Structural characteristics of irrational Type-II Twin interfaces

The Type-II Twin Boundary (TB) is a critical interface in functional materials whose irrational Miller-index identity has recently drawn significant research interest. This study establishes general structural characteristics of the Type-II twin interface, utilizing TBs in Shape Memory Alloys (SMAs) - TiPd, TiPt, and AuCd - as study targets. It is shown how the irrational identity of each TB is explained by the Terrace-Disconnection (T-D) structural topology. It is proposed that the terrace is the rational-plane nearest to the irrational TB in the reciprocal space, having integral Miller-indices of least magnitude. Crystallographic-registry on this terrace requires non-trivial coherence-strains. A novel kinematic-origin of the coherence-strain is proposed, coming directly from a transformation of the classical twinning deformation-gradient. This transformation revealed that the classical twinning-shear partitions into the coherence-strain and a new metric termed the “terrace-shear”. It is shown that the magnitude of shear relating the twin-structure to the matrix is the terrace-shear and not the twinning-shear, contrary to classical understanding. Furthermore, the Burgers vector of the twinning disconnection is shown to be related directly to the terrace-shear. The energy of each Type-II interface is determined from ab initio Density Functional Theory (DFT) calculations. It is shown that the energy-minimal atomic-structure on the terrace requires determination of a “lattice-offset” that is non-trivial and unknown apriori. In summary, this study expounds on T-D topological structure of Type-II twin interfaces, establishing methods to identify rational terraces, coherence strains, ab initio planar TB energies and revealing a unique partitioning of the twinning-shear exhibited by this class of interfaces.