Continuous transition from palladium clusters to nanocrystals simulated by machine learning potential
Phys. Rev. Materials 10, 046001 – Published 8 April, 2026
DOI: https://doi.org/10.1103/y1gy-9sfq
Abstract
The physical and chemical properties of clusters undergo significant changes with changes in size. Therefore, the evolution of cluster structure with size has always been an important issue in nanoscience. However, due to the complexity of cluster potential energy surfaces and limitations in computational simulation methods, the evolution of cluster structures has long been a challenge. Here, we developed a high-accuracy machine learning interatomic potential (MLIP) for palladium systems, including clusters, surfaces, and crystal. This MLIP enables a cross-scale () study of palladium systems from clusters to nanocrystal. For () clusters, simulated annealing revealed 32 new lower-energy structures. Small clusters (n < 85) show core-shell structures and repeated transitions from truncated to complete octahedra near FCC magic sizes (e.g., to to ). When the size exceeds 200, the Wulff construction becomes increasingly stable. There is competition among multiple structural modes (icosahedron, octahedron, and Wulff construction) within the range of 200–460. Beyond 460 atoms, Wulff constructions dominate and the system transfers from cluster to nanocrystal. Our work reveals continuous transition from Pd clusters to nanocrystal and the critical size, and paves the way for studies on other clusters.
Physics Subject Headings (PhySH)
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Machine Learning for Materials Discovery and Understanding
The Editors of Physical Review Materials are pleased to present the Collection on Machine Learning for Materials Discovery and Understanding, highlighting cutting-edge advances in machine learning method development and applications for materials discovery and fundamental understanding of the structure-property-function relationship. The Collection is being guest-edited by Deyu Lu of Brookhaven National Laboratory (USA) and Jinlan Wang of Southeast University (China). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.