Analysis of direct correlation measurements from adsorbed atom fluctuations

Despite its importance in theoretical studies of surface diffusion there ha s been limited experimental progress in developing methods to measure the d ynamic structure factor S(q,t). In this work we study gases adsorbed on sin gle-crystal surfaces and show that their equilibrium dynamics is measurable in a diffraction experiment through density fluctuations described by the dynamic correlation function [S(q,t)S(q,0)]. Using a lattice-gas model with nearest-neighbor repulsive interaction, we demonstrate how to separate out the microscopic dynamics caused by diffusion and adsorption-desorption fro m the form of (S(q,t)S(q,0)). Our analytical results show that (S(q,t)S(q,0 )) decays as an exponential with a time constant tau(cb) Significant deviat ions from the hydrodynamic dependence of 1/tau(q)= D(c)q(2) are found with and without desorption. These deviations have important consequences in ext racting diffusion constants from experiments.