Magnetization equilibrium

The equilibrium magnetization corresponds to a minimum free energy which implies that... 

B1.15.2.2 THERMAL EQUILIBRIUM, MAGNETIC RELAXATION AND LORENTZIAN UNESHAPE... 

Figure 1.17 A crosvsectional view of the /z-plane (longitudinal plane) after application of pulse Bi along the c -axis (perpendicular to this plane). The pulse B, applied along the -axis causes the equilibrium magnetization Mo to bend by an angle 0. The magnitude of the component M, along the y -axis is Mo sin 6.

Figure 1.18 Effect of applying a 90° pulse on the equilibrium magnetization Continuous application of a pulse along the x -axis will cause the magnetization vector (Ml) to rotate in the y z-plane. If the thumb of the right hand points in the direction of the applied pulse, then the partly bent fingers of the right hand point in the direction in which the magnetization vector will be bent.

Based on the right-hand thumb rule described in the text, and assuming that only an equilibrium magnetization directed along the z-axis exists, draw the positions of the magnetization vectors after the application of ... 

Figure 1.42 A90° pulse brings the equilibrium magnetization to the )i -plane. Itsorien-tation in the x y-plane depends on the direction of the pulse. Applying the pulse along one axis causes the magnetization to rotate in a plane defined by the other two axes.

Before the application of a pulse, only equilibrium magnetization exists, directed toward the z-axis corresponding to the zero coherence level for all coherence pathways. When the pulse is applied, two coherence levels, + 1 and —1, are created during the evolution period that evolve into M and respectively, where [Pg.74]

This equation is called the Curie law and relates the equilibrium magnetization M0 to the strength of the magnetic field B0. The constants have the following meaning I is the nuclear spin quantum number (see below), y is the gyromagnetic ratio specific for a given isotope, h is Planck s constant, kB is Boltzmann s constant, N is the number of nuclei and T is the temperature. 

Figure 6 The inversion-recovery experiment. The dynamic range is twice the equilibrium magnetization.

If M0 is the equilibrium magnetization along B and M- is the z-component under non-equilibrium conditions, then we assume that Mz approaches M0 with first-order kinetics ... 

NMR spin relaxation is not a spontaneous process, it requires stimulation by a suitable fluctuating field to induce an appropriate spin transition to reestablish equilibrium magnetization. There are four main mechanisms for obtaining relaxation dipole-dipole (most significant relaxation mechanism for I = 1/2 nuclei), chemical shift anisotropy, spin rotation, and quadrupolar (most significant relaxation mechanism for I > 1/2 nuclei) (Claridge, 1999). 

For the PP sequence, we need Mq = (equilibrium magnetization at the field Bp) so that we must keep... 

For a given number of nuclides placed in the sample coil volume, the inherent S/N ratio p is a parameter depending only on the probe and preamplifier assembly. It is usually measured in terms of the maximum FID amplitude after a 90° pulse applied after the sample has reached its equilibrium magnetization Ma in the acquisition field Ba- Defined in this way, it is independent of the details of any FFC sequence. 

In this equation, M oo) is the equilibrium magnetization, and B2 is the strength of the irradiating or decoupling rf field. 

A simple way to prepare a non-equilibrium state of the longitudinal magnetization is to invert the equilibrium magnetization (or its NOE-enhanced counterpart) by a tt pulse. This preparation is used in the classical inversion-recovery (IR) method as described by Void et al. [24] in the early... 

The terms pc and py correspond to 1/Tic and 1/Tih, respectively, and CTCH is the cross-relaxation rate. It should be stressed that the simplicity of the above equation is a consequence of the rareness of the I spins and of the dominant strength of the dipolar interaction between directly bonded nuclei. The situation for homonuclear proton spin systems is often more complicated, since the protons usually constitute a much larger spin system, and a separation into distinct two-spin systems may be not valid in this case. The broadband irradiation of the protons yields, in a steady state, Mhz = 0 and M z = Mj (1 rj). The factor 1 + 77 is called, as introduced above, the nuclear Overhauser enhancement factor. The NOE factor is related in a simple way to the equilibrium magnetizations of the I- and S-spins (which are proportional to the magnetogyric ratios 71 and 7s), the cross-relaxation rate and the relaxation rate of the I-spin ... 

The rehydrated samples were obtained by exposing dehydrated samples to water vapor at least three days over saturated NH4GI solution at room temperature. A duraction of 0.5 s between scans were allowed for nuclear spin to recover to their equilibrium magnetization. The one—dimensional Na NMR spectra were recorded by using the spin—echo technique. The strength of the radio-frequency field for the two dimensional nutation experiments was 80 kHz and 128 ti values were used (0 250 /is). Each two- dimensional experiment took about 12 hours of spectrometer time. 

Relaxation can be described in terms of the magnetization vector components. At resonance, the equilibrium magnetization M0 parallel to B0 decreases to Mz, due to the transitions between the nuclear magnetic energy levels caused by the alternating field B,. Following resonance, the equilibrium of the nuclear spins with their lattice and with each other is restored by relaxation. 

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