Classification and analysis of trigonal martensite laminate twins in shape memory alloys

In the trigonal martensite shape memory alloys (SMAs), typically only the well-known classic herringbone pattern satisfies the nonlinear compatibility theory. However, many other interesting trigonal patterns are still possible. Thus, geometrically linear compatibility theory is first used to obtain the full set of rank-2 laminate twin patterns which can possibly form in the trigonal SMAs. There are only seven families of twin pattern, including many new structures, such as checkerboard, toothbrush and non-classic herringbone patterns. These microstructures are confirmed in the trigonal R-phase Ti50.3Ni48.2Fe1.5 SMA. The interfaces separating the seven families and their parent phase (austenite) are also determined and observed. The results show that minor geometrical incompatibility of microstructures can be tolerated in the trigonal R-phase SMAs. Next, a numerical method based on non-linear compatibility theory is developed to evaluate the parameter for measuring the defect of disclination in these patterns. The greater the value of the parameter is, the less likely the pattern could be observed in the experiments. The likelihood of occurrence of all seven families in the typical trigonal SMAs is revealed in the current work. Moreover, 3-dimensional unit cell alignment of the patterns is illustrated. The loading conditions to avoid the disclination are also discussed.