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A crystal surface arbitrarily oriented is not necessarily stable. For some orientations, the crystal surface breaks up into a structure containing several new orientations, which we might call surface phases. A thermodynamic treatment which follows exactly the same lines as the theory of equilibrium of volume phases is presented to determine the conditions under which this happens. It shows that the equilibrium surface structure for a given average orientation will contain one, two, or three orientations (surface phases) depending on the number of points a tangent plane touches the surface, β, representing the surface tension per unit area of a reference surface as a function of orientation.
University of Virginia, Charlottesville, Va