Distribution widths, spin-lattice

Figure 2. Spin-lattice relaxation time, T, as a junction of correlation time, t, and distribution width, p, for the tog-%2 distribution (22.6 MHz) (8)...

Figure 4. Spin-lattice relaxation time as a function of correlation time for distribution widths of p 8 (-------------) and p = 100 (---------) for 67.9 and 22.6 MHz (8)...

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

Relaxation is the establishment of the equilibrium distribution of spins after perturbation. For nuclear spins, relaxation is indnced by coupling to fluctuating magnetic fields, described by rate constants (R = /T ) and (f 2 = 1/T2). T is the spin-lattice relaxation time and is modulated by high-frequency fluctuations, whereas T2 describes spin-spin relaxation, which in addition to high-frequency fluctuations is also modulated by low-frequency processes such as chemical exchange. T2 determines line widths according to... 

The distribution of spins over these levels is the result of spin-spin interactions during some characteristic time T2 that is of order of inverse width of the magnetic resonance line shape. As it follows from the experience usually in solids this time T2 is significantly shorter than spin-lattice relaxation time Tj. The distribution of spins over the energy levels entirely determines the thermodynamic state of a spin system. It was appeared to be very convenient to introduce two spin temperatures for describing this distribution. 

Below 7c, a slow relaxing 1/3-tail signal appears, suggesting very slow spin fluctixations in the ordered state, in agreement with the earlier Mossbauer results (Chappert et al. 1982). The (nearly) static depolarization is obviously much faster than in the crystalline material, an outcome due to the increased width of field distribution caused by the randomness of distribution of ions on the lattice sites. No effect of LF was seen at any temperature in the amorphous sample, but at the time, fields above 0.4 T were difficult to generate at xSR spectrometers, and separately, temperatures below 3 K were not easily attained (compare to the more-advanced technology used recently for LF xSR in quasicrystals, described below). 

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