A General Method for Twin Element Analysis and its Application in Cu-Zn-Al Shape Memory Alloys with M18R Martensite

Twins play a crucial role in elucidating the structure and deformation characteristics of materials. However, in materials with low-symmetry crystal structures, solving the twin relationships remains a challenging task. In this study, we propose a general method for determining twin elements K1, η1, K2, and η2, which are essential for twin analysis. The proposed method involves three main steps: (1) representing misorientation data measured by electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM) in matrix form, (2) identifying additional 180° rotation elements related to twin elements K1 or η1 by traversing all symmetrically equivalent misorientations, and (3) using a minimum and crystal structure-dependent uniform shear as the constraint to determine the other twin elements (K2andη2). By combining the experimental data and the proposed method, we systematically analyze the complex twin relationships of Cu-Zn-Al shape memory alloys (SMAs) with monoclinic martensite (M18R). This methodology has been demonstrated to be effective and possesses broad applicability.