A comparison of the phenomenological theory of martensitic transformations with a model based on interfacial defects

Abstract

Structural models of martensitic interfaces are those where the habit plane (HP) is comprised of coherent terraces reticulated by arrays of interfacial defects. Such interfaces are shown explicitly to exhibit no long-range displacements and to move in a glissile manner by lateral motion of disconnections along the interface. We quantify predictions of HP and orientation relationship (OR) between the parent and product crystals for such models in terms of a reference lattice in an approach called a topological model (TM). These crystallographic quantities for the TM are compared with those of the phenomenological theory of martensite crystallography (PTMC). For the case of transformations resembling α to β in Ti, but where lattice invariant deformation is suppressed, the two models agree when the interplanar spacings of the terraces in the two crystals are the same. However, although the OR’s according to the two approaches are very similar, the predicted HP’s differ systematically when the terrace plane spacings are varied. The differences arise because the PTMC interfaces are unrelaxed configurations that are invariant planes of the geometrical shape transformation, whereas TM interfaces are physically invariant planes as a transformation progresses.