Analytical O-line solutions to phase transformation crystallography in fcc/bcc systems

Abstract

This paper presents the progress in phase transformation crystallography of the fcc/bcc system based on the O-line model. In contrast to previous numerical methods, closed-form expressions have been derived to describe the orientation relationship (OR), habit plane (HP) normal, dislocation direction and spacing as functions of the lattice parameter ratio (λ) and the angle between the Burgers vectors of the dislocations. Possible directions of the dislocation and the HP normal are presented as elliptical curves in stereographic projections and explicit expressions for the curves are provided. In the 3-D space defined by the OR, the O-line criterion only restricts two degrees of freedom in the OR, while various constraints have been applied to the remaining degree of freedom. A comparison of the calculations with those from existing models indicates the general applicability of the method. Furthermore, the property that the HP normal lays on the surface of an elliptic cone can be readily extended to other systems.

Keywords:

• orientation relationship
• habit plane
• dislocation spacing
• O-line model
• transformation crystallography

Acknowledgement

XFG dedicates this paper to Dr. Walter Bollmann (1920–2009) for his contributions on our understanding of crystalline interfaces. The support from National Natural Science Foundation of China (Project No. 50971076) and 973 Program (Project No. 2009CB623704) is gratefully acknowledged.