Free induction decay

In Fourier Transform NMR, a free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetisation precessing about the magnetic field (conventionally along z). This non-equilibrium magnetisation is generally created by applying a pulse of resonant radio-frequency close to the Larmor frequency of the nuclear spins.

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If the magnetisation vector has a non-zero component in the xy plane, then the precessing magnetisation will induce a corresponding oscillating voltage in a detection coil surrounding the sample. This time-domain signal is typically digitised and then Fourier transformed in order to obtain a frequency spectrum of the NMR signal i.e. the NMR spectrum.

The duration of the NMR signal is ultimately limited by T₂ relaxation, but mutual interference of the different NMR frequencies present also causes the signal to be damped more quickly. When NMR frequencies are well-resolved, as is typically the case in the NMR of samples in solution, the overall decay of the FID is relaxation-limited and the FID is approximately exponential (with a time constant T₂ or more accurately T₂^*). FID durations will then be of the order of seconds for nuclei such as ¹H. If NMR lineshapes are not relaxation-limited (as is commonly the case in solid-state NMR), then the NMR signal will generally decay much more quickly e.g. microseconds for ¹H NMR.

Particularly if a limited number of frequency components are present, the FID may be analysed directly for quantitative determinations of physical properties, such as hydrogen content in aviation fuel, solid and liquid ratio in dairy products (Time-Domain NMR).