Faceted morphology is common in the microstructures resulting from solid-state phase transformations in a wide range of crystalline materials. This study explains the faceted interfaces based on the concept of singular interfaces, which are characterized by key interfacial structures at two levels: the singular dislocation structure and the preferred state existing between the dislocations. It identifies interface geometries required by these structures at two stages: before and after dislocation generation. Methods to determine the interface geometries are reviewed. These methods enable quantitative interpretation of phase transformation crystallography features, including the interface orientations and the orientation relationship between the two phases, irrespective of whether these features are described as rational or irrational. The agreement achieved across different systems indicates the crucial role of geometric matching in the development of phase transformation crystallography. An example is provided for an illustration of the application of the two-stage approach, especially with an analysis in reciprocal space using a superimposed diffraction pattern. [ABSTRACT FROM AUTHOR]

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