Induction decay

As was mentioned above, the observed signal is the imaginary part of the sum of and Mg, so equation (B2.4.17)) predicts that the observed signal will be tire sum of two exponentials, evolving at the complex frequencies and X2- This is the free induction decay (FID). In the limit of no exchange, the two frequencies are simply io3 and ici3g, as expected. When Ids non-zero, the situation is more complex. 

Acquisition of free induction decay data during the time interval m which the equi librium distribution of nuclear spins is restored... 

Spin-spin relaxation is the steady decay of transverse magnetisation (phase coherence of nuclear spins) produced by the NMR excitation where there is perfect homogeneity of the magnetic field. It is evident in the shape of the FID (/fee induction decay), as the exponential decay to zero of the transverse magnetisation produced in the pulsed NMR experiment. The Fourier transformation of the FID signal (time domain) gives the FT NMR spectrum (frequency domain, Fig. 1.7). 

FID Free induction decay, decay of the induction (transverse magnetisation) back to equilibrium (transverse magnetisation zero) due to spin-spin relaxation, following excitation of a nuclear spin by a radio frequency pulse, in a way which is free from the influence of the radiofrequency field this signal (time-domain) is Fourier-transformed to the FT NMR spectrum (frequency domain)... 

Figure 4-9. (Ai Precessing moment vectors in field tfo creating steady-state magnetization vector Afo. with//i = 0. (B) Immediately following application of a 90° pulse along the x axis in the rotating frame. (C) Free induction decay of the induced magnetization showing relaxation back to the configuration in A.

Now with Hx turned off, the induced magnetization must relax to its steady-state value. This is the free induction decay phase. Figure 4-9C shows an intermediate stage in the FID is increasing ftom zero toward Mq, and My is decreasing toward zero. As we have seen, relaxes with rate constant l/Ti, and My relaxes with rate constant l/T 2. 

Figure 1.4 (a) Free induction decay (FID) in the time domain, (b) Fourier transfor-... 

Figure 1.26 Free induction decay and corresponding frequency-domain signals after Fourier transformations, (a) Short-duration FIDs result in broader peaks in the frequency domain, (b) Long-duration FIDs yield sharp signals in the frequency domain.

Free induction decay A decay time-domain beat pattern obtained when the nuclear spin system is subjected to a radiofrequency pulse and then allowed to precess in the absence of Rf fields. 

Matched filter The multiplication of the free induction decay with a sensitivity enhancement function that matches exactly the decay of the raw signal. This results in enhancement of resolution, but broadens the Lorentzian line by a factor of 2 and a Gaussian line by a factor of 2.5. 

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-...

Fig. 3.4.1 Schematic description of the three-dimensional SPI technique. Gz, Cx and Gy are the phase encode magnetic field gradients and are amplitude cycled to locate each /(-space point. A single data point is acquired at a fixed encoding time tp after the rf excitation pulse from the free induction decay (FID). TR is the time between excitation (rf) pulses. Notice that the phase encode magnetic field gradients are turned on for the duration of the /(-space point acquisition.

Although the idea of generating 2D correlation spectra was introduced several decades ago in the field of NMR [1008], extension to other areas of spectroscopy has been slow. This is essentially on account of the time-scale. Characteristic times associated with typical molecular vibrations probed by IR are of the order of picoseconds, which is many orders of magnitude shorter than the relaxation times in NMR. Consequently, the standard approach used successfully in 2D NMR, i.e. multiple-pulse excitations of a system, followed by detection and subsequent double Fourier transformation of a series of free-induction decay signals [1009], is not readily applicable to conventional IR experiments. A very different experimental approach is therefore required. The approach for generation of 2D IR spectra defined by two independent wavenumbers is based on the detection of various relaxation processes, which are much slower than vibrational relaxations but are closely associated with molecular-scale phenomena. These slower relaxation processes can be studied with a conventional... 

---