Hierarchical twin microstructure in modulated 10M Ni-Mn-Ga single crystals. An analysis including shuffling of atomic layers

The trained and self-accommodated martensite microstructures of 10M Ni-Mn-Ga single crystals were studied by back scattered electron imaging and electron backscatter diffraction in a scanning electron microscope. These data were then compared with theoretical calculations using a long periodic commensurate modulated monoclinic lattice and Gautam and Howe (G-H) model in order to establish twin boundary (TB) hierarchy according to their surface energy. The whole spectrum of TBs including type I, type II, and compound twins were detected and theoretically predicted. Using the G-H model and long periodic structure along with a small displacement of atoms connected with lattice modulation allowed to calculate all twin elements including their surface energy. These data are then confronted with theoretical predictions of classical continuum mechanics and minimum shear approaches, which disregard the lattice modulation. As it is shown including the modulation modifies the twin systems (twinning plane and twinning direction) for some TBs. Moreover, it strongly affects the interfacial energy which allows to rank TBs in the 10M Ni-Mn-Ga system. Large differences in surface energy between different TBs are associated with atomic interface configurations and de-shuffling of atoms to form a coherent twin plane. Therefore, unlike the classical geometrical concepts, the G-H model allows to perform not only a quantitative but also qualitative analysis of all possible twin boundaries. As a result of new approach, a model that involves interfacial energy, shuffling of atoms and homogenous shear type deformation for TB determination is presented. In addition, irrational or step-like planes not only for type II but also for type I twin boundaries is predicted. Furthermore, a description of twin formation with respect to two different reference systems is completed, i.e. parent-based and monoclinic ones. In this way, a hierarchical twin microstructure of 10M martensite is established.