Chapter 5 – Detection and Imaging Tools that Use Nonoptical Waves 189
operate in shorter pulses and generate higher transient B-fields, for example, up to ~100 T
for millisecond-duration pulses.
Superconducting NMR solenoids of a coil length of ~100 km are composed of
superconducting wire made usually from an alloy of niobium with tin and titanium, for
example, (NbTaTi)3Sn, which is embedded in copper for mechanical stability and cooled to
~4 K using a liquid helium reservoir inside a Dewar, which is in turn thermally buffered from
the room temperature environment by a second outer Dewar of liquid nitrogen (Figure 5.4b).
The sample is lowered into the central solenoid bore, whose a diameter and length are both
typically a few centimeters, which enclose transmitter/receiver radio frequency coils that
surround the sample placed inside a narrow glass tube on the central solenoid axis. The size
of the Dewars required result in such machines occupying the size of a room often requiring
stair access to the sample’s entry port and the Dewar openings and are suitably expensive to
purchase and maintain, necessitating an NMR facility infrastructure.
The B-field inside a long solenoid of length s, a coil current I, and a number of turns n can
be modeled by the simple relation easily derived from the Biot–Savart law of (in reference to
Figure 5.4c) dB = μ0I sin θds/(4 πr2):
(5.23)
B
n
I
s
= µ0
where μ0 is the vacuum permeability. The signal-to-noise ratio of an NMR measurement
scales roughly as ~B3/2 (the bulk magnetization of the sample scales as ~B; see Worked Case
Example 5.2, but the absorbed power also scales with ν, which scales with ~B, whereas the
shot noise scales with ~√ν) so there is a motivation to generate higher fields. Field strengths
of ~12 T are possible with solenoid cooling at 4 K, which corresponds to an ~500 MHz reson
ance frequency for 1H. To generate higher field strengths requires cooling lower than the ~4 K
boiling point of helium, using the Joule–Thompson effect in a gas expansion unit to maintain
solenoid temperatures as low as ~2 K, which can result in a coil current of a few hundred
amperes, equivalent to a resonance frequency for 1H of up ~900 MHz.
Older NMR machines use a continuous wave (CW NMR) approach to sequentially probe
the sample with different radio frequencies. The primary limitation with CW NMR is one of
time, since multiple repeated spectra are usually required to improve signal-to-noise ratio,
which can result in experiments taking several hours. Modern NMR machines use a fre
quency domain method known as “Fourier transform NMR (FT NMR),” which dramatically
reduces the data acquisition time. Here, a sequence of short pulses of duration τ of a carrier
wave of frequency f is composed of a range of frequency components, which span ~f ± 1/2πτ.
The value of f used is catered to the unshielded resonance frequency of the magnetic atomic
nucleus type under investigation, while τ is usually in the range 10−6 to 10−3 s to give suffi
cient frequency resolution to probe shifts in the resonance frequency of <0.1 ppm (typically
~0.02 ppm), with an averaged NMR spectroscopy trace typically taking less than 10 min to
acquire.
As discussed previously, after the absorption of radio frequency energy, atomic nuclei
relax back to a state of thermal equilibrium. This relaxation process involves the ultimate
emission of tiny amounts of radio frequency energy from the high-energy-state nuclei. These
tiny signals can be detected by radio frequency detector coils around the sample, and it is
these that ultimately constitute the NMR signal.
5.4.6 NMR SPECTROSCOPY PULSE SEQUENCES
In practice, an NMR spectroscopy experiment is performed by using several repeated
radiofrequency driving pulses, as opposed to continuous wave stimulation. However, different
specific pulse sequences can generate different levels of information in regard to the spin
relaxation processes. The simplest pulse sequence is just a single pulse followed by the detec
tion of resonance signal, damped by relaxation (Figure 5.5a), known as the free induction