This work proposes a grain boundary (GB) structure prediction framework for A15 [001] symmetric tilt GBs, combining a modified Farey diagram (MFD) with an interface computational method based on the conserved Landau-Brazovskii model. We use MFD to predict GB structures for misorientation angles from $0^{\circ }$ to ${90}^{\circ }$, addressing the challenge of describing high-$\mathrm{\Sigma }$ coincidence site lattice (CSL) GBs. When the Farey fraction of a GB is irreducible, MFD predicts a unique structure. When reducible, it predicts two possible structures. The concrete GB structure is determined by the distance between lattice spheres and the GB plane, influenced by environmental parameters, such as temperature. Computer simulations demonstrate excellent agreement with MFD's theoretical predictions. The developed framework can also be used to predict CSL GB structures in other crystalline materials.

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• Grain boundaries
• Microstructure
• Intermetallic compounds
• Polycrystalline materials
• Numerical techniques
• Phase-field modeling