Abstract
The surface equation of motion in the continuum limit is derived by considering the diffusion of surface species along the gradient of their chemical potential in the presence of a bulk sink/source. This equation extends Mullins's equation and is distinct from the Cahn-Taylor equation. The characteristic length below which this equation leads to new solutions is in the length scale of many practical problems, e.g., in the interpretation of low-temperature flattening experiments. As an example, we discuss the application to the thermal groove motion.
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