The Spin Echo

Often a second, short spin echo is added to this sequence so that pulses shorter than 90° (e.g., 30°) can be used for the first pulse. A starting pulse of less than 90° is desirable to 

1 Measurement of T2 Values Using Multiple Spin Echoes CPMG 

We saw in Chapter 5 that in a perfectly homogeneous magnetic field the FID decays to zero in an exponential fashion with characteristic time 72. In the real world, field inhomogeneity makes the FID decay faster (Fig. 6.28), with a characteristic time we can call (T T2). The envelope of the FID drops to 63% (e-1) of its original size after this period of time 7J. If we look at decay rate rather than characteristic time, the intrinsic rate (Ri = 1/73) of decay of coherence is added to the rate of decay due to fanning out of individual vectors from different physical locations in the sample (R =1/ T, the inhomogeneity decay rate) to obtain the experimental rate of decay (R = 1 / 7J)  

The Fourier transform converts the FID into a Lorentzian peak with absorptive lineshape (after phase correction). The full width of this peak at one half of the peak s height (the linewidth ) is inversely related to the decay time constant of the FID,  

The interesting thing is that the maximum intensity of the FID at the top of the echo is still less that that at the start of the FID not all of the coherence is recovered by refocusing in the second half of the spin echo. The part that is lost is the intrinsic decay, the loss of coherence due to pure T2 relaxation, a fundamental relaxation process. The spin echo simply gets back the losses due to inhomogeneity of the magnetic field (T losses). This gives us a method to measure 7 We could repeat the spin-echo experiment a number of times with different echo delays (t values) and start the acquisition of the FID at the top of the echo  

In the case of a heteronuclear AX system, e.g. a CH bond with A = 1H and X = 13C, the transverse magnetization dephases to the doublet components with v0 + J(H and v0 — 7CI, because of CH coupling (Fig. 2.38(a)). A 13C- H pair thus responds to the echo sequence shown in (Fig. 2.37 (a-c), provided the 180 pulse covers the range of carbon-13 shifts At time 2z after the initial pulse, a spin-echo builds up along the negative y axis. Subsequent Fourier transformation computes a negative signal (Fig. 2.38(a)). 

In the homonuclear AX case, e.g. a proton-proton two-spin system, the 180 pulse affects both nuclei. The doublet vectors are reflected at the x z plane. Inverting the precession states of all other coupling nuclei, the 180 pulse also inverts rotation of both AX components (Fig. 2.38(c)). At time 2z, the vectors will be aligned antiparallel along + x (Fig. 2.38(c)) the resultant is zero and no signal will be detected. 

A 180 pulse irradiating the protons just inverts the rotation of the doublet vectors (Fig. 2.38(b)). At time 2t, the components refocus along the positive y -axis (Fig. 2.38(b)), so that a positive signal arises from Fourier transformation. 

Magnetic field inhomogeneities and chemical shifts additionally dephase each doublet component in Fig. 2.38. These effects are also refocussed by a 180 pulse, provided it rotates the components about the x -axis, as is the case in experiments (a) and (c) of Fig. 2.38. 

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This is followed by two field actions which again create a vibrational coherence but, now, with opposite phase to the first coherence. Hence one obtains a partial rephasing, or echo, of the macroscopic polarization. The final field action creates the seventh order optical polarization which launches the signal field (the eighth field). Just as for the spin echo in NMR or the electronic echo in 4WM, the degree of rephasing (tlie... 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

The spin-echo experiment therefore leads to the refocusing not only of the individual nuclear resonances but also of the field inhomogeneity components lying in front or behind those resonances, a maximum negative amplitude being observed at time 2t after the initial 90° pulse. The frequency of rotation of each signal in the rotating frame will depend on its chemical shift and after the vector has been flipped by the 180° pulse, it... 

Figure 2.3 Spin-echo experiment. The behavior of nucleus X in an AX spin system is shown. (A) Application of the second 180° pulse to nucleus X in the AX hetero-nuclear system results in a spin-flip of the two X vectors across the x -axis. But the direction of rotation of the two X vectors does not change, and the two vectors therefore refocus along the —y axis. The spin-echo at the end of the t period along the -y axis results in a negative signal. (B) When the 180° pulse is applied to nucleus A in the AX heteronuclear system, the spin-flip of the X vectors...

The spin-echo is used to suppress the production of spurious signals due to field inhomogeneities or to eliminate errors in the setting of pulse widths. It is also possible to use the spin-echo to follow the decay of transverse magnetization and to determine the transverse relaxation time (7 2). How might we do this in practice ... 

The spin-echo is an elegant method for the measurement of transverse relaxation time Tj. In practice, this is done by repeating the spin-echo experiment many times, with different delay intervals (2t, 4t, 6t,. . . etc.). The following sequence is used ... 

Nuclei resonating at different chemical shifts will also experience similar refocusing effects. This is illustrated by the accompanying diagram of a two-vector system (acetone and water), the nuclei of which have different chemical shifts but are refocused together by the spin-echo pulse (M, = magnetization vector of acetone methyl protons, M(v = magnetization vector of water protons). 

To understand how the chemical shift and multiplicity information is separated, we need to reconsider the spin-echo sequence described earlier. 

While the nuclear magnetic resonance (NMR) technique has widely been used to study diffusion processes of normal liquids, solids, or colloidal systems, there are only a few applications to molten salts. The spin echo self-diffusion method with pulsed field gradients was applied to molten salts by Herdlicka et al. "" There is no need to set up or maintain a concentration gradient. 

The spin echo amplitude M (2x, g )in the presence of a magnetic field gradient of strength g and duration 8 is given, as schematically shown in Fig. 20, by... 

In Fig. 11, the value of D of Na in molten NaNOj measured at 623 K by the spin-echo method is compared with those measured by some other methods. 

For the case of the spin-echo for diffusion weighting, the full kernel can be written as... 

For the spin-echo diffusion-relaxation experiment, they showed... 

In an experiment, tcp is to be varied systematically to obtain the 2D data matrix. For the spin-echo and stimulated-echo based sequences, molecular diffusion causes signal decay in the first segment, thus both are called diffusion-editing sequences. 

In many products, the spin-relaxation properties of the components can be different due to molecular sizes, local viscosity and interaction with other molecules. Macromolecules often exhibit rapid FID decay and short T2 relaxation time due to its large molecular weight and reduced rotational dynamics [18]. Mobile water protons, on the other hand, are often found to have long relaxation times due to their small molecular weight and rapid diffusion. As a result, relaxation properties, such as T2, have been used extensively to quantify water/moisture content, fat contents, etc. [20]. For example, oil content in seeds is determined via the spin-echo technique as described according to international standards [64]. 

The spin-echo successfully imaged water held in the cracks of cement paste. This technique can be used to resolve cracks much smaller than the nominal resolution by relying on water saturation of the crack, the connectivity of the crack structure and the fact that it is relatively easy to detect a high intensity structure on a low intensity background. 

The SHV flow regime has been studied systematically using the spin-echo and FLASH imaging sequences [39]. Figure 4.4.6 describes the steps for extracting... 

Self-Diffusion of Desmopressin and Monoolein by NMR. The self-diffusion coefficient was measured with the NMR diffusion technique using a Bruker MSL 100 spectrometer. Two magnetic field gradient pulses were applied at either side of the 180-degree pulse in a [90x-T-180y-T-echo] spin echo sequence (7,8) (Figure 2). Due to diffusion, the amplitude of a component in the spin-echo spectrum is attenuated according to (7)... 

Both find their origin in the spin-echo sequence, devised hy Hahn in 1952 and used for the determination of relaxation times. 

Fig. 15. Comparison of the viscosities either directly measured or calculated from the spin-echo results for polyethylene melts at 509 K as a function of molecular mass ( experimental result o viscosities calculated on the basis of mode analysis). (Reprinted with permission from [52]. Copyright 1993 The American Physical Society, Maryland)...

Figure 15B shows a screenshot displaying the spin echoes of 195Pt in platinum powder acquired by the CPMG sequence. The experiments were performed at a carrier frequency of 50.74 MHz. The 19SPt signal... 

This section introduces the reader to the basic principles of MRI and the concept of the k-space raster. The basic MRI pulse sequence, the spin-echo imaging sequence, is described at this point. For more detailed discussion of the background theory of MRI the interested reader should refer to texts by Callaghan5 and Kimmich.6... 

We describe in some detail the techniques of nuclear magnetic resonance which are used for studying alumina-supported platinum catalysts. In particular, we describe the spin-echo technique from which the Pt lineshape can be obtained. We also discuss spin echo double resonance between surface Pt and chemisorbed molecules and show how the NMR resonance of the surface Pt can be separately studied. We present examples of experimental data and discuss their interpretation. 

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