  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.
