The energy pathways associated with the martensitic transformation in shape memory alloys (SMAs), though the focus of extensive research over the past decades, are still unclear. In this work, we use a first-principles approach within the frame-work of density functional theory, as implemented in the Vienna ab initio simulation package (VASP), to model the transformation in transition metal alloys by tracking atomic motion via shear, shuffle and distortion during the transformation. We build a framework to investigate the f.c.c-h.c.p transformation in Co-based binary alloys which may be applied to ternary alloys as well. In the Co2NiGa Heusler system, by applying the Burgers transformation, we found a low-energy phase with orthorhombic symmetry (O) phase which is lower in energy than the experimentally observed L10. By performing a detailed analysis of the transformation paths (Burgers and Bain) taking into account perturbations on the ground state, it is seen that a phase selection problem exists: the ultimate crystal structure that the system transforms into, depends on the path that the system prefers. When coming from high temperature, the accessible path is that corresponding to the Bain transformation. Finally, we present a complete and unique 4-parameter model to describe the B2 -- B19' transformation in Ni --Ti. We eliminate the possibility of the B19 phase being an intermediate phase in the transformation and show that it is in fact a barrier-less transformation. Crystallographic analysis of intermediate states shows that the B2 -- B19' path follows a known crystallographic path.
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