Prediction of A15 Tilt Grain Boundary Structures

In this work, we present a theoretical method to predict all coincidence site lattice (CSL) tilt grain boundaries (GBs) in A15, especially high-$\mathrm{\Sigma }$ CSL GBs. This method includes a modified Farey diagram (MFD) and a computational framework based on the 3D phase field crystal model. Applied to [001] CSL symmetric tilt grain boundaries (STGBs) in A15, this method identifies building blocks of A15 GBs, known as structural units (SUs). The MFD predicts the quantity and proportion of SUs within GBs. The developed computational approach further determines the arrangement of these SUs. The predictive rule reveals the SU arrangement of A15 [001] CSL STGBs.