Larmor time scale

NMR spectroscopy is very sensitive to a wide timescale - on the order of seconds to nanoseconds. An accurate mathematical treatment of motional averaging in NMR spectroscopy is highly dependent on the relative timescale of the motional process, with respect to the Larmor time scale (the reciprocal of the NMR frequency), since nonsecular Hamiltonian terms (i.e., those that do not commute with the Hamiltonian) are mainly responsible for relaxation. Motional... 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

The dynamic window of a given NMR technique is in many cases rather narrow, but combining several techniques allows one to almost completely cover the glass transition time scale. Figure 6 shows time windows of the major NMR techniques, as applied to the study of molecular reorientation dynamics, in the most often utilized case of the 2H nucleus. Two important reference frequencies exist The Larmor frequency determines the sensitivity of spin-lattice relaxation experiments, while the coupling constant 8q determines the time window of line-shape experiments. 2H NMR, as well as 31P and 13C NMR, in most cases determines single-particle reorientational dynamics. This is an important difference from DS and LS, which access collective molecular properties. 

This means that the Larmor radius of the CM motion is completely determined by the initial distance between the electron and the nucleus in the plane perpendicular to the magnetic field. All amplitudes of the oscillations on the above-mentioned shorter time scales are small compared to this Larmor radius. We note that the above-mentioned effect of the classical self-stabilization of the ion on a Landau orbit is a generic phenomenon for regular phase space, i.e. it occurs for any regular initial conditions. 

Rates that are fast on the NMR linC Shape time scale (peaks fail to decoalesce at high temperatures) sometimes may be measured by observation at a different resonance frequency. Normally, nuclear spins precess around the field at their Larmor frequency. Application of the usual 90 pulse in the x direction places the spins in the xy plane, along they axis. (See Figure 1-15a). Continuous irradiation along the y axis (not a pulse) forces... 

One approach to improve the electron-nuclear polarization transfer rate in ONP experiments is to adapt time-tested Hartmann-Hahn-type approaches. Groups at Heidelberg and Leiden separately developed similar approaches (respectively dubbed Hartmann-Hahn ONP (HHONP) and nuclear orientation via electron spin locking (NOVEL) ) whereby a spin-lock mw pulse sequence is applied to the electrons such that their frequency in the rotating frame matches the Larmor frequency of the H nuclei in the lab frame. Thus, the formerly forbidden electron/nuclear flip-flop transitions effectively become thermodynamically allowed , improving the efficiency of the polarization transfer compared to MIONP experiments performed outside this Hartmann-Hahn condition. The polarization transfer typically occurs on the ps time scale, generally faster than both the electronic T and the triplet lifetime. ... 

Conventional X-ray diffraction measures a space and time average of the electronic density. Therefore, any dynamical disorder will be transformed into spatial disorder between positions whose probabilities are determined by the average time spent on each position. Certainly, one of the most tremendous advantages of NMR compared to X-ray diffraction is its ability to measure the occurrence of motion at different time-scales. Whether the motion correlation time is on the Larmor frequency scale, the linewidth scale or much slower (exchange NMR) will affect differently the NMR parameters like relaxation rates, apparent anisotropy and asymmetry of the interaction and ID or 2D lineshape. With suitable sequences, the motion correlation times and site probabilities as a function of an external parameter (temperature or pressure) can be explicitly measured. 

If the direction of the main component V z of the electric field gradient (EFG) fluctuates rapidly as a result of diffusion, the Mbssbauer spectrum may be changed in shape. Two atomic sites have very different isomer shift values and the jump between these two states also may show the time-dependent Mbssbauer spectra as a function of the jump firequency. The time scales over which the Mbssbauer effect can be used to observe the dynamical effect is determined by the characteristic times associated with the resonance the natural lifetime and the Larmor precession times of the hyperfine interactions. 

We assume a random walk, i.e., an incoherent motion, for the spin carrier. In practice this assumption is not restrictive. Coherence or incoherence of the motion is essentially a question of time scale. A motion appears coherent, i.e., ballistic, as long as it is not interrupted by any kind of collision. After a collision the memory is left and the motion appears incoherent. In spin dynamics studies the time scale to probe the motion corresponds to the Larmor periods in the applied magnetic fields, typically 10" and 10" s for the nuclear and electron spins, respectively. This is longer than the usual collision times of charge carriers in conducting materials. 

Fig. 2.6 Energy levels, drawn approximately to scale, for two spin systems. On the left is shown a homonuclear system (two protons) on this scale the a/3 and f)u states have the same energy. On the right is the case for a carbon-13 - proton pair. The Larmor frequency of proton is about four times that of carbon-13, and this is clear reflected in the diagram. The atf and fia states now have substantially different energies.

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