• View
• Edit
• History
• Print

FreeInductionDecay

< Practical aspects | Index | Nuclear Curie law and receptivity >

and the nuclear relaxation

When we succeed in turning the nuclear magnetization {$\mathbf{M}_n$} away from its equilibrium direction along the static magnetic field {$\mathbf{B}_0$} we obviously drive it out of equilibrium. This is the prerequisite in order to observe the nuclear induction of Felix Bloch. Optimized spin manipulation by radiofrequency pulses turns {$\mathbf{M}_n$} perpendicular to {$\mathbf{B}_0$} and the precession generates an induction signal in the coil.

The coherent induction signal will inevitably decay in time both because it looses the initial coherence and because the nuclear magnetization will be driven back towards equilibrium by inelastic events, ending up again aligned along the static field. This is a good reason why the induction signal in the pick-up coil is termed Free Induction Decay (FID, for short).

The relaxation due to the equilibrium recovery of the magnetization requires an energy exchange between the nuclear spin system and its surrounding, generally referred to as the lattice. The energy of the spin ensemble must return to its minimum, through a dissipative process, as dictated by:

{$ U = -\sum_i \mathbf{m}_i\cdot \mathbf{B} $}

This is therefore called a spin-lattice process.

However the FID will generally vanish before, often long before this type of relaxation is completed. This is because precessing spins may get out of phase and cease to produce an induction when still out of thermodynamic equilibrium. A fate of this kind takes place if the magnetic field is inhomogeneous, which may be a trivial artifact of the experimental setup, but it may also be an intrinsic property of the sample, if the sample provides an internal source of additional random magnetic fields. This is typically the case for the dipolar magnetic field produced on each nucleus by the other neighboring nuclei.

Because of the latter example the decay of the induction due to dephasing is termed a spin-spin process.

In any case relaxation is an essential aspect of NMR. Spin-lattice relaxation is also essential to produce a net magnetization in the first place, since one must make sure to wait enough to build it, before tilting it into the precession plane. In pratice the spin lattice relaxation rate may vary between fractions of microseconds (which make observation practically impossible, not enough time to perform the experiment) to hours (which again makes experiment very cumbersome), whereas the intermediate cases are the easiest.

Spin-spin relaxation rates are often larger then spin-lattice rates. When this is the case they may be countered by suitable radio-frequency spin manipulations that invert time evolution, refocusing the spin magnetization in an echo process.

< Practical aspects | Index | Nuclear Curie law and receptivity >