Phase Cycling and Gradient Pulses - The James Keeler Group

p
p
p
(a)
RF
2
1
0
–1
–2
(b)
RF
g
2
1
0
–1
–2
(c)
RF
g
2
1
0
–1
–2
The ideal pathway, shown in (a), preserves coherence orders p = ± 2 during the
inter-pulse delay. Gradients can be used to select the pathway –2 to –1 or +2 to
–1, shown in (b) and (c) respectively. However, no combination of gradients
can be found which will select simultaneously both of these pathways. In
contrast, it is easy to devise a phase cycle which selects both of these pathways
(section 9.5.5.4). Thus, selection with gradients will in this case result in a loss
of half of the available signal when compared to an experiment of equal length
which uses selection by phase cycling. Such a loss in signal is, unfortunately, a
very common feature when gradients are used for pathway selection.
9.6.3.2 Selection versus suppression
Coherence order zero, comprising z-magnetization, zz-terms and homonuclear
zero-quantum coherence, does not accrue any phase during a gradient pulse.
Thus, it can be separated from all other orders simply by applying a single
gradient. In a sense, however, this is not a gradient selection process; rather it
is a suppression of all other coherences. A gradient used in this way is often
called a purge gradient. In contrast to experiments where selection is achieved,
there is no inherent sensitivity loss when gradients are used for suppression.
We will see examples below of cases where this suppression approach is very
useful.
9.6.3.3 Gradients on other axes
The simplest experimental arrangement generates a gradient in which the
magnetic field varies in the z direction, however it is also possible to generate
gradients in which the field varies along x or y. Clearly, the spatially dependent
phase generated by a gradient applied in one direction cannot be refocused by a
gradient applied in a different direction. In sequences where more than one pair
of gradients are used, it may be convenient to apply further gradients in
different directions to the first pair, so as to avoid the possibility of accidentally
refocusing unwanted coherence transfer pathways. Likewise, a gradient which
is used to destroy all coherences can be applied in a different direction to
gradients used for pathway selection.
9.6.4 Refocusing and inversion pulses
Refocusing and inversion pulses play an important role in multiple-pulse NMR
experiments and so the interaction between such pulses and field gradient
pulses will be explored in some detail. As has been noted above in section
9.5.3, a perfect refocusing pulse simply changes the sign of the order of any
coherences present, p → –p. If the pulse is imperfect, there will be transfer to
coherence orders other than –p.
A perfect inversion pulse simply inverts z-magnetization or, more generally,
all z-operators: I z
→ –I z
. If the pulse is imperfect, it will generate transverse
magnetization or other coherences. Inversion pulses are used extensively in
heteronuclear experiments to control the evolution of heteronuclear couplings.
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