Phase Cycling and Gradient Pulses - The James Keeler Group

magnetic field is made spatially inhomogeneous for a short time. As a result,
transverse magnetization and other coherences dephase across the sample and
are apparently lost. However, this loss can be reversed by the application of a
subsequent gradient which undoes the dephasing process and thus restores the
magnetization or coherence. The crucial property of the dephasing process is
that it proceeds at a different rate for different coherences. For example,
double-quantum coherence dephases twice as fast as single-quantum coherence.
Thus, by applying gradient pulses of different strengths or durations it is
possible to refocus coherences which have, for example, been changed from
single- to double-quantum by a radiofrequency pulse.
Gradient pulses are introduced into the pulse sequence in such a way that
only the wanted signals are observed in each experiment. Thus, in contrast to
phase cycling, there is no reliance on subtraction of unwanted signals, and it
can thus be expected that the level of t 1
-noise will be much reduced. Again in
contrast to phase cycling, no repetitions of the experiment are needed, enabling
the overall duration of the experiment to be set strictly in accord with the
required resolution and signal-to-noise ratio.
The properties of gradient pulses and the way in which they can be used to
select coherence transfer pathways have been known since the earliest days of
multiple-pulse NMR. However, in the past their wide application has been
limited by technical problems which made it difficult to use such pulses in
high-resolution NMR. The problem is that switching on the gradient pulse
induces currents in any nearby conductors, such as the probe housing and
magnet bore tube. These induced currents, called eddy currents, themselves
generate magnetic fields which perturb the NMR spectrum. Typically, the eddy
currents are large enough to disrupt severely the spectrum and can last many
hundreds of milliseconds. It is thus impossible to observe a high-resolution
spectrum immediately after the application of a gradient pulse. Similar
problems have beset NMR imaging experiments and have led to the
development of shielded gradient coils which do not produce significant
magnetic fields outside the sample volume and thus minimise the generation of
eddy currents. The use of this technology in high-resolution NMR probes has
made it possible to observe spectra within tens of microseconds of applying a
gradient pulse. With such apparatus, the use of field gradient pulses in high
resolution NMR is quite straightforward, a fact first realised and demonstrated
by Hurd whose work has pioneered this whole area.
9.6.2 Dephasing caused by gradients
A field gradient pulse is a period during which the B 0
field is made spatially
inhomogeneous; for example an extra coil can be introduced into the sample
probe and a current passed through the coil in order to produce a field which
varies linearly in the z-direction. We can imagine the sample being divided into
thin discs which, as a consequence of the gradient, all experience different
magnetic fields and thus have different Larmor frequencies. At the beginning
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