Solid Spin-lattice Relaxation Research Articles

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.

Nuclear spin-lattice relaxation in the triply rotating frame and ultraslow molecular motions in solids

A method for measuring nuclear magnetic spin-lattice relaxation in solids in the effective field He3 acting in the triply rotating frame (TRF) is described. The method advances the previously described techniques whereby nuclear magnetic resonance and relaxation in the rotating (RF) and doubly rotating frames (DRF) are measured directly. In the present work, the RF and DRF are employed for suppressing the secular part of nuclear dipole-dipole (DD) interactions in the first two orders. As a result, the higher-order DD interactions (four- and five-particle ones) were separated, and their contribution to the nuclear spin-lattice relaxation in the TRF was studied experimentally. The experiments were carried out on protons in polycrystalline benzene. With the introduced technique, an overall spin-lattice relaxation decay in the TRF was recorded continuously during a single radio-frequency pulse with a length not exceeding 1 s. The contribution of multiproton nonsecular DD interactions to the proton spin-lattice relaxation in the TRF was observed selectively as a pronounced local minimum in the temperature dependence of the relaxation timeT 1ϱϱϱ. This contribution corresponds to ultraslow motion of benzene molecules with a rate about γHe3 ≈ 2π · (101-103) s-1 and is determined quantitatively by specific correlation functions corresponding to the multiparticle nonsecular DD interactions of protons. The prospects of using this method for studying ultraslow atomic and molecular dynamics in solids are discussed.

Spin diffusion and spin-lattice relaxation in pulse spin-locking in solids containing paramagnetic impurities

The spin diffusion and spin-lattice relaxation in solids containing paramagnetic impurities under the influence of a multiple-pulse spin-locking radio-frequency sequence are studied. The diffusion equation is obtained, providing the possibility of finding the time dependence of the magnetization. The spin-lattice relaxation time is calculated as a function of the correlation time and multiple-pulse field parameters.

Characterizing Nonexponential Spin-Lattice Relaxation in Solid-State NMR by Fitting to the Stretched Exponential

Spin-lattice relaxation in solids often deviates from the usual exponential law, for example, in dilute spin-12 solids like silicon carbide, when relaxation arises from fixed paramagnetic impurities. We examine nonexponential spin-lattice relaxation from the point of view of nonlinear regression to the stretched-exponential function M(τ) = a − bexp[−(τ/T′)n], where n is typically 1 or 0.5 but can have intermediate values. Criteria for error estimation as well as an optimal choice of delay times τ are examined in detail and tested on typical data from our studies on silicon carbide. Two methods are outlined for the estimation of confidence intervals which are typically found to be somewhat larger than the standard errors in the parameters. The typical experiment for determination of spin-lattice relaxation time is found to be robust even when relaxation is nonexponential. The determinant of the curvature matrix is a good experimental design criterion and correlates well with the estimated errors. While any reasonable choice of points yields good results, an optimal choice of delay times τ can be made by following the guidelines presented here.

Theory of the effect of random rotational jumps on the nuclear spin-lattice relaxation in solids

Starting from the weak collision limit, the BPP theory is applied to develop a theory of nuclear spin-lattice relaxation resulting from random rotational jumps of molecular groups in solids. The molecular motion modeled by an invariant continuous-time random walk on a finite group of rotations is assumed to modulate the dipole-dipole interaction between resonant nuclei. Straightforward group-theoretical techniques are used, yielding analytic expressions for the spin-lattice relaxation times T 1 and T 1 π , The tables included in the text allow our results to be applied to numerous cases of practical interest. The effect of a ( π 2 ) rotational jump of the PF 6 − ion is analyzed to illustrate the theory.

ChemInform Abstract: The Impact of the Symmetry Properties of Classical Reorienting and Tunnelling Methyl Groups on the Spin‐Lattice Relaxation in Solids

Chemischer InformationsdienstVolume 15, Issue 36 Reviews ChemInform Abstract: The Impact of the Symmetry Properties of Classical Reorienting and Tunnelling Methyl Groups on the Spin-Lattice Relaxation in Solids R. A. WIND, R. A. WINDSearch for more papers by this authorS. EMID, S. EMIDSearch for more papers by this authorD. J. LIGTHELM, D. J. LIGTHELMSearch for more papers by this authorJ. F. J. M. POURQUIE, J. F. J. M. POURQUIESearch for more papers by this authorJ. SMIDT, J. SMIDTSearch for more papers by this author R. A. WIND, R. A. WINDSearch for more papers by this authorS. EMID, S. EMIDSearch for more papers by this authorD. J. LIGTHELM, D. J. LIGTHELMSearch for more papers by this authorJ. F. J. M. POURQUIE, J. F. J. M. POURQUIESearch for more papers by this authorJ. SMIDT, J. SMIDTSearch for more papers by this author First published: September 4, 1984 https://doi.org/10.1002/chin.198436364Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume15, Issue36September 4, 1984 RelatedInformation

Spin-lattice relaxation in solids

Spin-lattice relaxation times ( T 1) contain information about molecular motion. We present a formalism for extracting this information from T 1 values measured for static and spinning polycrystalline solids. General equations are developed for orientation dependent line positions (frequencies) and values of T 1. The correlation functions in the general T 1 expressions are evaluated for various jump and diffusive models of motion, assuming an axially symmetric coupling mechanism. Explicit expressions for dipolar and quadrupolar values of T 1 are presented for two- and three-site jumps, and for continuous diffusion about a symmetry axis. It is shown that T 1measurements can readily distinguish between three-site jump and continuous diffusion models of methyl reorientation on the basis of the different angular dependence calculated for T 1 in these two models. In general, T 1 is axially asymmetric for the three-site jump model, resulting in nonexponential relaxation for the spectral lines in the axially symmetric powder pattern.

The influence of symmetry-restricted spin diffusion on the spin-lattice relaxation of molecular groups in solids

The influence of symmetry-restricted spin diffusion on the spin-lattice relaxation of rapidly reorienting molecular groups in solids is considered. Each group consists of three identical spin-12 nuclei at the corners of an equilateral triangle. First, the spin-lattice relaxation of isolated three-spin systems is considered. Then symmetry-restricted spin diffusion is treated and its influence on the spin-lattice relaxation in solids is discussed. The resulting coupled spin-lattice relaxation equations explain phenomena like non-exponential relaxations in solids. Previous works concerning the spin-lattice relaxation in the symmetry-restricted spin diffusion model are discussed briefly.

Quadrupolar spin-lattice relaxation in solids

Calculations have been carried out for quadrupolar spin-lattice relaxation in NMR experiments, involving nuclei in non-cubic environments, which extend and, in certain cases, correct previous treatments for I=3/2, 5/2, 7/2 and 9/2. In particular, pulsed NMR experiments are treated and the results are presented in a way which reveals non-exponential effects. Since it is not in general meaningful to introduce a spin-lattice relaxation time some emphasis is placed on possible methods for measuring the quantities W2 and W1 which are related to the transition rates for Delta m=+or-2 and Delta m=+or-1 transitions involved in two-phonon relaxation processes. Results for 59Co in K3Co(CN)6 are briefly discussed.

Influence of Sample Rotation on the NMR Spin-Lattice Relaxation of CH3Groups in Solids

When nuclear spin-lattice relaxation in solids is due to rapid random rotation of methyl groups, the Zeeman relaxation can be nonexponential. This is because the magnetization is dynamically coupled to the so-called rotational polarization. It is shown that rotating the sample perpendicular to the magnetic field with angular velocity large compared with the relaxation rate decouples these parameters, resulting in an almost exponential Zeeman relaxation close to that predicted by the spin-temperature theory.

Time reversal invariance and the nuclear quadrupole spin-lattice relaxation tensor

A theoretical study is made of the nuclear electric quadrupole spin-lattice relaxation in solids, for the case where the quadrupole interaction is small compared with the Zeeman interaction. It is shown that, provided the external magnetic field H0 has no effect on the lattice motions which cause the relaxation, the principle of time reversal invariance implies that the nuclear quadrupole spin-lattice relaxation tensor is real and the relaxation probabilities W1 and W2 are invariant with respect to reversal of H0. If the magnetic field does influence the 'lattice', it is found that W1 and W2 are still invariant with respect to reversal of H0 even though the relaxation tensor is not necessarily real. A simple, classical model is presented to illustrate the results obtained quantum mechanically. Finally, it is shown that the anomalous orientation dependence of W2/W1 recently observed for 23Na in NaNO3 cannot be attributed to failure of the principle of time reversal invariance.

Nuclear-Magnetic-Resonance Spin-Lattice Relaxation in High and Low Fields

An experimental and theoretical study is presented of the magnetic-field dependence of nuclear-magnetic-resonance (NMR) spin-lattice relaxation in solids. Theoretically, density-matrix methods are used along with the spin-temperature assumption to derive an expression for the field dependence of the relaxation time ${T}_{1}$ in the laboratory and rotating reference frames. It is shown that with the assumptions of extreme narrowing and cubic symmetry, the ratio of the Zeeman relaxation time to the dipolar relaxation time should be two for a one-ingredient crystal in both the laboratory and rotating reference frames. The ratio of the Zeeman ${T}_{1}$ to the dipolar ${T}_{1}$ is also calculated for two-ingredient crystals. To test the theory, measurements were made of the field dependence of the laboratory- and rotating-frame spin-lattice relaxation times of the sodium nuclei in NaCl. There is a large discrepancy between the calculated and measured ratios of high-field to low-field relaxation times in both frames. The origin of the discrepancy is not fully understood.

Saturation effects in nuclear spin-lattice relaxation in solids

Saturation effects in nuclear spin-lattice relaxation in solids

Nuclear quadrupole spin-lattice relaxation in solids

Nuclear quadrupole spin-lattice relaxation in solids has been investigated using pulsed nuclear induction techniques. By selective excitation of the quadrupolar spin system, several new modes of relaxation are observed. Measurements of these modes are used to determine the individual transition probabilities W 1 and W 2 associated with Δ m = ± 1 and ± 2 quadrupole spin-lattice relaxation. W 1, W 2, and the spin-lattice relaxation time T 1 of the Cl 35 pure quadrupole resonance in p-C 6H 4Cl 2, KClO 3, and NaClO 3 have been measured in the temperature range 77–300°K. The B ayer theory of quadrupole spin-lattice relaxation is applied to p-C 6H 4Cl 2 to calculate W 1 and W 2. From the B ayer theory and the separate measurement of W 1 and W 2, information is obtained about the lifetime of excited torsional states and the mode of torsional oscillation which provides the dominant relaxation contribution in p-C 6H 4Cl 2. Measurements of the spin-lattice relaxation in NaClO 3 and KClO 3 are compared with C hang's theory of quadrupole relaxation. The experimental results suggest that the model used by C hang to describe the fluctuating internal electric field gradient in NaClO 3 responsible for the Cl 35 relaxation is inadequate.