Biexponential I = 3/2 Spin-Lattice Relaxation in the Solid State: Multiple-Quantum 7Li NMR as a Probe of Fast Ion Dynamics.

Spin-lattice relaxation measurements are used in 7Li NMR studies of materials of potential use in solid-state Li-ion batteries as a probe of ion mobility on a fast (nanosecond to picosecond) time scale. The relaxation behavior is often analyzed by assuming exponential behavior or, equivalently, a single T1 time constant. However, the spin-lattice relaxation of spin I = 3/2 nuclei, such as 7Li, is in general biexponential; this is a fundamental property of I = 3/2 nuclei and unrelated to any compartmentalization within the solid. Although the possibility of biexponential 7Li (and other I = 3/2 nuclei) spin-lattice relaxation in the solid state has been noted by a number of authors, it can be difficult to observe unambiguously using conventional experimental NMR techniques, such as inversion or saturation recovery. In this work, we show that triple-quantum-filtered NMR experiments, as previously exploited in I = 3/2 NMR of liquids, can be used in favorable circumstances to observe and readily quantify biexponential 7Li spin-lattice relaxation in solids with high ion mobility. We demonstrate a triple-quantum-filtered inversion-recovery experiment on the candidate solid electrolyte material Li2OHCl at 325 K, which has previously been shown to exhibit fast ion mobility, and we also introduce a novel triple-quantum-filtered saturation-recovery experiment. The results of these solid-state NMR experiments are less straightforward than those in liquids as a consequence of the unwanted direct excitation of triple-quantum coherences by the weak (compared with the unaveraged 7Li quadrupolar interaction) pulses used, but we show that this unwanted excitation can be accounted for and, in the example shown here, does not impede the extraction of the two 7Li spin-lattice relaxation times.

Two-dimensional 1H and 1H-detected NMR study of a heterogeneous biocatalyst using fast MAS at high magnetic fields.

Nuclear magnetic resonance (NMR) is a powerful tool for investigating atomic-scale structure in heterogeneous or composite materials where long-range order is absent. In this work solid-state 1H and 1H-detected NMR experiments were performed with fast magic angle spinning (νR = 75 kHz) and at high magnetic fields (B0 = 20 T) and used to gain structural insight into a heterogeneous biocatalyst consisting of an enzyme, human carbonic anhydrase II (hCA II), covalently immobilized on epoxy-functionalized silica. Two-dimensional 1H-1H NOESY-type correlation experiments were able to provide information on 1H environments in silica, epoxy-silica and the immobilized enzyme. Two distinct signals originating from water protons were observed: water associated with the surface of the silica and the water associated with the immobilized enzyme. Additional two-dimensional 1H-1H double-single quantum (DQ-SQ) correlation experiments suggested that the immobilized enzyme is not in close contact with the silica surface. Most significantly, comparison of two-dimensional 1H-15N spectra of the immobilized enzyme and the solution-state enzyme confirmed that the structural integrity of the protein is well preserved upon covalent immobilization.

A high-resolution natural abundance 33S MAS NMR study of the cementitious mineral ettringite.

Despite the widespread occurrence of sulfur in both natural and man-made materials, the 33S nucleus has only rarely been utilised in solid-state NMR spectroscopy on account of its very low natural abundance (0.76%), low NMR frequency (ν0 = 30.7 MHz at B0 = 9.4 T), and significant nuclear quadrupole moment (spin I = 3/2, Q = -69.4 mb). Satellite-transition magic angle spinning (STMAS) is an NMR method for obtaining high-resolution spectra of half-integer quadrupolar nuclei (spin I > 1/2) in solids and is notable for its intrinsic sensitivity advantage over the similar multiple-quantum (MQMAS) method, especially for nuclei with low NMR frequencies. In this work we demonstrate the feasibility of natural abundance 33S STMAS NMR experiments at B0 = 9.4 T and 20.0 T using a model sulfate sample (Na2SO4 + K2SO4 in a 1 : 1 molar ratio). Furthermore, we undertake a natural abundance 33S STMAS NMR study of the cement-forming mineral ettringite (Ca6Al2(SO4)3(OH)12·26H2O) at B0 = 9.4 T and 20.0 T, resolving a discrepancy in the literature between two previous conventional 33S MAS NMR studies and obtaining an alternative set of 33S NMR parameters that is simultaneously consistent with the MAS and STMAS data at both field strengths.

The ambient hydration of the aluminophosphate JDF-2 to AlPO-53(A): insights from NMR crystallography.

The aluminophosphate (AlPO) JDF-2 is prepared hydrothermally with methylammonium hydroxide (MAH+·HO-, MAH+ = CH3NH3+), giving rise to a microporous AEN-type framework with occluded MAH+ cations and extra-framework (Al-bound) HO- anions. Despite the presence of these species within its pores, JDF-2 can hydrate upon exposure to atmospheric moisture to give AlPO-53(A), an isostructural material whose crystal structure contains one molecule of H2O per formula unit. This hydration can be reversed by mild heating (such as the frictional heating from magic angle spinning). Previous work has shown good agreement between the NMR parameters obtained experimentally and those calculated from the (optimized) crystal structure of JDF-2. However, several discrepancies are apparent between the experimental NMR parameters for AlPO-53(A) and those calculated from the (optimized) crystal structure (e.g. four 13C resonances are observed, rather than the expected two). The unexpected resonances appear and disappear reversibly with the respective addition and removal of H2O, so clearly arise from AlPO-53(A). We investigate the ambient hydration of JDF-2 using quantitative 31P MAS NMR to follow the transformation over the course of ∼3 months. The structures of JDF-2 and AlPO-53(A) are also investigated using a combination of multinuclear solid-state NMR spectroscopy to characterize the samples, and first-principles density functional theory (DFT) calculations to evaluate a range of possible structural models in terms of calculated NMR parameters and energetics. The published structure of JDF-2 is shown to be a good representation of the dehydrated material, but modification of the published structure of AlPO-53(A) is required to provide calculated NMR parameters that are in better agreement with experiment. This modification includes reorientation of all the MAH+ cations and partial occupancy of the H2O sites.

Spin-locking of half-integer quadrupolar nuclei in NMR of solids: The far off-resonance case.

Spin-locking of spin I=3/2 and I=5/2 nuclei in the presence of large resonance offsets has been studied using both approximate and exact theoretical approaches and, in the case of I=3/2, experimentally. We show the variety of coherences and population states produced in a far off-resonance spin-locking NMR experiment (one consisting solely of a spin-locking pulse) and how these vary with the radiofrequency field strength and offset frequency. Under magic angle spinning (MAS) conditions and in the "adiabatic limit", these spin-locked states acquire a time dependence. We discuss the rotor-driven interconversion of the spin-locked states, using an exact density matrix approach to confirm the results of the approximate model. Using conventional and multiple-quantum filtered spin-locking 23Na (I=3/2) NMR experiments under both static and MAS conditions, we confirm the results of the theoretical calculations, demonstrating the applicability of the approximate theoretical model to the far off-resonance case. This simplified model includes only the effects of the initial rapid dephasing of coherences that occurs at the start of the spin-locking period and its success in reproducing both experimental and exact simulation data indicates that it is this dephasing that is the dominant phenomenon in NMR spin-locking of quadrupolar nuclei, as we have previously found for the on-resonance and near-resonance cases. Potentially, far off-resonance spin-locking of quadrupolar nuclei could be of interest in experiments such as cross polarisation as a consequence of the spin-locking pulse being applied to a better defined initial state (the thermal equilibrium bulk magnetisation aligned along the z-axis) than can be created in a powdered solid with a selective radiofrequency pulse, where the effect of the pulse depends on the orientation of the individual crystallites.

Solid-state dynamics in the closo-carboranes: a (11)B MAS NMR and molecular dynamics study.

This work explores the dynamic behavior of the three closo-carborane isomers (formula C2B10H12) using modern solid-state magic angle spinning (MAS) NMR techniques and relates the experimental measurements to theoretical results obtained using molecular dynamics simulations. At high temperatures and at B0 = 9.4 T, the (11)B MAS line widths are narrow (40-90 Hz) for the three isomers. The rotational correlation times (τc) calculated by molecular dynamics are on the picosecond time scale, showing a quasi-isotropic rotation at these temperatures, typical for liquid systems. For all three isomers, the values of the (11)B spin-lattice relaxation times (T1) show discontinuities as the temperature is decreased, confirming the phase changes reported in the literature. At low temperatures, the (11)B MAS spectra of all three isomers exhibit much broader lines. The simulations showed that the molecular reorientation was anisotropic around different symmetry axes for each isomer, and this was supported by the values of the reduced quadrupolar parameter PQ(eff) derived from "dynamic shift" measurements using (11)B MQMAS NMR spectroscopy. The behavior of PQ(eff) as a function of temperature for p-carborane suggests that molecular reorientation is about the C5 symmetry axis of the molecule at low temperatures, and this was supported by the molecular dynamics simulations.

Deuterium MAS NMR studies of dynamics on multiple timescales: histidine and oxalic acid.

Deuterium ((2) H) magic-angle spinning (MAS) nuclear magnetic resonance is applied to monitor the dynamics of the exchanging labile deuterons of polycrystalline L-histidine hydrochloride monohydrate-d7 and α-oxalic acid dihydrate-d6 . Direct experimental evidence of fast dynamics is obtained from T1Z and T1Q measurements. Further motional information is extracted from two-dimensional single-quantum (SQ) and double-quantum (DQ) MAS spectra. Differences between the SQ and DQ linewidths clearly indicate the presence of motions on intermediate timescales for the carboxylic moiety and the D2 O in α-oxalic acid dihydrate, and for the amine group and the D2 O in L-histidine hydrochloride monohydrate. Comparison of the relaxation rate constants of Zeeman and quadrupolar order with the relaxation rate constants of the DQ coherences suggests the co-existence of fast and slow motional processes.

Imaging of the B1 distribution and background signal in a MAS NMR probehead using inhomogeneous B0 and B1 fields.

Several widely used methods for suppressing the "background" signal in (1)H magic angle spinning (MAS) NMR spectroscopy are based on the assumption of a significant difference between the B1 radiofrequency field experienced by the sample (within the MAS rotor) and that felt by static components of the probehead (where the background signal is believed to originate). In this work, a two-dimensional correlation experiment employing inhomogeneous B0 and B1 fields is used to image the B1 distribution in a MAS NMR probehead. The experiment, which can be performed on any spectrometer, allows the distribution of the B1 field to be measured and also correlated with the spatial location of the NMR signal within the probehead. The method can also readily be combined with various "depth pulse" techniques for background suppression, allowing their performances to be more rigorously evaluated.

Dual-compensated antisymmetric composite refocusing pulses for NMR.

Novel antisymmetric composite 180° pulses are designed for use in nuclear magnetic resonance (NMR) and verified experimentally. The pulses are simultaneously broadband with respect to both inhomogeneity of the radiofrequency (B(1)) field and resonance offset and, as a result of their antisymmetric phase schemes, can be used to form spin echoes without the introduction of a phase error. The new dual-compensated pulses are designed analytically, using symmetry arguments and a graphical interpretation of average Hamiltonian theory. Two families of composite refocusing pulses are presented, one (ASBO-9) consisting of sequences made up of 9 simple 180° pulses and one (ASBO-11) of sequences made up of 11 simple 180° pulses. There are an infinite number of composite pulses in each family owing to a free phase variable in the solution to the average Hamiltonian equations and this allows selection of individual composite pulses with particular properties. Finally, a comparison is made between composite pulses designed using average Hamiltonian theory and those proposed for use in quantum computing by NMR.

Improved background suppression in ¹H MAS NMR using composite pulses.

A well known feature of ¹H MAS NMR spectroscopy, particularly of solids where the concentration of ¹H nuclei is low, is the presence in the spectrum of a significant broad "background" signal arising from ¹H nuclei that are outside the MAS rotor and radiofrequency coil, probably located on the surfaces of the static components of the probehead. A popular method of suppressing this unwanted signal is the "depth pulse" method, consisting of a 90° pulse followed by one or two 180° pulses that are phase cycled according to the "Exorcycle" scheme, which removes signal associated with imperfect 180° pulses. Consequently, only spins in the centre of the radiofrequency coil contribute to the ¹H MAS spectrum, while those experiencing a low B1 field outside the coil are suppressed. Although very effective at removing background signal from the spectrum, one drawback with this approach is that significant loss of the desired signal from the sample also occurs. Here we investigate the ¹H background suppression problem and, in particular, the use of novel antisymmetric passband composite pulses to replace the simple pulses in a depth pulse experiment. We show that it is possible to improve the intensity of the ¹H signals of interest while still maintaining effective background suppression. We expect that these results will be relevant to ¹H MAS NMR studies of, for example, nominally perdeuterated biological samples or nominally anhydrous inorganic materials.

Use of composite refocusing pulses to form spin echoes.

The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.

High-resolution (19)F MAS NMR spectroscopy: structural disorder and unusual J couplings in a fluorinated hydroxy-silicate.

High-resolution (19)F magic angle spinning (MAS) NMR spectroscopy is used to study disorder and bonding in a crystalline solid. (19)F MAS NMR reveals four distinct F sites in a 50% fluorine-substituted deuterated hydrous magnesium silicate (clinohumite, 4Mg(2)SiO(4)·Mg(OD(1-x)F(x))(2) with x = 0.5), indicating extensive structural disorder. The four (19)F peaks can be assigned using density functional theory (DFT) calculations of NMR parameters for a number of structural models with a range of possible local F environments generated by F(-)/OH(-) substitution. These assignments are supported by two-dimensional (19)F double-quantum MAS NMR experiments that correlate F sites based on either spatial proximity (via dipolar couplings) or through-bond connectivity (via scalar, or J, couplings). The observation of (19)F-(19)F J couplings is unexpected as the fluorines coordinate Mg atoms and the Mg-F interaction is normally considered to be ionic in character (i.e., there is no formal F-Mg-F covalent bonding arrangement). However, DFT calculations predict significant (19)F-(19)F J couplings, and these are in good agreement with the splittings observed in a (19)F J-resolved MAS NMR experiment. The existence of these J couplings is discussed in relation to both the nature of bonding in the solid state and the occurrence of so-called "through-space" (19)F-(19)F J couplings in solution. Finally, we note that we have found similar structural disorder and spin-spin interactions in both synthetic and naturally occurring clinohumite samples.

Dynamics on the microsecond timescale in hydrous silicates studied by solid-state (2)H NMR spectroscopy.

Solid-state (2)H NMR spectroscopy has been used to probe the dynamic disorder of hydroxyl deuterons in a synthetic sample of deuterated hydroxyl-clinohumite (4Mg(2)SiO(4).Mg(OD)(2)), a proposed model for the incorporation of water within the Earth's mantle. Both static and magic angle spinning (MAS) NMR methods were used. Static (2)H NMR appears to reveal little evidence of the dynamic process, yielding results similar to those obtained from deuterated brucite (Mg(OD)(2)), where no dynamics on the relevant timescale are expected to be present. However, in (2)H MAS NMR spectra, considerable line broadening is observed for hydroxyl-clinohumite and a (2)H double-quantum (DQ) MAS NMR spectrum confirms that this is due to motion on the microsecond timescale. Using a model for dynamic exchange of the hydroxyl deuterons between two sites identified in previous diffraction studies, first-principles density functional theory (DFT) calculations of (2)H (spin I = 1) quadrupolar NMR parameters, and a simple analytical model for dynamic line broadening in MAS NMR experiments, we were able to reproduce the observed motional line broadening and use this to estimate a rate constant for the dynamic process. From analysis of the observed (2)H linewidths in variable-temperature MAS experiments, an activation energy for the exchange process was also determined. A simulated static (2)H NMR lineshape based on our dynamic model is consistent with the observed experimental static NMR spectrum, confirming that the motion present in this system is not easily detectable using a static NMR approach. Finally, a (2)H DQMAS NMR spectrum of fluorine-substituted (2)H-enriched hydroxyl-clinohumite shows how the dynamic exchange process is inhibited by O-DF(-) hydrogen-bonding interactions.

Spin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: second-order quadrupolar and resonance offset effects.

Spin-locking of spin I=3/2 and I=5/2 nuclei in the presence of small resonance offset and second-order quadrupolar interactions has been investigated using both exact and approximate theoretical and experimental nuclear magnetic resonance (NMR) approaches. In the presence of second-order quadrupolar interactions, we show that the initial rapid dephasing that arises from the noncommutation of the state prepared by the first pulse and the spin-locking Hamiltonian gives rise to tensor components of the spin density matrix that are antisymmetric with respect to inversion, in addition to those symmetric with respect to inversion that are found when only a first-order quadrupolar interaction is considered. We also find that spin-locking of multiple-quantum coherence in a static solid is much more sensitive to resonance offset than that of single-quantum coherence and show that good spin-locking of multiple-quantum coherence can still be achieved if the resonance offset matches the second-order shift of the multiple-quantum coherence in the appropriate reference frame. Under magic angle spinning (MAS) conditions, and in the "adiabatic" limit, we demonstrate that rotor-driven interconversion of central-transition single- and three-quantum coherences for a spin I=3/2 nucleus can be best achieved by performing the spin-locking on resonance with the three-quantum coherence in the three-quantum frame. Finally, in the "sudden" MAS limit, we show that spin I=3/2 spin-locking behavior is generally similar to that found in static solids, except when the central-transition nutation rate matches a multiple of the MAS rate and a variety of rotary resonance phenomena are observed depending on the internal spin interactions present. This investigation should aid in the application of spin-locking techniques to multiple-quantum NMR of quadrupolar nuclei and of cross-polarization and homonuclear dipolar recoupling experiments to quadrupolar nuclei such as (7)Li, (11)B, (17)O, (23)Na, and (27)Al.

Structure and NMR assignment in calcined and as-synthesized forms of AlPO-14: a combined study by first-principles calculations and high-resolution 27Al-31P MAS NMR correlation.

The high-resolution 27Al and 31P NMR spectra of two as-synthesized forms of the microporous aluminophosphate AlPO-14 and the corresponding calcined-dehydrated form were assigned using both "first-principles" calculations of NMR parameters (GIPAW, as implemented in NMR-CASTEP) and a 27Al-31P heteronuclear correlation NMR experiment (MQ-J-HETCOR) that exploits 27Al multiple-quantum coherences and J couplings to identify Al-O-P linkages. NMR parameters calculated from published AlPO-14 crystal structures, which are derived from powder X-ray diffraction (XRD) data, are in poor agreement with experiment and it was necessary to optimize the structure geometry using energy minimization before satisfactory agreement was obtained. Comparison of simulated powder XRD patterns from the experimental and the energy-minimized structures shows that the changes in relative atomic positions in the optimized structure are relatively small and yield only minor adjustments in the Bragg peak intensities. These results indicate that a combination of NMR spectroscopy and first-principles calculation of NMR parameters may soon be considered a generally useful step in the refinement of the structures of microporous materials derived from powder diffraction data.

Satellite transitions acquired in real time by magic angle spinning (STARTMAS): "ultrafast" high-resolution MAS NMR spectroscopy of spin I=3/2 nuclei.

The satellite transitions acquired in real time by magic angle spinning (STARTMAS) NMR experiment combines a train of pulses with sample rotation at the magic angle to refocus the first- and second-order quadrupolar broadening of spin I=3/2 nuclei in a series of echoes, while allowing the isotropic chemical and quadrupolar shifts to evolve. The result is real-time isotropic NMR spectra at high spinning rates using conventional MAS equipment. In this paper we describe in detail how STARTMAS data can be acquired and processed with ease on commercial equipment. We also discuss the advantages and limitations of the approach and illustrate the discussion with numerical simulations and experimental data from four different powdered solids.

17O and 29Si NMR parameters of MgSiO3 phases from high-resolution solid-state NMR spectroscopy and first-principles calculations.

The 29Si and 17O NMR parameters of six polymorphs of MgSiO3 were determined through a combination of high-resolution solid-state NMR and first-principles gauge including projector augmented wave (GIPAW) formalism calculations using periodic boundary conditions. MgSiO3 is an important component of the Earth's mantle that undergoes structural changes as a function of pressure and temperature. For the lower pressure polymorphs (ortho-, clino-, and protoenstatite), all oxygen species in the 17O high-resolution triple-quantum magic angle spinning (MAS) NMR spectra were resolved and assigned. These assignments differ from those tentatively suggested in previous work on the basis of empirical experimental correlations. The higher pressure polymorphs of MgSiO3 (majorite, akimotoite, and perovskite) are stabilized at pressures corresponding to the Earth's transition zone and lower mantle, with perovskite being the major constituent at depths >660 km. We present the first 17O NMR data for these materials and confirm previous 29Si work in the literature. The use of high-resolution multiple-quantum MAS (MQMAS) and satellite-transition MAS (STMAS) experiments allows us to resolve distinct oxygen species, and full assignments are suggested. The six polymorphs exhibit a wide variety of structure types, providing an ideal opportunity to consider the variation of NMR parameters (both shielding and quadrupolar) with local structure, including changes in coordination number, local geometry (bond distances and angles), and bonding. For example, we find that, although there is a general correlation of increasing 17O chemical shift with increasing Si-O bond length, the shift observed also depends upon the exact coordination environment.

Use of SPAM and FAM pulses in high-resolution MAS NMR spectroscopy of quadrupolar nuclei.

The merits of SPAM and FAM pulses for enhancing the conversion of triple- to single-quantum coherences in the two-dimensional MQMAS experiment are compared using (87)Rb (spin I=3/2) and (27)Al (I=5/2) NMR of crystalline and amorphous materials. Although SPAM pulses are more easily optimized, our experiments and simulations suggest that FAM pulses yield greater signal intensity in all cases. In conclusion, we argue that, as originally suggested, SPAM and FAM pulses are best implemented in phase-modulated whole-echo MQMAS experiments and that the use of SPAM pulses to record separate echo and antiecho data sets, which are then combined, generally yields lower signal-to-noise ratios.

First-principles calculations of solid-state (17)O and (29)Si NMR spectra of Mg(2)SiO(4) polymorphs.

The nuclear magnetic resonance (NMR) shielding and electric field gradient (EFG) tensors of three polymorphs of Mg(2)SiO(4), forsterite (alpha-Mg(2)SiO(4)), wadsleyite (beta-Mg(2)SiO(4)) and ringwoodite (gamma-Mg(2)SiO(4)), have been calculated using a density functional theory (DFT) approach with a planewave basis set and pseudopotential approximation. These Mg(2)SiO(4) polymorphs are the principal components of the Earth down to depths of 660 km and have been proposed as the hosts of water in the Earth's upper mantle and transition zone. A comparison of our calculations with single-crystal spectroscopic data in the literature for the alpha-polymorph, forsterite, shows that both the magnitude and orientation of the shielding and EFG tensors for O and Si can be obtained with sufficient accuracy to distinguish subtle differences in atomic positions between published structures. We compare calculated (17)O MAS NMR quadrupolar powder lineshapes directly with experimental lineshapes and show that we are able to reproduce them within the precision with which the NMR parameters may be determined from multi-parameter fitting. The relatively small amounts of sample available for the beta- and gamma-polymorphs, arising from the high pressures required for synthesis, has hindered the extraction of NMR parameters in previous work. The application of DFT calculations to these high-pressure polymorphs confirms previous spectral assignments, and provides deeper insight into the empirical correlations and observations reported in the literature. These first-principles methods are highly promising for the determination of local bonding in more complex materials, such as the hydrated forms of Mg(2)SiO(4), by aiding analysis of their multinuclear NMR spectra.