FID —See Free induction decay

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. 

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). 

How do we extract the chemical shifts of all nuclei in the sample from the free-induction decay signal The answer is our old friend the Fourier transform. The FID is called a time-domain signal because it is a plot of the oscillating and decaying RF intensity versus time, as shown in Fig. 10.4 (the time axis is conventionally labeled t2, for reasons you will see shortly). Fourier transforming the FID produces afrequency-domain spectrum, a plot of RF intensity versus the frequencies present in the FID signal, with the frequency axis labeled v2 for frequency or F2 for chemical shift, as shown in Fig. 10.1. So the Fourier transform decomposes the FID into its component frequencies, revealing the chemical shifts of the nuclei in the sample. 

The standardized pulse program for a proton decoupled 13C spectrum is shown in Figure 4.2a. The sequence is relaxation delay (Rd) (see Section 4.2.3), rf pulse (6), and signal acquisition (t2). The proton channel has the decoupler on to remove the H—13C coupling, while a short, powerful rf pulse (of the order of a few microseconds) excites all the 13C nuclei simultaneously. Since the carrier frequency is slightly off resonance FID (free induction decay), for all the 13C frequencies, each 13C nucleus shows a FID, which is an exponentially decaying sine wave. 

Actually, the spectroscopic data would more closely resemble the pattern in Figure 3.15, which is the same as the wave in Figure 3.14, except that the overall intensity of the signal decays exponentially with time. (Note that the decay does not affect the frequencies.) Such a pattern is called the modulated free induction decay (FID) signal (or time-domain spectrum). The decay is the result of spin-spin relaxation (Section 2.3.2), which reduces the net magnetization in the, y plane. The envelope (see Section 3.6.2) of the damped wave is described by an exponential decay function whose decay time is T, the effective spin-spin relaxation time. 

Figure 1. The effect of coherent excitation on hght transmission, (a) The incident and transmitted pulses through a sample having an optical density of 1.0. (b) The free induction decay created by the coherent excitations by the pulse in (a), (c) The Wigner distribution (see text) of the FID shown in (h).

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