Spatial and temporal scaling of oxide cluster aggregation on a liquid-gallium surface

Oxide clusters grow spontaneously on a liquid-gallium surface exposed to oxygen at room temperature. Clusters diffuse and aggregate to form larger and larger clusters with a fractal dimension ${\mathit{d}}_{\mathit{f}}$ of ∼1.5. The total number of clusters and the weighted average cluster size do not exhibit power-law dependence on time, while the typical linear dimension of the clusters exhibits a ${\mathit{t}}^{1/2}$ time dependence. The exponent appears to be consistent with Binder’s prediction for the phase separation of two-dimensional binary fluid mixture. For early stages of the aggregation, the structure function F(k,t) of the oxide patterns can be scaled as [${\mathit{k}}_{\mathit{m}}$(t)${]}^{\mathrm{-}{\mathit{d}}_{\mathit{f}}}$f(k/${\mathit{k}}_{\mathit{m}}$), where ${\mathit{k}}_{\mathit{m}}$ is the peak position of F(k,t) and f(k/${\mathit{k}}_{\mathit{m}}$) is a time-independent function. However, such a scaling behavior, which is a generalization of Furukawa’s theory for spinodal decomposition, does not hold for longer times. © 1996 The American Physical Society.