Fundamental thermodynamic issues are surveyed to establish limits of t
he degree of spatial ordering during phase separation processes on sem
iconductor surfaces. The study is based on a detailed experimental inv
estigation of diffusion-controlled coarsening (Ostwald ripening) of Sn
on Si(111). This late stage process is of particular interest due to
the self-similar evolution of the cluster morphology, allowing in prin
ciple to extrapolate observed properties to a wide range of length sca
les. Two basic concepts are discussed to understand the limitations of
ordering: (i) the role of screening of the interaction between cluste
rs during phase separation and (ii) the interplay between spatial orde
ring and size ordering of the clustered phase. (C) 1998 Elsevier Scien
ce B.V. All rights reserved.