Pulse Width Flip Angle

With the test sample in the magnet, the probe is tuned to H and the magnet homogeneity maximized. Next, a test spectrum is determined in which the tp used is unimportant. This spectrum then serves as a starting point for another spectrum, which has a reduced spectral width. The original sw is now reduced to about 500 Hz, and the transmitter offset is adjusted so that it is in the middle of the reduced sw. Many spectrometers have programs that do both operations with one command. Since sw has been considerably reduced, the number of data points should also be decreased, to approximately 4,000, so as to maintain an acquisition time of around 4 s. 

A reduced one-scan spectrum is then taken and displayed in the absolute-intensity mode, with tp set to about one-half of the value given for the 90° tp in the instrument specifications (e.g., set fp = 5 pis for a 90° /p = 10 pis). The resulting one-line spectrum should be processed with a 1-Hz line broadening, phased properly, and presented such that the baseline appears at about midscreen and the height of the signal occupies about one-half of the vertical size of the screen. 

As a general rule, the transmitter and decoupler power levels are set so that both the H and 90° /p s are in the range of 5-10 ps. Pulse widths less than 5 ps are inaccurate, because pulse rise and fall times are in the microsecond range. Probes having /p s appreciably greater than 10 ps may be unable to execute those pulse sequences which require several transmitters to be rapidly switched on and off. 

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Figure 7. Pulse sequence and coherence transfer pathway diagram for a H DQ MAS experiment using the BAB A recoupling sequence for the excitation and reconversion of DQCs. The rectangular blocks represent pulses of flip angle 90°, with the choice of the phases being described in, e.g., ref 25. If the q increment is set equal to a rotor period, a rotor-synchronized two-dimensional spectrum is obtained, while reducing q, and hence increasing the DQ spectral width, leads to the observation of a DQ MAS spinning-sideband pattern.

Fig. 8.1.2 Excitation by delta pulses in a strong field gradient Gz as a function of the space coordinate z- Normalized signals (a) and Sj,(z) (b) from an rf pulse with flip angle n/2 at z = 0. For the simulation, the gradient strength has been set to = 20T/m, and the amplitude of the rf field was yB = 100 kHz. The width of the excited slice is of the order of 100 p,m.

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. 

Spectra were determined using a pulse width of 4 yseconds, which corresponds to a flip angle of 18° and a 1 second pulse delay time. The 4000 Hz spectrum was described using 8192 data points. 

The H-FT-NMR spectra were obtained from a Bruker Avance 300 operating in the FT mode at 400 MHz under total proton decoupled conditions. The spectra were recorded at 40°C from 200 mg sample vanillin dissolved in 1 mL CDClj after 3,000 scans. A 90° pulse flipping angle, a 26.6 ps pulse width and a 1.74 s acqnisi-tion time were employed. There was no significant difference in the stractnre of vanillin precipitated from crystallization process and standard vanillin based on H-NMR analysis (Fig. 9.5). Incomplete dissolntion of the sample may becanse of the rmexpected high signaPnoise ratio. The peaks show that the chemical shifts for both of vanillins are very similar. 

The Gaussian pulse is truncated at 2.5% in order to keep its duration finite without introducing distortions in the profile its half-height full width is 43.5% of its total duration. The flip angle is calibrated to 270° in order to use the self-refocussing properties of this pulse [15]. 

A radio-frequency (rf) alternating field initiates any NMR experiment. At resonance, the field vector B, rotates with Larmor frequency (v, = v0) perpendicularly to the static field vector B0, as shown in Fig. 2.1. In this situation, the nuclear magnetic moments will precess about both fields B0 and B,. Provided B1 extends along the x axis at a certain instant, the double cone of precession will rotate about the x axis in the yz plane (Fig. 2.1 (a) -> (b)). The flip angle 0 relative to the z axis at a given field strength B, depends on the pulse width t of the rf field, in the range of some ps, so that... 

Flip angle Pulse width No. of scans Rep. time Weighting Line broad. Spectral resolution Instrument ... 

Let us review what happens to Mo while and after it is irradiated by a B, pulse. First, we set the power and pulse duration (pulse width tp) to result in a flip angle a of 90° (n/2 rad). Since in the present case B, is oriented along the x" axis of the rotating frame, we will refer to this as a 90y pulse. Figure 3.20a shows the initial orientation of M and Figure... 

M flips through 90°, and the pulse is called a 90° or tt/2 pulse. Pulse widths for other flip angles are determined in an analogous manner. 

In Fig. 2 we show a flow chart of the simulation program. Apart from the specification of the m.p. sequence, that is, of the spacings t of the pulses, their widths their flip angles /3 = (o tp, and phases a, the program requires as input parameters the dipole-dipole coupling strengths b.k, the chemical shifts and the offset Aw. 

Nonuniform widths, that is, nonuniform flip angles of the four types of pulses... 

Fig. 9. Sensitivity of BR-24 spectra to a combination of pulse errors. Shown is the dependence of the residual width on the average flip angle /3 for the following individual pulse errors pulses, phase error of +1° -x pulses, too long by 1% +y pulses, too short...

Spectrometer does not fall far behind the theoretical limitations, if it does at all. The quality of the pulses (uniformity and constancy of the flip angles and the rf phases) is sufficiently high that pulse errors hardly play a role as a resolution-limiting factor. The tightest theoretical limitation is the necessarily finite width of the rf pulses, which is particularly acute for the BR-24 sequence. The next significant step to enhance the resolution in solid state proton m.p. spectroscopy may well require either 90° pulses shorter than, say, 500 ns (this would be the brute force method) or another clever idea. 

The flip angle is related to the pulse width tp and on the field distribution BuyiR). Because the latter is proportional to the current I through the coil, the flip angle varies with the distance R of the volume element of interest from the centre of the coil. In return the distribution of flip angles produces a dependence of the excited transverse magnetization on the space coordinates. 

Nowadays almost all the NMR data are acquired by the pulsed Fourier transform (FT) method. In this method, the consideration of spin-lattice relaxation times (Tj) for the signals of interest, that is, proper selection of the observed pulse width (or flip angle) and of pulse repetition time (or pulse interval) is of primary importance for quantitative analysis.5-8... 

Inhomogeneity in the applied rf field means not all nuclei within the sample volume experience the desired pulse flip angle (Fig. 9.1b), notably those at the sample periphery. This is similar in effect to the (localised) poor calibration of pulse widths and references to rf (or Bi) inhomogeneity below could equally read pulse width miscalibration . Modifications that make sequences... 

As the duration of a pulse of a given flip angle is inversely proportional to the relationship can be expressed in terms of the initial and new pulse widths, Tinit and rnew ... 

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