中国物理B ›› 2024, Vol. 33 ›› Issue (1): 16109-16109.doi: 10.1088/1674-1056/acd5c2

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Geometries and electronic structures of ZrnCu(n =2-12) clusters: A joint machine-learning potential density functional theory investigation

Yizhi Wang(王一志)1,2, Xiuhua Cui(崔秀花)1,2,†, Jing Liu(刘静)1,2, Qun Jing(井群)1,2, Haiming Duan(段海明)1,2,‡, and Haibin Cao(曹海宾)3   

  1. 1 Xinjiang Key Laboratory of Solid State Physics and Devices, Xinjiang University, Urumqi 830017, China;
    2 School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China;
    3 Department of Physics, College of Sciences, Shihezi University, Shihezi 832000, China
  • 收稿日期:2023-01-11 修回日期:2023-05-04 接受日期:2023-05-16 出版日期:2023-12-13 发布日期:2023-12-20
  • 通讯作者: Xiuhua Cui, Haiming Duan E-mail:xjcxh0991@xju.edu.cn;dhm@xju.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11864040, 11964037, and 11664038).

Geometries and electronic structures of ZrnCu(n =2-12) clusters: A joint machine-learning potential density functional theory investigation

Yizhi Wang(王一志)1,2, Xiuhua Cui(崔秀花)1,2,†, Jing Liu(刘静)1,2, Qun Jing(井群)1,2, Haiming Duan(段海明)1,2,‡, and Haibin Cao(曹海宾)3   

  1. 1 Xinjiang Key Laboratory of Solid State Physics and Devices, Xinjiang University, Urumqi 830017, China;
    2 School of Physical Science and Technology, Xinjiang University, Urumqi 830017, China;
    3 Department of Physics, College of Sciences, Shihezi University, Shihezi 832000, China
  • Received:2023-01-11 Revised:2023-05-04 Accepted:2023-05-16 Online:2023-12-13 Published:2023-12-20
  • Contact: Xiuhua Cui, Haiming Duan E-mail:xjcxh0991@xju.edu.cn;dhm@xju.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11864040, 11964037, and 11664038).

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摘要： Zr-based amorphous alloys have attracted extensive attention because of their large glassy formation ability, wide supercooled liquid region, high elasticity, and unique mechanical strength induced by their icosahedral local structures. To determine the microstructures of Zr—Cu clusters, the stable and metastable geometry of ZrnCu (n=2—12) clusters are screened out via the CALYPSO method using machine-learning potentials, and then the electronic structures are investigated using density functional theory. The results show that the ZrnCu (n≥ 3) clusters possess three-dimensional geometries, ZrnCu (n≥ 9) possess cage-like geometries, and the Zr12Cu cluster has icosahedral geometry. The binding energy per atom gradually gets enlarged with the increase in the size of the clusters, and ZrnCu (n=5, 7, 9, 12) have relatively better stability than their neighbors. The magnetic moment of most ZrnCu clusters is just 1μB, and the main components of the highest occupied molecular orbitals (HOMOs) in the Zr12Cu cluster come from the Zr-d state. There are hardly any localized two-center bonds, and there are about 20 σ-type delocalized three-center bonds.

关键词: geometries and electronic structures, magnetic and chemical bonds, machine learning potentials, Zr—Cu clusters

Abstract: Zr-based amorphous alloys have attracted extensive attention because of their large glassy formation ability, wide supercooled liquid region, high elasticity, and unique mechanical strength induced by their icosahedral local structures. To determine the microstructures of Zr—Cu clusters, the stable and metastable geometry of ZrnCu (n=2—12) clusters are screened out via the CALYPSO method using machine-learning potentials, and then the electronic structures are investigated using density functional theory. The results show that the ZrnCu (n≥ 3) clusters possess three-dimensional geometries, ZrnCu (n≥ 9) possess cage-like geometries, and the Zr12Cu cluster has icosahedral geometry. The binding energy per atom gradually gets enlarged with the increase in the size of the clusters, and ZrnCu (n=5, 7, 9, 12) have relatively better stability than their neighbors. The magnetic moment of most ZrnCu clusters is just 1μB, and the main components of the highest occupied molecular orbitals (HOMOs) in the Zr12Cu cluster come from the Zr-d state. There are hardly any localized two-center bonds, and there are about 20 σ-type delocalized three-center bonds.

Key words: geometries and electronic structures, magnetic and chemical bonds, machine learning potentials, Zr—Cu clusters

中图分类号:  (Structure of clusters (e.g., metcars; not fragments of crystals; free or loosely aggregated or loosely attached to a substrate))

  • 61.46.Bc
31.15.ej (Spin-density functionals) 36.40.-c (Atomic and molecular clusters) 36.40.Cg (Electronic and magnetic properties of clusters)