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

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Abstract

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.

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Data Availability

The PRISMS-PF source code for this project is available at https://github.com/BryanKinzer/zener-pinning-PRISMS-PF. Raw data files are available upon request.

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Acknowledgements

The information, data or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), US Department of Energy, under Award Number DE-AR0001123 under cooperative agreement with Michigan State University and the University of Michigan. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Bala Chandran acknowledges startup funding from the College of Engineering and the Department of Mechanical Engineering at the University of Michigan. This research was supported in part through computational resources and services provided by Advanced Research Computing (ARC), a division of Information and Technology Services (ITS) at the University of Michigan, Ann Arbor. Authors acknowledge colleagues at the University of Michigan and Michigan State University: Dr. Luisa Barrera for sharing a MATLAB script to perform grain size analysis, Dr. Aditya Sundar, Dr. Andre Benard, Dr. Haseung Chung and Dr. Himanshu Sahasrabudhe for insightful conversations, and David Montiel for technical assistance on the PRISMS-PF software.

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Kinzer, B., Bala Chandran, R. A Phase-Field Study on the Effects of Nucleation Rate and Nanoparticle Distributions on Solidification and Grain Growth. JOM 76, 496–509 (2024). https://doi.org/10.1007/s11837-023-06221-7

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