SETTING UP YOUR EXPERIMENT
   
Acquire data (continued).
  Remember that the magnetization vector is actually the sum of many individual magnetic moments, some of which are precessing slightly faster than others. A simplified example, illustrating the behavior of only one faster (pink) and one slower (red) magnetic moment is shown below. Immediately after the pulse, the two are still coincident, and their magnitudes add together to give an observeable signal shown by the blue arrow (the pink and burgundy vectors are slightly offsest for clarity):
 
 

As time elapses, the pink and burgundy arrows dephase, or spread out, in the x-y plane, with the faster moments getting significantly ahead of the slower ones. Position your mouse over the image above to see the the system at a later time, still in the vicinity of the +x axis. The length of the blue arrow is, again, the sum of the projections of the two vectors onto the +x axis. The sum, in this case, is clearly less than in the original, as a result of this dephasing process, called spin-spin relaxation. In other words, as the spin system evolves, the magnitude of the maximum signal observed decreases for each cycle. Eventually, it becomes zero, and no signal can be detected. Click on the image below to see an animated representation of this process; move your mouse over it to replay.
 
  Note that, in the one-cycle example above, even though no signal is observed, the magnetization vectors continue to lie in the x-y plane; they have not yet returned to equilibrium. Spin-spin relaxation is, therefore, distinct from spin-lattice relaxation. Even though the signal is no longer observeable, the vectors should still be allowed to return to the +z axis before another pulse is imposed.
 
Spin-spin relaxation is characterized by a time constant T2, which describes how quickly the dephasing happens. If the frequency difference is only very small, then dephasing occurs slowly (T2 is long), and the signal takes a relatively long time to lose phase coherence, as illustrated below:
 
If, on the other hand, they dephase quickly (i.e., if there is a large difference between the precessional frequencies, indicating that T2 is short), then the signal decays quickly. Roll your mouse over the image above to see an example of a short-T2 signal. The acquisition time of the experiment only needs to be set as long as it takes for the signal to dissipate. Collecting data longer is a waste of time, because there is no more information to be gained during a simple, one-pulse experiment. The magnetization vectors are still precessing, and have not yet returned to equilibrium, but they are so "scrambled" in phase that no more useful data can be extracted. At the end of the acquisition time, the receiver is turned off, and the system is allowed to relax (T1) during the pulse delay, until equilbrium is regained.
 

So, what do all these vectors mean in terms of the final spectrum? Each spectral peak corresponds to a set of magnetic moments; this "bundle" of spins precesses at an average rate somewhat offset from the Larmor frequency; this is why they appear at distinct frequencies, or chemical shifts. Within a sample, the bundles are all affected nearly alike by the rf pulse, but each set will return to equilibrium at a particular rate. Each peak in the NMR spectrum, therefore, exhibits a disinct T1.

Within each spin bundle, the precessional frequencies also vary. If these variations are small, it takes a long time for the signal to decay, and such a long-T2 system will exhibit narrow peaks (i.e., the frequency, or chemical shift, spread within that peak is small). If, on the other hand, T2 is short, then the peaks will be broad because of the wide distribution of frequencies within the bundle.
What causes these differences in T1 and T2? While a complete answer is beyond the scope of this tutorial, some generalizations can be made. For small organic molecules in solution, T1 is generally related to the rate of molecular motion. For example, the carbons in methyl groups, which can undergo relatively rapid propellor-like spinning motions, tend to have longer T1's than the less mobile carbons in the molecule. The same holds true for T2, but this relaxation time is also affected by inhomogeneities in the magnetic field, which broaden the frequency distribution for a particular type of nucleus, resulting in wider peaks. This is why shimming, which minimizes the inhomogeneities, leads to narrower peaks.