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Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems

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Abstract

Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morphology is the periodic arrangement of lamellar plates with well-defined orientations of the solid–solid interface in a given eutectic grain. It is typically believed that this form of morphology develops due to the presence of solid–solid interfacial energy anisotropy. In this paper, we provide evidence using phase-field simulations where our focus is on alloys where the minority phase fraction is low. Our aim is to establish the role of solid–solid interfacial energy anisotropy in the stabilization of broken lamellar structures in such systems in contrast to the formation of a rod microstructure. In this regard, we conduct phase-field simulations for different strengths of anisotropy in both constrained and extended settings, using which we clarify the mechanisms by which a lamellar arrangement gets stabilized in the presence of anisotropy in the solid–solid interfacial energy.

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Acknowledgments

The authors would like to thank DST-SERB 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. The authors would also like to thank Prof. Mathis Plapp for insightful discussions during the course of the work.

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

    Sumeet Khanna, Shanmukha Kiran Aramanda & Abhik Choudhury

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  1. Sumeet Khanna
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Correspondence to Abhik Choudhury.

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Manuscript submitted June 7, 2020.

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Appendices

Appendices

A. Non-dimensionalization of Simulation Parameters

The parameters used in the simulation are obtained through non-dimensionalization of the physical parameters. The procedure is enlisted below, where the asterisked values are defined as: \(T^{*} = 471.7,\) \(f^{*} = \dfrac{RT^{*}}{V_{\text {m}}},\) \(l^{*} = \dfrac{\sigma }{f^{*}}\) and \(t^{*} = \dfrac{{l^{*}}^{2}}{D}.\) Here, the values of molar volume \(V_{\text {m}} = 1.6\times 10^{-5}\,{\hbox {m}}^{3},\) interface energy \(\sigma = 0.104\,{\hbox {J}}\,{\hbox {m}}^{-2}\) and diffusivity \(D = 3.5\times 10^{-9}\,{\hbox {m}}^{2}\,{\hbox {s}}^{-1}\) are obtained from References 40, 60. Dividing the dimensional parameters with the corresponding asterisked (*) variables gives their non-dimensional values.

B. Numerical Consistency and Grid Resolution

The simulations have been checked for numerical accuracy against different grid resolutions (dx) and interface widths as shown in Figure AI.

Fig. AI
figure 17

Numerical consistency and grid resolution, checked with different interface widths

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Khanna, S., Aramanda, S.K. & Choudhury, A. Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems. Metall Mater Trans A 51, 6327–6345 (2020). https://doi.org/10.1007/s11661-020-05995-8

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