Edge-to-edge plane matching as a criterion for interphase boundaries of low energy

As demonstrated by Aaronson and his colleagues over five decades or so, the structure, energy, and dynamic response of interphase boundaries in metallic systems are strongly correlated. It has also become clear that very few, if any, solid/solid transformation interfaces can be considered truly "incoherent." Most treatments of the geometry of irrational interfaces (facet planes) have focused on the density of coincidence sites or near-coincidence sites (NCS); this naturally involves consideration of the matching of densely packed atomic planes lying parallel to the facet. Edge-to-edge plane matching represents an alternative and, perhaps, more general approach to the geometry of transformation interfaces. For diffusional transformations, growth ledges are required to displace and reproduce the structure of the facet plane; their geometrical properties are distinct from those of the interfacial facets. The role of local thermodynamic driving force in determining the migration mode is assessed. Several recent observations of the transient faceting of irrational interfaces, for which the density of NCS is relatively low, have stimulated considerations of the significance of the invariant-line condition and of edge-to-edge plane matching as criteria for local minima in interfacial free energy.