Spin-echoes

Signal loss in the free induction decay (FID) can be partially refocused using a second application of with a duration and amplitude that produces an 180° flip angle of M (180° pulse). This has the effect of placing individual magnetic moments, which are no longer in phase with the central frequency, in a position to realign with spins at the central frequency. 

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Electron Spin Resonance Spectroscopy. Several ESR studies have been reported for adsorption systems [85-90]. ESR signals are strong enough to allow the detection of quite small amounts of unpaired electrons, and the shape of the signal can, in the case of adsorbed transition metal ions, give an indication of the geometry of the adsorption site. Ref. 91 provides a contemporary example of the use of ESR and of electron spin echo modulation (ESEM) to locate the environment of Cu(II) relative to in a microporous aluminophosphate molecular sieve. 

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... 

Figure Bl.12.5. Zr static NMR lineshapes from ZrO polymorphs using frequency-stepped spin echoes.

Meiboom S and Gill D 1958 Modified spin-echo method for measuring nuclear relaxation times Rev. Sci. Instrum. 29 688-91... 

Figure Bl.14.1. Spin warp spin-echo imaging pulse sequence. A spin echo is refocused by a non-selective 180° pulse. A slice is selected perpendicular to the z-direction. To frequency-encode the v-coordinate the echo SE is acquired in the presence of the readout gradient. Phase-encoding of the > -dimension is achieved by incrementmg the gradient pulse G...

The magnetization profile in the y-direction is recovered by Fourier transfonnation with respect to G. B1.14.2.4 2D SPIN-ECHO FT IMAGING AND K-SPACE... 

Figure Bl.14.5. J2-weighted images of the propagation of chemical waves in an Mn catalysed Belousov-Zhabotinsky reaction. The images were acquired in 40 s intervals (a) to (1) using a standard spin echo pulse sequence. The slice thickness is 2 nun. The diameter of the imaged pill box is 39 nun. The bright bands...

The mathematical description of the echo intensity as a fiinction of T2 and for a repeated spin-echo measurement has been calculated on the basis that the signal before one measurement cycle is exactly that at the end of the previous cycle. Under steady state conditions of repeated cycles, this must therefore equal the signal at the end of the measurement cycle itself For a spin-echo pulse sequence such as that depicted in Figure B 1.14.1 the echo magnetization is given by [17]... 

We first examine how this works for the case of coherent flow. A typical pulse sequence is shown in figure Bl.14.9. This sequence creates a spin echo using two unipolar gradient pulses on either side of a 180° pulse. The duration of each gradient pulse of strength G, is . The centres of the gradient pulses are separated by A. 

Figure Bl.14.9. Imaging pulse sequence including flow and/or diflfiision encoding. Gradient pulses before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G, (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatially...

This expression can be used for pulsed held gradient spin-echo experiments and also for spin-echo experiments in which the gradient is applied continuously. 

Mansfieid P 1977 Muiti-pianar image formation using NMR spin echoes J. Rhys. C Solid State Rhys. 10 L55-L58... 

Figure Bl.15.11. Fomiation of electron spin echoes. (A) Magnetization of spin packets i,j, /rand / during a two-pulse experiment (rotating frame representation). (B) The pulse sequence used to produce a stimulated echo. In addition to this echo, which appears at r after the third pulse, all possible pairs of the tluee pulses produce primary echoes. These occur at times 2x, 2(x+T) and (x+2T).

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-)... 

In electron spin echo relaxation studies, the two-pulse echo amplitude, as a fiinction of tire pulse separation time T, gives a measure of the phase memory relaxation time from which can be extracted if Jj-effects are taken into consideration. Problems may arise from spectral diflfrision due to incomplete excitation of the EPR spectrum. In this case some of the transverse magnetization may leak into adjacent parts of the spectrum that have not been excited by the MW pulses. Spectral diflfrision effects can be suppressed by using the Carr-Purcell-Meiboom-Gill pulse sequence, which is also well known in NMR. The experiment involves using a sequence of n-pulses separated by 2r and can be denoted as [7i/2-(x-7i-T-echo) J. A series of echoes separated by lx is generated and the decay in their amplitudes is characterized by Ty. ... 

Pulsed ENDOR offers several distinct advantages over conventional CW ENDOR spectroscopy. Since there is no MW power during the observation of the ESE, klystron noise is largely eliminated. Furthemiore, there is an additional advantage in that, unlike the case in conventional CW ENDOR spectroscopy, the detection of ENDOR spin echoes does not depend on a critical balance of the RE and MW powers and the various relaxation times. Consequently, the temperature is not such a critical parameter in pulsed ENDOR spectroscopy. Additionally the pulsed teclmique pemiits a study of transient radicals. 

Rowan L G, Hahn E L and Mims W B 1965 Electron-spin echo envelope modulation Phys. Rev. 137 A61-A71... 

Mims W B 1972 Envelope modulation in spin-echo experiments Phys. Rev. B 5 2409-19... 

Merks R P J and de Beer R 1979 Two-dimensional Fourier transform of electron spin-echo envelope modulation. An alternative for ENDOR J. Phys. Chem. 83 3319-22... 

Thurnauer M C and Norris J R 1980 An electron spin echo phase shift observed in photosynthetic algae. Possible evidence for dynamic radical pair interactions Chem. Phys. Lett. 76 557-61... 

In addition to the above techniques, inverse gas chromatography, swelling experiments, tensile tests, mechanical analyses, and small-angle neutron scattering have been used to determine the cross-link density of cured networks (240—245). Si soHd-state nmr and chemical degradation methods have been used to characterize cured networks stmcturaHy (246). H- and H-nmr and spin echo experiments have been used to study the dynamics of cured sihcone networks (247—250). 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

APT Attached proton test, a modification of the J-modulated spin-echo experiment to determine C//multiplicities, a less sensitive alternative to DEPT... 

Dipole-dipole (homonuclear) Afjfhomo) (mean-squared local field) Spin-echo NMR Intemuclear distances, number of surrounding nuclei... 

Dipole—dipole (heteronuclear) Af (hetero) Spin-echo double resonance (SEDOR) ... 

A number of other, more sophisdcated, selective averaging tools (includli spin echo, double resonance and two-dimensional techniques) are available, both for spectral editing purposes and for obtaining quantitadve information about inter-... 

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