Twin boundary structure and mobility

Twinning is an important mechanism of deformation in various crystalline materials, and in particular in shape memory alloys, where it is inherent to the shape memory and super-elasticity effects. This paper presents a generalized methodological approach for analyzing and modeling twin boundary dynamics with particular relevance for shape memory alloys. This approach combines the topological model description of the interface structure at the atomistic/lattice scale with analytical analysis of energy barriers and mechanisms of motion that provide macro-scale kinetic laws for the twin boundary motion. We emphasize the main differences between the topological structures of different types of twin interfaces and their implications for the mobilities of the different twin types. In particular, we elaborate on the relaxed topological structure of type II twin boundaries that contains a coherently facetted structure, where the facets are rational planes that accommodate misfit strain. Then, we clarify the lattice barriers’ role in determining the different regimes of the kinetics of twin boundary motion. Further, we develop models leading to analytical expressions for the activation energies of various nucleation processes that dictate the overall kinetics of twin boundary motion, and identify of the rate-limiting process for the different twin types. In the case of compound and type I twins, the analysis leads to an explicit expression for the magnitude of the twinning stress, revealing a strong dependency on the shear modulus and the twinning shear, which is in excellent quantitative agreement with experimental values reported for BaTiO₃, Ni-Ti, Cu-Al-Ni, and 10M and NM Ni-Mn-Ga. Moreover, our analysis reasons the different temperature dependencies of the twinning stress exhibited by the different twin types, and in particular the very low temperature sensitivity of type II twins.