Spontaneous spiral patterns etched on germanium

A thin metal film deposited on germanium, in the presence of water, results in a remarkable pattern-forming system. Here, we present an analysis of spirals spontaneously etched on the Ge surface. We obtain measurements of the growth dynamics of the spirals and measurements of the local strain field in the metal film. Both indicate that the near geometric order of the pattern originates from the unique far field of a singularity-a crystal defect. The measured engraving profile is found to be in quantitative agreement with a model of metal catalyzed corrosion of the Ge surface. Specifically, local etch depth is inversely proportional to the normal velocity of the Ge-metal contact line. The growth mechanism combines crack propagation, reaction-diffusion dynamics, and thin film mechanical instabilities, and illustrates how a defect's long range field can impose geometric order in a nonequilibrium growth process. General features relevant to other pattern-forming systems are the coupling of chemistry and mechanics and the singularity-driven order.