Nuclear Spin-Lattice Relaxation in Three-Spin Molecules

Abstract

urements 11 on uranium, L vacancies were produced by irradiating samples with x rays from molybdenum. This method of L vacancy production results in an appreciable proportion of Li vacancies (15-20%), so this result is not directly comparable with the present work.It may seem surprising that the L fluorescence yield measurements in this region do not appear to fall on a smoothly rising curve (see Fig. 5). It should be pointed out, however, that Coster-Kronig transitions of the Lu~>LniMy type are energetically possible at Z=90 and above, and those of the Lu -» LmMiv type at Z=94 and above. If the Lu and L m subshell yields are different, these Coster-Kronig transitions will introduce discontinuities in a plot of coj, versus Z.No theoretical computations of L fluorescence yields for these elements were found although a program was begun by Rose and Goertzel. 12 Theoretical computations of L fluorescence yields for elements with lower Z have been carried out by Pincherle. 13 ACKNOWLEDGMENTSThe authors wish to thank Paul Day for assistance in the use of the beta spectrometer and A. H. Jaffey for advice on the statistical treatment of the data. 11 The free longitudinal relaxation of the nuclear magnetization of systems of three identical spins J at the corners of an equilateral triangle is investigated using the semiclassical form of the density operator theory. The relaxation mechanism investigated is a fluctuating dipolar interaction between the spins. Assuming only that the symmetry of the thermal motion of the molecules preserves the complete equivalence of the three spins, the general relaxation equation is obtained before adopting models for this thermal motion. The effect of correlations between different pairwise interactions is studied; this effect can be more significant in the case of anisotropic reorientations possible in solids than for isotropic motion. For systems initially describable by a spin temperature, the effect of cross correlations always is to retard the relaxation. In general the relaxation is described by a sum of four exponentials, although three suffice for isotropic motion and two for the limit of long correlation times. An "effective relaxation time" is defined, the calculation of which is far simpler than that of the complete solution.

Methyl and t-butyl group rotation in a molecular solid:1H NMR spin-lattice relaxation and X-ray diffraction

“…The spin-lattice relaxation for an ensemble of randomly oriented and isolated methyl (CH 3 ) groups (which involves the modulation of only intraCH 3 1 H-1 H interactions) is inherently nonexponential because of the anisotropic nature of the rotation (the spin-spin vectors orient in a plane) and because the motion of the three spin-spin vectors are perfectly correlated. 17,18 CH 3 -nonCH 3 1 H-1 H interactions and interCH 3 1 H-1 H interactions tend to make the relaxation more exponential. 19,20 When the CH 3 rotation axis is moving on the NMR time scale (as is the case for a t-butyl group), the relaxation, also, tends to be more exponential.…”

Monitoring a simple hydrolysis process in an organic solid by observing methyl group rotation

“…When methyl group rotation is responsible for the relaxation, the relaxation is nonexponential near the maximum in the relaxation rate and at higher temperatures [2,[8][9][10][22][23][24][25][26][27][28]. The recovery of the perturbed magnetization M(0) at these higher temperatures can be fitted by a stretched exponential;…”

“…If the relaxation is exponential to within experimental uncertainty, β = 1 and R* is labeled R. This occurs in pure compounds like 1 and 2 at temperatures below the maximum in the relaxation rate [2,[8][9][10][22][23][24][25][26][27][28]. R* and β are not amenable to interpretation in any closed-form model and we use β solely as an indicator of the degree of nonexponentiality.…”

“…The solid state 1 H spin-lattice relaxation in all these samples results from CH 3 rotation and is modeled in terms of standard NMR relaxation theory [1], with appropriate modifications needed when the relaxation is caused by methyl group rotation [8][9][10]. The fitted NMR activation energies in the pure samples are in reasonable agreement with the barrier heights for methyl group rotation determined by electronic structure calculations in clusters of molecules based on the Xray structures of the pure crystals, both of which are reported here.…”

1H and 19F spin-lattice relaxation and CH3 or CF3 reorientation in molecular solids containing both H and F atoms

“…11,25,27 Independently and in addition, the nuclear spin-lattice relaxation of an ensemble of isolated CH 3 or CF 3 groups is inherently nonexponential. [28][29][30] Modeling the nonexponential relaxation in closed form and/or numerically due to both the crosstalk between 1 H Beckmann and Rheingold 3 and 19 F spins and due to the inherent nonexponential relaxation of the three-spin ½ system would be unwieldy. Fortunately, it is not necessary to consider both phenomenon simultaneously.…”