A Phase-Field Study on the Effects of Nucleation Rate and Nanoparticle Distributions on Solidification and Grain Growth

Nanoparticle-reinforced alloys offer the potential for high-strength, high-temperature alloys. While the classic Smith–Zener equation is widely used to predict grain size with pinning particles, it does not explicitly factor the influence of nucleation rate, which is a critical phenomenon that affects microstructure. A model is developed using the open-source phase-field modeling software, PRISMS-PF, to explore the impact of nucleation rate on alloy solidification for both random and clustered distributions of nanoparticles. Heterogeneous nucleation and grain boundary pinning are explicitly included, and a wide range of nanoparticle area fractions (0.01–0.1) and nucleation site densities (106–1012nuclei/m2), which affect nucleation rates, are modeled. Quantitative analyses inform a kinetically modified Smith–Zener relationship, which predicts grain size dependence on nucleation rate as dz ~ 1/J*0.15. Simulations also reveal a strong preference of nanoparticle pinning grains, especially at triple points. Total pinning fraction increases rapidly with nucleation rate before saturating between 0.85 and 0.90 for both random and clustered 2D distributions. At low area fractions (< 0.05), particle clustering increases grain size between 15% and 45% compared to random distributions. A main advancement of this work is the quantification of how nucleation rate, in addition to nanoparticle size and concentration, affects grain size and therefore alloy strength.