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arXiv · 2512.21067

From cluster to nanocrystal: the continuous evolution and critical size of copper clusters revealed by machine learning

Hongsheng Liu·Luneng Zhao·Yaning Li·Yuan Chang·Shi Qiu·Xiao Wang·Junfeng Gao·Feng Ding
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Abstract

The evolution of cluster structure with size and the critical size for the transition from cluster to nanocrystal have long been fundamental problems in nanoscience. Due to limitations of experimental technology and computational methods, the exploration of the continuous evolution of clusters towards nanocrystal is still a big challenge. Here, we proposed a machine learning force field (MLFF) that can generalize well to various copper systems ranging from small clusters to large clusters and bulk. The continuous evolution of copper clusters CuN towards nanocrystal was revealed by investigating clusters in a wide size range (7 <= N <= 17885) based on MLFF simulated annealing. For small CuN (N < 40), electron counting rule plays a major role in stability. For large CuN (N > 80), geometric magic number rule plays a dominant role and the evolution of clusters is based on the formation of more and more icosahedral shells. For medium size CuN (40 <= N <= 80), both rules contribute. The critical size from cluster to nanocrystal was calculated to be around 8000 atoms (about 6 nm in diameter). Our work terminates the long-term challenge in nanoscience, and lay the methodological foundation for subsequent research on other cluster systems.

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Hongsheng Liu, Luneng Zhao, Yaning Li, Yuan Chang, Shi Qiu, Xiao Wang, Junfeng Gao, Feng Ding. 2025-12-24. From cluster to nanocrystal: the continuous evolution and critical size of copper clusters revealed by machine learning. https://arxiv.org/abs/2512.21067

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