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Faceted interfaces are a key feature in self-resembling morphologies of manymicrostructures generated from solid state phase transformations.Interpretations, predictions and simulations of the faceted morphologies remaina challenge, especially for systems in which irrational orientationrelationships (ORs) between two phases and irrational interface orientations(IOs) are preferred. In terms of structural singularities, this work suggestsan integrated framework, which possibly encompasses all candidates of facetedinterfaces. The structural singularities are identified in a matching pattern,a dislocation structure and/or a ledge structure. The resultant singularinterfaces are discrete IOs, described with low index g's (rationalorientations) and/or Delta-g's (either rational or irrational orientations).Elimination of defects exerts restrictions on the OR and the latticeparameters. Various models are grouped according to their determined resultsregarding the OR and IO, and the links between the models are clarified in theintegrated framework. An irrational IO is usually due to elimination ofdislocations in one direction, i.e., an O-line interface. Analytical methodsusing both 3D and 2D models for quantitative determinations of O-lineinterfaces are reviewed, and a detailed example showing the calculation for anirrational interface is given. The association between structural singularitiesand local energy minima is verified by atomistic calculations of interfacialenergies in fcc/bcc alloys where it is found that the calculated equilibriumcross-sections are in a good agreement with observations from selected alloys.Comment: This paper has been withdrawn due to the error use of Figure

Faceted interfaces: a key feature to quantitative understanding of transformation morphology