Product phases from various phase transformations often exhibit fascinating morphologies. Facets of unique crystallographic orientations are characteristic of the morphologies. Based on a comparison of facets in the surfaces and interfaces of crystals, this paper proposes to use singularity as the common features of facets on a crystal. While association of facets with energy singularity has been established from the Wulff construction, we defined singularity in structure with an absence of one or more types of defects common to a vicinal surface or interface. Singularity in an interfacial structure is described in terms of both ledges and dislocations. When dislocations are involved, the candidates of the singular interfaces derive mainly from the principal O-lattice planes. The orientations of these planes are defined by Δg’s, which are measurable in diffraction patterns. Singularity with respect to the orientation relationship results from further eliminating defects, which is permitted by a special arrangement of Δg’s. The candidates of singular interface confined by the arrangement of discrete Δg’s are helpful for understanding the crystallographic morphology. One example from an Mg alloy is provided to show the association of the singular interfaces with Δg’s. The effect of the potential presence of a long-range strain and kinetic effects are briefly discussed.