Hahn-echo technique

Users of any NMR instrument are well aware of the extensive employment of what is known as pulse sequences. The roots of the term go back to the early days of pulsed NMR when multiple, precisely spaced RF excitation pulses had been invented (17,98-110) and employed to overcome instrumental imperfections such as magnetic field inhomogeneity (Hahn echo) or receiver dead time (solid echo), monitor relaxation phenomena (saturationrrecovery, inversion recovery, CPMG), excite and/or isolate specific components of NMR signals (stimulated echo, quadrupole echo), etc. Later on, employment of pulse sequences of increasing complexity, combined with the so-called phase-cycling technique, has revolutionized FT-NMR spectroscopy, a field where hundreds of useful excitation and detection sequences (111,112) are at present routinely used to acquire qualitatively distinct ID, 2D, and 3D NMR... 

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 quadrupole echo is generated similar to a Hahn echo by two pulses which are separated by half the echo time t = t /2 (Fig. 3.2.6(a)). However, the second pulse is a 90° and not a 180° pulse, and it is shifted in phase by 90° with respect to the first. The quadrupole echo appears at a time t2 = t j2 after the second pulse. The spectra shown in Fig. 3.2.5 have been simulated for the quadrupole echo technique with acquisition of the echo decay during h — t. Clearly, the lineshape strongly depends on type and time scale of the motion. In this way, molecular reorientation with correlation times in the range of 10 s < Tc < 10 s can be characterized by H NMR [Laul, Wehl]. Faster motion with correlation times in the range of 10 s < < 10" s can be investigated... 

Many NMR techniques rely on the formation of magnetization echoes [Bagl, Blu5]. Examples are (1) the measurement of T2 relaxation times by the Hahn echo (Section 2.2), (2) the analysis of slow motion by stimulated echoes for spins with / = 1/2, and for nuclei with spin / = 1 or pairs of coupled spins with / = 1/2 by the solid echo and the alignment echo (Section 3.2), (3) MAS, where echoes are generated by mechanical... 

Hydrochloride salts have been popular materials to study, particularly in recent years, as evidenced by the reports of Bryce et al., Chapman and Bryce, and Hamaed et al. (see Figure 11 for an example). Data are summarized in Table 4. To the best of our knowledge, the first chlorine SSNMR report for a powdered hydrochloride salt appears to be that of Pines and co-workers, who studied cocaine hydrochloride in 1995. The study utilized multiple techniques to study the hydrochloride salt, including N NQR. The chlorine-35 SSNMR experiment was carried out at 7.0 T using a Hahn-echo pulse sequence, and a chlorine-35 Cq of 5.027 MHz was reported. To avoid the intensity distortions that result from a finite pulse applied to a broad line shape, a variable frequency offset approach, in which the frequency was stepped in 2 or 4 kHz increments over the entire spectral width, was used to acquire the spectrum. 

In many cases, the NMR method of measuring D is superior to tracer diffusion studies. For liquids, at least, the diffusion coefficient of the tracer does not correspond to that of the major chemical species except for very small tracer concentrations (Ahn, et al., 1972). Furthermore, the NMR techniques do not contaminate the sample, the measured value of D is not disturbed by isotope effects, and the method is not limited to the availability of suitable isotopes, although it is, of course, limited to suitable NMR nuclei and the existence of Hahn echoes. 

Uniform excitation of the entire spectral region is not always possible, since the spectra may span hundreds of kHz. As for the CPMG experiment discussed above (Section 3.3), this problem can be overcome by acquiring several subspectra with different frequency offsets. Recently, Schurko and co-workers demonstrated that undistorted Al NMR spectra of CTs which span up to 700 kHz, in a series of three- and five-coordinate aluminum compounds, may be acquired using a frequency-stepped acquisition method.These spectra were acquired using the Hahn-echo or quadrupolar CPMG (QCPMG vide infra) techniques. 

Figure 8 Comparison of the Rb NMR signal intensity of an MAS powdered sample of RbCI04 obtained with the Hahn echo (left) and QCPMG (right) experiments. The bottom traces are obtained with no enhancement those above were obtained with the indicated enhancement techniques. Reprinted from Siegel, R. Nakashima, T. T. Wasylishen, R. E. Chem. Phys. Lett. 2004, 388, 441-445, with permission from Elsevier.

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... 

---