Oxide-growth kinetics and fractal-like patterning across liquid gallium surfaces

Gallium oxide initially forms fractal-like structures as it grows laterally across bounded clean surfaces of liquid gallium. The growing oxide film is no more than a few monolayers thick. During later growth, the oxide perimeter becomes rounded and uniform gaps develop between neighboring growth fronts. The measured fractal dimension of the oxide patterns increases from less than 1.6 to 2.0. In this experiment, the oxide is constrained to grow over liquid surfaces ≤(80 μm${)}^2$. To good approximation, for fixed growth time, liquid temperature, and ambient oxygen pressure, the fractional oxide coverage is independent of the area enclosed by the original boundary. The liquid area decreases exponentially with time as it is blanketed by the oxide film. These results suggest that the oxidation is the result of an irreversible nonequilibrium diffusion aggregation process across the liquid surface, modified by the action of (undetected) impurities on the interface between the oxide and clean liquid. The change in oxide coverage is modeled as a function of time, liquid temperature, ambient oxygen pressure, and area of the original enclosing boundary. The data were acquired using imaging secondary-ion mass spectrometry, with a spatial resolution of 100 nm.