Free induction decay pulses

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.

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. 

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... 

When the pulse is switched off, the excited nuclei return slowly to their original undisturbed state, giving up the energy they had acquired by excitation. This process is known as relaxation. The detector is switched on in order to record the decreasing signal in the form of the FID (free induction decay). You can observe the FID on the spectrometer s computer monitor, but although it actually contains all the information about the NMR spectrum we wish to obtain, it appears completely unintelligible as it contains this information as a function of time, whereas we need it as a function of frequency. 

At the very beginning of our discussion in 1.1.1, we mentioned that any pulse experiment begins with a delay period. This is necessary so that the spins can return to equilibrium before they are excited. After excitation (when the pulse is turned off) we observe the FID, the free induction decay What decays The induced magnetization of the spins, and this process is known as relaxation. It may be slow or fast, as we shall see, and can also occur via a number of processes, which are discussed in detail in the monographs we have recommended for further reading. We will only treat relaxation very briefly here. 

After the pulse, we wait for a short whilst (typically a few microseconds), to let that powerful pulse ebb away, and then start to acquire the radio frequency signals emitted from the sample. This exhibits itself as a number of decaying cosine waves. We term this pattern the free induction decay or FID (Figure 1.3). 

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. 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.

Also, the high mobility present in elastomers creats a weak dipolar coupling so that the cross polarization is inefficient and results in weak enhancement compared to standard free induction decay spectra. As far as material identification is concerned, the spectrum resulting from acquiring a standard pulsed free induction decay at an elevated temperature is adequate. Further research will probably show the narrow lines from the magic angle spectra of natural rubber may allow assignments to lesser components. ... 

So-called multidimensional NMR techniques can provide important information about macromolecular conformation. In these cases, the sequence of a protein is aheady known, and establishing covalent connectivity between atoms is not the goal. Rather, one seeks through-space information that can reveal the solution conformation of a protein or other macromolecule. Two-or three-dimensional techniques use pulses of radiation at different nuclear frequencies, and the response of the spin system is then recorded as a free-induction decay (FID). Techniques like COSY and NOESY allow one to deduce the structure of proteins with molecular weights less than 20,000-25,000. 

In pulsed NMR, the magnetic field is turned on for the time necessary to rotate the magnetization vector into a plane called the 90° rotation or 90° pulse. The field is turned off and the magnetization vector rotates at a nuclear precession frequency relative to the coil. This induces an NMR signal that decays with time as the system returns to equilibrium. This signal is called the free induction decay (FID). 

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