Strain-sensitive topological evolution of twin interfaces

Abstract

Twin Boundaries (TBs) are fundamental interfaces in materials science which, despite over a century of research, continue to surprise us. A longstanding anomaly in the field is the experimental observation of a Type II TB in NiTi with two distinct indicial identities: (0.720511¯)≈(344¯) and (899¯). The nanostructure of this interface is still unclear, with varying propositions put forth over the past 4 decades. We consider multi-scale energetics, employing Molecular Statics simulations and anisotropic elasticity formalisms, to establish a Terrace-Disconnection (TD) topology as the energy-minimal nanostructure. A theoretical framework is developed based on continuum strain-energy arguments to determine the influence of microstructural strain and local twin volume fraction on interface topology. It is shown that it is energetically favorable for the topology to evolve across a continuous spectrum of indicial identities under coupled influence of both parameters. Consequently, experimental observations that were thus far considered contrasting are proposed as distinct states within this spectrum, transposing as evidence of the proposed evolving capability in the Type II TB. This topological evolution fundamentally arises from a strain-mediated change of the dislocation-spacing (equivalently, a change in the interface dislocation-density). We further propose the prevalence of this evolving behavior in both Type I and Compound TBs (in NiTi) exhibiting a seamless transition between coherent and semi-coherent states, significantly changing dislocation-densities (upto 8-fold) and exhibiting irrational Miller-index identities under non-zero strain. An “Evolving Interface” theory is proposed as an extension to the Topological Modeling framework, allowing determination of equilibrium topologies at non-zero strain and unsymmetric twin volume fractions.