# T1 Measurement by Inversion Recovery

### From NMR Wiki

## Inversion Recovery

Here the spins are flipped to the 180° position, and sampled at different times until the spins are back in equilibrium. This will give a characteristic set of spectra, which can be used to accurately measure T_{1}-Times for the sample. The delay τ is varied and the intensities in the spectra are plotted agains τ.

## T_{1} fitting

Using a nonlinear regression algorithm, the data is fitted to the following model:

Which can be simplified (when using a normalised plot which has very little *noise*) to:

For an inversion recovery experiment 1 < *p*_{1} < 2 is normally true. In the optimal case, *p*_{1} would be 2, but since in reality one does not get a negative signal which is as strong as the maximum positive signal, the parameter *p*_{1} compensates for that. The parameter *p*_{2} is equal to T_{1}.

When trying to fit multiple T_{1}-Times in a samle, one simply fits a sum of several of the previous model. For two T_{1}-Times, one would use:

Here *p*_{1} is used as bevore, but *p*_{2} now serves as a parameter determining how much each of the two components contribute to the relaxation behaviour. The parameters *p*_{3} and *p*_{4} are the two contributing T_{1}-Times.