Towards a continuum theory for phase transformations using atomistic calculations

We develop a continuum theory for martensitic phase transformations in which explicit use is made of atomistic calculations based on density functional theory. Following the work of Rabe and coworkers, branches of the phonondispersion relation with imaginary frequencies are selected to construct a localized basis tailored to the symmetry of the crystal lattice. This so-called Wannier basis helps to construct an effective Hamiltonian of a particularly simple form. We extend the methodology by incorporating finite deformations and passing the effective Hamiltonian fully to continuum level. The developments so far are implemented on a one-dimensional unstable di-atomic chain.