Structure and Kinetics of Twin Boundaries in Shape Memory Alloys

Shape memory alloys (SMAs) are functional materials that recover from large strains without permanent deformation. In magnetic shape memory alloys (MSMAs), the reversible deformation is driven either magnetically or mechanically. Two underlying phenomena are responsible for the shape memory effect: (a) a diffusionless, martensitic transformation and (b) twinning in the martensite phase. In MSMAs, the reversible plastic deformation occurs via twinning in the martensite phase, particularly via the movement of twinning disconnections (TDs) along the twin boundaries (TBs). A geometric algorithm called the classical model (CM) of deformation twinning describes operative twinning modes of a given crystal system. There are four types of twins - compound, non-conventional (NC), type I, and type II, which are distinguished based on the crystal's orientation relationship (OR) across the TB. Recently, Pond, Hirth, and coworkers developed a dislocation model of twinning called the topological model (TM) to describe the formation and growth of twins. We apply the TM to characterize the defect structure of junction lines and TBs. We show that the relaxed structure of type II TBs differs distinctly from those of type I and compound TBs. Furthermore, depending on the crystal, the type II interface can either relax into a coherently faceted structure (e.g., NiTi) or remain inherently irrational (e.g., 10M Ni-Mn-Ga (NMG)). One of the characteristic features of type II twins is that chains of quadruple junction lines (QJLs) appear in the vicinity of the TB. Our analysis shows that QJLs have no long-range stress field. Triple junction lines (TJLs), on the other hand, contain a rotational displacement field, i.e., a disclination. A stable chain of TJLs requires a local minimum of the strain energy associated with the disclinations. A disclination quadrupole approximation shows that the system’s total energy scales with the distance of the defects. So, as we approach larger defect spacing, two TJLs may coalesce to form a QJL, thus minimizing the system's energy. A complete description of twinning includes the kinetic relation, i.e., the relationship between the driving force acting on the TB and the resulting velocity of TB motion. In 2014, Faran and Shilo presented an analytic kinetic relation for TB motion, a general kinetic law typical of viscous interface motion in a periodic potential. We refine the model by incorporating the structural differences between type I and type II twins in the kinetic relation. We establish the structure of type II TBs in various alloys and correlate their kinetic properties with the interface's structure. Our work helps establish the kinetic relation for type II twins. Our model predicts the mechanism responsible for the high mobility and temperature insensitivity of type II TBs. Furthermore, we correctly predict the twinning stress of an alloy for compound and type I twins. Our investigation and discovery help enhance the understanding of the dynamic behavior of SMAs.