Estimating solid-liquid interfacial anisotropy using phase-field simulations and machine learning

G. Kim, S. Hyun, H. Ko
Korea Institute of Ceramics Engineering and Technology,

Keywords: CNN, Solid-liquid interface parameters, Solidification, Phase-field simulation


A dendrite is one of the most common growing patterns in solidification microstructures of metallic materials. The morphology of dendrite is primarily determined by anisotropy of solid-liquid interfacial energy, which is described by two anisotropy parameters e1 and e2. These parameters characterize and growth, respectively. Traditionally, only an effect of e1 has been considered in most of phase-field simulations for dendritic growth in cubic crystals, as the preferred growth direction in cubic crystals is generally assumed to be . However, it was reported that the growth morphology of Al-Zn alloy shifts from dendrite to seaweed and dendrite as Zn concentration increases [1]. This phenomenon implies that anisotropy parameters are influenced not only by the crystal structure but also by solute concentration. Therefore, it is important to accurately measure or estimate anisotropy parameters including their concentration dependency. However, the experimental measurements of these parameters are challenging. In this presentation, we introduce a novel approach for estimating anisotropy parameters (e1, e2) by integrating phase-field simulations with machine learning techniques [2]. We conducted phase-field simulation for isothermal solidification and continuous cooling in fcc binary alloy using various sets of e1 and e2. The resulting diverse microstructures were quantified into Interfacial Shape Distribution (ISD) map, which represents the probability of local interface curvedness and shape characteristics [3]. These ISD maps, with their corresponding (e1, e2) values, were trained using deep neural networks, particularly convolutional neural networks (CNN). We evaluated the accuracy of model, including the layer design, optimizer selection, and hyperparameter tuning for two distinct solidification processes: isothermal solidification and continuous cooling. [1] T. Haxhimali, A. Karma, F. Gonzales and M. Rappaz, Nat. Mater. 5 (2006) 660. [2] G. Kim, R. Yamada, T. Takaki, Y. Shibuta, and M. Ohno, Comput. Mater. Sci. 207 (2022) 111294. [3] J. Gibbs, K. Mohan, E. Gulsoy, A. Shahani, X. Xiao, C. Bouman, M. Graef, and P. Voorhees, Sci. Rep. 5 (2015) 11824.