The Density and Molecular Phase Field Methods
Density phase field (DPF) methods have arisen as a means of more closely linking free energy functionals with grain boundary physics as opposed to using functionals that are purely phenomenological. In their current form, DPF methods exhibit a number of theoretical and computational problems that limit their applicability. These issues include the following:(1) being unable to simulate moving grain boundaries, (2) low computational performance due to high order gradient energy terms, and (3) failing to predict stable bulk equilibriums. We solve the mobility and performance issues mentioned above by coupling the density field of DPF simulations with traditional order parameters. The stable equilibrium problem is solved through the development of a criteria list that can be used to determine the set of DPF free energy functionals that correctly predict bulk equilibrium states. A subset of the free energy functionals that meet aforementioned criteria were identified and studied further because of their direct connection with atomistic physics. Termed the Molecular Phase Field (MoPF) method, these free energy functionals are constructed from interatomic potentials. Grain boundaries simulated using the MoPF method are material specific and their calculated excess energies are a natural consequence of the interatomic potential parameters used as model inputs. Lennard Jones, M-N, Mie, and Morse potential parameters have been calculated for over 30 different transition metals such that MoPF simulations of these metals may be carried out. Finally, MoPF models allow for the thermodynamic description of specific grain boundaries to be incorporated within phase field models such that the large variation in properties over the grain boundary phase space might be more accurately represented in phase field simulations.