Spin echo decay

In an NMR analysis of the effects of /-irradiation induced degradation on a specific polyurethane (PU) elastomer system, Maxwell and co-workers [87] used a combination of both H and 13C NMR techniques, and correlated these with mechanical properties derived from dynamic mechanical analysis (DMA). 1H NMR was used to determine spin-echo decay curves for three samples, which consisted of a control and two samples exposed to different levels of /-irradiation in air. These results were deconvoluted into three T2 components that represented T2 values which could be attributed to an interfacial domain between hard and soft segments of the PU, the PU soft segment, and the sol... 

NMR relaxometry Free induction decay (T2 ) or solid echo Spin echo decay (T2) Magnetization recovery curve (7)) Eads (1998)... 

Fig. 3 Temperature dependence of the transverse relaxation time Ti for D-RADP-20 as obtained from a bi-exponential fit to the Rb spin echo decay. The fact that T2 changes discontinuously at the phase transition clearly indicates the first order character of the transition...

The methodology described in this procedure is limited to systems that do not contain free moisture. In cases when both oil and water signals are refocused after the second pulse (e.g., when free water is present), the spin-echo decay curve can be collected over varying x values. Log of the echo amplitudes versus x can be further analyzed to deconvolute the contribution of various components, in this example water and oil would result in a biexponential decay curve. Extrapolating each decay curve to X 0 gives the signals amplitudes due to the oil and the water fractions (A0 and Aw Fig. A1.3.4). 

Leisen, J., Schmidtrohr, K., and Spiess, H. W. (1993). Nonexponential relaxation functions above T(G) analyzed by multidimensional NMR and novel spin-echo decay techniques. Physica A 201,79-87. 

Figure 7. Spin-echo decay of signals from...

Illustration of modulation of two pulse electron spin echo decay envelope. Microwave pulses 1 and 2 separated by the time x produce the echo signal at time x after pulse 2. As x is increased the echo amplitude changes and traces out an echo envelope which may be modulated. 

The spin echo decay under homonuclear couplings only (as opposed to decay by relaxation) is often called the slow beat, even if no periodic modulation is observed. A real beat usually occurs when a scalar coupling between unlike nuclei is the main decay mechanism, e.g., for Pt in dilute bulk alloys. Dipolar coupling usually leads to a monotonic decay, which initially is Gaussian (at the origin all its odd time derivatives are zero) and becomes more exponential at longer times. 

Fig. 2 Timing diagram of the spin echo decay spectroscopy method devised for the measurement of homonuclear dipole-dipole interactions...

Serious complications arise, however, if the spins are subject to strong nuclear electric quadrupolar interactions, which tend to modify the echo amplitudes measured. In such cases, it is still possible to extract dipole-dipole coupling information from spin echo decay spectroscopy, if the 71-pulses are applied entirely selectively to the central l/2>o -l/2> transition [6]. If the resonance frequencies between the coupled nuclei are sufficiently similar to allow for spin-exchange via the flip-flop mechanism, Eq. (5) turns into... 

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 ... 

Cation Distributions in Singie Aikaii Giasses Studied by Na Spin Echo Decay Spectroscopy... 

As illustrated by the model compound work summarized in Fig. 3, Na spin echo decay spectroscopy is suitable in principle for elucidating the spatial distribution of sodium ions in sohds [11,44-47]. Meaningful results can be obtained provided that the measurement is carried out by selective excitation of the central j 1/2> -1/2> transition, which needs to be ascertained by nutation NMR. Furthermore, sub-ambient temperatures may be required to suppress any potential influence of sodium dynamics. To date, promising applications have been pubhshed using Na spin echo decay spectroscopy (1=3/2) on sodium-containing glasses, to address the vital issue of cation clustering. Fig-... 

At the present time it is unclear whether the spin echo decay spectroscopy approach successfully demonstrated for Na is generally transferable to other alkali ion nuclei such as Li and Cs. The latter two isotopes have moderately small electric quadrupole moments causing first order quadrupolar splittings that are comparable to the radio frequency excitation window. As a result, the 7i-pulse length is ill-defined in many situations and the contribution of dipolar coupling of the observed spins to nuclei in the outer Zeeman levels is difficult to quantify. Nevertheless, some promising initial results on cesium borate... 

Figure 7. Spin-echo decay of Si signals from samples A and D (A and B). Lines 1-4 refer to signals from Si (3A1), Si (2A1), Si (1A1) and Si (0A1), respectively.

In general the Cooper pairs in conventional superconductors induced by phonons have. -symmetry where the gap opens uniformly on the Fermi surface and the temperature dependence of physical quantities below Tc is exponential. On the other hand, when the attractive force originates from spin or electron charge fluctuations, the Cooper pair has p- or d-wavc symmetry where the gap disappears on lines or points on the Fermi surface and the physical quantities have power-law temperature dependences. The quantities that are measured by NMR and nuclear quadrupole resonance (NQR) are the nuclear spin-lattice relaxation rate, 1 / T, the Knight shift, K, the spin echo decay rate, 1/T2 and the NQR frequency, vq. The most important quantities, K and 1/77 for the determination of the symmetry of the Cooper pairs are reviewed in the following sections. 

Bulut and Scalapino58 calculated the Gaussian spin echo decay rate, 1 / Tjq which is proportional to Xq the, v and d-wave model and proposed the measurement of 1 /Tig to distinguish between the d- or. v-wave. The experiment by Itoh et al,59 coincided well with the calculation on the d-wave model. 

The Gaussian spin echo decay rate 1/72G through the spin fluctuations is expressed as... 

Fig. 34. A plot of 1/T2G for Ni-doped YBCO7 against (a) T and (b) T/Tc.n The inset shows the spin echo decay curve at Tc values for x = 0 and 3%.

B. Robertson, "Spin-echo decay of spins diffusing in a bounded region," Phys. Rev. 151, 273-277 (1966). 

Finally, NMR has been used to characterize the structural features of surface-fluorinated aluminas and amorphous aluminosilicates. Both the F NMR chemical shifts and spin-spin relation times differentiate sensitively between Si-F and Al-F bonds. Lineshape and spin echo decay data suggest that the homonuclear F- F dipolar interactions are much weaker than in AlFj-hydrate, indicating that in samples containing up to 5 wt% fluorine, most of the Al-F species are isolated from each other [78]. 

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