Diffusion measurements with the pulsed gradient nonlinear spin echo method

Spin echo signal attenuation by diffusion is examined for coherence evoluti on in the course of ordinary pulsed gradient spin echoes and for nonlinear evolution in the presence of a spatially modulated demagnetizing field. It is shown, that, for given field gradient pulse widths (or equivalently for a given gradient strength), echo attenuation by diffusion is much more effi cient for nonlinear echoes than for Hahn echoes. Remarkably, in the case of nonlinear echoes the refocusing process is spoiled by diffusion not only d uring the gradient intervals but also thereafter. The effect of displacemen ts occurring in the gradient intervals is enhanced according to the order o f the nonlinear echo the pulse sequence is adjusted for. A second attenuati on mechanism takes place after the gradient pulses due to displacements in the presence of the spatially modulated demagnetizing field. This effect ev en occurs when the gradient intervals are too short to contribute. A comple te formalism is presented describing all features of the test experiments. It is shown that nuclear magnetic resonance diffusometry based on nonlinear echo signals permits one to measure small diffusion coefficients with mode rate field gradients. Nonlinear echo experiments demonstrate that the coher ence pathway dominating by far is of a purely single-quantum nature. (C) 20 00 American Institute of Physics. [S0021-9606(00)00312-3].