Full length articleInfluence of growth velocity variations on the pattern formation during the directional solidification of ternary eutectic Al-Ag-Cu
Graphical abstract
Introduction
It is well known that the scale of eutectic microstructures is dependent on solidification velocity. The relationship was first described by Jackson and Hunt, who observed that the lamellar or rod spacing is equal to the square root of velocity multiplied by some material-specific parameter [1]. These geometrically simple structures are convenient to treat, because a single characteristic length can be used to define the system, controlling both, solid-liquid interfacial curvature and diffusion length. Subsequent works showed the Jackson-Hunt scaling behavior to be consistent for more complex and faceted structures as well [2], [3], [4], including various arrangements of three-phase eutectic patterns [5]. In order to accommodate changes in length scale due to velocity adjustments, it is necessary for growing phases to split or overgrow at the solid-liquid interface. This has been extensively studied for binary eutectic growth using both, metallic and transparent organic systems [4], [6], [7], [8], in which these adjustment mechanisms are generally well understood. However, patterns in higher order eutectics can be far more complex, requiring different adjustment behaviors to respond to velocity changes. Likewise, a variety of patterns have been identified in three-phase eutectics, sometimes with different patterns occurring under the same experimental conditions [9], [10], [11], [12], [13], [14]. The way in which such three-phase eutectic systems respond to imposed changes in growth velocity has not previously been studied. Understanding the way in which pattern adjustment occurs is an important step to identify the fundamental parameters that control morphology development in multi-phase, multi-component systems.
In order to gain a more complete understanding of this complex behavior, a combination of experimental and simulation work was carried out. Recent advances in computer science now allow for large-scale, three-dimensional simulations to be carried out that reasonably approximate the behavior of the physical system [15], [16], [17], [18], [19]. Using Al-Ag-Cu as a model system, full 3D phase-field simulations of directionally solidified ternary eutectic growth are carried out. The results are compared to experimental results of the same alloy system. In order to capture the specific spacing adjustment mechanisms in three dimensions, X-ray synchrotron tomography is performed on small regions of the experimental samples where the velocity change have been imposed. Because tomography results are necessarily limited in scale, additional experimental work was done to measure the behavior of the system over longer length scales using individual cross-sectional images taken across the length of the sample.
The paper is structured in the following way: first, details of the experiments and simulations are provided. Then the results obtained by experiment and simulation are discussed and compared. Qualitative analysis is done via comparison of cross-sectional images of the microstructures; quantitative analysis is done via statistical analysis of phase fractions, shape factor and number of nearest neighbors. Finally, the implications and conclusions of these findings are discussed.
Section snippets
Setup
Experiments with Bridgman furnaces and simulations with a phase-field model based on the Grand potential approach are conducted to study the influence of growth velocity changes during the directional solidification of the ternary eutectic system Al-Ag-Cu. First, the experimental setup and the procedures to obtain the microstructures are described. Subsequently, the applied phase-field model and the simulation setup is presented.
Results and discussion
In the following, experimental and simulation results of the directionally solidified ternary eutectic Al-Ag-Cu are presented. First, qualitative analysis of the cross-sectional images is presented and afterwards statistics of phase fractions, average shape factors as well as nearest neighbor statistics are analyzed. In all statistics, simulations with velocity variations of , show trends similar to those found in the simulations, but less pronounced.
The phases Al, Ag2Al and Al2Cu are
Conclusion
In this work, combined experimental and simulation studies are conducted to investigate the influence of growth velocity variations on the microstructure evolution during the directional solidification of the ternary eutectic system Al-Ag-Cu. For this, the effects of velocity increases and decreases are studied with large-scale phase-field simulations as well as with experiments, analyzed by SEM and synchrotron tomography, providing information across widely varying length scales. The results
Acknowledgment
We thank the High Performance Computing Center Stuttgart and the Leibniz Rechenzentrum in Munich for computational resources. The authors from KIT acknowledge the funding of the cooperative graduate school “Gefügeanalyse und Prozessbewertung” by the Ministry of Baden-Wuerttemberg and financial support through the German Research Foundation (NE 822/14-2) within the project NE 822/14–2. Also authors from KIT and HSKA gratefully acknowledge the founding through the BMBF project “SKAMPY”. Anne
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The authors contributed equally.