Magnetization precession

One may say that the magnetic precession ( the magnetic term ) is added to the relaxation at a rate rp, 7s or T. One must keep in mind the fact that, since all approximations adopted in Section 3.1 are in force, the... 

Of course, along with magnetic precession, relaxation processes take place in molecules after pulsed excitation. If the relaxation of a If-rank polarization moment is characterized by a rate constant IV, then the absolute value, i.e., Modpg of pq, diminishes over time ( decays ) exponentially ... 

The rate at which the nuclear magnet precesses (v0) is also proportional to yB0. As with any electrical generator, if you turn the crank faster you get a higher voltage out of the generator. 

Evolution the magnetization precesses in the x-y plane for a period t, encoding its chemical shift as a function of t. ... 

Equation 2.45, often called the Larmor equation, is the basic mathematical expression for NMR. The precession (or Larmor) frequency is directly proportional to the applied magnetic field and is also proportional to y (or (Ji/I), which varies from one nuclide to another. One significant feature of the Larmor equation is that the angle 0 does not appear. Hence the magnetization precesses at a frequency governed by its own characteristic properties and that of the magnetic field. On the other hand, the energy of this spin system does depend on d, because... 

A positive rotation about z then leads to magnetization precessing in the order x — y —x — —y. ... 

FIGURE 9.1 Use of a spin echo pulse sequence to refocus two magnetizations precessing at different frequencies because of difference in chemical shift. 

The fundamental premise of 2D NMR is that magnetization precesses during the fj period and, as we have seen, thus introduces a modulation into the magnetiza-... 

We now look at the evolution of the density matrix for the one spin system as the magnetization precesses in the rotating frame. Once more, we apply Eq. 11.16 in the same manner we did in Section 11.2 to take into account the effect of the rotating frame. In this case we obtain... 

The transformation of the density matrix by a 90° pulse and its subsequent evolution as the magnetization precesses freely depend on whether the pulse is applied only to one nucleus or to both I and S. We treat first the situation that would normally occur in a heteronuclear system, where a 90x pulse is applied only to the I spins—a 90pulse. This treatment is, of course, also applicable to a homonu-clear system subjected to a selective rf pulse. 

The expressions for Sx and Sy are redundant. They are both detected in quadrature by the normal phase-sensitive detection scheme. Note that from /, where we gain the intensity factor of y,/ys = 4 for H/13C, the a magnetization precessing at fi — tt/ has intensity of 4, while from S this gives — 1, for an overall intensity of 3. For the /3 magnetization both components are negative to give a total of—5. 

NMR frequency, the magnetization precesses around the z-axis with the offset frequency Qq. In this case the transverse magnetization components are described by... 

The magnetization precesses about this effective field at frequency coeff given by... 

In this situation the motion of the magnetization vector is very simple. Just as in Fig. 3.7 the magnetization precesses about the field, thereby rotating in the zy-plane. As we have seen above the precession frequency is co. If the RF field is applied for a time tp, the angle, fi, through which the magnetization has been rotated will be given by... 

So, if we have created some transverse magnetization (for example by applying a 90° pulse) overtime relaxation will cause this magnetization to decay away to zero. The free induction signal, which results from the magnetization precessing in the xy plane will therefore decay away in amplitude. This loss of v- and y-magnetization is called transverse relaxation. 

In words this says that the magnetization precesses from -y towards +x. 

In the static field Hq the nuclear magnets precess around the z axis, but a signal is only induced in the detector if they are in phase so that the resultant vector in the XY plane is not zero. The loss of this phase coherence is associated with T2 such that... 

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