In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable NMR signal generated by non-equilibrium nuclear spin magnetization

precessing Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...

about the

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...

(conventionally along z). This non-equilibrium magnetization can be created generally by applying a pulse of radio-frequency close to the Larmor frequency of the

nuclear spin In atomic physics, the spin quantum number is a quantum number (designated ) which describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. The phrase was originally used to describe ...

s. If the magnetization

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

has a non-zero component in the xy plane, then the precessing magnetisation will

induce Induce may refer to: * Induced consumption * Induced innovation * Induced character * Induced coma * Induced menopause * Induced metric * Induced path * Induced topology * Induce (musician) Ryan Smith, better known by his stage name Induce, i ...

a corresponding oscillating voltage in a detection coil surrounding the sample. This time-domain signal (a sinusoid) is typically digitised and then Fourier transformed in order to obtain a frequency spectrum of the NMR signal i.e. the NMR

spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of color ...

. 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 the time constant T₂ changed, indicated by T₂^*). FID durations will then be of the order of seconds for nuclei such as ¹H. 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). Advances in the development of quantum-scale sensors, particularly NV centres, have enabled the observation of the FID of single nuclei. When measuring the precession of a single nucleus, quantum mechanical measurement

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has to be considered. In this special case, also the measurement itself contributes to the decay as predicted by quantum mechanics.

References

{{DEFAULTSORT:Free Induction Decay Nuclear magnetic resonance