Nonexponential decay of velocity correlations in surface diffusion: The role of interactions and ordering

We study the diffusive dynamics of adparticles in two model systems with st rong interactions by considering the decay of the single-particle velocity correlation function phi (t). In accordance with previous studies, we find phi (t) to decay nonexponentially and follow a power-law phi (t)similar tot (-x) at intermediate times t, while at long times there is a crossover to a n exponential decay. We characterize the behavior of the decay exponent x i n detail in various ordered phases and in the vicinity of phase boundaries. We find that within the disordered phase, the behavior of x can be rationa lized in terms of interaction effects. Namely, x is typically larger than t wo in cases where repulsive adparticle-adparticle interactions dominate, wh ile attractive interactions lead to x <2. In ordered phases, our results su ggest that the behavior of x is mainly governed by ordering effects that de termine the local structure in which adatoms diffuse. Then the decay is cha racterized by 1 <x <2 under conditions where diffusion is truly two-dimensi onal, while in phases where adatoms diffuse in a one-dimensional fashion al ong ideal rows of vacancies, we find a regime characterized by x <1. Also, changes in the qualitative behavior of x are closely related to phase bound aries and local ordering effects. Our studies suggest that phi (t) can be u sed to obtain information about the ordering of the system and about the na ture of predominant interactions between adparticles. Our predictions can b e tested experimentally by techniques such as scanning tunneling microscopy , in which phi (t) can be measured in terms of discrete adparticle displace ments as shown in this work. Finally, our studies suggest that the decay of velocity correlations in collective diffusion follows, qualitatively, the same behavior as the decay of single-particle velocity correlations in trac er diffusion. (C) 2000 American Institute of Physics. [S0021- 9606(00)70246 -7].