DIFFUSION-LIKE MOTION OF THE MODULATION WAVE IN INCOMMENSURATE SOLIDSSTUDIED BY NMR AND NQR IN A SINUSOIDAL-ELECTRIC-FIELD GRADIENT

Slow random-walk-type motion of the modulation wave in structurally in commensurate systems represents a collective atomic self-diffusion in solids. The diffusion constant D for the thermally induced modulation wave motion has been determined using a technique based on NMR and nuc lear quadrupole resonance (NQR) in an inhomogeneous electric-field gra dient which varies sinusoidally with space. This technique is generall y applicable to solids with a modulated superstructure. It is capable of measuring extremely low D values such as 10(-15) cm(2)/s, so that s patial motion is observed on a nanometric scale. The diffusive motion is discussed analytically on a scale small compared to the wavelength of the modulation wave, whereas large-scale diffusion is treated numer ically. For small-scale motion, spin-echo decay curves in a NMR/NQR ex periment show an exponential decay with the exponent proportional to t he cube of time and the decay strongly varies over the incommensurate spectrum. For large-scale motion, the spin-echo decay is less strong a nd the variation over the spectrum vanishes. The diffusion constant ha s been determined experimentally in Rb2ZnCl4 by Cl-35 NQR and in K2SeO 4 by K-39 NMR. In both cases, D behaves critically in the vicinity of the para-to-incommensurate transition and rapidly decreases on going d eeper into the incommensurate phase. This can be explained by the mech anism of thermally induced depinning of the modulation wave at the imp urity pinning centers.