MATERIALS 兴 HIENGE& ENGIEERING ELSEVIER Materials Science and Engineering A 438-440(2006)109-112 www.elsevier.com/locate/msea Kinematic and topological models of martensitic interfaces R C. Pond a,*X. Maa. J. P. Hirth Department of Engineering, University of Liverpool. Brownlow Hill, Liverpool L69 3BX, UK Received 19 April 2005; received in revised form 12 January 2006: accepted 2 February 2006 A new model of martensitic transformations has been presented recently where the habit plane consists of segments of coherent terraces reticulated by an array of line defects. These defects accommodate any coherency strains present and the transformation is effected by lateral motion of disconnections across the terraces. Provided the terraces and line defects satisfy certain criteria, the mechanism of transformation is onservative. Moreover, the topological parameters of the defects( Burgers vectors and step heights) can be determined rigorously enabling the overall habit plane inclination and orientation relationship to be determined The objective of the present paper is to compare predictions for the habit planes according to this topological method with those of the classical theories in the case of transformations in ZrO2 and Ti. The two approaches lead to disparate solutions, and the origin and magnitude of the disparities are elucidated. Unlike habit planes in the classical model, which are invariant planes, topological ones are misfit-relieved semi-coherent o 2006 Elsevier B v. All rights reserved Keywords: Martensitic phase transformation; Interface structure; Martensitic crystallography 1. Introduction that coherency strains may be partitioned unequally between the A new model of martensitic transformations was presented Clearly, the physical basis of the TM is different from that recently [1]; this model is known as the topological model (TM) of the Phenomenological Theory of Martensite Crystallogra- because the interface structure is comprised of coherent terrace phy (PTMC)[6, 7]. In general, predictions for the HP, orien- gments reticulated by an array of line defects. In general, this tation relationship(OR), and transformation displacement are array has two sets of defects, crystal or twinning dislocations not expected to be identical according to the two approaches (lattice-invariant deformation or LID)and transformation dis- [1]. The objective of the present paper is to elucidate the ori- locations or disconnections [2]. The array accommodates any gin of discrepancies between HP orientations predicted by the coherency strains and also provides the mechanism of transfor- TM and PTMC. For clarity, we consider transformations where mation through synchronous lateral motion of disconnections one of the principal strains is zero, which simplifies the analy- across the terraces. The overall interface plane or habit plane sis because no LId need be invoked [5]. We demonstrate that (HP)deviates from the terrace plane(TP) because disconnec- the two approaches lead to the same HP prediction in a sp tions, unlike LID, exhibit"overlap"step heights, h [3]. Dis- cial crystallographic circumstance, referred to as the congruent connection motion in this manner is diffusionless provided the case, but differ systematically otherwise. Martensitic transfor- TP and Burgers vector/step height couple of the disconnections, mations in ZrO2 [8] and Ti [9] are used for illustration; one b, h, satisfy certain criteria [4]. In addition, it also leads to a principal strain is zero in the former and is small in the latter transformation displacement and is hence consistent with exper- Transmission electron microscopy (TEM) has been used to study imental observations of martensitic transformations in metals the parent/martensite interface structure in these materials [1, 8 d ceramics [5]. Moreover, the TM is adaptable in the sense and both were observed to consist of terraces and disconnec tions as imagined in the tM. Furthermore the magnitude of the coherency strain on the terrace plane is very similar in the two Corresponding author. Tel. +44 151 794 4660: fax: +44 151 4675 materials, whereas the b, h values for the disconnections differ, E-lmail address: r.c. pond @liv. ac uk(RC. Pond) and hence comparison of the two cases is valuable 0921-5093/S-see front matter e 2006 Elsevier B doi:10.1016/msea.200602.132Materials Science and Engineering A 438–440 (2006) 109–112 Kinematic and topological models of martensitic interfaces R.C. Pond a,∗, X. Ma a, J.P. Hirth b a Department of Engineering, University of Liverpool, Brownlow Hill, Liverpool L69 3BX, UK b 114 E. Ramsey Canyon Road, Hereford, AZ 85615, USA Received 19 April 2005; received in revised form 12 January 2006; accepted 2 February 2006 Abstract A new model of martensitic transformations has been presented recently where the habit plane consists of segments of coherent terraces reticulated by an array of line defects. These defects accommodate any coherency strains present and the transformation is effected by lateral motion of disconnections across the terraces. Provided the terraces and line defects satisfy certain criteria, the mechanism of transformation is conservative. Moreover, the topological parameters of the defects (Burgers vectors and step heights) can be determined rigorously enabling the overall habit plane inclination and orientation relationship to be determined. The objective of the present paper is to compare predictions for the habit planes according to this topological method with those of the classical theories in the case of transformations in ZrO2 and Ti. The two approaches lead to disparate solutions, and the origin and magnitude of the disparities are elucidated. Unlike habit planes in the classical model, which are invariant planes, topological ones are misfit-relieved semi-coherent configurations. © 2006 Elsevier B.V. All rights reserved. Keywords: Martensitic phase transformation; Interface structure; Martensitic crystallography 1. Introduction A new model of martensitic transformations was presented recently [1]; this model is known as the topological model (TM) because the interface structure is comprised of coherent terrace segments reticulated by an array of line defects. In general, this array has two sets of defects, crystal or twinning dislocations (lattice-invariant deformation or LID) and transformation dis￾locations or disconnections [2]. The array accommodates any coherency strains and also provides the mechanism of transfor￾mation through synchronous lateral motion of disconnections across the terraces. The overall interface plane or habit plane (HP) deviates from the terrace plane (TP) because disconnec￾tions, unlike LID, exhibit “overlap” step heights, h [3]. Dis￾connection motion in this manner is diffusionless provided the TP and Burgers vector/step height couple of the disconnections, b, h, satisfy certain criteria [4]. In addition, it also leads to a transformation displacement and is hence consistent with exper￾imental observations of martensitic transformations in metals and ceramics [5]. Moreover, the TM is adaptable in the sense ∗ Corresponding author. Tel.: +44 151 794 4660; fax: +44 151 794 4675. E-mail address: r.c.pond@liv.ac.uk (R.C. Pond). that coherency strains may be partitioned unequally between the parent and product crystals, or incompletely accommodated [4]. Clearly, the physical basis of the TM is different from that of the Phenomenological Theory of Martensite Crystallogra￾phy (PTMC) [6,7]. In general, predictions for the HP, orien￾tation relationship (OR), and transformation displacement are not expected to be identical according to the two approaches [1]. The objective of the present paper is to elucidate the ori￾gin of discrepancies between HP orientations predicted by the TM and PTMC. For clarity, we consider transformations where one of the principal strains is zero, which simplifies the analy￾sis because no LID need be invoked [5]. We demonstrate that the two approaches lead to the same HP prediction in a spe￾cial crystallographic circumstance, referred to as the congruent case, but differ systematically otherwise. Martensitic transfor￾mations in ZrO2 [8] and Ti [9] are used for illustration; one principal strain is zero in the former and is small in the latter. Transmission electron microscopy (TEM) has been used to study the parent/martensite interface structure in these materials [1,8] and both were observed to consist of terraces and disconnec￾tions as imagined in the TM. Furthermore, the magnitude of the coherency strain on the terrace plane is very similar in the two materials, whereas the b, h values for the disconnections differ, and hence comparison of the two cases is valuable. 0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.02.132