The magnitude of the magnetic moment in the z axis builds up according to the equation

M₀ - M = k [exp(-t/T₁)]

The spin-lattice (T₁) relaxation time of the various ¹ H nuclei of a molecule may be determined by using the inversion recovery pulse sequence. The inversion recovery experiment yields a signal of intensity I₀[1 - 2exp(-t/T₁)].
The experiment is repeated many times and the resulting intensities used to find the value of T₁. Notice that if the recovery delay time is very short, the detected signal has full, negative intensity. On the other hand, if the delay is very long, full T ₁ relaxation occurs, and the detected signal has full positive intensity. T₁ can be determined by repeating the experiment with several different recovery delay values, processing the results identically, and plotting peak intensity with respect to recovery delay time. The resulting curve is an exponential with rate 1/T ₁ . (Notice that for some intermediate value of the recovery delay, the peak intensity is zero and
T₁ = t_null/ ln 2; however, the accuracy of this measure of T₁ is usually low.)

The inversion recovery experiment uses the pulse program t1ir and requires a variable delay list to provide all the values of the recovery time vd. To create the variable delay list, type edlist and select vd from this menu. This calls up a menu of existing vdlist filenames and gives the user the option of creating a new file (‘ Type new name'). Simply type the name t1delay and enter the delays desired, e.g.: 10, 5, 3, 2, 1, 0.5, 0.25, 0.1, 0.01 and 0.001 sec. Set the loop counter l4 to number of entries in vdlist .
A 1D spectrum is obtained for each value of vd , and the results are stored in a 2D data set. The 2D data set is used by the T1 calculation routine, which allows the user to determine T₁ for any number of peaks of the 1D spectrum. Although inversion recovery is not technically a 2D experiment, it does generate an array of 1D spectra, which are most easily handled as one 2D file. Thus, the PARMODE must be changed (in eda ) into a 2D data set ( PARMODE = 2D). It should be indicated that the F1 acquisition parameter td should be set to the number of delays in the vdlist (= l4), and the relaxation delay, d1, should be long (~10sec). The spectra can be processed by the automation program proc_t1 (see Bruker’s manual), or manually by entering xf2 .