Hahn spin-echo technique

The Hahn spin echo technique may be used to remove the inhomogeneous broadening. A n pulse at tJ2 changes to —q, allowing a refocusing of the coherence at ti for all orders. However, this n pulse also removes the separation of the orders which was a result of the frequency offset. 

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 ... 

A few relatively recent published examples of the use of NMR spectroscopy for studying polymer degradation/oxidation processes will now be discussed briefly. At the early stages of degradation, the technique can be used to provide chemical identification and quantification of oxidised species for polyolefins, oxidation sites can be identified by the chemical shifts of -CH2- groups a and ji to carbons bonded to oxygen [85]. Spin-spin relaxation times may be determined by a pulse sequence known as the Hahn spin-echo pulse sequence. 

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... 

With the use of a constant appHed magnetic field, field-swept techniques for acquisition ofbroad Zr powder patterns were no longer feasible, necessitating alternative techniques for Zr nuclei in lower-symmetry environments. Bastow introduced the stepped spin-echo technique for acquisition ofbroad Zr SSNMR powder patterns in 1992 [38]. This new technique permitted study of Zr in a variety of lower-symmetry environments, and Bastow et al. made extensive use of traditional one-pulse and Hahn-echo experiments as well as stepped spin-echoes to examine Zr in a variety of environments [38,43,48—52], including zirconia phases and zirconia-based materials with practical appfications. Flartmann and Scheler [35] also explored the feasibifity of Zr SSNMR through echo... 

The zircon study was followed up with Zr SSNMR experiments in 1992 by Bastow et al. on seven Zr-based metals and oxides at room temperature [38]. Zr chemical and Knight shifts, EFG parameters, and some relaxation times were reported. The stepped spin-echo technique was introduced for Zr spectral acquisition in this work (see Section 2 for further details, vide supra). As a proof of concept, the Zr SSNMR powder pattern of hep Zr metal was acquired at 9.4 T via a traditional 90—180° Hahn-echo experiment as well as the stepped spin-echo technique (Fig. 7). The Hahn-echo experiment produced an imperfect, lopsided Zr powder pattern in ca. 27.5 h the authors credited this to a combination of instrumental factors, most likely excitation bandwidth limitations associated with hard pulses. In contrast, the stepped-echo technique produced a relatively weU-defmed, superior powder pattern in an experimental time of ca. 28 h, which clearly illustrated the benefits of the stepped-echo technique. 

Measurements of diffusion and motion were the first application of the spin echo as detailed in Hahn s famous 1950 paper. The advent of good pulsed gradients has improved this technique dramatically, and both the physiological and the materials applications in restricted geometries have attracted much recent attention. Callaghan and Stepisnik s review lays out both the mathematical framework and the range of applications in a very clear manner. 

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. 

Only a brief mention of this technique will be possible. The Spin Echo method, as such, was first developed by Hahn (1950). The essential features are the application of a short intense radio-frequency pulse which matches the condition at the Larmor frequency... 

In 1950, Hahn [17] described his ingenious spin echo NMR techniques in which he first used a radio frequency pulse to flip nuclear spins by 90°, allowed the signal to disappear by field inhomogeneihes or T2 relaxation and then x seconds after the first pulse he applied a 180°... 

The so-called SEDOR technique (spin-echo double resonance [9, 47, 48], see Fig. 5) allows the determination of internuclear distances, rjs, for isolated spin pairs consisting of a resonating J-spin and a non-resonating S-spin. Hahn s echo [49] of the resonating J-spins is observed with a time between the 7i/2-pulse and the 7T-pulse. A rr-pulse applied to the S-spins after a variable time ti (0characteristic damping of Hahn s echo of the resonating /-spins. The damped amplitude, of Hahn s echo under SEDOR conditions is determined by ... 

The "spin echo correlated spectroscopy" technique retains the basic two-pulse sequence, but delays acquisition of a free induction decay until the maximum of the Hahn echo 50 51... 

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