The Jeener echo

Mansfield, Multiple-pulse nuclear magnetic resonance transients in solids , Phys. Rev. 137, A961-A974 (1965). 

Moskvich, N. A. Sergeev, and G. I. Dotsenko, Two-pulse echo in solids containing isolated three-spin systems, Phys. Stat. Solidi (a) 30, 409-418 (1975). 

Powles and P. Mansfield, Double pulse nuclear-resonance transients in Solids , Phys. Letters 2, 58-59 (1962). 

---

Any of the above ADRF methods, in principle, can convert Zeeman order into dipolar order with an efficiency approaching 100%. In contrast, the Jeener echo technique (to be discussed in IV.B.4.) can only achieve approximately 50% conversion. 

The Jeener echo sequence (Jeener and Broekaert, 1967 Goldman, 1970) is... 

The requirements on the phases of the pulses is somewhat less stringent than implied by the sequence above. The second pulse must be in quadrature with the first but the third pulse can have any arbitrary phase because the dipolar order is not referenced by any external directions. To observe the Jeener echo, the reference phase of the receiver must be 90° out of phase with the third pulse. When the detector reference phase is identical with that of the third pulse, a Zeeman signal can be observed which is simply the FID resulting from the magnetization which has relaxed back to the z direction in the time since the first pulse. 

Thus, the sequence stated at left and illustrated above is the most convenient one to set up. The reference phase for the receiver should be set to maximize the FID following the first pulse, in this case. In searching for it, it is good to know that the Jeener echo is typically an order of magnitude smaller than the FID. 

The appearance of a Jeener echo depends upon the existence of a dipolar reservoir so that some dipolar interaction not averaged out by molecular motions is necessary. This does not nessarily restrict the application to rigid solids. For example, liquid crystals, including soaps and lipids in certain phases yield valuable information when studied by the Jeener echo sequence (Bloom, et al., 1977). 

The most obvious application of the Jeener echo is to measure T by plotting echo amplitude vs. time spent in a state of dipolar order. If the system under study is homogeneously broadened, then the location on the echo where the amplitude is measured, provided it is chosen consistently, is immaterial for the measurement of T - In an inhomogeneously broadened system, such as a poly crystalline material, the Jeener echo may be a superposition of Jeener echoes with different shapes and different T- s. If so, it may matter where the echo amplitude is sampled. The most obvious test is to plot relaxation curves from different parts of the echo to determine whether the echo is relaxing uniformly. For a crystalline material, one expects that the dipolar relaxation time T p will be independent of the crystal orientation in the external field because the state of dipolar order is independent of this external field. 

A second application of the Jeener echo is to determine lineshape parameters such as the second moment (Bloom, et al. 1977). As the echo starts with zero magnitude at the third rf pulse and evolves in time from that point, it is less susceptible to problems of receiver deadtime than the FID is. From the equation for the expansion of the FID in terms of its moments... 

This method requires evaluation of the initial slope of the Jeener echo which is linear in time. This linearity can be assumed for times shorter than t. Therefore it is less susceptible to errors from the recovery of the system after the third pulse. One must also obtain the initial height of the FID following the first pulse by extrapolating back to time zero. However, the extrapolation to obtain the magnitude of the FID is far less susceptible to errors than the estimate of the FID slope at time zero which is what most other methods require. Note also that this determination requires accurate knowledge of the rotation angles of the last two pulses. 

There are two more ways to analyze the Jeener echo. From the relation... 

A more sophisticated analysis indicates that we can evaluate Sg from the Jeener echo without requiring knowledge of A or of G(0). This is because, for a homogeneous system, the shape f(t) of the Jeener echo as opposed to its magnitude, is independent of x and Xg. In the linear region... 

It differs from the Jeener echo in that the dipolar state is prepared by an off-resonance saturation radiation rather than the first two pulses in the Jeener sequence. The application of the saturation method to short relaxation times comparable to the Jeener echo is discussed by Emid, et al. (1980). 

Fig. 6. The generalized Jeener-Broekaert three pulse sequence. Note that FT of the solid echo and the alignment echo starts at times delayed by the pulse separation r, after the second and third pulse, respectively...

To bypass receiver deadtime effects, wideline spectra are derived by Fourier transformation of the decay of an echo. By use of the Hahn echo and the stimulated echo (Section 2.2.1), wideline spectra of and other spin-5 nuclei can be measured, for example, but not the spectra of dipolar coupled spins and of quadrupolar nuclei like H. The magnetization of nuclei with spin / = 1 can be refocused by the quadrupole echo or the solid echo, and by the Jeener-Broekaert echo or the alignment echo [Slil] (Fig. 3.2.6). 

Equation (3.2.14) is the starting point for numerical simulation of dynamic wideline NMR spectra. With the Jeener-Broekaert echo the imaginary part of the exponential depending on h is measured, and with the stimulated echo the real part is measured. The lineshapes of solid-echo spectra follow from (3.2.14) with t , = 0. 

These composite pulses can be used in liquid- and solid-state multi-pulse experiments such as the //V PT experiment (insensitive nuclei enhanced by polarization transfer) and the Jeener-Broekaert echo experiment [Wiml]. 

In the stimulated echo experiment, also shown in Fig. 6.2.3, the second pulse transfers the system into a mixture of Zeeman and double quantum order (alongandpg). Here, the relevant relaxation times are Ti (longitudinal Zeeman) and T q (double quantum), for which the 45 pulses of the Jeener-Broekaert sequence are replaced by 90v pulses. Again, two echos evolve at T] around the third pulse, and are refocussed by the fourth pulse. The two negative echo amplitudes vary as function of T2, with -[exp(-T2/Tiz) + exp(-T2/Ti3Q)], and both Ti and Tqq can be determined as separate values [14]. 

Pulses which are multiples of n/2 pulses are the easiest to set, but other pulse lengths are occasionally needed, like a 45 degree pulse for Jeener echoes (IV.B.4.), or arbitrary length pulses for variable nutation T experiments (III.D.5.) and the DANTE sequence (II.D.2.). For any submultiple of n/2 pulses, the trick is to repeat the pulse an appropriate number of times so that the combined effect is that of a n/2 pulse or multiples thereof. For example, you could go for 30 degree pulses by having three identical pulses act like a 90 degree pulse. Any odd length pulses must be interpolated after that. 

Jeener and Broekaert introduced, in 1%7, a three-pulse B,(r) sequence to measure the relaxation time Tm of the dipolar order of / = 1 spin systems in the presence of a conventional high Zeeman field, Bq, which is based on the decay time of the so-called Jeener echo . It was later extended by Spiess and Kemp-Harper and Wimperis to study in a similar way the quadrupolar order in / a 1 systems. The appearance of a Jeener echo depends upon the existence of interactions that are not averaged out by molecular motions on the considered time scale. The method has become of great importance in recent relaxation studies, in particular of liquid crystals because, in standard spin relaxation theories, it provides a power l means to separate and analyse the spectral densities / v) and /2) j. i4,is,2025 ggg... 

Li and Be work has gained from the application of the stimulated-echo spectroscopy to study the ultra-slow dynamics of nuclear spin-3/2 probes. Apart from the dominant first-order quadrupolar interaction, the impact of the homonuclear dipolar interactions was also considered. Explicit analytical expressions describing various aspects of a coupled quadupolar pair subjected to a Jeener-Broekaert pulse sequence have been derived. Extensions to larger spin systems are also briefly discussed. These results are compared with experimental data on a single-crystalline Li ion conductor. 

The Jeener-Broekaert (J-B) pulse sequence [2.18] shown in Fig. 2.5 allows the creation of spin alignment and the observation of a stimulated echo [2.19] for a spin-1 system. The density matrix at the end of second pulse... 

In systems with non-zero average interactions, a Jeener echo may be observed after a convenient pulse sequence, whose decay is sensitive to very slow motions (in the range 1 to 100 Mz) . These motions should be related to slow eventual rearrangements of junction points, involving many chain collective motions. An exponential decay, with characteristic rate T- = 3/5 is observed experimentally, up to 0.3 s, which means that... 

This is illustrated in Fig. 9. The 2D spectra refer to quadrupole echo sequences and characterize two possible reorientation mechanisms of a methyl group (three-site jumps vs continuous diffusion). Drastic spectral differences are observed. Ajqjarratly, these 2D relaxation spectra sensitively indicate the type of motion. The same is true for the corresponding normalized contour dots (see Fig. 9). We note that similar 2D spectra can be obtained from inversion recovery or Jeener-Broekaert sequences (see Fig. 6) [68]. Thus, by applying this 2D technique to different pulse sequoic, the various motions can be differentiated over an extremely wide dynamic range, extending from the fast-rotational to the ultraslow motional re me. Sin<% the different motions (see Fig. 4) modulate different kinds of molecular order (see Fig 3) these orders can be differentiated, likewise. 

In another work the MAS NMR technique is compared to the static powder quadrupole echo (QE) and Jeener-Brockaert (JB) pulse sequences for a quantitative investigation of molecular dynamics in solids. The line width of individual spinning sidebands of the ID MAS spectra were found to be characteristic of the correlation time from 10 to s so that the dynamic range is increased by approximately three orders of magnitude when compared to the QE experiment. As a consequence, MAS NMR is found to be more sensitive to the presence of an inhomogeneous distribution of correlation times than the QE and JB experiments which rely upon line shape distortions due to anisotropic T2 and Tiq relaxation, respectively. All these results have been demonstrated experimentally and numerically using the two-site flip motion of dimethyl sulfone and of the nitrobenzene guest in the a-p-tert-butylcalix[4]arene-nitrobenzene inclusion compound. 

---