Diffusion measurements using the second echo

Abstract

We present a tutorial discussion of diffusion measurements by NMR, aimed around a specific problem. To measure diffusion in the presence of convective flow, one may use the second echo using the well-known cancellation of phase effects from flow for the second echo. In testing this with a simple organic liquid and a static (dc) gradient at room temperature, where no convection can occur, we noticed the data from the second echo implied a substantially larger rate of diffusion than for the first echo. The error is due to the second echo being a superposition of a spin (Hahn) echo (an echo of the first echo) and a stimulated echo. We show that the stimulated echo is more attenuated by diffusion (it has a larger b value), explaining our result. A simple phase cycle is presented that suppresses the stimulated echo and leads to the correct diffusion value from the second echo. That is, the diffusion values taken from the first and second echoes are now identical.