Equilibrium shape of crystals
نویسنده
چکیده
2014 The physical mechanisms governing the equilibrium shape of crystals are described. The roughening transition of a given crystal face is associated with the vanishing of the free energy of a step on that surface. Below the roughening transition, facets of finite size coexist with rounded parts of the surface. Near the boundary of a facet, the shape of the crystal is determined by a fluctuation-induced long-range interaction between steps. A simple transfer-matrix method is used to derive the 3/2-power-law for the crystal shape near the boundary (implying diverging curvature), as well as some other features of the facet shape. If there are long-range repulsive interactions between steps, facets of higher and higher order can form at low temperatures, leading to a devil’s staircase at T = 0. Formulae for the width and roughening temperature of the high index facets are given. If there is attraction between steps, the devil’s staircase disappears partly or completely, and edges between different facets can be stable at nonzero temperatures. J. Physique 46 (1985) 257-269 FTVRIER 1985,
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