Hahn spin-echo experiment

Figure 2. Pulse sequence diagram of a Hahn spin-echo experiment with field gradient pulses. Rf- and field gradient pulses are denoted by 90°, 180° and FGP, respectively. The FGP pulses have a length 5 and are separated by an interval A as in the spin-echo sequence given in Fig. 1. VD is a time delay which may be variable in which case also A is variable. A PFG NMR experiment may also be performed with variable 5 or gradient strength (G) and fixed A. Normally, 6 is chosen between 0 and 10 ms and A between 0 and 400 ms. The time delay t depends on the T1 relaxation time of the pure oil of the emulsion but is normally between 130 and 180 ms.

Many NMR experiments are described using this model. For example, the Hahn spin-echo experiment involves measurement of the signal (or echo ) following a 90°, t, 180°, T sequence, t being the interval between two pulses. The behavior of the spin system in the spin echo experiment is shown in Figure 6. 

Figure 6. The Hahn spin echo experiment in the rotating frame, (a) Tipping of M into the x y plane by 90° pulse, (b) Decrease in M,. as spins dephase. (c) Application of a second (180°) pulse, (d) Increase in M. as spins refocus , (e) Complete refocusing, (f) Decay in M,. as spins dephase. From [2].

All these sequences include a (90°) preparation pulse which flips the magnetization of the spin system into the xy plane. The evolution period is then the period of free precession of the spin system in the xy plane, in the Hahn spin echo experiment (Fig. 6). The almost infinite variations in the mixing strategies serve the purpose of bringing out those features of the correlated motions in the system of coupled spins which one wishes to observe. 

The self-diffusion coefficients described below were measured by the pulsed-field technique proposed by Stejskal and Tanner. The pulse sequence applied is a modification of the classical Hahn spin-echo experiment for the determination of the spin-spin relaxation time,72- Fourier transformation of the second half of the spin-echo permits the simultaneous study of complex mixtures. The limit for the number of compounds that can be measured in one experiment is set solely by the requirement that there is at least one... 

The precision which is obtainable for self-diffusion coefficients obtained by NMR depends critically on exact determination of the two pulse widths in the Hahn spin-echo experiment and on the coil constant, k. 

Fig. 2.9.7 Hahn spin-echo rf pulse sequence combined with bipolar magnetic field gradient pulses for hydrodynamic-dispersion mapping experiments. The lower left box indicates field-gradient pulses for the attenuation of spin coherences by incoherent displacements while phase shifts due to coherent displacements on the time scale of the experiment are compensated. The box on the right-hand side represents the usual gradient pulses for ordinary two-dimensional imaging. The latter is equivalent to the sequence shown in Figure 2.9.2(a).

In this section, three experiments are going to be discussed. Two of them, a broadband inversion and a Hahn spin echo, are well-known in the rotating frame. They need to meet the requirement of the phase coherence in PIPs in order to work properly in the Eigenframe. The third is a composite pulse with offset modulation. 

For the basic PFGE experiment a spin-echo experiment (either the two-pulse Hahn echo sequence, Fig. la, or the three-pulse stimulated echo sequence. Fig. lb) is combined with two magnetic field gradient pulses with duration 8 and separated by the time duration A. The gradient pulses generate a magnetic... 

In principle, Ti and T2 can be measured experimentally by the inversion recovery sequence (180°—x—90°) and the Hahn spin-echo sequence, respectively. In practice, these experiments can be easily performed only when the 33S signal is very narrow. If the signal is broad, the difficulties in obtaining 33S spectra with a good S/N make the direct measurements very time-consuming and less precise. The problem can be easily circumvented because T2 (and Ti) can be obtained with good precision directly from line width. 

Static spin echo decay spectroscopy also forms the basis for the measurement of magnetic dipole-dipole interactions between two unlike nuclei I and S. While this interaction is refocused by the Hahn spin echo, it can be recoupled by applying a 7i-pulse to the S-spins during the dipolar evolution period [12]. This manipulation inverts the sign of the heterodipolar Hamiltonian, and thereby interferes with the ability of the Hahn spin echo technique to refocus this interaction. The corresponding pulse sequence, termed SEDOR spin echo double resonance) shown in Fig. 4, compares the I-spin echo intensity as a function of dipolar evolution time (a) in the absence and (b) in the presence of the ti(S) pulses. Experiment (a) produces a decay F(2ti)/Fo, which is dominated by homonuclear dipole-dipole interactions, while experiment (b) results in an accelerated decay, reflecting the contribution from the heteronuclear I-S dipole-dipole interaction, which is now re-introduced into the spin Hamiltonian. For multi-spin systems, a Gaussian decay is expected ... 

We now apply the above theory to modelling of the pulse-and-collect , Hahn spin-echo and triple-quantum filtered T2 experiments. 

Figure 53 (a) Hahn s original spin echo experiment. The pulse spacing is t. (b) The SEDOR experiment as proposed by Kaplin and Hahn. Again the pulse spacing in t. (c) The SEDOR experiment as proposed by Slichter, et al. [74]. The abundant spin it pul.se here is at All times begin at the end of the first pulse. 

Fig. 5. Schematic representation of a SEDOR experiment. The pulse sequence applied to the resonating S-spins corresponds to the weU-known Hahn s echo experiment...

The long transverse relaxation times could be exploited to determine experimentally the difEision constant D of the charge carriers [36], [34]. For this measurement, Hahn sequences and other electron-spin-echo experiments were carried out in applied magnetic fields Bo, with a constant magnetic field gradient G superposed parallel to Bo. When the spins difiuse within the time interval 2r, i.e. the time between the first 90° pulse and the echo afier the 180° pulse at time r, they arrive at locations where the coherence of the spin precession is destroyed owing to the field gradient This leads to an additional decay of the echo amplitude A(r) ... 

Fig. 2.9.2 Radiofrequency, field gradient and current distributions requires a three-dimen-ionic current pulse sequences for two-dimen- sional imaging sequence [see Figure 2.9.1(a)] sional current density mapping. TE is the Hahn and multiple experiments with the orientation spin-echo time, Tc is the total application time of the sample relative to the magnetic field of ionic currents through the sample. The 180°- incremented until a full 360°-revolution is pulse combined with the z gradient is slice reached. The polarity of the current pulses...

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