Simple model for crystal shapes: Step-step interactions and facet edges

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Abstract
The terrace-step-kink model for equilibrium crystal shapes is considered. Noninteracting steps are known to correspond to a free-fermion model which leads to a continuous transition from facets to curved surfaces. We study both short- and long-ranged interactions between steps within meanfield theory. For nearest-neighbor step interactions, the model can be solved exactly, and details are given. The possibility of a slope discontinuity between facets and curved surfaces is explored within the interacting terrace-step-kink model (which ignores voids and overhangs); this possibility is realized only for sufficiently long-ranged attractive interactions. As physical examples of such interactions we consider both elastic and dipolar interactions between steps. These have the same range, and may be comparable in magnitude. It is argued that elastic interactions (which are repulsive) do not change the free-fermion predictions for the exponent governing the facet-curved surface edge while dipolar interactions, if attractive, can lead to slope discontinuities and associated tricritical phenomena.