Building Blochs

Felix Bloch

Nobel Prize in Physics lecture, 11th December 1952:

“To follow the analogue of mechanical resonance we must now come back to relaxation, which can be seen to act like a friction, and which counteracts the tilt produced by the alternating field.”

Since the net magnetisation of a sample is the vector sum of many protons, and since there is a constant interaction growth rate of the protons with the lattice, we can write

T1 recovery of Mz: eqn

where M0 is the equilibrium magnetisation, T1 is the longitudinal, or spin-lattice relaxation time, which is the time constant of the exponential recovery of Mz.

The transmission of energy to the local environment of a magnetic moment in a magnetic field which mediates this relaxation is primarily due to its thermal “contact” with that environment (fluctuating magnetic fields).

It is possible to perceive why Bloch likened relaxation to friction.

Take the general Bloch equation (dM/dt=γMxB, derivation), and rewrite it in terms of parallel and perpendicular components of M to the external, static main magnetic field: dMz/dt=0 and dMxy=γ(MxyxB). From the former we may write the equation in the post above, and from the latter, dMxy/dt=γ(MxyxB)-(1/T2)Mxy (or simply dMxy/dt=-(1/T2)Mxy in the rotating frame).