# Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/Spin echo

File:Spinecho.JPG
Spin echo: Pulse sequence (above) and Signal (below)

In nuclear magnetic resonance, spin echo refers to the refocusing of precessing nuclear spin magnetisation by a 180° pulse of resonant radiofrequency.

The NMR signal observed following an initial excitation pulse (orange in diagram) decays with time due to both spin-spin relaxation and any inhomogeneous effects which cause different spins to precess at different rates e.g. a distribution of chemical shifts or magnetic field gradients. Relaxation leads to an irreversible loss of magnetisation (decoherence), but the inhomogeneous dephasing can be reversed by applying a 180° or inversion pulse (blue in diagram) that inverts the magnetisation vectors. If the inversion pulse is applied after a period T of dephasing, the inhomogeneous evolution will rephase to form an echo at time 2T. The intensity of the echo relative to the initial signal is given by ${\displaystyle \exp(-2T/T_{2})}$ where ${\displaystyle T_{2}}$ is the time constant for spin-spin relaxation.

Another method for generating spin echoes is to apply three successive 90° pulses. After the first 90° pulse, the magnetization vector is exchanging energy through dipole, dipole interactions and in a time τ, forms what is often referred to as a “pancake” in the x’-y’ plane. A further 90° pulse is then applied such that our “pancake” is now in the x’-z’ plane. When considering the two types of relaxation, spin – lattice and spin – spin (T1 and T2) we assume the former to take an infinite amount of time as such allowing the spin vectors to precess about the z axis. Now, the angle each spin makes with the z’ axis is equal to the angle it previously made about the y’ axis. At this point any change in angle that now takes place will require a change in energy thus implying a spin – lattice interaction is necessary. This implies a permanent memory of the state of the system as it was at time τ. After a further time τ2 a third pulse is applied and our Magnetization vector is back in the x’ – y’ plane and will lie in the same direction as for a (90 – τ – 180) spin echo sequence formally discussed. Then after final delay of τ we see what is commonly referred to as a stimulated echo. This technique is commonly used when studying T1 relaxation times. This is because by measuring the magnitude of the correct echo and its decay with pulse width separation we can determine T1. The echo magnitude will depend on the relation, exp(-τ2/T1).

Echo phenomena are important features of coherent spectroscopy which have been observed and used in various fields from magnetic resonance to laser spectroscopy. They are fundamental to magnetic resonance imaging. Echoes were first detected in nuclear magnetic resonance by Erwin Hahn in 1950.[1]

## How it works

The spin echo concept of Erwin Hahn was fully explained in his 1950 paper, but it was further developed by Carr who pointed out more aspects of a full 180 degree refocusing pulse.[2][3]

The fundamental concept may be better understood by considering the following symbolic representation:

The spin echo concept. (A) - The vertical green arrow is the average magnetic moment of a group of protons. All are vertical in the main field and spinning on their long axis. (B) A 90 degree pulse (orange arrow) has been applied that flips the arrow into the horizontal (x-y) plane. The black arrow shows the precession of the net magnetic moment. (C) & (D) Due to T2* effects, as the net moment precesses, some protons slow down due to lower local field strength (and so begin to progressively trail behind) while some speed up due to higher field strength and start getting ahead of the others. This makes the signal broaden progressively, dephasing and decaying. (E) A 180 degree pulse is now applied (orange arrow) so now the slower protons lead ahead of the main moment and the fast ones trail behind. (F) Progressively, the fast moments catch up with the main moment and the slow moments drift back toward the main moment. (G) Complete refocusing has occurred and at this time, an accurate T2 echo can be measured with all T2* effects removed. Quite separately, return of the green arrow towards the vertical (not shown) would reflect the T1 relaxation.

## References

1. E. L. Hahn, Physical Review 80, 580–594 (1950)
2. Carr, HY: Effects of diffusion on free precession in nuclear magnetic resonance, Physical Review 94, 630-638 (1954)
3. Carr, HY: Sharper images of MRI's origins. "Physics Today" "46:93-36 (1993)