Three-pulse sequences

Fig. 6. The generalized Jeener-Broekaert three pulse sequence. Note that FT of the solid echo and the alignment echo starts at times delayed by the pulse separation r, after the second and third pulse, respectively...

Fig. 1.—Diagrammatic Representation of the Recovery of Magnetization along the z-Axis (Mj), from Its Initial Value (-M ) to +Mo, Following Its Inversion by a 180° Pulse. The exponential recovery curve shown in [A] depicts the return of magnetization that would be found in a typical inversion-recovery experiment. The curve in [B] would be obtained from a three-pulse sequence, and is a plot of which decreases from an initial value of...

Fig. 1. The pulse sequences for the pulsed field gradient echo NMR experiment (a) Hahn echo, (b) stimulated or three-pulse sequence.

Fig. 1. Feynman diagrams for the interaction of a three-pulse sequence with a two-level system.

The third method involves a three pulse sequence, 90 — r — 180° — x — 90°, with a repetition time of tr s. This pulse sequence refocuses the magnetization vector M0 into its equilibrium position within the repetition time, thus representing a pulse driven relaxation acceleration. This technique, known as DEFT NMR [23, 24] (driven equilibrium Fourier transform NMR) can be understood by following the behavior of the magnetization vector Mq under the influence of the pulse sequence in the rotating frame of reference (Fig. 2.17(a-e)). 

In 2D NMR spectroscopy, a two-dimensional data set is acquired as a function of two time variables tx and t2 as shown schematically in Figure 14.4 [1, 7]. Figure 14.4a shows the general case while the three pulse sequence of Figure 14.4b represents a typical example. 

Figure 14.5 Two-dimensional magnetisation-exchange spectra of a SBR sample recorded with the three-pulse sequence of Figure 14.4b. Different mixing times have been used tm = 2.5 ms, (a) 5 ms, (b) 15 ms, (c) and 30 ms (d). The 2D surface representation for tm=30 ms in (e) shows that all cross-peaks are positive [36]...

In order to interpret the results of our experiments, optimal-control calculations were performed where a GA controlled 40 independent degrees of freedom in the laser pulses that were used in a molecular dynamics simulation of the laser-cluster interactions for Xejv clusters with sizes ranging from 108 to 5056 atoms/cluster. These calculations, which are reported in detail elsewhere [67], showed optimization of the laser-cluster interactions by a sequence of as many as three laser pulses. Detailed inspection of the simulations revealed that the first pulse in this sequence initiates the cluster ionization and starts the expansion of the cluster, while the second and third pulse optimize two mechanisms that are directly related to the behaviour of the electrons in the cluster. We consistently observe that the second pulse in the three-pulse sequence arrives a time delay where the conditions for enhanced ionization are met. In other words, the second pulse arrives at a time where the ionization of atoms is assisted by the proximity of surrounding ions. The third peak is consistently observed at a delay where the collective oscillation of the quasi-free electrons in the cluster is 7t/2 out of phase with respect to the driving laser field. For a driven and damped oscillator this phase-delay represents an optimum for the energy transfer from the driving force to the oscillator. 

Fig. 21. The new five-pulse sequence for recording static 2H exchange spectra.51 The experiment differs from the simple three pulse sequence in Fig. 19 in the addition of r-90°-r (or A — 90° - A) echo sequences before the t and h periods to avoid spectral distortions caused by receiver deadtime and finite pulse width problems. The broader pulses are 90° pulses the narrower ones 54.7° pulses.

Due to the dead time, the correlation functions Fcos,sin(rm rp) for short tp cannot be measured with three-pulse sequences, but a further pulse is necessary to refocus the stimulated echo, leading to four-pulse sequences such as (tc/2)x — tp — (n/2) x - tm - (n/2)x - A - (rc/2)y, where the echo forms at a time tp + A after the last pulse.6,102 So far, we assumed x > tp so that molecular dynamics during the evolution time can be neglected. In the studies of relaxation processes in glasses, this assumption is not justified since very broad distributions of correlation times G( 1 n x) exist. Then, it is necessary to explicitly calculate the phases (h, tf) according to Eq. (8) so that, in general, correlation functions resulting from the above four-pulse sequence can be written as... 

Fig. 2.—Multiple quantum spectrum of benzene (15 mol %) in />-ethoxybenzylidene-n-butylaniline (EBBA) at 20 C. The three pulse sequence was PI = n/2, P2 = 7t/2, P3 = k/2. The magnitude spectra obtained for 11 values of t spaced at 0.1 ms intervals from 9.6 to 10.7 ms were added. The value of /i ranged from 0 to 13.824 ms in 13.5 fis increments for each t. A single sample point was taken at 2 = r after Pj, One half of a symmetrical spectrum is shown.

The pulse sequences for the amplitude-modulated z-filter MQMAS experiment are shown in Fig. 5, with Fig. 5b showing the regular three pulse sequence and Fig. 5c... 

The three-pulse sequence and the split-tj version of the z-filter scheme yield pure absorptive lineshapes, and may be combined with either TPPI or STATES for frequency sign discrimination. For the split-fj version no shearing is required, however, its coherence pathway, and thus the phase cycling depends on the values of I and desired p after the excitation pulse. For a pQMAS experiment, if Ip I < II, the second pulse transfer has a value of Ap = (p -I- 1) (for 3QMAS in spins- j,, y, 5QMAS in spins-1, 2, and 7QMAS in spins- ), indicated by the dotted line in Fig. 5c, and for Ipl = 2/, Ap = (p — 1), indicated by the solid line in Fig. 5c. 

The multiple-quantum (MQ)/MAS NMR is one of the 2D NMR methods, which is capable of averaging out the second-order quadrupolar interaction in nuclei with spin > 1/2 such as H, "B, O, etc. The "B MQ/ MAS NMR measurements on boron as contained in silyl-carborane hybrid Si-based polymer networks considered here. The molded samples are cut into small pieces to insert them into a 4-mm NMR rotor and spun at 12 kHz in a MAS probe. The observation frequency of the "B nucleus (spin number I = 3/2 and isotope natural abundance = 80.42%) is 96.3 MHz. Excitation of both the echo (—3Q) and anti echo (+3Q) coherences is achieved by using a three-pulse sequence with a zero quantum filter (z-filter). The widths of the first, second, and third pulses are 3.0 4.1 ps, 1.1-1.6 ps, and 19-28 ps, respectively. The z-filter is 20 ps. The recycle delay time is 6-15 s and the data point of FI (vertical) axis is 64 and for each the number of scans is 144. Then, the total measurement time is 15-38 h. The phase cycling used in this experiment consists of 12 phases. Boron phosphate (BPO4 3 = 0 ppm) is used as an external standard for "B. The chemical shift value of BPO4 is —3.60 ppm from BF3 O(C2H5)2 which is used as a standard reference in " B NMR in the liquid state. The transmitter frequency of " B is set on peak of BPO4 for a trustworthy chemical shift after Fourier transform." " ... 

Other pulse sequences are in use such as the three-pulse sequence (Figure 3.16) and hyperfine sublevel correlation (HYSCORE) spectroscopy, the latter being a two-dimensional technique.P ]... 

We can see that the total size of a phase cycle grows at an alarming rate. With four phases for each pulse the number of steps grows as 4l where / is the number of pulses in the sequence. A three-pulse sequence such as NOESY or DQF COSY would therefore involve a 64 step cycle. Such long cycles put a lower limit on the total time of an experiment and we may end up having to run an experiment for a long time not to achieve the desired signal-to-noise ratio but simply to complete the phase cycle. 

Coherence transfer pathways (CT pathway) fall in the domain of spherical product operators instead of CARTESIAN operators. Before proceeding any further it is recommended to a necomer to read section 2.2.2 and for addition information references [2.20 - 2.31]. To illustrate the use of coherence transfer pathways in coherence selection, three pulse sequences will be examined. 

Altliougli EPR is very sensitive to tlie surroundings of the paramagnetic cation, it cannot provide directly infonnation concerning the fine interactions with the framework. Such interactions can, however, be measured by ESEEM. This teclmique is particularly useful for the measurement of weak hyperfine interactions. The modulation frequencies are the NMR frequencies of the coupled nuclei. In disordered systems, the modulation frequencies are essentially the Lannor frequencies of the coupled nuclei, which serve to identify the coupled nuclei. The modulation depth can be related to the distance between the electron spin and the coupled nuclei, and to their number. The ESEEM measurements described here were carried out at 4 K using an operating frequency of 9.1 GHz. Both two-pulse and three-pulse sequences were employed. 

Fig. 7a-t Pulse sequences for the pulsed ESR technique a single pulse followed by a free induction decay b two pulse sequence c three pulse sequence (reprinted from reference [20]. Copyright 1987 R.OldenbourgVerlag)... 

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