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Role of interfacial energy and liquid diffusivities on pattern formation during thin-film three-phase eutectic growth

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Abstract

In this paper, we investigate three-phase eutectic growth during thin-film directional solidification of a model symmetric ternary eutectic alloy. In contrast to two-phase eutectics that have only a single possibility, \(\alpha \beta \alpha \beta \ldots \), as the growth pattern, during three-phase eutectic growth infinite possibilities exist. Here, we explore the possible existence of pattern selection influenced by the change in the solid–solid interfacial energies and the diffusivities. We begin the study by estimating the undercooling vs. spacing variation for the simplest possible configurations of pattern lengths 3 and 4, where phase-field simulations are utilized to quantify the influence of the solid–solid interfacial energy and the contrast in the component diffusivities. Subsequently, extended simulations consisting of multiple periods of \(\alpha \beta \delta \ldots \) as well as \(\alpha \beta \delta \beta \ldots \) are carried out for assessing the stability of the configurations to long-wavelength perturbations in spacing. Thereafter, growth competition among the simplest patterns is investigated through phase-field simulations of coupled growth of configurations of the type \(\left[ \alpha \beta \delta \right] _m\left[ \alpha \beta \delta \beta \right] _n\), (m, n) being the respective number of periods. Finally, pattern selection is studied by initializing with random initial configurations and classifying the emerging patterns based on the phase sequences. The principal finding is that, while there is no strong phase selection, between the solid–solid interfacial energies and the contrast in the component diffusivities, we find the latter to strongly influence pattern morphology.

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Acknowledgements

The authors would like to thank DST-SERB, India for funding through the project (DSTO1679). SK would like to thank SERC and TUE-CMS, IISc for providing access to high-performance computational resources, including the use of the SahasraT (Cray XC40) machine at SERC.

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  1. Department of Materials Engineering, Indian Institute of Science, Bengaluru, 560012, India

    Sumeet Khanna & Abhik Choudhury

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  1. Sumeet Khanna
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Correspondence to Abhik Choudhury.

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This study was funded by DST-SERB, India, through the project (DSTO1679). The authors declare that they have no conflict of interest.

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All the data required for the reproduction of the results in the paper are already mentioned in the paper. The phase-field code used for the generation of the results cannot be shared at this point of time; however all the details of the model formulation are present in the paper from which the code can be created.

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Khanna, S., Choudhury, A. Role of interfacial energy and liquid diffusivities on pattern formation during thin-film three-phase eutectic growth. J Mater Sci 56, 17646–17664 (2021). https://doi.org/10.1007/s10853-021-06434-8

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