Free induction decay

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A free induction decay (FID) is the simplest NMR signal which is generated as excited nuclei relax in an NMR spectrometer. In NMR spectroscopy, a sample is introduced into a magnetic field, which generates an excess of nuclear spins aligned with the external magnetic field. This excess population causes an observable magnetization, that can be manipulated with radio frequency pulses, which can rotate it into the xy-plane orthogonal to the equilibrium state. This magnetization will relax back to the equilibrium state over time. During this relaxation process a FID can be recorded. The FID is a sinusoidal or more accurately exponential function modulated by a decay function. In most liquid cases, the decay function is an exponential or a combination of two or more exponential functions. In rigid solids, the decay function is more complicated. It can be a mixture of Gaussian, Lorentz and sine functions. The sine function is reflecting the spin's precession around its own axis at the Larmor frequency, where as the exponential function reflects the relaxation. The FID is then manipulated via Fourier Transform in order to create the spectrum. The FID can also be applied directly for quantitative determinations of many physical properties, such as hydrogen content in aviation fuel, solid and liquid ratio in dairy products, and many more Time-Domain NMR applications.