The Roughening Transition
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The idea that there could be a “roughening” of the interface of a crystal in equilibrium with its vapor at a particular temperature TR was first suggested by Burton and Cabrera (1949) and further developed in a now classic article by Burton, Cabrera and Frank (BCF) (1951). Representing the crystal surface by a two-dimensional (2D) Ising model they suggested that there would be large fluctations in the surface structure at the Ising model’s critical temperature TC(2D) and a disappearance of the nucleation barrier to crystal growth. Jackson (1953, 1967) further developed and extended these ideas to the case of melt growth and showed that the morphology and growth mechanism of a wide class of crystals could be understood by assuming they were grown above or below the appropriate surface roughening temperature.
KeywordsPartition Function Ising Model Planar Model Universality Class Interface Width
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