New Aspects of Spin Diffusion and Cross Relaxation in Solid-State NMR

Secondary water relaxation in a water/dimethyl sulfoxide mixture revealed by deuteron nuclear magnetic resonance and dielectric spectroscopy

We exploit the potential of a combined dielectric spectroscopy (DS) and deuteron nuclear magnetic resonance ((2)H NMR) approach to investigate the molecular dynamics in a supercooled 2:1 molar mixture of deuterated water (D(2)O) and dimethyl sulfoxide (DMSO). While DS probes the rotational motion of both components, application of (2)H NMR allows us to single out the dynamical behavior of the water molecules. Combining the results of both methods, we can follow the slowdown of the α-process of the mixture over more than 10 orders of magnitude in time, revealing that the Vogel-Fulcher-Tammann (VFT) equation describes well its temperature dependence down to the glass transition temperature, T(g) = 146 K. While the (2)H NMR data do not provide evidence for a secondary relaxation process in the weakly supercooled regime, they indicate that, in the deeply supercooled regime, T(g) ≤ T ≤ 160 K, the water molecules do show a secondary dynamical process, which is faster and exhibits a weaker temperature dependence than the α-process of the mixture. Consistently, the shape of the dielectric spectra changes in this temperature range. (2)H NMR rotational correlation functions reveal that this faster secondary water process destroys essentially all orientational correlation. In addition, these data show that the water reorientation process is characterized by a mean elementary jump angle smaller than 13°. Possible origins of the faster secondary water process in the deeply supercooled mixture are discussed.

Spin relaxation and ultra-slow Li motion in an aluminosilicate glass ceramic

The ion dynamics in a lithium aluminosilicate glass ceramic was studied using stimulated-echo 7Li-NMR. For temperatures 300 K<T<450 K the hopping correlation times, tau(C), were determined from the decay of the quadrupolar spin-alignment amplitude. The decay times were thermally activated with an energy barrier of 0.61 eV, in agreement with conductivity measurements. For T<300 K the temperature dependence of the decay times, now corresponding to T1Q, was much weaker. The T1Q times followed the same trend as the independently measured spin-lattice relaxation times, T1, but were a factor of about three shorter than those. The theoretical ratio of T1/T1Q is shown to be 25/8 in the slow-motion regime if quadrupolar spin relaxation prevails. This result explains the present observation and similar ones made for several Li ion conductors. The relaxation of the octupolar spin-alignment order is discussed.

Spectral spin diffusion and magnetic dipolar energy in the NMR of 13CH3 compounds

Spin diffusion between 13CH3 groups in solids is studied both theoretically and experimentally. It is shown to be dominated by mutual spin flip-flops of protons belonging to neighbouring methyl groups. Also nonmethyl protons may contribute significantly if present in the sample. The spin-rotational ground state of 13CH3 consists of 16 sublevels. When their populations are used to describe spin diffusion, eight population combinations are shown to be important, two of them corresponding to the 13C-proton and proton-proton intra-methyl magnetic dipolar energies, Dc and Dp, respectively. Spin-diffusion transitions modulate these combinations so that a further reduction to two sets of four combinations is possible, with no coupling between the sets. Coupled differential equations are derived to describe the time dependence of the combinations in each set. They are solved numerically and compared with experimental results on a single crystal of aspirin with 13C-labelled methyl groups at the carbon resonance. The 13C NMR induction signal was observed as a function of time after the preparation either at the carbon resonance (a two-pulse sequence) or at the proton resonance (proton saturation). Usually carbon spectra were computed first and then three of the mentioned population combinations were obtained from the individual spectral components. Some results on the time dependence of Dc were also obtained directly from the amplitude of the out-of-phase induction signal. Theoretical predictions are found to describe semiquantitatively the overall time dependence of these three combinations and especially their variation with different initial conditions, which are discussed in detail. Also the partial transfer of the magnetic dipolar energy between Dc and Dp is nicely explained. Reasons for discrepancies are discussed.

The proton nuclear magnetic shielding tensors in biphenyl: experiment and theory

Line-narrowing multiple pulse techniques are applied to a spherical sample crystal of biphenyl. The 10 different proton shielding tensors in this compound are determined. The accuracy level for the tensor components is 0.3 ppm. The assignment of the measured tensors to the corresponding proton sites is given careful attention. Intermolecular shielding contributions are calculated by the induced magnetic point dipole model with empirical atom and bond susceptibilities (distant neighbours) and by a new quantum chemical method (near neighbours). Subtracting the intermolecular contributions from the (correctly assigned) measured shielding tensors leads to isolated-molecule shielding tensors for which there are symmetry relations. Compliance to these relations is the criterion for the correct assignment. The success of this program indicates that intermolecular proton shielding contributions can be calculated to better than 0.5 ppm. The isolated-molecule shielding tensors obtained from experiment and calculated intermolecular contributions are compared with isolated-molecule quantum chemical results. Expressed in the icosahedral tensor representation, the rms differences of the respective tensor components are below 0.5 ppm for all proton sites in biphenyl. In the isolated molecule, the least shielded direction of all protons is the perpendicular to the molecular plane. For the para proton, the intermediate principal direction is along the C-H bond. It is argued that these relations also hold for the protons in the isolated benzene molecule.

Simple modeling of dipolar coupled 7Li spins and stimulated-echo spectroscopy of single-crystalline beta-eucryptite

Stimulated-echo spectroscopy has recently been applied to study the ultra-slow dynamics of nuclear spin-3/2 probes such as 7Li and 9Be in solids. Apart from the dominant first-order quadrupolar interaction in the present article also the impact of the homonuclear dipolar interactions is considered in a simple way: the time evolution of a dipole coupled pair of spins with I = 3/2 is calculated in an approximation, which takes into account that the satellite transitions usually do not overlap. Explicit analytical expressions describing various aspects of a coupled quadrupolar pair subjected to a Jeener-Broekaert pulse sequence are derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor.

Stimulated-echo NMR spectroscopy of 9Be and 7Li in solids: method and application to ion conductors

The generation of pure quadrupolar stimulated-echo spectra is successfully demonstrated for the spin-3/2 probe 9Be in a single crystal of triglycine fluoberyllate. This solid exhibits a paraelectric-to-ferroelectric phase transition. From experiments carried out for various mixing times no indications for a slow soft mode could be detected in this crystal. Then ion conducting lithium metal phosphates were studied using 7Li, another spin-3/2 probe which allows for a non-selective excitation of the entire NMR spectrum. In the indium and the scandium phosphates ultra-slow Li hopping processes could be detected directly via the stimulated-echo technique in a time range of up to four orders of magnitude. Due to the relatively large gyromagnetic ratio and thus strong dipolar interactions of 7Li no pure quadrupolar echoes could be generated. However, from a variation of the evolution times the quadrupolar effects could be separated from the dipolar ones. Finally, the differences in the ion hopping times of lithium indium phosphate and of lithium scandium phosphate are briefly discussed.

Deuteron NMR study of the diverse mobility of the ammonium ions in the ordered phase of (ND4)2PtCl4

A detailed description of the diverse mobility of the ND4+ ions in the low-temperature ordered phase of (ND4)2PtCl4 is developed on the basis of single-crystal deuteron NMR spectra and site-selective T1 measurements. The ordered phase of (ND4)2PtCl4 consists of two kinds of domains in which the orientation of the ND4+ tetrahedra differs by a 90 degrees rotation about an axis which otherwise is a two-fold symmetry axis of the tetrahedra. Inside the domains, the ND4+ ions do not reorient at low temperatures. The domains are separated by domain walls which contain, according to the deuteron NMR spectra, about 10% of all ND4+ ions. These ions are highly mobile even at 10 K. On rising the temperature, the thickness of the domain walls increases, that is, the ions in more and more layers become mobile. Moreover, we provide evidence for fluctuations of the locations of the domain walls. The central resonance of the domain-wall ions shows a complicated structure below 36 K. On the basis of a tunnelling hypothesis we make an attempt to account for this structure. There are indications that the tunnelling process is incoherent.

One- and two-dimensional 15N exchange CP/MAS NMR studies of the structure and electronic properties of the intermolecular N-H...N hydrogen bond in imidazole crystal

The hydrogen bond of the type N-H...N in imidazole crystal has been studied by one and two-dimensional 15N exchange CP/MAS NMR measurements as well as the powder NMR spectrum. The chemical shift anisotropies for -N= and -N< were determined from the powder 1D spectrum. In 2D exchange CP/MAS NMR spectrum, the cross peaks between the 15N main resonance peaks for -N= and -N< were observed, implying that magnetization exchange between -N= and -N< takes place. The 1D exchange CP/MAS NMR measurements determined the exchange rate of magnetization at 289 K to be 1.3 and 1.5 s(-1) for -N= and -N<, respectively. The proton-driven spin-diffusion model interprets the experimental values, and the exchange rate depends strongly on the RF power of the proton decoupling field, suggesting that the magnetization transfer between -N= and -N< takes place by the 1H-driven spin-diffusion mechanism.

Precision measurement of the quadrupole coupling and chemical shift tensors of the deuterons in alpha-calcium formate

Using calcium formate, alpha-Ca(DCOO)2, as a test sample, we explore how precisely deuteron quadrupole coupling (QC) and chemical shift (CS) tensors Q and sigma can currently be measured. The error limits, +/-0.09 kHz for the components of Q and +/-0.06 ppm for those of sigma, are at least three times lower than in any comparable previous experiment. The concept of a new receiver is described. A signal/noise ratio of 100 is realized in single-shot FT spectra. The measurement strategies and a detailed error analysis are presented. The precision of the measurement of Q is limited by the uncertainty of the rotation angles of the sample and that of sigma by the uncertainty of the phase correction parameters needed in FT spectroscopy. With a 4-sigma confidence, it is demonstrated for the first time that the unique QC tensor direction of a deuteron attached to a carbon deviates from the bond direction; the deviation found is (1.2+/-0.3 degrees ). Evidence is provided for intermolecular QC contributions. In terms of Q, their size is roughly 4 kHz. The deuteron QC tensors in alpha-Ca(DCOO)2 (two independent deuteron sites) are remarkable in three respects. For deuterons attached to sp2 carbons, first, the asymmetry factors eta and, second, the quadrupole coupling constants C(Q), are unusually small, eta1=0.018, eta2=0.011, and C(Q1)=(151.27+/-0.06) kHz, C(Q2)=(154.09+/-0.06) kHz. Third, the principal direction associated with the largest negative QC tensor component lies in and not, as usual, perpendicular to the molecular plane. A rationalization is provided for these observations. The CS tensors obtained are in quantitative agreement with the results of an earlier, less precise, line-narrowing multiple-pulse study of alpha-Ca(HCOO)2. The assignment proposed in that work is confirmed. Finally we argue that a further 10-fold increase of the measurement precision of deuteron QC tensors, and a 2-fold increase of that of CS tensors, should be possible. We indicate the measures that need to be taken.