High resolution NMR scattering : the first measurement of spin diffusion rates in a homogeneous solid

Abstract

The first direct measurement of the rate of spin diffusion through a homogeneous sample was performed as an incoherent NMR scattering experiment. The experiment consists of a combination of pulsed gradient spin echo methods with multiple pulse/ pulsed gradient spatial encoding met.hods. The NMR scattering experiment involves the creation of an initial spatial magnetization grating, a period of spin evolution including the displacement of spin magnetization, followed by the detection of the residual magnetization grating. The essence of NMR scattering measurements is to record the extent of microscopic motion of spin magnetization through a sample by directly observing amplitude and phase changes of a well defined spin magnetization grating. The spin diffusion measurement records the rate of destruction of a magneti­zation grating by the random offset of spin magnetization associated with the flip-flop term of the homonuclear dipole-dipole interaction. Since the microscopic motion driven by di- polar coupling is very slow, only fine magnetization gratings are sensitive to the small spatial offsets. Strong pulsed mag­netic field gradient techniques were developed for these studies which generate switched gradients with strengths up to 103T /m (a factor of 100 stronger than those commer­cially available, and a factor of 25 stronger than the highest previously reported). These gradients are able to create a spatial magnetization grating with a pitch of from l[mu]m to 1nm for solid state NMR scattering experiments. Gradients on the order of 200T /m were applied in the spin diffusion measurement experiment. For single crystal CaF2, the measured parallel components of the spin diffusion rates are 7.1 x 10-12cm2 /s along the [0,0,1) direction and 5.3 x 10-12cm2/s along the [1,1,1) direction, in good agreement with theoretical predictions. Additional work has been done on flow measurement. A novel approach is intro­duced to measuring flow velocities using a probe with a spatially varying RF field, and without using other magnetic field gradients. The velocities of the spins are measured as a modulation of the NMR signal from the translatlation of a spatial mag­netization grating through a detection coil with a spatially periodic field profile. Since the same coil can be employed to create the initial magnetization grating, the overall measurement is as simple as recording the signal modulation frequency following a single excitation pulse. The design principles are discussed for a probe that has a spatially periodic field constructed from a series of lumped element x-circuits. Spa­tial modulation of the amplitude or the phase of the RF field can easily be achieved, and either of these may be used t.o characterize a flow field. Examples are shown of measurements of pipe flow using a probe with an amplitude modulated RF field.