Project title: Atomistic-to-continuum Theory of Martensitic Transformations
Supervisors: Dimitri Vvedensky, Lev Kantorovich (KCL), Carla Molteni (KCL)
A martensitic transformation, a non-diffusive phase transformation involving the coordinate shifts of atoms, is subjected to residual stresses generated at interfacial boundaries between variants within bulk materials, such as steels and alloys. The materials which undergo a reversible martensitic transformation exhibit hysteresis so, for example, they can be used as shape memory materials. An example of such a material is NiTi, which has been experimentally and theoretically studied for the understanding of the martensitic transformation. However, a full description including multiscale modelling of the martensitic transformation in NiTi has not yet been carried out. The equiatomic NiTi system is chosen as the main prototype in this work.
Previous research has calculated harmonic phonon dispersion curves of B2 structure along high- symmetry directions using density functional perturbation theory  and a direct method . The curves exhibit imaginary frequencies, which indicate the instability of B2 at the ground state. Thus, the quasi-harmonic approximation cannot be used to calculate thermodynamic properties of this system. A possible way to treat this problem is to use ab initio molecular dynamics (AIMD) to simulate the system at finite temperature and apply the method of temperature dependent effective potential (TDEP) [3,4] to obtain the phonon spectrum. For example, TDEP has been successfully used to construct the non-imaginary-frequencies phonon dispersion of Zr, which is highly anharmonic and unstable at zero temperature. This method is to use the information of forces, atomic displacements and energies from AIMD to fit with a model Hamiltonian, which, in principle, can include high-order terms of potential energy. Thus, one of the scopes of the present work is to implement the TDEP method and perform AIMD simulations of NiTi in order to construct phonon spectrum and calculate its phase diagram.
The data from first-principles calculations will be parametrised to time-dependent Ginzburg-Landau (TDGL) functional. The TDGL modelling can be used to study the kinetics of martensitic t!ransformation in NiTi microstructures.
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