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稳态Cu-Zr二十面体团簇电子结构的密度泛函研究

蒋元祺 彭平

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稳态Cu-Zr二十面体团簇电子结构的密度泛函研究

蒋元祺, 彭平

Electronic structures of stable Cu-centered Cu-Zr icosahedral clusters studied by density functional theory

Jiang Yuan-Qi, Peng Ping
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  • 采用第一原理对以Cu为心的低能稳态CunZr13-n(n=6,7,8,9)二十面体团簇的电子结构进行计算,结果表明:同一化学组分下,以Cu为心的Cu-Zr二十面体团簇中出现的同类原子聚集现象可以增强团簇的稳定性,降低费米能级(EF)上的电子数N(EF),这为低能稳态团簇拥有较小的N(EF)提供了深层次的理论解释.进一步的差分电子密度与Mulliken布居分析得知,Cu-Zr二十面体中共价键与离子键共存,成键态与反键态共存,且团簇在形成时壳层Zr与中心Cu原子是电子的提供者,壳层Cu是电子的获得者.该电荷转移方向是金属玻璃中以Cu为心的Cu-Zr二十面体团簇普遍遵循的规律,不随团簇的化学序参数及化学组分的变化而变化.计算的红外振动谱为实验上准确表征不同二十面体原子团提供了一种新的思路.
    Cu-Zr alloy system,as a representative of transition metal-transition metal (TM-TM) metallic glass (MG),has attracted considerable attention due to its high glass-forming ability in a wide range of compositions.Many researchers have realized that the GFA of Cu-Zr alloy is intimately related to Cu-centered Cu-Zr icosahedral atomic cluster in supercooled liquid and rapidly solidified into amorphous solid.And lots of molecular dynamics simulations have shown that Cu-centered Cu-Zr icosahedral clusters not only affect the thermo-dynamical properties of metal or alloy melts,but also exhibit excellent structural stability and configuration heredity ability during the rapid solidification.Hereof a model of the metallic glass structure based on like icosahedron has become widely accepted,which plays an important role in the glass transition and its strong kinetic constraint on nucleation.However,though more and more standard and distorted Cu-Zr icosahedral clusters have been found and reported in Cu-Zr metallic glass,the fundamental understanding of these Cu-Zr icosahedral clusters of MGs is still lacking.More essential properties of Cu-centered Cu-Zr icosahedral cluster, especially on the electronic structure are still unclear.Based on this,as a further step towards in depth understanding the electronic structures of those icosahedral clusters,we will investigate the electronic structures of the stable Cucentered CunZr13-n (n=6,7,8,9) icosahedral clusters in this work,and consider all the possible atomic configurations for given chemical composition in view of originate in theory And a DMol3 molecular orbital package based on density functional theory (DFT) is adopted to calculate the energetics and electronic structures of Cu-centered Cu-Zr icosahedral clusters.During optimization and total energy calculation,electronic exchange-correlation energy functions in reciprocal space with the Perdew-Burke-Emzerhof type under general gradient approximate are used.A double-numerical basis set together with d-polarization functions (DNP) is chosen to describe the electronic wave functions of Cu and Zr atoms. And only core electrons described by the DFT Semi-core Pseudopots are calculated.All atomic positions in Cu-centered CunZr13-n (n=6,7,8,9) icosahedral clusters are relaxed by geometry optimization under a root mean square (RMS) force of 0.002 Ha/ and RMS displacement of 0.005 .The calculations of total energy and electronic structure are followed by the geometry optimization with self-consistent field tolerance of 110-5 Ha.It is found that homogeneous atoms in the shell of clusters with low binding energy prefer to bond to each other.In this case,the results of electronic structures reveal this segregation at low energy and stable configurations can be attributed to their low N (EF) at EF to some extent.A further analysis of Mulliken'population shows that these 4s and 4p of shell Cu atoms are all donees in the formation of icosahedral cluster,different from the donations of 3d and 4s of core Cu atoms and 5s of shell Zr atoms, and this charge transfer tendency does not change with order parameter nor chemical composition of Cu-centered Cu-Zr icosahedral cluster.In addition,calculating the infrared vibration spectrum of Cu-Zr icosahedral cluster is a new idea for accurately characterizing the cluster structure.
      通信作者: 蒋元祺, yuanqi325@163.com
    • 基金项目: 江西省青年科学基金(批准号:20171BAB216001)、江西省教育厅科技项目(批准号:GJJ161242)、南昌师范学院博士启动基金(批准号:NSBSJJ2015034)和国家自然科学基金(批准号:51071065)资助的课题.
      Corresponding author: Jiang Yuan-Qi, yuanqi325@163.com
    • Funds: Project supported by the Jiangxi Provincial Natural Science Foundation of China (Grant No. 20171BAB216001), the Scientific Research Project of Jiangxi Provincial Education Department, China (Grant No. GJJ161242), the Start-up Foundation of Doctor Scientific Research Projects of Nanchang Normal University, China (Grant No. NSBSJJ2015034), and the National Natural Science Foundation of China (Grant No. 51071065).
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  • [1]

    Klement W, Wiliens R H, Duwez P 1960 Nature 187 870

    [2]

    Wang W H 2013 Prog. Phys. 33 177 (in Chinese) [汪卫华 2013 物理学进展 33 177]

    [3]

    Cheng Y Q, Ma E 2011 Prog. Mater. Sci. 56 379

    [4]

    Jiang Y Q, Peng P, Wen D D, Han S C, Hou Z Y 2015 Comput. Mater. Sci. 99 156

    [5]

    Li M Z 2017 Acta Phys. Sin. 66 176107 (in Chinese) [李茂枝 2017 物理学报 66 176107]

    [6]

    Jiang Y Q, Wen D D, Peng P 2017 J. Molec. Liquids 230 271

    [7]

    Hirata A, Kang L J, Fujita T, Klumov B, Matsue K, Kotani M, Yavari A R, Chen M W 2013 Science 341 376

    [8]

    Yang L, Guo G Q, Chen L Y, Huang C L, Ge T, Chen D, Liaw P K, Saksl K, Ren Y, Zeng Q S, LaQua B, Chen F G, Jiang J Z 2012 Phys. Rev. Lett. 109 105502

    [9]

    Shen Y T, Kim T H, Gangopadhyay A K, Kelton K F 2009 Phys. Rev. Lett. 102 057801

    [10]

    Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419

    [11]

    Wen D D, Peng P, Jiang Y Q, Tian Z A, Liu R S 2013 Acta Phys. Sin. 62 196101 (in Chinese) [文大东, 彭平, 蒋元祺, 田泽安, 刘让苏 2013 物理学报 62 196101]

    [12]

    Hwang J, Melgarejo Z H, Kalay Y E, Kalay I, Kramer M J, Stone D S, Voyles P M 2012 Phys. Rev. Lett. 108 195505

    [13]

    Lee M, Lee M, Lee C, Lee K, Ma E, Lee J 2011 Acta Mater. 59 159

    [14]

    Deng Y H, Wen D D, Peng C, Wei Y D, Zhao R, Peng P 2016 Acta Phys. Sin. 65 066401 (in Chinese) [邓永和, 文大东, 彭超, 韦彦丁, 赵瑞, 彭平 2016 物理学报 65 066401]

    [15]

    Leocmach M, Tanaka H 2012 Nat. Commun. 3 974

    [16]

    Wen D D, Peng P, Jiang Y Q, Tian Z A, Liu R S, Dong K J 2014 J. Non-Cryst. Solids 388 75

    [17]

    Liu A C Y, Neish M J, Stokol G, Buckley G A, Smillie L A, de Jonge M D, Ott R T, Kramer M J, Bourgeois L 2013 Phys. Rev. Lett. 110 205505

    [18]

    Lekka C E, Evangelakis G A 2009 Scripta Mater. 61 974

    [19]

    Bokas G B, Lagogianni A E, Almyras G A, Lekka Ch E, Papageorgiou D G, Evangelakis G A 2013 Intermetallics 43 138

    [20]

    Sha Z D, Pan H, Pei Q X, Zhang Y W 2012 Intermetallics 26 8

    [21]

    Jiang Y Q 2015 Ph. D. Dissertation (Changsha: Hunan University) (in Chinese) [蒋元祺 2015 博士学位论文 (长沙: 湖南大学)]

    [22]

    Sha Z D, Pei Q X 2015 J. Alloys Compd. 619 16

    [23]

    Wang D, Zhao S J, Liu L M 2015 J. Phys. Chem. A 119 806

    [24]

    Delley B 2000 J. Chem. Phys. 113 7756

    [25]

    Delley B 1990 J. Chem. Phys. 92 508

    [26]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865

    [27]

    Nagel S R, Tauc J 1975 Phys. Rev. Lett. 35 380

    [28]

    Moruzzi V L, Oelhafen P, Williams A R 1983 Phys. Rev. B 27 7194

    [29]

    Goldberg A, Halls M D, Kung P, Liang J J 2009 J. Phys. B: Atomic, Molecular and Optical Physics 42 125103

    [30]

    Mulliken R S 1955 J. Chem. Phys. 23 1833

    [31]

    Mulliken R S 1955 J. Chem. Phys. 23 1841

    [32]

    Mulliken R S 1962 J. Chem. Phys. 36 3428

    [33]

    Peng L, Peng P, Wen D D, Liu Y G, Wei H, Sun X F, Hu Z Q 2011 Modell. Simul. Mater. Sci. Eng. 19 065002

    [34]

    Segall M D, Pickard C, Shah J R, Payne M C 2010 Mol. Phys. 89 571

    [35]

    Ohmura S, Shimojo F 2010 Phys. Rev. B. 81 014208

    [36]

    Segall M D, Shah R, Pickard C J, Payne M C 1996 Phys. Rev. B 54 16317

    [37]

    Yang L, Ge T, Guo G Q, Huang C L, Meng X F, Wei S H, Chen D, Chen L Y 2013 Intermetallics 34 106

    [38]

    Zhao L Z, Ma C L, Fu M W, Zeng X R 2012 Chem.Phys. Lett. 549 44

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出版历程
  • 收稿日期:  2018-02-06
  • 修回日期:  2018-04-19
  • 刊出日期:  2018-07-05

稳态Cu-Zr二十面体团簇电子结构的密度泛函研究

  • 1. 南昌师范学院物理系, 南昌 330032;
  • 2. 湖南大学材料科学与工程学院, 长沙 410082
  • 通信作者: 蒋元祺, yuanqi325@163.com
    基金项目: 江西省青年科学基金(批准号:20171BAB216001)、江西省教育厅科技项目(批准号:GJJ161242)、南昌师范学院博士启动基金(批准号:NSBSJJ2015034)和国家自然科学基金(批准号:51071065)资助的课题.

摘要: 采用第一原理对以Cu为心的低能稳态CunZr13-n(n=6,7,8,9)二十面体团簇的电子结构进行计算,结果表明:同一化学组分下,以Cu为心的Cu-Zr二十面体团簇中出现的同类原子聚集现象可以增强团簇的稳定性,降低费米能级(EF)上的电子数N(EF),这为低能稳态团簇拥有较小的N(EF)提供了深层次的理论解释.进一步的差分电子密度与Mulliken布居分析得知,Cu-Zr二十面体中共价键与离子键共存,成键态与反键态共存,且团簇在形成时壳层Zr与中心Cu原子是电子的提供者,壳层Cu是电子的获得者.该电荷转移方向是金属玻璃中以Cu为心的Cu-Zr二十面体团簇普遍遵循的规律,不随团簇的化学序参数及化学组分的变化而变化.计算的红外振动谱为实验上准确表征不同二十面体原子团提供了一种新的思路.

English Abstract

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