Local Larmor frequency

Spatial localization in imaging is by means of magnetic field gradients, which impose local Larmor frequencies dependent upon position. The resonance offset frequency (in radians per second) of a spin at position x in a field gradient Gx is equal to yxGx. 

It is appropriate here to provide only brief details of the principles behind MRI methods. An excellent book on the subject, particularly with regard to porous media, is that of Callaghan. Nuclear spins in a magnetic field gradient G will have different Larmor precession frequencies depending on their spatial location. Thus, during a field gradient, the local Larmor frequency will be... 

Fig. 4 Stacked Fourier transforms of the NMR spin echoes in D-RADP-25 versus echo delay time at T = 65 K. In contrast to D-RADP-20 (Fig. 2) there are still two rims present at this low temperature indicating the coexistence of two different phase states. The rim at the Larmor frequency vl originates from Rb spins localized in short range ordered glass clusters, whereas the rim at vl + 8 kHz is produced by spins sitting in FE clusters [17]...

In spin-lattice relaxation, the excited nuclei transfer their excitation energy to their environment. They do so via interaction of their magnetic vectors with fluctuating local fields of sufficient strengths and a fluctuation frequency of the order of the Larmor frequency of the nuclear spin type. Depending upon the atomic and electronic environment of a nucleus in a molecule and the motion of that molecule, there are five potential mechanisms contributing to spin-lattice relaxation of the nucleus. 

The power spectrum of the local magnetic field fluctuations shows different features at different Larmor frequency and temperature. The interpretation of the results is that the dominant source of these fluctuations is spatial transport of the electrons along the polymer chains and the frequency and temperature dependences reflect the details of their motions. 

NMR has become such an invaluable technique for studying the structure of atoms and molecules because nuclei represent ideal noninvasive probes of their electronic environment. If all nuclei of a given species responded at their characteristic Larmor frequencies, NMR might then be useful for chemical analysis, but little else. The real value of NMR to chemistry comes from minute differences in resonance frequencies dependent on details of the electronic structure around a nucleus. The magnetic field induces orbital angular momentum in the electron cloud around a nucleus, thus, in effect, partially shielding the nucleus from the external field B. The actual or local value of the magnetic field at the position of a nucleus is expressed as... 

Time development caused by local variations of the Larmor frequency... 

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