Pulsed dephase, rephase

An example of a velocity-encoding method is the bipolar-gradient method.35 Here, two identical pulses are applied during the dephasing and rephasing periods of a spin-echo sequence. Since the two pulses are in opposite polarity with respect to the time domain, the phase shift (p(t) in Eq. (28) is dominated by the velocity term, i.e. the first-order term of t in the expansion. 

A further advance in the use of pulse technique is the spin echo method (Hahn, 1950 Waugh et al., 1968 Mehring, 1978 Emerson and Bray, 1993). Briefly in this technique, a 90 pulse is applied at t = to- 90 pulse is that for which Op = 7112. This causes an induction, which then dephases and begins to decay. After a time r, a 180 pulse is imposed, which now rotates the spins by 180 . As a consequence, the same mechanism which was responsible for dephasing of spins in the xy plane, now acts to rephase the spins. After a time interval of 2r, a spin echo is formed. The spin echo therefore represents cumulative action of two FIDs taking place from opposite directions. The FT of the second half of the spin echo gives the absorption spectrum. 

Following the second pulse the systems proceed with its free evolution marked by the grey arrow in panel (d). However, this free evolution now causes rephasing of the dephased molecular dipoles After time t, which is equal to the time elapsed between the two light pulses, the system will be completely rephased as indicated by the final (ftill-line) vector in panel (d). This analysis then predicts that at that point in time the superradiance emission by the molecular system will resume. In other words, following a second light-pulse at time t after the first pulse, the system will respond with an echo at time It. An experimental example is shown in Fig. 18.14. 

The use of PFG NMR for measurement of translational motion is illustrated in Fig. 5.4.4 [Cal2]. Narrow gradient pulses of amplitude G and width S are inserted into the dephasing and rephasing intervals of an echo sequence. The first gradient pulse defines the initial pitch of the magnetization in terms of the initial wave vector... 

Fig. 5.4.4 Pulsed-field gradient NMR. (a) The Hahn echo is attenuated by translational diffusion during the time interval A between two short gradient pulses applied in the dephasing and in the rephasing periods of the echo (top). By use of flie gradient pulses initial position T and final position Tj of the magnetization are labelled to identify migrating magnetization components (bottom), (b) The sensitivity of the method towards slower processes can be increased if the stimulated echo is used in place of the Hahn echo. Adapted from [Cal2] with permission from Oxford University Press.

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