Echo experiment

Accurate modelling of the field radiated by ultrasonic transducers is an essential step forward considering the final goal of the complete simulation of pulse echo experiments. 

Figure Al.6.22 (a) Sequence of pulses in the canonical echo experiment, (b) Polarization versus time for the pulse sequence in (a), showing an echo at a time delay equal to the delay between the excitation pulses.

Although the early photon echo experiments were cast in tenns of Ji/2 and n pulses, these precise inversions of the population are by no means necessary [Ml- hr fact echoes can be observed using sequences of weak... 

An alternative fifth order Raman quasi-echo experiment can also be perfomied [130. 131. 132. 133 and 134]. Unlike the true Raman echo which involves only two vibrational levels, this process requires the presence of tliree very nearly evenly spaced levels. A WMEL diagram for the Raman quasi-echo process is shown in figure Bl.3.8. Here again the first two field actions create a vibrational coherence which is allowed to dephase. This is followed by a second pair of... 

Vanden Bout D and Berg M 1995 Ultrafast Raman echo experiments in liquids J. Raman Spectrosc. 26 503-11... 

Muller L J, Vanden Bout D and Berg M 1993 Broadening of vibrational lines by attractive forces ultrafast Raman echo experiments in a CH2l CDCl2 mixture J. Chem. Phys. 99 810-19... 

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. 

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

Tokmakoff A, Zimdars D, Urdahl R S, Francis R S, Kwok A S and Fayer M D 1995 Infrared vibrational photon echo experiments in liquids and glasses J. Phys. Chem. 99 13 310-20... 

Tokmakoff A and Fayer M D 1995 Homogeneous vibrational dynamics and inhomogeneous broadening in glass-forming liquids infrared photon echo experiments from room temperature to 10 KJ. Chem. Phys. 103 2810-26... 

Tokmakoff A and Fayer M D 1995 Infrared photon echo experiments exploring vibrational dynamics in liquids and glasses Acc. Chem. Res. 28 439—45... 

Rector K D, Rella C W, Hill J R, Kwok A S, Sligar S G, Chien E Y T, DIott D D and Fayer M D 1997 Mutant and wild-type myoglobin-CO protein dynamics vibrational echo experiments J. Phys. Chem. 

Schematic diagrams of modem experimental apparatus used for IR pump-probe by Payer and co-workers [50] and for IR-Raman experiments by Dlott and co-workers [39] are shown in figure C3.5.3. Ultrafast mid-IR pulse generation by optical parametric amplification (OPA) [71] will not discussed here. Single-colour IR pump-probe or vibrational echo experiments have been perfonned with OP As or free-electron lasers. Free-electron lasers use...

The vibrational echo experiments yielded exponential decays at all temperatures. The Fourier-transfonn of the echo decay gives the homogeneous lineshape, in this case Lorentzian. The echo decay time constant is AT, where is... 

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). 

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

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...

Will the vectors of a doublet be refocused at time 2t in a spin-echo experiment ... 

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 ... 

No. Since the direction of precession of the vectors is reversed during the second half of the sequence, they continue to diverge from each other. The effect of a spin-echo experiment on spin-spin coupling in a first-order homonuclear spin system is shown in the following vector representation ... 

Fig. 1.2 Behavior of the magnetization in a simple echo experiment. Top a free induction decay (FID) follows the first 90° pulse x denotes the phase of the pulse, i.e., the axis about which the magnetization is effectively rotated. The 180° pulse is applied with the same phase the echo appears at twice the separation between the two pulses and its phase is inverted to that of the initial FID. Bottom the magnetization vector at five stages of the sequence drawn in a coordinate frame rotating at Wo about the z axis. Before the 90° pulse, the magnetization is in equilibrium, i.e., parallel to the magnetic field (z) immediately aftertbe 90° pulse, it has been rotated (by90° ) into the transverse (x,y) plane as it is com-...

The short relaxation time of the 3D spin-echo experiment caused some saturation, otherwise the gain in SNR at the higher field would have been even larger, but at the expense of a longer experiment time. 

One of the fastest growing areas in NMR over the past decade has been the use of pulsed field gradients , or PFG-NMR, for selective ID and 2D experiments. The basic pulsed gradient spin-echo (PGSE) experiment [174] relies on the use of pulsed linear magnetic field gradients (of amplitude g, duration 8 and separation A) that are applied during a spin-echo experiment [184],... 

Modem NMR diffusion measurements are all based on the Stejskal-Tanner (S-T) pulsed field gradient spin-echo experiment [174] in which a gradient pulse is... 

Several NMR pulse sequences have been developed for measuring the diffusion coefficient. The most successful and currently used experiment is the modified spin-echo experiment (PGSE) proposed by Stejskal in 1967.62 As the echo signal is due to the transversal components of magnetic moments, the echo attenuation normalized for the attenuation due to relaxation can be written as63 ... 

This experiment has two limitations (a) nuclei with short T2 are difficult to be detected and (b) multiplets produce a distorted signal phase after n pulse which inverts the coupled spin states. Both limitations are partially overcome by the stimulated echo experiment (STE).64,65 The main difference with the experiment previously described is that the echo attenuation due to the diffusion competes with Tx rather than with T2. The equation analogous to Equation (13) is now ... 

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