Kinetic laws for the motion of twin boundaries in ferroic materials: the role of twinning disconnections

Twinning is a shear dominated material transition that plays a significant role in metal plasticity, geological processes, and actuation of shape memory and ferroelectric materials. In these materials, twinning transformation proceeds through the motion of twin boundaries as a result of a mechanical / electrical / magnetic driving force. At the atomic scale, the motion of a twin boundary involves the propagation of twinning disconnections, which are interface line defects having both dislocation and step characters. The disconnection`s burgers vector represents the lattice distortion carried by the defect, while the step height determines the amount of transformed volume from one twin to another as the disconnection propagates on the twin boundary.

In this work, we combine direct experimental observations at the level of individual interfaces with analytical modeling, which lead to the extraction and validation of the kinetic relations for twin boundary motion in a ferromagnetic Ni-Mn-Ga crystal. We show that at low velocities, twin boundary follows thermally activated kinetics that are controlled by the nucleation and propagation rates of two dimensional steps whose edges are twinning disconnections. At higher velocities, the twin boundary advances a-thermally as a flat plane. The transition between the two kinetic behaviors takes place at a driving force value that is determined by the magnitude of the lattice barrier for twin boundary motion. Fitting the analytical models to the experimental results allows the extraction of several atomic scale material properties that control twin boundary kinetics. In particular, we evaluate and discuss the magnitude of the line-energy of a twinning disconnection, for both type I and type II twins in Ni-Mn-Ga.