# The Basics of NMR

## PULSE SEQUENCES

### Introduction

You have seen in Chapter 5 how a time domain signal can be converted into a frequency domain signal. In this chapter you will learn a few of the ways that a time domain signal can be created. Three methods are presented here, but there are an infinite number of possibilities. These methods are called pulse sequences. A pulse sequence is a set of RF pulses applied to a sample to produce a specific form of NMR signal.

### The 90-FID Sequence

In the 90-FID pulse sequence, net magnetization is rotated down into the X'Y' plane with a 90o pulse. The net magnetization vector begins to precess about the +Z axis. The magnitude of the vector also decays with time. A timing diagram is a multiple axis plot of some aspect of a pulse sequence versus time. A timing diagram for a 90-FID pulse sequence has a plot of RF energy versus time and another for signal versus time.   When this sequence is repeated, for example when signal-to-noise improvement is needed, the amplitude of the signal after being Fourier transformed (S) will depend on T1 and the time between repetitions, called the repetition time (TR), of the sequence. In the signal equation below, k is a proportionality constant and is the density of spins in the sample.

S = k ( 1 - e-TR/T1 )

### The Spin-Echo Sequence

Another commonly used pulse sequence is the spin-echo pulse sequence.  Here a 90o pulse is first applied to the spin system. The 90o degree pulse rotates the magnetization down into the X'Y' plane. The transverse magnetization begins to dephase. At some point in time after the 90o pulse, a 180o pulse is applied. This pulse rotates the magnetization by 180o about the X' axis. The 180o pulse causes the magnetization to at least partially rephase and to produce a signal called an echo. A timing diagram shows the relative positions of the two radio frequency pulses and the signal. The signal equation for a repeated spin echo sequence as a function of the repetition time, TR, and the echo time (TE) defined as the time between the 90o pulse and the maximum amplitude in the echo is

S = k ( 1 - e-TR/T1 ) e-TE/T2

### The Inversion Recovery Sequence

An inversion recovery pulse sequence can also be used to record an NMR spectrum. In this sequence, a 180o pulse is first applied. This rotates the net magnetization down to the -Z axis. The magnetization undergoes spin-lattice relaxation and returns toward its equilibrium position along the +Z axis. Before it reaches equilibrium, a 90o pulse is applied which rotates the longitudinal magnetization into the XY plane. In this example, the 90o pulse is applied shortly after the 180o pulse. Once magnetization is present in the XY plane it rotates about the Z axis and dephases giving a FID.

Once again, the timing diagram shows the relative positions of the two radio frequency pulses and the signal. The signal as a function of TI when the sequence is not repeated is

S = k ( 1 - 2e-TI/T1 ) It should be noted at this time that the zero crossing of this function occurs for TI = T1 ln2.