When the magnetic spin of the measured nucleus interacts with the magnetic field, it is accepted practice to think of the magnetic spin as a moment with a certain direction. An NMR experiments measures a large number of moments. If they were in random orientations it would be impossible to observe them. However, it is apparent that at equilibrium there is some directionality of the moments in the direction of the magnetic field. This directionality is called the bulk magnetization of the sample. It is possible to represent the magnetization by a vector in the direction of the magnetic field. The magnetization vector can be shown against coordinates x,y,z with it on the z-axis of a fixed or laboratory frame.

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Larmor precession

Say that we somehow managed to move the magnetization vector by an angle β from the z-axis. (How this is done will be explained later.) In this case the magnetic vector will move around the z-axis describing a cone with the z-axis at its center. The vector's motion has a specific frequency that is representative of it and is called Larmor precession.

If the magnetic field is B₀ then the Larmor precession frequency will be according to equation 1.

The frequency, ν₀ is the same frequency that will be observed in the NMR spectrum. In the magnetic there is a detector (electric coil) that measures the Larmor frequency. The measurement is carried out with a detector in the x,y plane and when the magnetic vector crosses it during precession it induces a measurable electric current in the coil. The process is similar to the way electric current is generated by a rotating magnet in a coil.

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Pulses

We will now deal with how to move the magnetic vector away from equilibrium. The magnetic field is along the z-axis as is the magnetization vector. The vector is moved by transmitting a signal (a radiofrequency signal – rf) from a coil in the detector in the x,y plane. The problem that we have to deal with is that the induced magnetic field that we have to deal with is much stronger than any electrical signal that can be transmitted through the probe coil of the spectrometer. Instead of using a fixed frame of reference, we use a coordinate framework where the x,y plane rotates about the z-axis at the aobservation frequency close to the Larmor precession rate of the material under study. Then the induced field in on the zz-axis becomes manageable and the transmitted rf signal becomes a fixed electric field vector (E) in the x,y plane relative to the rotating frame. The correct choice of the rf signal frequency allows the movement of the magnetization vector from the z-axis to the x,y plane.

The magnetization vector is moved by an angle proportional to the length and intensity of the pulse. If the vector is moved by 90° then the process is called a 90° pulse (fig. 1). It is possible to arrange a 180° pulse so that the magnetization vector goes from +z to –z.

Fig. 1. Effect of a 90°x pulse

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Hard pulse

Most NMR spectroscopic measurements are concerned with measuring more than one signal and each of them has a different Larmor frequency. A sufficiently strong rf pulse is needed to overcome the induced field to move all the signals at different Larmor frequencies away from equilibrium. This is called a hard pulse.

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Soft pulse

When the pulse is weaker it is possible to excite a single signal within the spectrum. This is done by choosing a radio frequency identical to the selected signal reducing the influence of the pulse on other signals. Such pulses are known as selective pulses or soft pulses.

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Decoupling

When the signal is split by heteronculear coupling, for example proton couplings in a carbon spectrum, it is possible to decouple them by continuous irradiation of the coupling nucleus.

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Magnetic gradient pulse

It is possible to apply a magnetic gradient to the sample. A gradient affects the signal in the following manner. At the start of the experiment it disperses the signal, making it disappear. Then the application of a gradient in the opposite direction allows the signal to be seen again. In combination with rf pulses that act as quantum filters it is possible to observe correlations between nuclei. Likewise, it is possible to measure physical movement in the sample such as diffusion.

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Acquisition

At the end of the pulse sequence (fig. 2) the required signal for measurement is obtained.

Fig. 2. Symbols used in pulse sequences

The process is called free induction decay (fid). Fig. 3 shows the regular pulse sequence for 1D acquisition.

Fig. 3. Basic 1D-NMR pulse sequence

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Multi-channel pulse sequences

Fig. 4 shows an example of a three-channel pulse program. In two of them, pulses are transmitted in the rf region and in the third, magnetic gradients are applied. Note that each of the rf channels are at different frequencies, matched to different nuclei. In the diagram below, the proton channel is the observed channel and is also the acquisition channel while the second channel is that of the nucleus couple to proton. Transmission on all the channels is in parallel. The diagram shows a pulse sequence for a 2D experiment, HMBC that measures proton-carbon correlation.

Under each rf pulse its pulse angle and phase are written. Under the rf channels there is a time-scale (Δ and t₁). The evolution time, t₁, is the time that is incremented between each row of a 2D acquisition and makes up the extra dimension. In a 2D the symbol for the acquisition time axis is t₂. The grey lines on the diagram are not usually drawn but have been added here (and only here) for clarity. The relative gradient intensities are shown under the gradient channel. The pulse widths are not to scale.

Fig. 4. Pulse sequence for HMBC

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