RESUMO
We present a simple, quantitative, and thermodynamically self-consistent method of capturing density and pressure variation in continuum phase-change models. The formalism shows how the local state of homogenous dilation may be entirely given by species concentration in an Eulerian formulation. A hyperelastic contribution to the thermodynamic potential generalizes the lattice constraint while permitting composition, temperature, and phase-dependent specific volumes. We compare the results of models implementing this paradigm to those with the lattice constraint by examining the composition and size-dependent equilibrium of a Ni-Cu nanoparticle in its melt and free dendritic growth.
RESUMO
Highly anisotropic interfaces play an important role in the development of material microstructure. Using the diffusive atomistic phase-field crystal (PFC) formalism, we determine the capability of the model to quantitatively describe these interfaces. Specifically, we coarse grain the PFC model to attain both its complex amplitude formulation and its corresponding phase-field limit. Using this latter formulation, in one-dimensional calculations, we determine the surface energy and the properties of the Wulff shape. We find that the model can yield Wulff shapes with missing orientations, the transition to missing orientations, and facet formation. We show that the corresponding phase-field limit of the complex amplitude model yields a self-consistent description of highly anisotropic surface properties that are a function of the surface orientation with respect to the underlying crystal lattice. The phase-field model is also capable of describing missing orientations on equilibrium shapes of crystals and naturally includes a regularizing contribution. We demonstrate, in two dimensions, how the resultant model can be used to study growth of crystals with varying degrees of anisotropy in the phase-field limit.
