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Universality of the Tangential Shape Exponent at the Facet Edge of a Crystal

Y. Akutsu·N. Akutsu·T. Yamamoto
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Abstract

Below the roughening temperature, the equilibrium crystal shape (ECS) is composed of both facets and a smoothly curved surface. As for the ``normal'' profile (perpendicular to the facet contour), the ECS has the exponent 3/2 which is characteristic of systems in the Gruber-Mullins-Pokrovsky-Talapov (GMPT) universality class. Quite recently,it was pointed out that the ECS have a ``new'' exponent 3 for ``tangential'' profile. We first show that this behavior is universal because it is a direct consequence of the well-establised universal form of the vicinal-surface free energy. Second, we give a universal relation between the amplitudes of the tangential and the normal profiles, in close connection with the universal Gaussian curvature jump at the facet edge in systems with short-range inter-step interactions. Effects of the long-range interactions are briefly discussed.

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Y. Akutsu, N. Akutsu, T. Yamamoto. 1998-03-15. Universality of the Tangential Shape Exponent at the Facet Edge of a Crystal. https://arxiv.org/abs/cond-mat/9803189

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