method (SCAM-STMAS) that is self-compensated for angle missets of up to ±1° via coherence transfer between the two different satellite transitions ST+ (mI = +3/2 - +1/2) and ST- (mI = -1/2 - -3/2) midway through the t1 period [11, 12]. We have described in detail the implementation of SCAM-STMAS and demonstrated its wider utility through 23Na (I = 3/2), 87Rb (I = 3/2), 27Al (I = 5/2) and 59Co (I = 7/2) NMR. We have discussed linewidths in SCAM-STMAS and the limits over which angle-misset compensation is achieved and we have demonstrated that SCAM-STMAS is more tolerant of temporary spinning rate fluctuations than STMAS, resulting in less "t1 noise" in the two-dimensional spectrum. In addition, alternative correlation experiments, for example involving the use of double-quantum coherences, that similarly display self-compensation for angle misset have been investigated. The use of SCAM-STMAS has also been considered in systems where other high-order interactions, such as third-order quadrupolar effects, are present. Finally, we have shown that the sensitivity of the experiment can be improved through the use of amplitude-modulated pulses.
V. Spin-locking of quadrupolar nuclei. Spin-locking of half-integer quadrupolar nuclei, such as 23Na (I = 3/2) and 27Al (I = 5/2), is of renewed interest owing to the development of variants of the MQMAS and STMAS NMR experiments that either utilise spin-locking directly or offer the possibility that spin-locked states may arise. However, the large magnitude and, under MAS, the time dependence of the quadrupolar interaction often result in complex spin-locking phenomena that are not widely understood. We have shown that, following the application of a spin-locking pulse, a variety of coherence transfer processes occur on a timescale of ~1/wQ before the spin system settles down into a spin-locked state which may itself be time dependent if MAS is performed [13]. We have shown theoretically for both spin I = 3/2 and 5/2 nuclei that the spin-locked state created by this initial rapid dephasing typically consists of a variety of single- and multiple-quantum coherences and non-equilibrium population states and we have discussed the subsequent evolution of these under MAS. In contrast to previous work, we have considered spin-locking using a wide range of radiofrequency field strengths, i.e., a range that covers both the "strong-field" (w1 >> wQPAS) and "weak-field" (w1 << wQPAS) limits. Single- and multiple-quantum filtered spin-locking experiments on NaNO2, NaNO3 and Al(acac)3, under both static and MAS conditions, have been used to illustrate and confirm the results of the theoretical discussion.
VI. High-resolution 17O NMR of dense silicates. (Mg,Fe)2SiO4 is the principal compositional component of the Earth's mantle to a depth of 660 km and transforms from olivine (a) to wadsleyite (b) and, finally, to ringwoodite (g) with increasing pressure. Wadsleyite, occurring between depths of 410 and ~530 km, has been intensively studied owing to its probable relationship to a major seismic discontinuity and its potential as the repository for the largest reservoir of water in the Earth. MQMAS is an established method for obtaining high-resolution 17O NMR spectra of silicates, complementing diffraction techniques by, e.g., providing indirect information on the structural chemistry of hydrogen. Unfortunately, the method is insensitive and typically requires amounts of 17O-enriched material an order of magnitude greater than can be synthesised at the very high pressures needed to form wadsleyite. Recently, however, with the advent of the STMAS experiment and of very high field magnets, great advances have been made in the sensitivity of high-resolution NMR of quadrupolar nuclei. In collaboration with Dr A. J. Berry of the Research School of Earth Sciences, ANU, Canberra, we have reported the first 17O NMR study of b-Mg2SiO4 (9.6 mg of 35% 17O-enriched material) [14]. Using STMAS at magnetic fields of B0 = 9.4 T and 11.7 T and MQMAS at B0 = 18.8 T, we have resolved and assigned all four crystallographically distinct O sites and determined their chemical shift and quadrupolar parameters. Similar work has commenced on ringwoodite (g-Mg2SiO4) and the eventual aim is to study hydrated forms of all these minerals.
VII. Quadrupolar-CSA cross-terms effects in STMAS. In collaboration with Dr S. Wi of the University of California, Berkeley and Professor L. Frydman of the Weizmann Institute of Sciences, Israel we have investigated the nature of higher-order effects arising in solid-state NMR when quadrupolar nuclei are subject to significant chemical shift anisotropies [15]. It is known that the quadrupole interaction can give rise to shielding-derived terms that are not entirely averaged away by conventional MAS. These terms are proportional to the square of the z component of the spin angular momentum and therefore leave unaffected both the central and other -mI - +mI symmetric multiple-quantum transitions, yet lead to noticeable effects when monitoring other non-symmetric transitions within the spin manifold. The recently developed STMAS NMR method for the simultaneous averaging of the first- and second-order quadrupole effects makes such quadrupole-shielding cross terms observable. Thus it opens up new possibilities for determining the coupling parameters of the quadrupolar nucleus - particularly the relative orientation between its quadrupole and shielding tensors. Average Hamiltonian derivations of these effects have been explored and employed to derive analytical expressions for the resulting splittings. These predictions have then been successfully compared with variable-field STMAS NMR spectra of a 59Co-containing material.
VIII. MQMAS of amorphous zeolite precursors. In a collaboration with Dr H. Yang and Dr R. I. Walton of the University of Exeter, amorphous precursors to sodium gallium silicate and zeolite-A have been studied using 23Na, 27Al, 71Ga (I = 3/2) and 29Si (I = 1/2) MAS and, where applicable, MQMAS NMR with a view to increasing our understanding of the mechanism of hydrothermal synthesis [16, 17].
IX. Motional broadening in STMAS. In spite of the close similarity of the MQMAS and STMAS experiments, in a variety of materials it is observed that certain STMAS peaks are very broad compared with the corresponding MQMAS peaks, sometimes so broad that they are unobservable. We have presented 17O (I = 5/2) NMR spectra of two materials, chondrodite (2Mg2SiO4.Mg(OH)2) and clinohumite (4Mg2SiO4.Mg(OH)2), exhibiting this phenomenon and shown that the cause is a form of motional broadening arising from the combined effects of molecular motion, the quadrupolar interaction and MAS [18].
X. Refocussing of shift anisotropies in quadrupolar echoes. A simple two-pulse spin-echo experiment has been shown to refocus inhomogeneous broadening arising from both chemical and/or paramagnetic shift anisotropy and a first-order I = 1 quadrupolar interaction [19]. The method has been demonstrated to yield 2H NMR spectra of a paramagnetic solid (CuCl2.2D2O) and of a non-paramagnetic solid (D2C2O4.2D2O) that are significantly less distorted than those provided by the conventional quadrupolar-echo method. This technique should thus prove useful in studies of motion and dynamics where detailed analysis of the 2H lineshape is performed.
XI. High-resolution NMR in inhomogeneous B0 and B1 fields. Recently, there has been much interest in methods for obtaining high-resolution NMR spectra in inhomogeneous B0 and B1 fields and in their application to so-called "ex situ" spectroscopy, where the sample and magnet/probe assembly are spatially separated. In something of a departure from the rest of the work funded by GR/N07622, we have discussed the implementation of the well-known two-dimensional nutation experiment as a method for correlating B0 and B1 inhomogeneities and, hence, achieving a high-resolution NMR spectrum [20]. The advantages of this approach lie in its simplicity, its spatial ("depth") resolution, and in its not requiring a linear correlation of fields, i.e., B1 = aB0 + k, across the sample.
Project Plan Review
In essence, the project proceeded as originally envisaged. The advent of the STMAS experiment in mid-2000 (and our subsequent development of the SCAM-STMAS technique) could not have been foreseen in our original proposal, and it was necessary for us to adapt our work accordingly. In particular, we felt that the already high sensitivity of the STMAS method meant that we should concentrate mainly on this technique rather than on trying to improve the sensitivity of the older MQMAS experiment. Overall, we believe that the quality and quantity of our published results show that our research planning and practice are outstanding.
Research Impact and Benefits to Society
The research supported by this grant and described in the 15 published papers (so far) and in Sasa Antonijevic's PhD thesis (in preparation) is, in my opinion, internationally leading. I base this judgement upon the quality of the journals that we have published in, the level of interest and comments of my peers in this research area, the variety and very distinctive and original nature of our research, the awards of a Royal Society Leverhulme Trust Senior Research Fellowship to myself and a Royal Society Dorothy Hodgkin Research Fellowship to Dr Ashbrook, and the unsolicited (and mostly coming from people we were barely familiar with) invitations to both Dr Ashbrook and myself to give a number of plenary lectures at conferences in the USA. I believe that the quality of the research, combined with the vigour with which we have communicated our results through publications, conference lectures and poster presentations, means that the work supported by GR/N07622 has had the very highest impact in the international arena. There will be great benefits to broader society as well but it is in the nature of this type of work that these may take decades to emerge.
Explanation of Expenditure
The was no significant deviation of the expenditure from the original plans; Dr Ashbrook was employed for 24 months as a postdoctoral fellow; Mr Sasa Antonijevic has studied for his PhD for 36 months and should submit his thesis shortly; our MSL 400 and 200 spectrometers were upgraded (very successfully!) by Bruker to the latest Avance systems and a number of new probeheads were obtained (for pictures of our upgraded spectrometers go to: http:/nmr/Equipment/specroom.html). One minor deviation was that, in order to give talks at international conferences (even invited talks are rarely fully funded in my research area) and to present our work as posters (see list below), we had to spend more money on travel than EPSRC's "standard" amounts envisaged and had to use some consumables money for this purpose. In view of the importance of communicating high-quality results on the international stage, I consider this to be a sensible modification of the original spending plan.
Further Research and Dissemination Activities
As mentioned above, there should be at least one more full paper to be written based on the research described in Sasa Antonijevic's PhD thesis; this will be done when time allows. This final report will be posted on our group website (enter via: http://www.ex.ac.uk/chemweb/research/staff/scw.html).
In addition to the papers published in refereed international journals, the research supported by this grant was presented on the following occasions. Invited talks: British Radiofrequency Spectroscopy Group (London, 2002); 44th Experimental NMR Conference (USA, 2003); Gordon Research Conference on Magnetic Resonance (Dr Ashbrook, USA, 2003); 45th Rocky Mountain Conference (USA, 2003). Contributed talks: 2nd Alpine Conference on Solid-State NMR, Chamonix (Dr Ashbrook, France, 2001); Anglo-French NMR Meeting (Southampton, 2002); Bruker Users' Meeting (USA, 2003). Departmental talks: Department of Chemistry (Cambridge, 2002); Ecole Normale Supérieure, Lyon (France, 2002); Department of Physics (Warwick, 2003). Posters: 42nd Experimental NMR Conference (USA, 2001); 15th International Meeting on NMR Spectroscopy (Durham, 2001); 2nd Alpine Conference on Solid-State NMR, Chamonix (France, 2001); 43rd Experimental NMR Conference (USA, 2002); Anglo-French NMR Meeting (Southampton, 2002); British Radiofrequency Spectroscopy Group (London, 2002); 44th Experimental NMR Conference (USA, 2003); 3rd Alpine Conference on Solid-State NMR, Chamonix (France, 2003).
As a result of the variety and novelty of the work that we have done with the STMAS technique, Dr Ashbrook and myself have been commissioned (with remuneration!) to write a major review of our recent research.
Much further research is planned - if only we can obtain funding.
Summary
This has been a tremendously successful research project and represents great value for money. The major points to note are: (i) a major new state-of-the-art NMR facility (based on 400 MHz and 200 MHz spectrometers) established at the University of Exeter; (ii) a total of 15 papers published (so far) in refereed international journals; (iii) 12 papers produced by Dr Ashbrook and 5 (so far) by Mr Antonijevic; (iv) Mr Antonijevic will submit his PhD thesis within 3.25 years of starting his PhD and has obtained a postdoctoral position with Professor G. Bodenhausen at the EPFL, Lausanne, Switzerland; (v) Dr Ashbrook awarded a Royal Society Dorothy Hodgkin Research Fellowship to work at the University of Cambridge; (vi) the results of the research also presented at a significant number of national and international meetings and conferences; (vii) the reputation of UK science enhanced by top-class research that is, beyond question, internationally leading.
References
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[6] N. G. Dowell, S. E. Ashbrook, J. McManus and S. Wimperis, Relative Orientation of Quadrupole Tensors from Two-Dimensional Multiple-Quantum MAS NMR, J. Am. Chem. Soc. 123, 8135-8136 (2001). [Correction: 124, 1125 (2002).]
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[8] Z. Gan, Isotropic NMR Spectra of Half-Integer Quadrupolar Nuclei using Satellite Transitions and Magic-Angle Spinning, J. Am. Chem. Soc. 122, 3242-3243 (2000).
[9] K. J. Pike, S. E. Ashbrook and S. Wimperis, Two-Dimensional Satellite-Transition MAS NMR of Quadrupolar Nuclei: Shifted Echoes, High-Spin Nuclei and Resolution, Chem. Phys. Lett. 345, 400-408 (2001).
[10] S. E. Ashbrook and S. Wimperis, Satellite-Transition MAS NMR of Spin I = 3/2, 5/2, 7/2 and 9/2 Nuclei: Sensitivity, Resolution and Practical Implementation, J. Magn. Reson. 156, 269-281 (2002).
[11] S. E. Ashbrook and S. Wimperis, High-Resolution NMR Spectroscopy of Quadrupolar Nuclei in Solids: Satellite-Transition MAS with Self-Compensation for Magic-Angle Misset, J. Am. Chem. Soc. 124, 11602-11603 (2002).
[12] S. E. Ashbrook and S. Wimperis, SCAM-STMAS: Satellite-Transition MAS NMR of Quadrupolar Nuclei with Self-Compensation for Magic-Angle Misset, J. Magn. Reson. 162, 402-416 (2003).
[13] S. E. Ashbrook and S. Wimperis, Spin-Locking of Half-Integer Quadrupolar Nuclei in NMR of Solids: Creation and Evolution of Coherences, J. Chem. Phys. submitted.
[14] S. E. Ashbrook, A. J. Berry, W. O. Hibberson, S. Steuernagel and S. Wimperis, High-Resolution 17O NMR Spectroscopy of Wadsleyite (b-Mg2SiO4), J. Am. Chem. Soc. 125, 11824-11825 (2003).
[15] S. Wi, S. E. Ashbrook, S. Wimperis and L. Frydman, Second-Order Quadrupole- Shielding Effects in Magic-Angle Spinning Solid-State Nuclear Magnetic Resonance, J. Chem. Phys. 118, 3131-3140 (2003).
[16] S. Antonijevic, S. E. Ashbrook, R. I. Walton and S. Wimperis, A Multiple-Quantum 23Na MAS NMR Study of Amorphous Sodium Gallium Silicate Zeolite Precursors, J. Mater. Chem. 12, 1469-1474 (2002).
[17] H. Yang, R. I. Walton, S. Antonijevic and S. Wimperis, Local Order of Amorphous Zeolite Precursors from 29Si {1H} CPMAS and 23Na and 27Al MQMAS NMR and Evidence for the Nature of Medium-Range Order from Neutron Diffraction, in preparation.
[18] S. E. Ashbrook, S. Antonijevic, A. J. Berry and S. Wimperis, Motional Broadening: an Important Distinction between Multiple-Quantum and Satellite-Transition MAS NMR of Quadrupolar Nuclei, Chem. Phys. Lett. 364, 634-642 (2002).
[19] S. Antonijevic and S. Wimperis, Refocussing of Chemical and Paramagnetic Shift Anisotropies in 2H NMR using the Quadrupolar-Echo Experiment, J. Magn. Reson. 164, 343-350 (2003).
[20] S. Antonijevic and S. Wimperis, High-Resolution NMR Spectroscopy in Inhomogeneous B0 and B1 Fields by Two-Dimensional Correlation, Chem. Phys. Lett. 381, 634-641 (2003).