Free-induction decay, FID

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. 

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

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.

Free Induction Decay (FID) Interference pattern of decaying cosine waves collected by Fourier Transform spectrometers, stored digitally prior to Fourier Transformation. 

The zincblende (ZB), or sphalerite, structure is named after the mineral (Zn,Fe) S, and is related to the diamond structure in consisting entirely of tetrahedrally-bonded atoms. The sole difference is that, unlike diamond, the atoms each bond to four unlike atoms, with the result that the structure lacks an inversion center. This lack of an inversion center, also characteristic of the wurtzite structure (see below), means that the material may be piezoelectric, which can lead to spurious ringing in the free-induction decay (FID) when the electric fields from the rf coil excite mechanical resonances in the sample. (Such false signals can be identified by their strong temperature dependence due to thermal expansion effects, and by their lack of dependence on magnetic field strength). 

Three parameters affect an NMR spectrum the chemical shift, coupling, and nuclear relaxation. These must be accounted for when obtaining the NMR spectrum from the spectrometer s output. Obtaining the NMR spectral plot from the output (the free induction decay, FID) of a modern NMR spectrometer involves the analysis of the mathematical relationship between the time (0 and frequency (go) domains known as the Fourier relationship ... 

This effect induces a free induction decay (FID) signal in the detection circuit. The FID can be measured, and the normal absorption spectrum can be obtained by means of an inverse Fourier transform. A variety of experimental extensions have been developed for this approach. By means of particular pulse sequences it is possible to detect spin resonances selectively on the basis of a broad ensemble of properties such as spatial proximity and dipolar coupling strengths. The central fundamental quantity of interest is, however, still the energy spectrum of the nuclear spin,... 

Fig. 10.1. The top panel shows the free induction decay (FID) acquired for a sample of strychnine (1) at an observation frequency of 500 MHz. The spectrum was digitized with 16 K points and an acquisition time of 2 s. Fourier transforming the data from the time domain to the frequency domain yields the spectrum of strychnine presented as intensity versus frequency shown in the bottom panel.

A pre-requisite for the successful extraction of key NMR parameters from an experimental spectrum is the way it is processed after acquisition. The success criteria are low noise levels, good resolution and flat baseline. Clearly, there are also experimental expedients that can further these aims, but these are not the subject of this review per se. In choosing window functions prior to FT, the criteria of low noise levels and good resolution run counter to one another and the optimum is just that. Zero filling the free induction decay (FID) to the sum of the number acquired in both the u and v spectra (in quadrature detection) allow the most information to be extracted. 

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

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