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Cr-C体系材料是重要硬质防护涂层的代表，具有共晶特征.我们的前期工作指出，共晶合金满足双团簇近程序结构模型，由两种稳定液体亚单元构成，各自满足理想非晶团簇成分式，这里的第一近邻团簇来自相关共晶相.显然共晶成分解析的关键在于获得团簇，而相结构中往往存在多种团簇，进入到非晶/共晶团簇成分式的主团簇定义是关键环节.本文通过应用Friedel振荡理论及原子密堆，以团簇分布的球周期性及孤立度为判据，以Cr-C共晶相为例，进一步细化了共晶相中的主团簇选择流程，再搭配以2，4或6个连接原子，获得了描述共晶成分Cr86C14和Cr67.4C32.6的双团簇成分式：[Cr-Cr14+C-Cr9]CrC3和[C-Cr9+C-Cr8]C6，其中四种团簇分别来自共晶相Cr，Cr23C6，Cr7C3和Cr3C2.该工作进一步证实了团簇加连接原子模型在共晶点解析中的普适性，并从理论上支持了相关的材料设计.Cr-C system is an important protective coating material for its high hardness, good corrosion resistance and electrical conductivity. It is also a typical eutectic system, where all stable phases are involved in the eutectic reactions. According to our previous work, binary eutectic liquids satisfy the dual-cluster short-range-order structural model, i.e., a eutectic liquid is composed of two stable liquid subunits respectively issued from the two eutectic phases and each one formulates the same ideal metallic glass [cluster] (glue atom)1 or 3, where the nearest-neighbor cluster is derived from a devitrification phase. Therefore a eutectic liquid can always be formulated as two nearest-neighbor clusters plus two, four, or six glue atoms. The key step towards understanding a eutectic composition is then to obtain the right clusters from the two eutectic phases for use in the formulation of the glassy/eutectic composition, which we call the principal clusters. In this paper, Friedel oscillation and atomic dense packing theories are adopted to identify the principal clusters of Cr-C eutectic phases for the objective of establishing the dual cluster formulas for the eutectic compositions. First, clusters in eutectic phases Cr, Cr23C6, Cr7C3 and Cr3C2 are defined by assuming that all the nearest neighbors are located within the first negative potential minimum zone in Friedel oscillation, which causes a cutoff distance to be less than 1.5 times the innermost shell distance. Second, by comparing all the radial distribution profiles of total atomic density centered by each cluster in a given phase structure, the one exhibiting the most distinct spherical periodicity feature is selected as the principal cluster. Moreover, the principal clusters are the most separated from each other among all the clusters in the same phase, showing the highest degree of cluster isolation. Under the criteria of the cluster distribution following spherical periodicity order and of the cluster isolation, the following principal clusters are derived: rhombidodecahedron CN14 [Cr-Cr14] from Cr, capped trigonal prism CN9 [C-Cr9] from Cr23C6 and Cr7C3, and [C-Cr8] from Cr3C2. Via these examples, the principal cluster identification procedures are detailed. Third, the thus selected principal clusters are matched with appropriate glue atoms to construct the dual cluster formulas for the Cr-C eutectics Cr86C14 and Cr67.4C32.6, i.e., [Cr-Cr14+C-Cr9]CrC3Cr86.2C13.8 and [C-Cr9+C-Cr8]C6Cr68.0C32.0, respectively. This work proves the universality of the cluster-plus-glue-atom model in explaining the composition of binary eutectics and lays a theoretical foundation for the composition design of Cr-C based materials.
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Keywords:
- Cr-C /
- cluster-plus-glue-atom model /
- eutectics /
- principal cluster
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[1] Jellad A, Labdi S, Benameur T 2009 J. Alloy. Compd. 483 464
[2] Jelinek M, Kocourek T, Zemek J, Mikovsky J, Kubinov , Remsa J, Kopeček J, Jurek K 2015 Mater. Sci. Eng. C 46 381
[3] Taherian R 2014 J. Power Sources 265 370
[4] Wang H, Turner J A 2010 Fuel. Cells 10 510
[5] Miracle D B 2006 Acta Mater. 54 4317
[6] Tian H, Zhang C, Zhao J, Dong C, Wen B, Wang Q 2012 Physica B 407 250
[7] Shi L L, Xu J, Ma E 2008 Acta Mater. 56 3613
[8] Mudry S, Shtablavyi I, Shcherba I 2008 Arch. Mater. Sci. Eng. 34 14
[9] Pasturel A, Jakse N 2011 Phys. Rev. B 84 134201
[10] Sterkhova I V, Kamaeva L V 2014 J. Non-Cryst. Solids 401 241
[11] Guo J, Liu L, Liu S, Zhou Y, Qi X, Ren X, Yang Q 2016 Mater. Design 106 355
[12] Miracle D B 2004 Nat. Mater. 3 697
[13] Sheng H W, Luo W K, Alamgir F M, Bai J M, Ma E 2006 Nature 439 419
[14] Dong C, Wang Q, Qiang J B, Wang Y M, Jiang N, Han G, Li Y H, Wu J, Xia J H 2007 J. Phys. D: Appl. Phys. 40 R273
[15] Ma Y P, Dong D D, Dong C, Luo L J, Wang Q, Qiang J B, Wang Y M 2015 Sci. Rep. 5 17880
[16] Luo L J, Chen H, Wang Y M, Qiang J B, Wang Q, Dong C, Hussler P 2014 Philos. Mag. 94 2520
[17] Dong D D, Zhang S, Wang Z J, Dong C, Hussler P 2016 Mater. Design 96 115
[18] Miracle D B, Sanders W S, Senkov O N 2003 Philos. Mag. 83 2409
[19] Dong D D, Zhang S, Wang Z R, Dong C 2015 J. Appl. Crystallogr. 48 2002
[20] Friedel J 1958 Nuovo. Cimento. 7 287
[21] Hussler P 1992 Phys. Rep. 222 65
[22] Pearson W B, Villars P P, Calvert L D 1985 Pearson's Handbook of Crystallographic Data for Intermetallic Phases (Materials Park, Ohio: ASM International)
[23] Du J, Wen B, Melnik R, Kawazoe Y 2014 Acta Mater. 75 113
[24] Wu Z W, Li M Z, Wang W H, Liu K X 2015 Nat. Commun. 6 6035
[25] Wang Z R, Qiang J B, Wang Y M, Wang Q, Dong D D, Dong C 2016 Acta Mater. 111 366
[26] Oberle R, Beck H 1979 Solid State Commun. 32 959
[27] Nagel S R, Tauc J 1975 Phys. Rev. Lett. 35 380
[28] Hussler P 1985 J. Phys. Colloques 46 C8-361
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