Primary echo

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).

For a two-pulse (90° - t - 180°), or primary echo experiment, the integrated intensity of the spin echo, which occurs at time t after the 180° pulse, is measured as a fimction of increasing t from the probe s dead-time ( 100 ns) to a time where the echo amplitude has decayed to a few percent of its initial amplitude (2-8 ps for most powder samples). A two-pulse ESE decay envelope for the type-1 Cu(II) site of a multi-copper oxidase, Fet3p, is shown in Figure 1(a). The data show an overall decay characterized by a phase memory time, Tm or T, of < 1.0 ps. Superimposed on this decay are echo modulations that arise ft om hyperfine coupling to the N nuclei of two histidyl imidazole ligands and the protons of the snrronnding matrix. 

Analytical expressions for the primary echo modulation function of an B = 1 /2, / = 1/2 system were worked out for some of the earliest ESEEM studies that appeared in the literature. Perhaps the most general of these theoretical treatments is that of Mims where the two-pulse ESEEM function is given by... 

Fig. 2.2.10 Echoes in NMR. (a) Two-pulse Hahn echo, (b) CPMG sequence with multiple refocusing pulses, (c) Stimulated echo sequence showing both, the Hahn echo (HE) or primary echo and the stimulated echo (SE). (d) Gradient echo.

Fig. 7.2.20 [Ziml] Comparison of primary and stimulated echoes for a curing series of carbon-black filled NR measured in inhomogeneous Bo and Bj fields. The amplitudes of the primary echoes have been normalized to 100%. The amplitudes of the stimulated echoes are very sensitive to the change in cross-link density with increasing curing time, tn = 15 ms.

Phase memory times in solids are usually determined by the Hahn or primary echo sequence, 7i/2-T-7i-T-echo, by variation of t [144]. For quantum computation... 

Electron spin echo spectroscopy (ESE) monitors the spontaneous generation of microwave energy as a function of the timing of a specific excitation scheme, i.e. two or more short resonant microwave pulses. This is illustrated in Fig. 7. In a typical two-pulse excitation, the initial n/2 pulse places the spin system in a coherent state. Subsequently, the spin packets, each characterized by their own Larmor precession frequency m, start to dephase. A second rx-pulse at time r effectively reverses the time evolution of the spin packet magnetizations, i.e. the spin packets start to rephase, and an emission of microwave energy (the primary echo) occurs at time 2r. The echo ampHtude, as a fvmction of r, constitutes the ESE spectrum and relaxation processes lead to an irreversible loss of phase correlation. The characteristic time for the ampHtude decay is called the phase memory time T. This decay is often accompanied by a modulation of the echo amplitude, which is due to weak electron-nuclear hyperfine interactions. The analysis of the modulation frequencies and ampHtudes forms the basis of the electron spin echo envelope modulation spectroscopy (ESEEM). 

In the basic two-pulse or primary echo experiment, two pulses separated by a time T are applied. The second pulse is twice as long as the first. At time t after the last pulse a transient response appears from the sample, the so called spin echo. By monitoring the echo amplitude as a function of the time t, a spin echo envelope can be recorded. The hyperfine couplings are obtained either by trial-and-error simulations to reproduce the modulations superimposed on the decaying echo amplitude (the original procedure) or by a Fourier transform to obtain nuclear frequencies in modern instruments as in Fig. 2.20. The frequencies are the same as obtained in ENDOR. Contrary to ENDOR, combination peaks at the sum and difference frequencies may also occur. 

The envelope of the primary echo of the PS n/Tris/DjO samples and its corresponding frequency domain spectrum are shown in Fig. 

Fig. 5. Pulse sequences for basic time-domain ESR and pulsed ENDOR experiments, (a) Primary echo experiment, (b) Inversion recovery experiment (variation of T) or Davies ENDOR. (c) Stimulated echo experiment or Mims ENDOR. For ENDOR experiments, the horizontal bar in (b) and (c) indicates a radiofrequency pulse, whose frequency is varied while all interpulse delays are fixed.

Pulsed ELDOR. Distances between electron spins can be measured by double electron-electron resonance (DEER) experiments such as the four-pulse experiment illustrated in Figure 6 (34). Similar to measurements of electron-nucleus distances, this technique is based on the r dependence of the magnetic dipole interaction between electron spins and can determine larger distances, in the range 1.5-5 nm. One of two spins (color-coded green, observer) is observed by a refocused primary echo with fixed interpulse delays ti and t2, so that relaxation does not induce variations in the echo amplitude during the experiment. The second spin (color-coded red, pumped) imposes a local dipole field at the site of the first spin, with a magnitude that depends on the distance. At a variable delay t with respect... 

Fig. 6. The four-pulse DEER experiment, (a) Pulse sequence consisting of a refocused primary echo subsequence with fixed interpulse delays for the observer spins (top) and a pump pulse at variable delay t with respect to the first primary echo (bottom), (b) The pump pulse inverts the local field at the site of the observer spin (left arrow in each panel) imposed by a pumped electron spin (right arrow in each panel), (c) Observer and pump positions in an echo-detected EPR spectrum of a nitroxide.

In the two-pulse ESEEM experiment (Fig. 5a), the intensity of the primary echo is recorded as a function of the time interval r between the Jt/2 and it pulses. The modulation formula for an 4 = A, I = A spin system is given by... 

Figure 5. Pulse sequences making use of the ESEEM effect, (a) Two-pulse sequence and the primary echo, (b) Three-pulse sequence and the stimulated echo, (c) Four-pulse sequence for the HYSCORE experiment.

The main shortcoming of the two-pulse experiment is that the primary echo decays within the phase memory time, 7m, which is often very short. This can prevent the observation of low-frequency modulations, and thus the estimation of the magnetic parameters can become uncertain. Another important limitation arises from the spectrometer deadtime u (typically 100-150 ns at X-band frequencies), which restricts the observation of the signal to times t > ti. The loss of the initial part of the time trace can cause severe distortions in the frequency-domain spectrum, especially in disordered systems where destructive interference from differ-... 

In Davies ENDOR the first selective m.w. n pulse inverts the polarization of a particular EPR transition (Fig. 15a). During the miKing period a selective r.f. a pulse is applied. If the r.f pulse is resonant with one of the nuclear frequencies (Fig. 15b), the polarization of this transition is inverted, which also alters the polarization of the electron spin echo observer transition (1,3) detected via a primary echo, a/2 - T - % - X - echo. The ENDOR spectrum is thus recorded by monitoring the primary echo intensity as the r.f frequency is incremented stepwise over the desired frequency range. 

The pulse sequenees for a Davies-type, a Mims-type, and a Chirp-ENDOR-HYSCORE are shown in Figure 24 [82]. In the Davies-type sequence (a), the nuclear coherence generator consists of the first m.w. and r.f. chirp pulse, followed by a variable free evolution time T, and the nuclear coherence detector consisting of the second r.f chirp pulse and the m.w. primary echo sequence. The time-domain trace is thus measured by incrementing T and recording the echo intensity. FT gives the ENDOR spectrum. The Mims-type sequence, shown in Figure 24b, functions in a similar way. 

Figure 26. (a) EZ-EPR experiment consisting of a primary echo sequence and a sinusoidal Bo variation (b) model calculation for an S = A, I = 3/2 spin system. Modified with permission from [7]. Copyright 2001, Oxford University Press. 

By the method of electron spin echo, weak hyperfine interactions of a number of imidazoline nitroxides with the magnetic nuclei of the surrounding molecules of the matrix were investigated (in frozen solution). Analysis of modulation effects in the primary echo made it possible to determine the number oi the nearest molecules of the solvent surrounding the radicals and the effective distances to them the results were compared with the structure of free radicals (Yudanov et a/., 1976 Dikanov et al, 1977). 

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