W.-Z. Zhang

Formulas for periodic dislocations in general interfaces

The present work has advanced the calculation method for determining the configuration of periodic dislocations in general interfaces, especially for three sets of dislocations that are usually unsolvable by other methods. In terms of a newly introduced reciprocal Burgers vector (bi*), the configuration and the Burgers vector of the interfacial dislocations are related by a simple expression with general validity. Existing formulas for spacing of the dislocations in various special interfaces can be integrated in a concise form of D=1∕∣Δbi*∣.

Structures in irrational singular interfaces

We consider periodic good matching bands (which are centered at the O-lines) as the characteristic feature of the structures in irrational singular interfaces in the primary preferred state. This feature is shared by various structures described by different models for irrational singular interfaces, and it can be used to consolidate different descriptions. We have made a quantitative analysis on the distribution of good matching zones (GMZs) in a relationship with plane matching geometry. This analysis emphasizes that matching of one set of principal planes does not represent good lattice matching. Good lattice matching is possible only at the locations of 0-d intersections, where three sets of nonlinearly related Moiré planes intersect. Matching of one or more sets of principal planes in an interface usually implies the possible presence of periodic GMZs in the interface. The analysis also explains why and in what condition a dislocation configuration can be described by the traces of Moiré planes. The distribution of exact 0-d intersections can be determined based on the O-lattice theory. The approximate 0-d intersections can be used for determining a possible interfacial structure when periodic O-elements do not exist.

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

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.

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

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.