Pulsed Echo Experiments

In practice, hard rf-pulses are used for uniform excitation of broad lines. Our own work has tended to use an echo sequence with the phase cycling first proposed by Kun-war. Turner and Oldfield (1986) which combines quadrature phase cycling with further cycling designed to cancel direct magnetisation (the remaining FID) and ringing effects  

Phase pulse 1 Phase pulse 2 Receiver phase  

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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. 

Three-pulse echo experiments on isolated chromophores probe the 1 —> 2 transition in addition to the fundamental Therefore, in order to model nonlinear spectra, in addition to the trajectories for mp(t) and (t), one needs the trajectory for this 1 > 2 transition frequency and in addition to the excited... 

P. Gaspard Concerning multiple-pulse echo experiments, I would like to know if there are results on the decay of the amplitude of the echo as the number of pulses increases with equal-time spacing between pulses. If the decay is exponential, the rate of decay may characterize dynamical randomness since it is closely related to the so-called Kolmogorov-Sinai entropy per unit time [see P. Gaspard, Prog. Theor. Phys. Suppl. 116, 369 (1994)]. 

Figure 4. Schematic diagram of the experimental configuration for an ultrasonic pulse-echo experiment.

The electron spin echo of Ag°(B) has a very short phase memory time but relatively strong aluminum modulation can be identified. However, the phase memory time is too short to carry out a quantitative analysis of the modulation. This also precludes us from getting analyzable modulation from deuterated adsorbate molecules in a three pulse echo experiment. So the data is insufficient to locate Ag°(B) in the zeolite lattice without additional information. 

From the above discussion, it is clear that observation of ESEEM requires that the microwave pulses affect branching of the EPR transitions. This places a quantum mechanical constraint on the ESEEM experiment, in that each energy level must be involved in at least two different microwave transitions, and an experimental constraint that requires the microwave pulse bandwidth to cover the spread in frequencies needed to fully excite the branching . The experimentally observed ESEEM function is a product of the quantum mechanically derived modulation function and a decay function that describes the loss of magnetization due to spin relaxation. These decay functions are typically modeled with exponential forms exp(-T/To) where n = 1,2 or 0.5. Fora 90° - t - 180° or two-pulse echo experiment, Tq = a time that is typically on the order of 1 qs, as evidenced by the data shown for the Cu(II) center in Figure 1. This... 

The DME method has many possible applications. Inclusion of the external electromagnetic field into the mixed quantum lassical simulation is possible and offers a possibility for computational support of the pulse-echo experiments in the infrared region. See for example Ref. [35]. 

From magnetic resonance spectroscopy [49] it is well-known that IB effects are adequately circumvented by the tricks of a spin echo experiment. For instance, in a two-pulse echo experiment, IB effects are averaged out and one probes spin dephasing determined by time-dependent fluctuations characteristic of HB only (and not IB). More specifically, a nll-r-n microwave pulse sequence is applied, where the first nil pulse creates a coherent superposition state for which a la = 1 and the n pulse, applied at time r after the first pulse, generates a spin coherence (the echo) at time 2r after the initial pulse. The echo amplitude is traced with r. The echo amplitude decay time is characteristic of the pure dephasing dynamics. For phosphorescent triplet states it is possible to make the echo optically detectable by means of a final nil probe pulse applied at time f after the second pulse [44]. In Fig. 3b, the optically detected echo amplitude decay for the zero-field transition at 2320 MHz of... 

Fortunately, both of these problems can be solved by performing three-pulse echo experiments (Figure 3) in which the stimulated echo (SE) amplitude is used to plot the envelope. The mechanism underlying stimulated echo generation is as follows. The first two pulses impose a cosine-shaped toothed pattern of pitch Af = 1/t on an initially smooth resonance line. This toothed pattern is then subsequently detected by the method of free induction spectroscopy, i.e., by applying an additional pulse (pulse III). The resulting Fourier transform of the toothed pattern consists of a single pulse (SE) offset from pulse III by an interval t. 

A related RF technique to NMR is nuclear quad-rupole resonance (NQR). In NQR, transitions between nuclear quadrupole levels of nuclei in a solid material are induced by the applied radiation. The electric field gradients in the solid orient the quad-rupolar nuclei I>1/2) and give rise to quantized energy levels that yield transitions in the MHz range. FT-NQR spectroscopy measures these splittings and the relaxation times by free induction decay or various pulse echo experiments. FT-NQR spectroscopy provides information about the local environment around the quadrupolar nucleus in a crystal. 

To measure the longitudinal relaxation time Ti, an inversion or saturation pulse is applied, followed, after a variable time T, by a two-pulse echo experiment for detection (Fig. 5b). The inversion or saturation pulse induces a large change of the echo amplitude for T < T. With increasing T, the echo amphtude recovers to its equilibriiun value with time constant Ti. The echo amphtude of the stimulated echo (Fig. 5c) decays with time constant T2 when the interpulse delay T is incremented, and with the stimulated-echo decay time constant Tse < T1 when the interpulse delay T is incremented. A faster decay, compared to inversion or saturation recovery experiments, can arise from spectral diffusion, because of a change of the resonance frequency for the observed spins, of the order of Av = 1/t on the time scale of T. Quantitative analysis of spectral diffusion can provide information on the reorientation dynamics of the paramagnetic centers. 

Fig. 12. Two-pulse echo experiment, (a) Pulse sequence, (b) Evolution of the magnetization vectors corresponding to spin packets with difference resonance offsets Q.s.

Consider a two-pulse echo experiment consisting of an mw n/2 pulse for excitation of transverse magnetization an interpulse delay X in which this magnetization defocuses due to a dispersion of resonance frequencies a n pulse that inverts the... 

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

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