Phase-Field Modeling of Polycrystalline Solidification: From Needle Crystals to Spherulites—A Review

Quantitative PF simulations: In principle, quantitative computations are possible using the PF models, provided that the physical interface thickness is used (~1 nm). However, this would require an enormous computational power, especially if noise representing fluctuations is also considered. Prescribing a reasonable numerical resolution across the solid-liquid interface (say, 10 points), the spatial step falls on the Angstrom scale. A cubic micron requires then a grid of 10,000³, which is accessible at present only for the largest supercomputers. A further problem is that in the case of finite difference methods, the accessible time scale is restricted to nanoseconds, which means that only extreme undercoolings/fast processes can be addressed. While advanced methods (implicit scheme, adaptive grid) may ease these problems to some extent, they are difficult to parallelize efficiently. Evidently, one may perform the computations with a broad interface. However, it is accompanied with unwanted side effects such as enhanced solute trapping, different dynamics, etc.; so computations with broad interfaces can only be regarded as qualitative. To circumvent this impasse, methods were developed that use broad interfaces, however, with corrections that restore the proper growth dynamics and compositions.[55] These are termed as “quantitative PF models.” Unfortunately, in such models, nucleation cannot be realized by adding fluctuation-dissipation noise to the EOMs.