Time- and frequency-domain signals

We can think of the magnetization vector of a homonuclear AX spin system with J =0 as consisting of two parts, one formed by the A spins and the other by the X spins. When the 90° pulse is applied, both magnetization vectors are rotated into the xy-plane. However, because the A and X nuclei precess at different frequencies, they induce two signals in the detector coils, and the overall FID curve may resemble that in Fig. 15.32a. The composite FID curve is the analogue of the struck bell emitting a rich tone com posed of all the frequencies at which it can vibrate. The problem we must address is how to recover the resonance frequencies present in a free-induction decay. We know that the FID curve is a sum of oscillating functions, so the problem is to analyse it into its component frequencies by carrying out a Fourier transformation (Further information 13.2 and 15.1). When the signal in Fig.15.32a is transformed in this way, we get the frequency-domain spectrum shown in Fig. 15.32b. One line represents the Larmor frequency of the A nuclei and the other that of the X nuclei. The FID curve in Fig. 15.33 is obtained from a sample of ethanol. The frequency domain spectrum obtained from it by Fourier transformation is the one that we have already discussed (Fig. 15.6). We can now see why the FID curve in Fig. 15.33 is so complex: it arises from the precession of a magnetization vector that is composed of eight components, each with a characteristic frequency.

Fig. 15.32 (a) A free induction decay signal of a sample of AX species and (b) its analysis into its frequency components.

Fig. 15.33 A free induction decay signal of a sample of ethanol. Its Fourier transform is the frequency-domain spectrum shown in Fig. 15.6. The total length of the image corresponds to about 1s.

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Units

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Working galvanic cells

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The rate laws

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Catalytic activity at surfaces

Mechanisms of heterogeneous catalysis

Mobility on surfaces

The rate of desorption