Temperature Dependence of Pure Nuclear Quadrupole Spin—Lattice Relaxation in SnI4

Abstract

The pure nuclear quadrupole spin—lattice relaxation times for 127I in SnI4 have been measured over the temperature range from 4.2° to 300°K. Measurements were performed on both the 208- and 416-Mc/sec transitions. From the solution of the rate equations the transition probabilities, W1 and W2, corresponding to Δm=±1 and Δm=±2 transitions, are evaluated using the experimentally determined relaxation times. The ratio of the two required relaxation times is found to have a rather insensitive dependence upon W2/W1 and could be determined only at temperatures below 77°K. For temperatures below about 15°K a third relaxation time was required to describe the observed relaxation curves. Since cross-relaxation or spin—diffusion effects were not observed, the determination of the spin—lattice relaxation times from the stimulated echo was found to give far more accurate results than the conventional two-pulse technique. The theory of quadrupolar relaxation developed by Bayer and the modification given by Woessner and Gutowsky have been reformulated for nuclei with spin 53. The third time constant required to fit the low-temperature data is predicted by either theory even though the details of the theory do not agree well with experiment results. The ratio W2/W1 is found from the experimental observations to increase by a factor of about 2 as the temperature decreases from 77° to about 7°K. The results obtained from Bayer and from Woessner and Gutowsky indicate an opposite effect. However, by assuming a temperature dependence for the molecular vibrational frequencies, better agreement can be obtained between the expressions for W2/W1 and the experimentally determined values. The temperature dependence of the lifetime of the molecular torsional oscillations has not been determined in detail and remains as a second parameter of poor definition. Because of the limited information describing the molecular torsional oscillations, relatively poor agreement is obtained between the theoretical and experimental determinations of the individual W1 and W2 transitions.

Short-range ion dynamics in methylammonium lead iodide by multinuclear solid state NMR and127I NQR

“…Again according to the Bayer theory, 67 this temperature dependence can be used to calculate an accurate estimate of the correlation time t a of the torsional vibrations, albeit a closed solution for a spin 5/2 nucleus does not exist. 72 Under certain assumptions, a partial solution can still be found for our system, but only in a very narrow temperature range (290-340 K), making the obtained t a values of 2 Â 10 À10 s (290 K) and 4 Â 10 À10 s (340 K) only indicative. We refer the reader to the ESI, † (Section 8) for the complete treatment and related assumptions.…”

Separation of Quadrupolar and Magnetic Contributions to Spin–Lattice Relaxation in the Case of a Single Isotope

“…The literature contains mainly calculations of multiexponential magnetization recovery laws for the case of either purely magnetic or purely quadrupolar fluctuations, with Andrew et al 1 being the first to treat the case of a static quadrupolar perturbed Zeeman Hamiltonian (spin I = 3/2, 5/2). These calculations were extended to higher spins [2][3][4] and to the case of a static quadrupolar Hamiltonian [5][6][7][8] . MacLaughlin et al 9 treated the case of a static quadrupolar Hamiltonian (η = 0) with mixed fluctuations in a kind of perturbation expansion, whereas Rega 10 presented, for this case, an exact solution in the limit of time approaching zero.…”

“…These calculations were extended to higher spins [2][3][4] and to the case of a static quadrupolar Hamiltonian [5][6][7][8] . MacLaughlin et al 9 treated the case of a static quadrupolar Hamiltonian (η = 0) with mixed fluctuations in a kind of perturbation expansion, whereas Rega 10 presented, for this case, an exact solution in the limit of time approaching zero.…”

Untitled

“…The literature contains mainly calculations of multi-exponential magnetization recovery laws for the case of either purely magnetic or purely quadrupolar fluctuations, with Andrew and Tunstall [1] being the first to treat the case of a static quadrupolar perturbed Zeeman Hamiltonian (spin I = 3/2, 5/2). These calculations were extended to higher spins [2][3][4] and to the case of a static quadrupolar Hamiltonian [5][6][7][8]. MacLaughlin et al [9] treated the case of a static quadrupolar Hamiltonian (η = 0) with mixed fluctuations in a kind of perturbation expansion, whereas Rega [10] presented, for this case, an exact solution in the limit of time approaching zero.…”