The 90 Pulse

The signal is in the form of a simple free induction decay (FID) of a sample of spins, with a single resonance frequency. 

As time passes, the individual spins move out of step, so the magnetization vector M shrinks exponentially with a time constant Tc and induces an even weaker signal in the detector coil. 

After a 90° pulse, the numer of a-spins equals the number of p-spins. The populations revert to their thermal equilibrium values. But, as described earlier, at thermal equilibrium the spins have a Boltzmann distribution, with more a-spins than p-spins. By giving up energy to the surrounding area (the lattice), the p-spins again revert to a-spins. The time required for this reversion is T, the spin-lattice relaxation time. 

A 90° pulse is defined as that length of time necessary to rotate the magnetization through 90°. The transmitter is turned off at that point. The relaxation times T and T2 of different orientations are recorded. The resonance data obtained by the pulse method is the collection of signals expressed in time sequence, X(t), which is now ready for Fourier analysis. 

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Precisely controllable rf pulse generation is another essential component of the spectrometer. A short, high power radio frequency pulse, referred to as the B field, is used to simultaneously excite all nuclei at the T,arm or frequencies. The B field should ideally be uniform throughout the sample region and be on the order of 10 ]ls or less for the 90° pulse. The width, in Hertz, of the irradiated spectral window is equal to the reciprocal of the 360° pulse duration. This can be used to determine the limitations of the sweep width (SW) irradiated. For example, with a 90° hard pulse of 5 ]ls, one can observe a 50-kHz window a soft pulse of 50 ms irradiates a 5-Hz window. The primary requirements for rf transmitters are high power, fast switching, sharp pulses, variable power output, and accurate control of the phase. 

Next a period of time T (T > T ) is allowed for the entire system to relax to its steady-state configuration. Then the pulse sequence is repeated, with a different value for t. In this way the decay of M is measured by sampling it via the 90° pulse. The sequence is called a 18(f, t, 90° sequence. l/T, is found from a semilogarithmic plot. 

After the 90° pulse is applied, all the magnetization vectors for the different types of protons in a molecule will initially come to lie together along the y -axis. But during the subsequent time interval, the vectors will separate and move away from the y -axis according to their respective precessional frequencies. This movement now appears much slower than that apparent in the laboratory frame since only the difference between the... 

Since there is a slight delay between when a pulse is switched on and when it reaches full power, an error may be introduced when measuring 90° or smaller pulses directly. If the 90° pulse width is required with an accuracy of better than 0.5 fi, then it may be determined more accurately by using self-compensating pulse dusters that produce accurate flip angles even when there are small (<10%) errors in the setting of pulse widths. 

Figure 1.41 Applying the first incorrectly adjusted 90° pulse (actually, 85° pulse) bends the z-magentization vector 5° above the y -axis. The 180 pulse at this stage will bring the magnetization vector 5° below the y -axis (to the mirror image position). Applying another similarly maladjusted 90° pulse causes a further bending of the magnetization vector precisely to the — z-axis. The composite pulse sequence (i.e., 90°-180°-90°) is thus employed to remove imperfections in the 90° pulse.

After the 90° pulse, the transverse magnetization vectors of C nuclei of C, CH, CH2, and CHj do not rotate synchronously with one another but rotate with characteristically different angular velocities during the same delay interval. This results in their appearing with differing (positive or negative) amplitudes. This forms the basis of the APT experiment. 

The pulse sequence used in homonuclear 2D y-resolved spectroscopy is shown in Fig. 5.18. Let us consider a proton, A, coupled to another proton, X. The 90° pulse bends the magnetization of proton A to the y -axis. During the first half of the evolution period, the two vectors (faster... 

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-...

We carried out two sets of experiments in which we set the pulse angle first at 90°, then at 30°. Using these two values we then varied the relaxation delay. Since the greatest difference in the relaxation times is that between the OH proton and the aromatic protons, we show in Fig. 11 the comparison between the integration values of the aromatic protons (set equal to 2.0) and of the OH proton for 90° pulses and for 30° pulses. The values approach each other with a relaxation delay of 10 sec and are virtually equal for a delay of 25 sec, but the 90° pulses give values which are completely wrong if a conventional delay of 1-2 sec is used On the other hand, the error is quite low if the delay is set at 2 sec and the pulse length is 30°. 

One last comment about pulse widths it is important that we know what the 90° pulse width is for the nuclei that we observe as accurate pulse widths are required for many pulse sequences (as mentioned previously). Failure to set these correctly may give rise to poor signal to noise or even generate artifacts in the spectrum. When instruments are serviced, these pulse widths are measured and entered into a table to ensure that the experiments continue to work in the future. 

The spin-spin relaxation time can, in principle, be measured from the FID following the 90° pulse (one-pulse experiment Fig. 10a). However, the application of this simple experiment is limited only to very short FIDs, and consequently short T2s, because of the inhomogenities in the laboratory field. The line width in magnetic resonance is proportional to T2, but the observed linewidth,- T, has also a contribution from the magnetic field term ... 

Fig. 2.12. Adjustment of the 90 pulse width sample methanol, 80% by vol. in deuterium oxide at 30 °C and 20 MHz computer-controlled experiment with variable pulse width. The 90 pulse width is found to be 7 ps.

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