# 2D NMR Experiments

- Page ID
- 1804

## The experiment

When \(\omega_1 \neq \omega_o\): 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 \(\omega_1 \approx \omega_o\): \(B_1\) and \(\mu\) are in accordance. Thus the couple applied by \(B_1\) modifies the angle \(\alpha\) of *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 \(M_y\).

## The Rotating Coordinate System

Impulsion angle and position of the \(\vec{M}\) vector (Figure \(\PageIndex{1}\)) 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 \(\alpha = 90^o\).

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

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 Deca**y (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) .

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).

= 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 *B _{1} *occurs around the x and the emission will occur in the y axis, the third impulsion along the - x and the reception in -y, etc.

There are other variations of this cycle like the following:

\[\Phi = x,-x, y,-y\]

or

\[\Phi = 0,2,1,3.\]

or still:

\[\Phi = x,x,-x,-x,y,y,-y,-y\]

or

\[\Phi 0,0,2,2,1,1,3,3.\]

This last one implies a multiple of eight transient cycles in the accumulation.

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