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NMR Spectroscopy: Spin Echo Experiment

How does one experimentally measure T2?

T2 is the time constant for relaxation of the bulk magnetization in the xy plane, and NMR spectroscopy employs detection coils along both the x and y axes. Consequently it should be straightforward to determine T2. Indeed, in a previous experiment it was noted that the peak width depends upon T2.

Unfortunately there is a complication. The Larmor frequency (ν) is strongly dependent upon the strength of the static magnetic field B, and therein lies the problem. B is not perfectly uniform across a sample and therefore ν varies from place to place within a sample. This magnetic field inhomogeneity provides an additional source of broadening for NMR peaks. One uses shims to obtain as uniform a magnetic field as possible, but it is impossible to eliminate all variations in B.

The actual peak width w, measured as the full-width at half-maximum, is related to T2 by w = (π T2*)-1 = w* + (π T2)-1

The effective relaxation time T2* accounts for the actual peak width w. The natural line width is (π T2)-1 and describes the width in the absence of inhomogeneity in B. The additional broadening w* arises from the inhomogeneities in B.

Exercise

There are several variations in the pulse sequence for the Spin Echo experiment. One form is       90ox - τ - 180oy - τ - FID

This simulation lets you step through each component of the Spin Echo sequence and observe the effect on the bulk magnetization. Carefully examine the response of the system to each pulse. Vary τ between 0 and 0.3 sec and observe its effect on the spectrum. Three spins, in different positions of the sample, are shown in the animation. All three spins have the same T2, but owing to their different positions in the sample they all have different T2*. (Only the data after the vertical blue line is part of the FID and is put through the FFT to obtain the spectrum.)

Answer the following questions.

The steps of the simulation have been slowed, to varying degrees, to make visualization easier. The simulation time is plotted on the graph and shows the actual time scale for the experiment.

τ (sec) =
     
     

     



 


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