Magnetization vector pulse effects

Figure 1.14 Effect of radiofrequency pulses of different durations on the position of the magnetization vector.

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.

The effect of pulses on magnetization vectors is much easier to understand in the rotating frame than in the fixed frame. How do we arrive at the chemical-shift frequencies in the rotating frame ... 

Figure 2.4 (A) Pulse sequence for the gated spin-echo (GASPE) or attached proton test (APT) experiment. (B) Effect of the pulse sequence on the C magnetization vectors of a CH group.

Nuclei resonating at different chemical shifts will also experience similar refocusing effects. This is illustrated by the accompanying diagram of a two-vector system (acetone and water), the nuclei of which have different chemical shifts but are refocused together by the spin-echo pulse (M, = magnetization vector of acetone methyl protons, M(v = magnetization vector of water protons). 

Figure 5.10 (A) Selective spin-flip pulse sequence for recording heteronuclear 2D / resolved spectra. (B) Its effect on magnetization vectors. The selective 180° pulse in the middle of the evolution period eliminates the large one-bond coupling constants, /< ...

Fig. 1.2 Behavior of the magnetization in a simple echo experiment. Top a free induction decay (FID) follows the first 90° pulse x denotes the phase of the pulse, i.e., the axis about which the magnetization is effectively rotated. The 180° pulse is applied with the same phase the echo appears at twice the separation between the two pulses and its phase is inverted to that of the initial FID. Bottom the magnetization vector at five stages of the sequence drawn in a coordinate frame rotating at Wo about the z axis. Before the 90° pulse, the magnetization is in equilibrium, i.e., parallel to the magnetic field (z) immediately aftertbe 90° pulse, it has been rotated (by90° ) into the transverse (x,y) plane as it is com-...

Now consider the effect of a 180° pulse on the ensemble of spins represented in Fig. 5.3. The RF pulse is actually a rotation, and we will see in Chapter 6 that this rotation is exactly analogous to the precession of magnetic vectors around the B0 field. The pulse itself can be viewed as a magnetic field (the Bi field) oriented in the x-y plane, perpendicular to the B0 field, and for the short period when it is turned on it exerts a torque on the individual nuclear magnets that makes them precess counterclockwise around the B field. This is shown in Fig. 5.4. Each magnetic vector is rotated by 180°, so the entire structure of two cones is turned upside down, with the upper cone and all its magnetic vectors turned down to become the lower cone, and the lower cone turned up to become the upper cone. This... 

We usually ignore relaxation during short delays (e.g., 1/(2J) is usually milliseconds or tens of milliseconds) and consider it only when relaxation is essential to the experiment (e.g., inversion-recovery or nuclear Overhauser effect (NOE) experiments, typically hundreds of milliseconds or seconds for small molecules). Pulses are very short (tens of microseconds), so we do not usually worry about either evolution or relaxation during pulses. Although pulses may look fat in pulse sequence diagrams, they are really much shorter than most delays and their duration is not important in terms of evolution. Pulses lead to rotation of the net magnetization vector around the B axis, always in the counterclockwise direction. 

S0 field interacting with the 13C nucleus) is sensitive only to 13C pulses, because only these can rotate the 13C net magnetization vectors. But /-coupling evolution is a mutual interaction between the 13C nucleus and the1H nucleus, so both of the 180° pulses affect it, and effectively they cancel each other out, just as the product of two negative numbers is a positive number. 

Note that the 180 -y pulse on the 13C channel has no effect on Sv. The cosine term is just the product operator we started with, unaffected by the1H pulse, and the sine term is the operator we would get with a full 90° 1H pulse. Note that rotation of the lx magnetization vector by a XH B field on the / axis goes from x to — z to — x to +z as is incremented from 0° to 90° to 180° to 270° in the trigonometric expression. The first term is DQC/ZQC, which will not be observable in the FID—there are no more pulses in the sequence to convert it to observable magnetization. Only the second term represents full coherence transfer to antiphase 13C coherence, which will refocus during the final 1/(27) delay into in-phase 13C coherence ... 

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