The kinetics of interfaces is inevitably very important for phase transformations. It causes in particular deviations from local equilibrium situations, as described by the bulk phase diagrams, at the interfaces between different phases. In particular for alloys it affects the entire microstructure formation and the concentrations in the growing phases. It can provoke the trapping of impurities in the growing phases and sometimes causes instabilitities of the growing fronts, which can lead to dendrites or banded structures.
In the bulk regions during isothermal solidification of alloys the dynamics is essentially described by diffusion equations. The interface, however, exhibits a much more complex behavior, as this is the region of the phase transformation additionally to diffusional exchange. In many cases the physical thickness of this interface region is small in comparison to the dimensions of the appearing patterns and can therefore be modeled as infinitely thin. This allows to link diffusional fluxes of the different atomic species to independent driving forces, which are related to the chemical potentials of the atoms. This link is established by Onsager relationships, which are strongly connected to deep physical symmetries.
In recent years, phase field models have become very popular for the modeling of alloy solidification. The most straightforward models are derived variationally from a free energy functional. However, these models typically suffer from limited accuracy of their predictions, as the phase field interface thickness, which is introduced as a numerical length scale parameter, needs to be small in comparison to the physical scales in order to provide quantitative results. For practical purposes, this is often hard to achieve due to the very large range of length scales present in the problem. The thin interface approach provides a way out of this dilemma, by leads to non-variational models. They, however, can lead to violations of the above Onsager symmetries.