Mechanism for BCC to HCP Transformation: Generalization of the Burgers Model

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Many structural transformations involve a group-nonsubgroup relationship between the initial and transformed phases, and hence are beyond the purview of conventional Landau theory. We utilize a systematic and robust methodology to describe such reconstructive martensitic transformations by coupling group-theoretical arguments to first-principles calculations. In this context we (i) use a symmetry-based algorithm to enumerate transformation paths, (ii) evaluate the energy barriers along these transformation paths using all-electron first principles calculations, (iii) deduce the full set of primary and secondary order parameters for each path to establish the appropriate Ginzburg-Landau free-energy functionals, and (iv) for each path, identify special points of the primary order parameter, as a function of local distortions, corresponding to the end product phase. We apply this method to the study of a pressure driven body-centered cubic (bcc) to hexagonal close-packed (hcp) transformation in titanium. We find a generalization of the Burgers mechanism, and also find that there is no energy barrier to this transformation. In fact, surprisingly, we also find a region of volumes in which the intermediate path becomes more stable than either of the end-points (bcc or hcp). We therefore predict a new orthorhombic phase for Ti between 51 and 62 GPa.