Ambiguity of Anisotropic Interface Tension for Complex Crystals

Abstract

For two-dimensional (2D) lattice gas which consists of more than one sublattices, we show that microscopic interface energy cannot be determined uniquely. Accordingly, the interface tension has unavoidable ambiguity in choice of the origin (Wulff point) of the Wulff plot. On the other hand, interface stiffness, equilibrium crystal shape and interface entropy are free from the ambiguity. For anisotropic systems, it has been known that the interface tension in various “physical” formulas is replaced by the interface stiffness, which can be naturally understood from the ambiguity argument. As a demonstration, we consider a step (regarded as a 1D interface) on the (10\overline{1}0) surface of the hexagonal ZnS-type crystal, and calculate interface (step) quantities at finite temperatures. Critical curve is successfully obtained from zeros of the interface stiffness.