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Predicting grain boundary structure and energy in BCC metals by integrated atomistic and phase-field modeling
We predict structure and energy of low-angle (110) pure twist grain boundaries (GBs) in five BCC transition metals (β-titanium, molybdenum, niobium, tungsten, and tantalum) using a combination of atomistic and microscopic phase-field (MPF) modeling. The MPF model takes as inputs solely the generalized stacking fault energy surfaces (i.e., the γ-surface) and elastic constants obtained from the atomistic simulations. Being an energy-based method, the MPF model lifts the degeneracy of the geometric models in predicting GB structures. For example, the multiple indefinite solutions offered by the Frank-Bilby equation are shown to converge to exactly the same equilibrium structure. It predicts a transition of the equilibrium GB structure from a pure screw hexagonal network (Mo and W) to mixed hexagonal networks (Nb and Ta) to a rhombus network (β-Ti) of dislocations. Parametric simulation studies and detailed analyses of the underlying dislocation reactions that are responsible for the formation of the rhombus and hexagonal structures reveal a close correlation between material properties (including the elastic anisotropic ratio and the local curvature on the γ-surface) and the GB structure and energy in BCC metals. This integrated approach allows one to explore, through high throughput calculations, the potential to tailor the structure and energy of special GBs in BCC metals by alloying.