# 2D NMR Experiments

### The experiment

When : There is no interaction between the field *B _{1}* and

*µ*(they are not in accord) and the precession is kept around the axis Oz.

When : *B _{1}* and

*µ*are in accordance. Thus the couple applied by

*B*modifies the angle of

_{1}*µ*with O

_{z}, and then causes transitions between the magnetic sublevels.

There is resonance. The value of the z magnetization decreases and it appears, in the y direction, the transverse magnetization My.

### The Rotating Coordinate System

Impulsion angle and position of the M vector (Fig. 5) is given by the following relation , with *B _{1}* which represents the amplitude or the power of the impulsion and t

_{p}the width or duration of the impulsion. It is possible to make these two values vary together in such a way that particularly interesting rotation angles appear. One of these is the angle = 90°.

In this case all the magnetization is orientated in the plane xy and the signal reaches its maximum of intensity. (7)

**FIG. 5**: Location of the M vector after an impulsion time allowing an angle of 90°

An other angle allows the inversion of the M vector by the application of an impulsion or = 180°. In this experiment, the vector M is orientated in –z. Practically, one uses the angle = 45° in order to get a good compromise between measurement time/quality of the response.

### The Free Induction Decay Signal

The signal given by the receiver coil is known under the name of interferogram: Free Induction Decay (FID). In opposition to the continue wavelength signal, the time dependent signal we monitor in this case is an emission signal, because the radiofrequency field* B _{1}* is turned off upon the signal acquisition. The experiment gives us practically a variable field which is linear at high frequency following the y axis. In fact it is an oscillator or an emitter with the Larmor frequency of the nuclei under study (7) .

**Fig. 6**: FID made of several superimposed damped sine wave.

The time signal S(t) generated in the receiver coil by the xy component of M weakens under the relaxation process.

**The notion of phase cycle**

The phase cycles or phase programs allow to:

- choose the relevant signals and to neglect these ones which do not contain information and which, eventually, are susceptible to hide some other useful signals.
- discriminate the sign of the frequencies in the fl dimension.
- compensate the inhomogeneity from one or several impulsion in the sequence,
- to achieve an optimal quadratic detection in the f2 axis. (5)

Any impulsion in a sequence has its own phase cycle which may be more or less complex. The ideal number of scans must be a multiple of the phase number of the longer cycle. For a better understanding of this method, a standard nomenclature has been defined (Fig. 7).

**Fig. 7: **Standard nomenclature for the phase cycles.

Example 1: The Cyclops Cycle |
---|

= x,y,-x,-y. 0,1,2,3. This cycle involves the accumulation of a multiple of 4 numbers between each free precession. The first impulsion There are other variations of this cycle like the following: = x,-x, y,-y or 0,2,1,3. This last one implies a multiple of 8 transient cycles in the accumulation. |

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