Dislocation mediated twin boundary faceting in $β$-Sn
Grain boundaries (GBs), including twin boundaries (TBs), play a critical role in plastic deformation by interacting with dislocations. The deformation and strengthening mechanisms in $β$-Sn are of significant interest because Sn-based alloys are widely used as solder materials. Recent experiments have shown deformation-induced faceting in $β$-Sn arising from twin-dislocation interactions. Using molecular dynamics (MD) simulations informed by a recently developed machine-learned interatomic potential (MLIP), we demonstrate a $\langle c\rangle$ dislocation-absorption mediated faceting reaction along $(301)$ TBs in $β$-Sn in which facet length grows with the number of absorbed dislocations. We show that the predicted facet length is consistent with isotropic elasticity theory only when the disclination character of the asymmetric twin facet is taken into account. We discuss analogies to faceting reactions in other low symmetry metals and hypothesize that the ubiquity of $(301)$ twins in $β$-Sn stems from their ability to grow rapidly through a forest of dislocation obstacles.