Multi-phase-field modeling of the dissolution behavior of stoichiometric particles on experimentally relevant length scales

Abstract

The dissolution of stoichiometric particles within a melt plays a crucial role in various material processes. This study presents a comprehensive phase-field model to analyze the dissolution behavior of these stoichiometric particles under experimental conditions. Our approach addresses the classical phase-field challenges related to modeling stoichiometric compounds and scaling to experimentally relevant lengths in a multi-phase, multi-component context. To overcome the difficulties posed by stoichiometric compounds, we rederive the classical phase-field evolution equations for a multi-phase system, adopting a composition-independent free energy expression for the stoichiometric compound. Additionally, we extend Feyen’s high driving force model [Feyen and Moelans, Acta Materialia, 256 (2023)] to multi-component systems, allowing us to perform quantitative simulations for technologically relevant material systems at experimental length scales within a reasonable computing time. The model’s precision in capturing diffusion-controlled transformations, including dissolution, growth, and the Gibbs–Thomson effect, is validated against analytical solutions for a hypothetical system. The quantitative nature of the model is validated by applying it to the dissolution of Al₂O₃ particles in CaO–Al₂O₃–SiO₂ slags. We break new ground by conducting three-dimensional simulations for a system size of $875\mu m\times 875\mu m\times 875\mu m$, directly comparable to confocal scanning laser microscopy experiments, where previous models were limited to two-dimensional simulations and a system size of $2\mu m\times 2\mu m$. This validation underscores the model’s proficiency to quantitatively describe the diffusion-controlled dissolution of Al₂O₃ at the experimentally relevant length scales.