Faceted interfaces: a key feature to quantitative understanding of   transformation morphology
  Faceted interfaces are a key feature in self-resembling morphologies of many microstructures generated from solid state phase transformations. Interpretations, predictions and simulations of the faceted morphologies remain a challenge, especially for systems in which irrational orientation relationships (ORs) between two phases and irrational interface orientations (IOs) are preferred. In terms of structural singularities, this work suggests an integrated framework, which possibly encompasses all candidates of faceted interfaces. The structural singularities are identified in a matching pattern, a dislocation structure and/or a ledge structure. The resultant singular interfaces are discrete IOs, described with low index g's (rational orientations) and/or Delta-g's (either rational or irrational orientations). Elimination of defects exerts restrictions on the OR and the lattice parameters. Various models are grouped according to their determined results regarding the OR and IO, and the links between the models are clarified in the integrated framework. An irrational IO is usually due to elimination of dislocations in one direction, i.e., an O-line interface. Analytical methods using both 3D and 2D models for quantitative determinations of O-line interfaces are reviewed, and a detailed example showing the calculation for an irrational interface is given. The association between structural singularities and local energy minima is verified by atomistic calculations of interfacial energies in fcc/bcc alloys where it is found that the calculated equilibrium cross-sections are in a good agreement with observations from selected alloys. 
W.-Z. Zhang, X.-F. Gu and F.-Z. Dai
cond-mat.mtrl-sci