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.

中文翻译：

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非合理Type-II Twin接口的结构特点


II 型孪生边界 (TB) 是功能材料中的一个关键界面，其非理性米勒指数特性最近引起了人们的广泛研究兴趣。本研究利用形状记忆合金 (SMA) 中的 TB（TiPd、TiPt 和 AuCd）作为研究目标，建立了 II 型孪晶界面的一般结构特征。它显示了如何通过阶断连接 (T-D) 结构拓扑来解释每个 TB 的非理性身份。提出平台是倒易空间中最接近无理 TB 的有理平面，具有最小量值的积分米勒指数。这个平台上的晶体登记需要不平凡的相干应变。提出了一种新颖的相干应变运动学起源，直接来自经典孪生变形梯度的变换。这种转变揭示了经典的孪生剪切分为相干应变和称为“阶地剪切”的新度量。结果表明，将孪晶结构与基体相关的剪切大小是平台剪切，而不是孪晶剪切，这与经典理解相反。此外，孪生断开的伯格斯矢量被证明与阶地剪切直接相关。每个 II 型界面的能量由从头开始的密度泛函理论 (DFT) 计算确定。结果表明，平台上的能量最小原子结构需要确定一个非平凡且未知的先验“晶格偏移”。 总之，本研究阐述了II型孪生界面的T-D拓扑结构，建立了识别有理阶、相干应变、从头算平面TB能量的方法，并揭示了此类界面所表现出的孪生剪切的独特划分。