A Generalized Frank-Bilby Equation for Interfaces in Crystalline Materials

The classical Frank-Bilby equation (FBE) is commonly used to predict the structure of interfaces in crystalline materials in terms of interfacial dislocation networks. However, in general, the line defects in interfaces are disconnections, possessing both dislocation and step character, which are not captured by the classical FBE. As a result, the FBE cannot fully describe the structure of most interfaces of practical interest. To address this issue, we derive a generalized Frank-Bilby equation (GFBE) that explicitly incorporates both dislocation and step components of interfacial defects. We demonstrate its application to several representative interface systems.