Kinematic and Topological Models of Martensitic Interfaces
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Kinematic and Topological Models of Martensitic Interfaces Robert C. Pond1, Xiao Ma1, Yaw W. Chai1 and John P. Hirth2 1 Department of Engineering, University of Liverpool, Brownlow Hill, Liverpool, L69 3BX, U.K. 2 114 E. Ramsey Canyon Road, Hereford, AZ 85615, U.S.A. ABSTRACT The Phenomenological Theory of Martensite Crystallography, developed fifty years ago, envisages martensitic interfaces to be invariant planes of the shape transformation. This theory has been very successful, but neither incorporates the notion of atomic relaxations at martensitic interfaces, nor explicitly demonstrates that such interfaces are glissile. A new model, called the Topological Model, is proposed that addresses these issues. Predictions of the habit plane and relative orientation of the crystals according to the two models are compared and contrasted.
INTRODUCTION Martensitic transformations have been studied for many years [1], and our understanding of their crystallography has been based on the treatment devised by Wechsler, Lieberman and Read [2], and Bowles and Mackenzie [3]. These works are often referred to as the ‘Phenomenological Theory of Martensite Crystallography’ (PTMC). The central proposition of the PTMC is that the habit plane is an invariant plane (IP) of the shape transformation, the latter involving a latticeinvariant deformation (LID), a lattice deformation and a rigid body rotation. Being a phenomenological approach, the PTMC does not provide insight into the mechanism of martensitic transformations. To address this issue, a model of martensitic transformations in terms of interfacial dislocations has been developed recently by Pond, Hirth and co-workers [4,5]. This approach, referred to as the topological model (TM), is based on previous suggestions [6,7] and is consistent with high resolution transmission electron microscope images of martensitic interfaces [8,9] which reveal relaxed structures to comprise coherent terraces reticulated by arrays of transformation dislocations and LID. The crystallographic features of martensite in stiff engineering materials, such as metals and ceramics, predicted by the PTMC and TM are considered here. Differences arise because of the relaxations that occur in the interfacial region, these being incorporated in the TM but not in the PTMC. Thus, according to the PTMC, habit planes are geometrically invariant, whereas in the TM they are both glissile and physically invariant in the sense that their structure does not change on average as the interface advances. The objective of this paper is to compare and contrast the predictions of the PTMC and TM for a particular case. The case chosen is Ti and its alloys; Fig.1 is a high resolution transmission electron micrograph of a martensitic interface in Ti-(10wt%)Mo showing relaxation into a disconnection-coherent terrace structure [10]. The terraces in Fig.1 are 2 1 1 β / 1 1 0 0 α . To
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elucidate the key differences between the PTMC and TM, we consider two special cases where no coherency strains arise along orth
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