Dephasing of Hahn echo in rocks by diffusion in susceptibility-induced field inhomogeneities

The decay of the Hahn spin echo of water in the pore space of many porous media is dominated by the dephasing of spins in internal-field inhomogeneities, produced by susceptibility contrasts, rather than surface or bulk relaxation. This is particularly the case for measurements at moderate and high fields in samples such as fluid-saturated sedimentary rocks and some biological materials. Here, we study the behavior of the Hahn-echo decay in rocks with grains much larger and smaller than the average dephasing length, which is typically of the order of a few microns. It is shown that the decay in these two cases is qualitatively different. For coarse-grained rocks, the decay can be modeled to first order by a distribution of local, effective field gradients. This is in contrast to the case of fine-grained rocks, where motional narrowing of the field inhomogeneities occurs. These interpretations are supported by measurements of the temperature dependence of the Hahn echo decay and the diffusion time dependence of the diffusion coefficient.