A two-dimensional analytical method for the transformation crystallography based on vector analysis

Abstract

A simple 2-D analytical method has been developed for calculating the crystallographic features, including the orientation relationship (OR), habit plane (HP) and the direction and spacing of dislocations in the HP, under the condition that a pair of Burgers vectors from both phases are parallel to each other lying in the HP. In contrast to previous 2-D models for the OR and HP, which are on the plane normal to the parallel Burgers vectors, the present 2-D model is based on vector analysis in the HP. Closed-form expressions for the crystallographic features have been derived as functions of lattice parameter ratios. While the results are in agreement with those from a 2-D method based on the O-line model, the present method is simpler and improves our understanding of crystallographic features.

Keywords:

• orientation relationship
• habit plane
• interfacial structure
• O-line model
• edge-to-edge matching model

Acknowledgements

Support from National Natural Science Foundation of China (Project No. 50971076) and from National Basic Research Program with Grant No. 2007CB613704 is gratefully acknowledged.