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Phase Field Modeling
Definition:A computational method for simulating microstructure evolution.
Explanation:A central challenge in the modeling of microstructure formation is the fact that the position of the interfaces is not known in advance and it is regarded as the part of the solution of the problem. This is obvious during solidification, where latent heat is emitted at freezing fronts and solute is also partitioned. On the other hand, the motion of these interfaces depends on the local concentration and heat fluxes; i.e. diffusive transport couples with boundary conditions and front propagation conditions at the a priori unknown interface positions.

In contrast to sharp interface methods where complex interface tracking is pursued, phase field modeling follows an alternative strategy by introducing an order parameter or phase field, which discriminates among different phases. For example, a value of 1 would correspond to a local solid state, whereas 0 represents the melt phase. At the interfaces, the order parameter changes smoothly over a certain length scale. The crucial point is now that the evolution of the order parameter is described via partial differential equations in the entire computational domain, and a tracking of the interfaces is no longer needed.

Typical applications are related to solidification and solid state transformations. More recently, aspects as fracture have also been studied. Further recent extensions are the phase field crystal model, which resolves an atomic structure and are therefore capable to simulate grain boundaries. Moreover, amplitude equations methods contain atomic resolution, but are able to simulate large systems as entire polycrystalline structures.
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Diagram:

Left: Phase field modeling of dendritic solidification. Right: Polycrystalline solidification of iron, simulated with amplitude equations.
SFB-Link:In the project A5 and A9, phase field models are used for the description of hydrogen embrittlement. Solidification modeling using phase field techniques is done in project A8. Amplitude equations are used for modeling of grain boundary premelting and solid-melt gamma surfaces in project A9.
References:I. Steinbach, Modelling Simul. Mater. Sci. Eng. 17 (2009) 073001.
L.-Q. Chen, Annu. Rev. Mater. Res. 32 (2002) 113.
R. Spatschek, E. Brener, A. Karma, Phil. Mag. 91 (2010), 75.
K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. Lett. 88 (2001) 245701
R. Spatschek, A. Karma, Phys. Rev. B, 214201 (2010).