Fig. 1: Topological analysis of the potential twinning shuffles in \(\left\{11\bar{2}1\right\}\) twinning of the HCP metals.

a Dichromatic pattern for the \(\left(11\bar{2}1\right)\) twinning viewed along the \(\left[1\bar{1}00\right]\) direction. The filled gray circles and squares represent atoms in the matrix; the open red circles and squares represent atoms in the twin. Solid circles, dash circles, solid squares, and dash squares indicate atoms of different levels along the \(\left[1\bar{1}00\right]\) direction. Stacking sequence of basal planes in the matrix A^mB^mA^mB^m changes to A^tB’^tA^tB’^t after the homogeneous shear (cyan arrows). b A^tB’^tA^tB’^t stacking sequence of the basal planes viewed along the \(\left[0001\right]\) direction of the twin. Arrows with the same color indicate one shuffling mode; there are a total of four shuffling modes. c The \(\left(11\bar{2}1\right)\) plane (green-colored) in a HCP unit cell. Atoms belong to two \(\left(22\bar{4}2\right)\) sub-planes and are colored blue with solid outlines and dash outlines, respectively.