What is Free Induction Decay in NMR?

Hello I will give you a basic run down of what these two things meen. Then a couple of ideas of there applications.

Nuclear Magnetic Resonance = NMR

Free Induction Decay = FID

Very basic the FID is the acctual measurement of the NMR.

If you web search FID+NMR you will get many great related articles for univeristies all over the world. It is used in chemisrty as well as bioligy and magnetic resonance  

Now for a dictionary explanation.

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.

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

Again brief but more detail, the actual NMR spectrum acquired by a modern pulse fourier transform NMR spectrometer is called a free-induction decay or fid. This spectrum results when a sample in the presence of a large external magnetic field is subjected to a short (several microseconds), high-power pulse (50-1,000W) of radio-frequency energy at the resonance frequency of the nuclei of interest. This burst of energy is released by the sample over a much longer period of time (typically seconds) as the nuclear spins return to their equilibrium energy states. The released energy is emitted as a radio wave.

The frequency of this wave is dependent upon the local magnetic environment of the nuclei. If the excited nuclei in a sample are all in the same magnetic environment, the observed signal will consist of a single decaying radio frequency (sine wave). If there are several magnetically in-equivalent nuclei, each will release its absorbed energy at a slightly different frequency. The observed signal will consist of a decaying waveform which is the sum of the individual decaying sine waves from each of the in-equivalent nuclei. This signal induces a current in the NMR probe and the signal decays as the nuclei freely release their absorbed energy, hence the term free-induction decay.

The actual spectral data acquired by the NMR is the free-induction decay, or fid. The "spectrum" we always plot and interpret results from a mathematical manipulation (ft) of the acquired spectral data. In pulse ft-NMR, the fid is fourier transformed. The ft converts the AMPLITUDE vs. TIME domain information in the fid to the AMPLITUDE vs. FREQUENCY domain seen in the typical NMR "spectrum".

in Bioligy 

A theory of the NMR signal dephasing due to the presence of tissue-specific magnetic field inhomogeneities is developed for a two-compartment model. Randomly distributed magnetized objects of finite size embedded in a given media are modeled by ellipsoids of revolution (prolate and oblate spheroids). The model can be applied for describing blood vessels in a tissue, red blood cells in the blood, marrow within trabecular bones, etc. The time dependence of the dephasing function connected with the spins inside of the objects, si, is shown to be expressed by Fresnel functions and creates a powder-type signal in the frequency domain. The short-time regime of the dephasing function for spins outside the objects, se, is always characterized by Gaussian time dependence, sesimexp[-zetak(t/tc)2], with zeta being a volume fraction occupied by the objects, tc being a characteristic dephasing time, and the coefficient k depending on the ellipsoid's shape through the aspect ratio of its axes (a/c). The long-time asymptotic behavior of se is always “quasispherical”-linear exponential in time, sesim exp(-zetaCt/tc), with the same “spherical” decay rate for any ellipsoidal shape. For long prolate spheroids (a/c)«1, there exists an intermediate characteristic regime with a linear exponential time behavior and an aspect-ratio-dependent decay rate smaller than (zetaC/tc).

Hope this gives you some insite as to what the two things are for. 

free induction decay