Pulse sequences

PULSE SEQUENCE 2.1. Spin exchange at the magic angle 

T2 (laboratory frame) to T p (rotating frame), and suppresses the chemical shifts of I and S nuclei. 

As discussed later, the application of the SEMA sequence is not limited to the 2D PISEMA experiment, but it can be used to design a variety of sophisticated pulse sequences. For example, the selective transfer of magnetization between strongly coupled heteronuclei by SEMA is the key feature of the sequence that can be utilized in experiments such as HETCOR, H-detected experiments, and experiments to selectively measure relaxation parameters of a proton bonded to S nuclei. 

5 -spin-lock and an rf irradiation of /-spins at an offset A, while -X-LG means a -X-phase A-spin-lock and an rf irradiation of /-spins at an offset —A. The phase of the first cycle of FFLG in t has to be inverted relative to the /-spin-lock phase in CP for polarization inversion as discussed in Section 2.2. The rf field strength of the spin-lock applied to A-spins is matched to the 

Line-narrowing efficiency of several 2D SLF methods was examined by performing experiments on a [ C , N]-labeled A-acetyl, D,L-valine single crystal at an arbitrary orientation with respect to Bo- All these experiments were performed on a Chemagnetics/Varian Irffinity 400 MHz solid-state NMR spectrometer at room temperature under identical conditions using a home-built (4-mm solenoid coil) probe. Line widths of and 

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Additionally, more sophisticated pulse sequences (the procedure is called spectral editing) enable one to obtain spectra, after addition or subtraction, where only the following are present (see, for example Bouquet, 1986) ... 

An idea of investigation of AE response of the material to different types of loads and actions seems to be useful for building up a dynamic model of the material. In this ease AE is representing OUT data, and it is possible to take various AE parameters for this purpose. It is possible to consider a single AE pulse in time or frequency domain or AE pulses sequence as... 

The -frmction excitation is not only the simplest case to consider it is the frmdamental building block, m the sense thatv the more complicated pulse sequences can be interpreted as superpositions of 5-frmctions, giving rise to superpositions of M avepackets which can in principle interfere. 

Figure Al.6.22 (a) Sequence of pulses in the canonical echo experiment, (b) Polarization versus time for the pulse sequence in (a), showing an echo at a time delay equal to the delay between the excitation pulses.

Figure Al.6.28. Magnitude of the excited-state wavefimction for a pulse sequence of two Gaussians with time delay of 610 a.u. = 15 fs. (a) (= 200 a.u., (b) ( = 400 a.u., (c) (= 600 a.u. Note the close correspondence with the results obtained for the classical trajectory (figure Al. 6.27(a) and (b)). Magnitude of the ground-state wavefimction for the same pulse sequence, at (a) (= 0, (b) (= 800 a.u., (c) (= 1000 a.u. Note the close correspondence with the classical trajectory of figure Al.6.27(c)). Although some of the amplitude remains in the bound region, that which does exit does so exclusively from chaimel 1 (reprinted from [52]).

Figure Al.6.30. (a) Two pulse sequence used in the Tannor-Rice pump-dump scheme, (b) The Husuni time-frequency distribution corresponding to the two pump sequence in (a), constmcted by taking the overlap of the pulse sequence with a two-parameter family of Gaussians, characterized by different centres in time and carrier frequency, and plotting the overlap as a fiinction of these two parameters. Note that the Husimi distribution allows one to visualize both the time delay and the frequency offset of pump and dump simultaneously (after [52a]).

The next step, therefore, is to address the question how is it possible to take advantage of the many additional available parameters pulse shaping, multiple pulse sequences, etc—m general an E(t) with arbitrary complexity—to maximize and perhaps obtain perfect selectivity Posing the problem mathematically, one seeks to maximize... 

Tannor D J and Rice S A 1988 Coherent pulse sequence control of product formation in chemical reactions Adv. Chem. Rhys. 70 441 -524... 

Tannor D J, Kosloff R and Rice S A 1986 Coherent pulse sequence induced control of selectivity of reactions exact quantum mechanical calculations J. Chem. Rhys. 85 5805-20, equations (1)-(6)... 

Figure Bl.12.9. Pulse sequence used for CP between two spins (/ S).

Figure Bl.12.12. Pulse sequences used in multiple quantum MAS experiments and their coherence pathways for (a) two-pulse, (b) z-filter, (c) split-t with z-filter and (d) RIACT (II).

Advantages. The experiment can be readily carried out with a conventional probe-head, although the fastest spiiming and highest RF powers available are usefid. The pulse sequences are relatively easy to set up (compared to DAS and DOR) and the results are usually quite straightforward to interpret in temis of the number of sites and detemiination of the interactions. 

Figure Bl.12.15. Some double-resonance pulse sequences for providing distance infomiation in solids (a) SEDOR, (b) REDOR, (c) TEDOR and (d) TRAPDOR. In all sequences the narrow pulses are 90° and the wide pulses 180°. For sequences that employ MAS the luimber of rotor cycles N is shown along the bottom.

Figure Bl.13.5. Some basic pulse sequences for measurements for carbon-13 and nitrogen-15.

Figure Bl.14.1. Spin warp spin-echo imaging pulse sequence. A spin echo is refocused by a non-selective 180° pulse. A slice is selected perpendicular to the z-direction. To frequency-encode the v-coordinate the echo SE is acquired in the presence of the readout gradient. Phase-encoding of the > -dimension is achieved by incrementmg the gradient pulse G...

From a more general point of view, components k-, ]=x,y,z of a wave vector k which describes the influence of all gradient pulses may be defined as follows k i) = yCi,U ) dif For the 2D unaging pulse sequence... 

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

Figure Bl.14.5. J2-weighted images of the propagation of chemical waves in an Mn catalysed Belousov-Zhabotinsky reaction. The images were acquired in 40 s intervals (a) to (1) using a standard spin echo pulse sequence. The slice thickness is 2 nun. The diameter of the imaged pill box is 39 nun. The bright bands...

The mathematical description of the echo intensity as a fiinction of T2 and for a repeated spin-echo measurement has been calculated on the basis that the signal before one measurement cycle is exactly that at the end of the previous cycle. Under steady state conditions of repeated cycles, this must therefore equal the signal at the end of the measurement cycle itself For a spin-echo pulse sequence such as that depicted in Figure B 1.14.1 the echo magnetization is given by [17]... 

We first examine how this works for the case of coherent flow. A typical pulse sequence is shown in figure Bl.14.9. This sequence creates a spin echo using two unipolar gradient pulses on either side of a 180° pulse. The duration of each gradient pulse of strength G, is . The centres of the gradient pulses are separated by A. 

Figure Bl.14.9. Imaging pulse sequence including flow and/or diflfiision encoding. Gradient pulses before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G, (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatially...

A measure of the echo attenuation within each pixel of an image created using the pulse sequence of figure Bl.14,9 perhaps by repeating the experiment with different values of and/or 8, gives data from which a true diffusion map can be constructed [37, 38],... 

The practical goal for pulsed EPR is to devise and apply pulse sequences in order to isolate pieces of infomiation about a spin system and to measure that infomiation as precisely as possible. To achieve tliis goal it is necessary to understand how the basic instnunentation works and what happens to the spins during the measurement. 

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

In electron spin echo relaxation studies, the two-pulse echo amplitude, as a fiinction of tire pulse separation time T, gives a measure of the phase memory relaxation time from which can be extracted if Jj-effects are taken into consideration. Problems may arise from spectral diflfrision due to incomplete excitation of the EPR spectrum. In this case some of the transverse magnetization may leak into adjacent parts of the spectrum that have not been excited by the MW pulses. Spectral diflfrision effects can be suppressed by using the Carr-Purcell-Meiboom-Gill pulse sequence, which is also well known in NMR. The experiment involves using a sequence of n-pulses separated by 2r and can be denoted as [7i/2-(x-7i-T-echo) J. A series of echoes separated by lx is generated and the decay in their amplitudes is characterized by Ty. ... 

More sophisticated pulse sequences have been developed to detect nuclear modulation effects. With a five-pulse sequence it is theoretically possible to obtain modulation amplitudes up to eight times greater than in a tlnee-pulse experunent, while at the same time the umnodulated component of the echo is kept close to zero. A four-pulse ESEEM experiment has been devised to greatly improve the resolution of sum-peak spectra. 

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