# T1 spin-lattice relaxation times, deviation from exponential relationship

For longitudinal relaxation, one would think that the magnetic moment obeys this simple relationship

$$M_z = M_0\left[1 - 2\exp\left(\frac{-t}{T_1}\right)\right].$$

However there is always a point of inflection when magnetisation is zero. Does anyone knows why?

edit: I deleted the image and added some from my own experiment for mineral oil.

In this scenario, the sample is placed under a large longitudinal z-magnetic field. To measure T1, a 180 degree pulse is applied to flip Mz, then a 90 degree pulse after time t. Mo is the equilibrium longitudinal magnetic moment.

I don't think this is due to the mixture of compounds, because it is observed in all samples I tried e.g glycerine, Fe(NO3)3.

• Please cite the source of the image and/or data and define the variables in the equation to avoid ambiguity. – andselisk Feb 28 '20 at 4:02
• Possibly the data refers to a mixture of compounds whose chemical shift are overlapping. Look for data on a known pure compound for comparison. – porphyrin Feb 28 '20 at 9:16
• Can you clarify the question, please? I don't see any inflection point there -- your graph is quite clearly concave -- and I don't think I've ever seen an inflection point in the inversion-recovery experiments I've done before (example). Btw, your equation is missing a minus sign inside the exponential. – orthocresol Feb 29 '20 at 14:46
• The inflection point is quite slight, if you look at the ln(Mz) against time plot, there is a small difference between the gradient below ~0.02s and after. It occurs when the sign of the Mz flips. Maybe because your data started at positive Mz ? @orthocresol (also added a -ve sign) – Fusedpie Feb 29 '20 at 15:28
• No, it doesn't start at positive Mz. I don't have an explanation for what you're seeing, unfortunately; I just can't say I've seen it before myself. – orthocresol Feb 29 '20 at 15:30