Echo formation

SPIN-ECHO FORMATION IN HOMONUCLEAR AND HETERONUCLEAR SYSTEMS... 

Spin-Echo Formation in Homonuclear and Heteronuclear Systems... 

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

Echo Formation Between Two Correlated Anisotropic Interactions... 

Figure 3. Spin echo formation with (a-b) non-inverted and (c) inverted 90° pulse.

N. Gelman, R.F. Code, A simple model of F spin-echo formation in polycrystalline fluorapatite, J. Magn. Res. A 107 (1994) 185-193. 

In this section, we provide an outline of the theoretical and practical aspects of diffusometry NMR experiments that are the core of chrom-NMR. This issue has been reviewed at large38,39 and thus only the key and most relevant aspects will be mentioned below. The displacement of a given molecular tracer is followed by a classical Stejskal-Tanner experiment. In this, pulses of magnetic field gradients are used to label the initial position of the tracer, and to follow its displacement along the direction of the gradient, Az. Indeed, in a spin-echo experiment, any displacement corresponds to a reduction of the efficiency of the echo formation. 

In equation (2) f 1 corresponds to the period of echo formation while t2 corresponds to the time during which the echo is sampled coi and a>2 correspond to the dispersion within individual J-spectra and to the normal spectral spread respectively. The resulting two-dimensional spectrum S((Ui,a)2) is of course made up of real and imaginary parts according (26) to equation (3) where terms such as 5 (co 1,0)2) are defined by equation (4), the superscripts s and c referring to sine and cosine respectively. 

Consider the free procession signal acquired as a function of time t after the spin-echo formation at time t. We shall presume that the sole term acting in the Hamiltonian after the echo center is due to the Larmor precession at frequency in the uniform field, where the use of the subscript i allows for the range of chemical shifts in the NMR spectrum. This precession contributes an evolution operator exp(iWo,t ->, ) to the density matrix so that we can rewrite Eq. (39) as... 

We now consider the simple case of a spin echo in which two rectangular linear gradient pulses are applied as shown in Fig. 1. In this pulsed gradient spin-echo (PGSE) experiment, the time t used in Eq. (41) will refer to the position of the spin-echo formation. In analyzing this experiment, we will assume the weak inhomogeneous field limit and the uniform... 

In the following, we show how an MQMAS echo is formed. The quadmpolar Hamiltonian under MAS will be derived as a perturbation to the strong static magnetic field Bq. The evolution of the density matrix under this Hamiltonian will be then shown to form an echo under a suitable selection of symmetric coherences. The manipulation of spin coherences by RF pulses will be assumed to be ideal here. The effects of nonidealities were discussed by the group of Vega. From the expression for the elements of the quadmpolar Hamiltonian, line narrowing by DOR experiment and echo formation by two alternative experiments, DAS and STMAS, will also be demonstrated and briefly discussed. Finally, some additional line narrowing schemes will be mentioned. 

Since we will be discussing only the echo formation, for details regarding the MAS spectra and expressions of the NMR lineshapes of quadrupolar nuclei, the reader is directed to some excellent reviews concerning quadmpolar nuclei by Freude, Smith and VanEck, Man, Frydman, " " and Kentgens. Additional reviews of interest on MQMAS include those of Amoureux and Pmski, and Goldbourt and Madhu. ... 

Since the experiment relies on a second echo formation, either the echo or the antiecho pathway can be chosen. However, choosing the antiecho pathway requires a much longer echo delay, which can lead to unwanted relaxation or exchange effects generating antisymmetric echoes. It is, therefore, preferable to choose the echo pathway, which is also the choice depicted in Fig, 5d and 5e. 

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