The magnetic field gradient nuclear magnetic resonance (NMR) stimulate
d echo experiment measures the incoherent (or self) part of the interm
ediate scattering function S(Q, t) similar to [exp[ -iQr(0)] exp [iQr(
t)]] with a 'generalized' scattering vector Q = gamma.g.tau (gamma is
the gyromagnetic ratio, g is the magnetic field gradient, tau is the e
volution time). With ultrahigh static field gradients up to approximat
e to 180 T/m, a prototype of which has recently been installed in Main
z, Q-values up to > 10(-2) Angstrom(-1) become accessible. The first p
art of the paper focusses on details of this technical development and
points out the close analogy with incoherent neutron scattering. In t
he second part, the enormous new possibilities of this kind of gradien
t NMR are demonstrated through a collection of most recent application
s: the measurement of small self-diffusion coefficients down to about
10(-15) m(2) s(-1) in supercooled liquids and in molecular crystals, l
ong chain polymer dynamics, restricted diffusion in systems of confine
d mesoscopic geometries and anomalous diffusion on fractal structures.