NUCLEAR MAGNETIC RESONANCE

Nuclear magnetic resonance (NMR) involves the interaction of a population of nuclear spins in a d.c. magnetic field with an r.f. field at their precession frequency. This frequency is given by

The apparatus required for NMR consists of a magnet to produce a uniform d.c. field H₀, a small coil surrounding the spin-containing sample to allow application of an r.f. magnetic field H₁, and another (or the same) coil to pick up the induced magnetic flux produced by the precessing spins. The electronic components described here allow the generation of suitable r.f. pulses and the detection of the induced flux.
 

Setup:

Magnet power supply - Harvey-Wells Magnet with Walker Scientific Power Supply

• Turn on water to magnet ~50% (Don't forget - there is no interlock protection). Monitor that exiting water becomes neither very warm nor so cold as to induce condensation.
• Turn "power" on (switch on left.)
• [IMPORTANT] Set "current adjust" "coarse" to 0 and "fine" at midrange.
• [IMPORTANT] Wait 60 sec.  Then push "dc on" button.
• Turn "current adjust" "coarse" to LED readout of 80.2 (this number is "% of max" and gives about 7kG, as required for proton resonance at 30 MHz.)
• Search for resonance using "current adjust, coarse" very slowly in the range 80.0 - 80.5 with r.f. pulses set as described below and observing the output signal on the scope.
• Use single pulse "A", approximately 10 µs long; Power Amplifier gain ~1/5 of knob range (horizontal, left)
• Scope sweep 10 or 20 µs/div. Watch just to the right of the pulse.
• Probe in the center of the magnet.
• Mineral oil or dirty water sample in the probe.

Shut down:

1. [IMPORTANT] Turn "course current" adjust to 0.
2. When current = 0, push "dc off" button. [VERY IMPORTANT to do step 2 before 3!]
3. Turn off power switch.
4. Turn off water.

Spectrometer: Digital Timing Panels

Modules

Procedure:

Monitor the "detected output" from the receiver on the oscilloscope, using about 1 ms/div and enough gain to see just a little noise. Adjust the magnetic current slightly to find the resonance. When you find something, adjust the current a little farther to make sure it is not a sideband (due to gating r.f. into pulses). Fine adjust the magnet current to maximize the period of the beat between the free precision and the 30 MHz reference. After the magnet drift has decreased to a reasonable rate, engage the flux stabilization circuit (see below).

Set up a p-pulse: (Channel A -> 1)

Start with the analog pulse width vernier fully CCW (1 ms). Turn CW until the initial amplitude of the free induction decay (FID) signal is maximum and continue until it decreases to zero. You may have to go to the 10-100 ms range, but start on 1-10 ms to be sure you get the first zero. Connect the scope to an unused "pulse output" jack on module "B" and measure the pulse width.

Set up a p/2-pulse: (Channel b ->2)

(1) Adjust for the (first) maximum initial FID amplitude; or better: (2) set width to half that of a p-pulse. For more precise setting, use the multiple pulse procedure described later.

Set phase adjustments:

Since only relative phases matter, the three sets of phase controls (Channel 1, Channel 2, and reference) are redundant. Therefore leave the Channel 1 settings fixed (unless it is convenient to introduce a 90^o or 180^o shift there; but leave the continuous adjustments fixed in any case). With an approximately p/2 pulse from Channel A/Channel 1, adjust the reference phase to maximize the initial amplitude of the FID.  [NOTE: Due to a bad relay, the channel 1 switch "0/90 deg" should be left on 0 deg.  Change the phase of the receiver instead.]
 

Standard pulse sequences

1. Slichter, 2nd edition, pp. 1-42, especially classical sections, especially pp. 1-10 and 38-42.
2. Fukushima and Roeder, pp. 1-35, especially pp. 25-35.
3. Gerstein and Dybowski, (Reference for pulse sequences).

(1) Single p/2-pulse (or any pulse length not equal to np):

This will tilt the magnetization rom the z-direction to the y-direction (for a p/2-pulse with H₁ in the x-direction) or in general will tilt some component into the x - y plane, where it will precess, and this precessing magnetization can be picked up by the receiver. Its magnitude will decay at a rate 1/T_m = 1/T₂ + 1/T₂*. For a liquid sample normally T₂ >> T₂*, so T_m @ T₂*.

The initial p-pulse tilts the magnetization from the +z to the -z direction (from an energy level point of view, it inverts the population of the nuclear Zeeman levels). The magnetization then relaxes towards equilibrium (+z) with time constant T₁. So far we see nothing because only magnetization precessing in the x - y plane can be detected. The p/2 pulse after delay tilts whatever z-magnetization M_z (t) exists at that time, whether negative or positive, into the y-direction. This gives a signal whose initial magnitude is proportional to M_z (t). The experiment is repeated for different values of t and compared to the predicted relation: M_z(t) = M₀[1 - 2exp(-t/T₁)]

to obtain T₁. Note that M_z (t) = 0 at = T₁ln2.

The p/2 pulse tilts the magnetization to the y axis in the rotating frame. It then fans out in the x - y plane during the period due to inhomogeneity of H₀. The p rotates each spin 180^o around the x axis. Each spin then continues to precess at the same rate as before. Consequently, regardless of its precession rate, it reaches the - y axis after an addition time t. This gives the "echo" or "refocusing."  The half-width of the echo pulse is characterized by T₂*. The decay of the echo amplitude as a function of delay 2t is determined by T₂.

(4) Flip-flop sequence, [(p/2)_x , t]ⁿ:

This is a sequence of identical p/2 pulses at interval t. If the pulses are in fact exactly p/2, then after any even number of pulses the magnetization should be in the ±z direction and the output zero. This is illustrated in Gerstein and Dybowski, p. 176, Figs. 5-6 and 5-7. Figure 5-8 shows what happens if the sample is too large: H₁ is then not uniform over the whole sample, and the pulse strength cannot be p/2 for all parts. This sequence can be used to trim the pulse length to p/2.

In this sequence, alternate p/2 pulses are phase-shifted by 180^o, i.e. the sign of H₁ is reversed for alternate pulses. Thus the magnetization is tilted from z to y and then back to z. If the x pulses (generated by Channel A, say, with f_A = 0^o) and the -x pulses (generated by Channel B with f_B = 180^o) are both exactly p/2 in strength but are not exactly 180^o out of phase, then there will be a cumulative error in returning the magnetization to the z direction, which will modulate the signal envelope. This can be used to set the phase of Channel B relative to Channel A

This is a "spin-echo" technique, used to measure T₂. The effect of inhomogeneity of H₀, which causes the FID to decay with time constant T₂* << t < T₂. In this sequence it is critical that the p pulses be exactly p, otherwise the magnetization will develop a cumulative tilt out of the x - y plane, and the apparent decay time will be less than T₂.

This differs from the Carr-Purcell sequence only in that the p pulses are phase shifted 90^o relative to the p/2 pulse. This means that the spins fanning out from the y- axis are rotated 180^o about the y (instead of x) axis to set up the echoes. See F & R, p. 32 and G & D, p. 193 ff, especially Fig. 5-15. The advantage of this is that a p pulse width error does not have a cumulative effect, and in fact cancels out for even-numbered echoes (see G & D, Fig. 5-16).

(The width of the p-pulse could be adjusted to the correct value by observing in the CPMG sequence when the odd echoes fall on the same exponential decay envelope as the even echoes, or in the CP sequence by maximizing the decay time.)

This is a four-pulse cycle which suppresses the effect of dipole-dipole interactions. We cannot do it at U.Va. because it requires two dual pulse generators.

Experiments:

1. Find the resonance in "dirty"* water and observe FID. (* dilute solution of NiCl, barely yellow, to reduce T₁ to a reasonable value.)  Or use mineral oil.
2. Setup p and p/2 pulses and study various pulse sequences qualitatively, getting rough delay times.
3. Measure T₂*, T₂, and T₁ by one or more methods and try to understand any differences in values for different methods.
4. See effect of different impurity concentrations in the water; look at protons in mineral oil or possibly methanol.
5. Possibly look at ¹⁹F in a compound such as CCl₂F₂ (freon).

Probe

• L₁: 18 turns of 0.7 mm diameter wire on 9.0 mm OD glass tube, approximately 15mm long.
• L₂: 4 turns on Bakelite (non-magnetic) toroid.

Front Panel Coax Connections