Stability analysis of the martensitic phase transformation inCo2NiGaHeusler alloy

Abstract

Phase competition and the subsequent phase selection are important characteristics of alloy systems exhibiting numerous states of distinct symmetry but comparable energy. The stoichiometric ${\mathrm{Co}}_{2}\mathrm{NiGa}$ Heusler alloy exhibits a martensitic transformation with concomitant reduction in symmetry from an austenitic $L{2}_{1}$ phase (cubic) to a martensitic $L{1}_{0}$ phase (tetragonal). A structural search was carried out for this alloy and it showed the existence of a number of structures with monoclinic and orthorhombic symmetry with ground state energies comparable to and even less than that of the $L{1}_{0}$ structure, usually reported as the ground state at low temperatures. We describe these structures and focus in particular on the structural transition path from the $L{2}_{1}$ to tetragonal and orthorhombic structures for this material. Calculations were carried out to study the Bain ($L{2}_{1}\ensuremath{-}L{1}_{0}$) and Burgers ($L{2}_{1}\ensuremath{-}\text{hcp}$) transformations. The barrierless Burgers path yielded a stable martensitic phase with orthorhombic symmetry ($O$) with energy much lower---beyond the expected uncertainty of the calculation methods---than the known tetragonal $L{1}_{0}$ martensitic structure. This low-energy structure ($O$) has yet to be observed experimentally and it is thus of scientific interest to discern the cause for the apparent discrepancy between experiments and calculations. It is postulated that the ${\mathrm{Co}}_{2}\mathrm{NiGa}$ Heusler system exhibits a classic case of the phase selection problem: although the unexpected $O$ phase may be relatively more stable than the $L{1}_{0}$ phase, the energy barrier for the ($L{2}_{1}\ensuremath{-}O$) transformation may be much higher than the barrier to the ($L{2}_{1}\ensuremath{-}L{1}_{0}$) transformation. To validate this hypothesis, the stability of this structure was investigated by considering the contributions of elastic and vibrational effects, configurational disorder, magnetic disorder, and atomic disorder. The calculations simulating the effect of magnetic disorder/high temperature as well as the atomic disorder simulations showed that the transformation from $L{2}_{1}$ to $L{1}_{0}$ is favored over the Burgers path at high temperatures (large magnetic disorder). These conditions are prevalent upon cooling the material from high temperatures (the usual synthesis route), and this provides a plausible explanation of why $L{1}_{0}$ and not the $O$ phase is observed. Other ground states (not observed in experiments but predicted through calculations) are ruled out in terms of symmetry relations as well as through considerations of elastic barriers to their nucleation.