Michael Kellner

Quantitative Comparison of Ternary Eutectic Phase-Field Simulations with Analytical 3D Jackson–Hunt Approaches

For the analytical description of the relationship between undercoolings, lamellar spacings and growth velocities during the directional solidification of ternary eutectics in 2D and 3D, different extensions based on the theory of Jackson and Hunt are reported in the literature. Besides analytical approaches, the phase-field method has been established to study the spatially complex microstructure evolution during the solidification of eutectic alloys. The understanding of the fundamental mechanisms controlling the morphology development in multiphase, multicomponent systems is of high interest. For this purpose, a comparison is made between the analytical extensions and three-dimensional phase-field simulations of directional solidification in an ideal ternary eutectic system. Based on the observed accordance in two-dimensional validation cases, the experimentally reported, inherently three-dimensional chain-like pattern is investigated in extensive simulation studies. The results are quantitatively compared with the analytical results reported in the literature, and with a newly derived approach which uses equal undercoolings. A good accordance of the undercooling–spacing characteristics between simulations and the analytical Jackson–Hunt apporaches are found. The results show that the applied phase-field model, which is based on the Grand potential approach, is able to describe the analytically predicted relationship between the undercooling and the lamellar arrangements during the directional solidification of a ternary eutectic system in 3D.

Large-Scale Phase-Field Simulations of Directional Solidified Ternary Eutectics Using High-Performance Computing

The combination of different chemical elements allows to obtain new and improved materials, as required for novel applications. Especially directionally solidified multicomponent eutectic alloys exhibit a wide range of patterns in the microstructure, which are correlated to the mechanical properties. The pattern formation during solidification depends on the chemical elements and the applied process parameters. Large-scale phase-field simulations are used to study the pattern formation of directional solidified ternary eutectics. Three different systems, starting from a model system towards the system Al-Ag-Cu are investigated, using three growth velocities. The three-dimensional simulation results are quantitatively compared and a broad variety of arising patterns for the studied systems is found. The results of the velocity variation follow the predictions from the analytic Jackson-Hunt approach.

The Impact of Pores on Microstructure Evolution: A Phase-Field Study of Pore-Grain Boundary Interaction

Among the most important issues of today’s materials research ceramic materials play a key role as e.g. in Lithium batteries, in fuel cells or in photovoltaics. For all these applications a tailored microstructure is needed, which usually requires sintering: A pressed body of compacted powder redistributes its material and shrinks to a compact body without pores. In a very porous polycrystal, pores constrain the motion of interfaces (pore drag) and no grain growth occurs. During further sintering the number and size of pores decreases and the pore drag effect fades away. Accordingly, in the final stage of sintering grain growth emerges. This grain growth decreases the driving force for sintering and is undesirable, but hard to avoid. Since application of ceramic materials usually requires a dense and fine-grained microstructure, it is of high interest to control the interplay of remaining pores and interface migration during sintering.