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三元Hf-C-N体系的空位有序结构及其力学性质和电子性质的第一性原理研究

彭军辉 TikhonovEvgenii

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三元Hf-C-N体系的空位有序结构及其力学性质和电子性质的第一性原理研究

彭军辉, TikhonovEvgenii

First-principles study of vacancy ordered structures, mechanical properties and electronic properties of ternary Hf-C-N system

Peng Jun-Hui, Tikhonov Evgenii
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  • 采用第一性原理方法, 研究了三元Hf-C-N体系的空位有序结构及其力学性质和电子性质. 首先采用第一性原理和进化算法, 预测得到8种可能存在的热力学稳定的Hf-C-N空位有序结构; 这些结构都具有岩盐结构, 与实验发现的无序固溶体的结构类型一致. 本文的预测结果证明了Hf-C-N空位化合物能够以有序结构形式存在, 空位与C, N原子都位于[Hf6]八面体间隙, 这一结构特点与HfCx的相同. 然后采用第一性原理方法, 计算了Hf-C-N空位有序结构的力学性质, 发现除C∶N = 1∶4外, 相同C/N下, 随着空位浓度的增大, Hf-C-N的体模量、剪切模量、弹性模量、Pugh比、维氏硬度等降低; 而Hf6CN4 (空位浓度为1/6)的维氏硬度高于Hf5CN4 (无空位), 表现出空位硬化现象. 最后, 计算了Hf-C-N空位有序结构的态密度和晶体轨道哈密顿分布, 发现其具有强共价性和金属性; 且随着空位浓度增大, 总体键强减弱, 因而模量减小.
    The thermal-mechanical properties of transition metal carbonitrides can be affected by the concentration and ordering of vacancies besides the C/N atomic ratio. However, there are few reports on the vacancy ordered structure of ternary transition metal carbonitrides. In the present paper, the first-principles method is used to study the vacancy ordered structures, mechanical properties, electronic properties and the effect of vacancies on the ternary Hf-C-N system. Firstly, the crystal structures of Hf-C-N system is examined by the first-principles and evolutionary algorithms implemented in USPEX under ambient pressure, and eight thermodynamical stable vacancy ordered structures are found, each of which has a rock-salt structure, and is also dynamical and mechanical stable, which are verified by the calculations of their phonon dispersion curves and elastic constants. The vacancies are occupied at the [Hf6] octahedral interstices, which replace the positions of non-metal atoms. Their crystallographic data such as space group, lattice constants are also predicted. To the best of our knowledge, there is no report on the Hf-C-N vacancy ordered structures and these structures investigated here in this work are all found for the first time. Then their mechanical properties are calculated. The Hf-C-N vacancy ordered structures all have very high bulk, shear and elastic modulus and hardness. It is found that except for C∶N = 1∶4, for the Hf-C-N system with the same C/N ratio the moduli, Vickers hardness values, and Pugh’s ratios decrease with the increase of the concentration of vacancy. However, the Vickers hardness of Hf6CN4 (the concentration of vacancy is equal to 1/6) is higher than that of Hf5CN4 (no vacancy), that is so-called vacancy hardening. Finally, the electronic density of states and the crystal orbital Hamilton populations are calculated. The chemical bonding of Hf-C-N vacancy ordered structure is analyzed, which is a mixture of covalence and metallic and is similar to that of binary transition metal carbides and nitrides. With the increase of the concentration of vacancy, the total bond strength decreases, and then the modulus decreases for Hf-C-N compound.
      通信作者: TikhonovEvgenii, tikhonov.e@nwpu.edu.cn
    • 基金项目: 外国人才引进与学术交流项目(批准号: B08040)资助的课题
      Corresponding author: Tikhonov Evgenii, tikhonov.e@nwpu.edu.cn
    • Funds: Project supported by the Foreign Talents Introduction and Academic Exchange Program of China (Grant No. B08040)
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  • 图 1  (a) 常压下, 三元Hf-HfC-HfN体系的能量凸包图, 黑色球表示热力学稳定结构, 其他为亚稳结构; (b) Hf-C-N空位有序结构的X射线衍射模拟图谱, 衍射源为Cu Kα射线

    Fig. 1.  (a) Enthalpy convex-hull of ternary Hf-HfC-HfN system at ambient pressure. The black sphere indicates stable structure, and others are metastable structure. (b) The simulated X-ray diffractions of Hf-C-N vacancy ordered structures with a copper Kα X-ray source.

    图 2  Hf-C-N空位有序结构在某一晶面上的空位分布 (a) Hf6C4N-$C2 $/m (0 0 1); (b) Hf6C3N-$C2 $ (1 0 0); (c) Hf6C3N2-$C2 $/m (1 0 0); (d) Hf3CN-$C2 $ (1 0 0); (e) Hf6C2N3-$C2 $ (1 0 0); (f) Hf4CN2-Cmmm (0 0 1); (g) Hf6CN3-$C2 $/m (1 0 0); (h) Hf6CN4-$C2 $/m (0 0 1)

    Fig. 2.  Vacancies on the crystallographic plane: (a) Hf6C4N-$C2 $/m (0 0 1); (b) Hf6C3N-$C2 $ (1 0 0); (c) Hf6C3N2-$C2 $/m (1 0 0); (d) Hf3CN-$C2 $ (1 0 0); (e) Hf6C2N3-$C2 $ (1 0 0); (f) Hf4CN2-Cmmm (0 0 1); (g) Hf6CN3-$C2 $/m (1 0 0); (h) Hf6CN4-$C2 $/m (0 0 1).

    图 3  Hf-C-N空位有序结构的声子谱曲线 (a) Hf6C4N-$C2 $/m; (b) Hf6C3N-$C2 $; (c) Hf6C3N2-$C2 $/m; (d) Hf3CN-$C2 $; (e) Hf6C2N3-$C2 $; (f) Hf4CN2-Cmmm; (g) Hf6CN3-$C2 $/m; (h) Hf6CN4-$C2 $/m

    Fig. 3.  Phonon dispersion curves of (a) Hf6C4N-$C2 $/m, (b) Hf6C3N-$C2 $, (c) Hf6C3N2-$C2 $/m, (d) Hf3CN-$C2 $, (e) Hf6C2N3-$C2 $, (f) Hf4CN2-Cmmm, (g) Hf6CN3-$C2 $/m, (h) Hf6CN4-$C2 $/m. They are all dynamical stable because no imaginary frequencies were found in Brillouin zone.

    图 4  三元Hf-HfC-HfN体系的力学性质-组分相图 (a) 体模量(B); (b) 剪切模量(G ); (c) 弹性模量(E ); (d) 维氏硬度(HV); (e) Pugh比(G/B); (f) 泊松比(μ)

    Fig. 4.  Mechanical properties-composition diagrams of ternary Hf-HfC-HfN system: (a) Bulk modulus (B); (b) shear modulus (G ); (c) elastic modulus (E ); (d) Vickers hardness (HV); (e) Pugh’s ratio (G/B); (f) Poisson’s ratio (μ).

    图 5  (a) Hf6C4N-$C2 $/m, (b) Hf6C3N-$C2 $, (c) Hf6C3N2-$C2 $/m, (d) Hf3CN-$C2 $, (e) Hf6C2N3-$C2 $, (f) Hf4CN2-Cmmm, (g) Hf6CN3-$C2 $/m和(h) Hf6CN4-$C2 $/m的态密度和分态密度; (i) Hf3CN和Hf2CN的总态密度对比; 其中Fermi能级位于0 eV

    Fig. 5.  Density of state (DOS) and partial density of state (PDOS) normalized by per HfCxNy of (a) Hf6C4N-$C2 $/m, (b) Hf6C3N-$C2 $, (c) Hf6C3N2-$C2 $/m, (d) Hf3CN-$C2 $, (e) Hf6C2N3-$C2 $, (f) Hf4CN2-Cmmm, (g) Hf6CN3-$C2 $/m and (h) Hf6CN4-$C2 $/m; (i) the total DOS of Hf3CN and Hf2CN normalized by per HfCxNy. The Fermi level is at 0 eV.

    图 6  Hf-C-N化合物的晶体轨道哈密顿分布(–COHP), Fermi能级位于0 eV

    Fig. 6.  Crystal orbital Hamilton populations (–COHP) of Hf-C-N compounds. The Fermi level is at 0 eV.

    表 1  Hf-C-N空位有序结构的空间群、晶格常数、反应焓ΔH (eV/atom)、Hf原子的配位数(CN) 和空位浓度(CV)

    Table 1.  Space group, lattice constants, the enthalpy of reaction ΔH (eV/atom), coordination number (CN) of Hf and the concentration of vacancy (CV) of Hf-C-N vacancy ordered structures.

    CompoundSpace groupLattice constants/ÅΔH/(eV·atom–1)CNCV
    Hf6C4N$C2 $/ma = 5.679, b = 9.799, c = 5.671, β = 70.6o–0.089951/6
    Hf6C3N$C2 $a = 5.658, b = 9.763, c = 9.262, β = 144.8o–0.098041/3
    Hf6C3N2$C2 $ma = 5.660, b = 9.783, c = 5.619, β = 109.6o–0.103851/6
    Hf3CN$C2 $a = 5.632, b = 9.705, c = 5.625, β = 109.8o–0.110741/3
    Hf6C2N3$C2 $a = 5.624, b = 9.725, c = 5.602, β = 109.6o–0.104751/6
    Hf4CN2Cmmma = 6.427, b = 9.147, c = 3.235–0.10824/51/4
    Hf6CN3$C2 $/ma = 5.592, b = 9.658, c = 6.455, β = 125.3o–0.089441/3
    Hf6CN4$C2 $/ma = 5.580, b = 9.681, c = 5.587, β = 70.3o–0.081551/6
    下载: 导出CSV

    表 2  Hf-C-N空位有序结构的弹性常数Cij (单位: GPa)

    Table 2.  Calculated elastic constants Cij (in GPa) of Hf-C-N vacancy ordered structures.

    CompoundsC11C22C33C44C55C66C12C13C23
    Hf6C4N-$C2 $/m414.3406.6415.6158.0170.6148.794.1116.1104.5
    Hf6C3N-$C2 $358.5362.8352.2100.0114.3132.387.598.391.6
    Hf6C3N2-$C2 $/m414.6417.4407.6152.2157.6147.8111.9115.0116.3
    Hf3CN-$C2 $354.5363.5348.790.6103.6128.7102.1109.5101.3
    Hf6C2N3-$C2 $409.7418.7418.1149.6160.2148.9123.4122.9126.5
    Hf4CN2-Cmmm373.4368.8406.8142.2133.1135.8146.4112.0124.4
    Hf6CN3-$C2 $/m361.1358.4351.784.999.8124.9108.1121.7114.2
    Hf6CN4-$C2 $/m401.2414.1403.5146.5157.2139.8134.0139.9147.8
    下载: 导出CSV

    表 3  Hf-C-N空位有序结构和HfC1–xNx[19]的力学性质—体模量(B)、剪切模量(G )、弹性模量(E )、泊松比(μ)、Pugh比(G/B)、维氏硬度(HV)等

    Table 3.  Mechanical properties—bulk modulus (B), shear modulus (G ), elastic modulus (E ), Poisson’s ratio (μ), Pugh’s ratio (G/B), Vickers hardness (HV) of Hf-C-N vacancy ordered structures and HfC1–xNx[19].

    CompoundB /GPaG /GPaE /GPaμG/BHV /GPa
    Hf6C4N229.0140.8350.60.24490.614817.5
    Hf5C4N[19]260.6201.3480.30.19280.772729.9
    Hf6C3N180.9121.5297.90.22560.671717.8
    Hf4C3N[19]262.2202.1482.40.19340.770729.9
    Hf6C3N2214.0151.1366.90.21430.705922.1
    Hf3CN188.0113.4283.30.24890.603114.6
    Hf2CN[19]268.1198.5477.60.20310.740328.1
    Hf6C2N3221.3149.7366.60.22390.676620.7
    Hf4CN2212.7132.8329.70.24170.624217.1
    Hf3CN2[19]272.8185.1452.80.22330.678623.9
    Hf6CN3195.4108.9275.60.26500.557412.7
    Hf4CN3[19]276.2179.6442.80.23280.650422.2
    Hf6CN4207.2156.1374.40.19890.753524.6
    Hf5CN4[19]279.0171.5427.00.24490.614720.0
    下载: 导出CSV

    表 4  Hf-C-N化合物的晶体轨道哈密顿分布的积分值(–ICOHP)

    Table 4.  Integrated crystal orbital Hamilton populations (–ICOHP) of Hf-C-N compounds.

    Compound–ICOHPCompound–ICOHP
    Hf—CHf—NHf—HfHf—CHf—NHf—Hf
    Hf6C4N3.3733.5670.529Hf6C3N23.1812.9900.571
    Hf5C4N3.3733.0330.459Hf4CN23.4743.1110.650
    Hf6C3N3.3503.0670.718Hf3CN23.5513.0910.541
    Hf4C3N3.3193.0290.454Hf6CN33.4083.2110.570
    Hf6C3N23.6073.1030.530Hf4CN33.3213.1590.520
    Hf3CN3.2773.2110.737Hf6CN43.6753.1790.591
    Hf2CN3.4832.8020.490Hf5CN43.3193.0170.500
    下载: 导出CSV
  • [1]

    Squire T, Marschall J 2010 J. Eur. Ceram. Soc. 30 2239Google Scholar

    [2]

    Opeka M M, Talmy I G, Zaykosk J A 2004 J. Mater. Sci. 39 5887Google Scholar

    [3]

    Levine S R, Opila E J, Halbig M C, Kiser J D, Singh M, Salem J A 2002 J. Eur. Ceram. Soc. 22 2757Google Scholar

    [4]

    Ushakov SV, Navrotsky A 2012 J. Am. Ceram. Soc. 95 1463Google Scholar

    [5]

    Grill A, Aron P R 1983 Thin Solid Films 108 173Google Scholar

    [6]

    Helmersson U, Todorova S, Barnett S A, Sundgren J E, Markert L C, Greene J E 1987 J. Appl. Phys. 62 481Google Scholar

    [7]

    Mirkarimi P B, Hultman L, Barnett S A 1990 Appl. Phys. Lett. 57 2654Google Scholar

    [8]

    Veprek S, Veprek-Heijman M G J, Karvankova P, Prochazka J 2005 Thin Solid Films 476 1Google Scholar

    [9]

    Hultman L, Bareno J, Flink A, Soderberg H, Larsson K, Petrova V, Oden M, Greene J E, Petrov I 2007 Phys. Rev. B 75 155437Google Scholar

    [10]

    Shin C S, Gall D, Hellgren N, Patscheider J, Petrov I, Greene J E 2003 J. Appl. Phys. 93 6025Google Scholar

    [11]

    Jhi S H, Louie S G, Cohen M L, Ihm J 2001 Phys. Rev. Lett. 86 3348Google Scholar

    [12]

    Shin C S, Rudenja S, Gall D, Hellgren N, Lee T Y, Petrov I, Greene J E 2004 J. Appl. Phys. 95 356Google Scholar

    [13]

    Lee T, Ohmori K, Shin C S, Cahill D G, Petrov I, Greene J E 2005 Phys. Rev. B 71 144106Google Scholar

    [14]

    Holleck H 1986 J. Vac. Sci. Technol., A 4 2661Google Scholar

    [15]

    Yang Q, Lengauer W, Koch T, Scheerer M, Smid I 2000 J. Alloys Compd. 309 L5Google Scholar

    [16]

    Jhi S H, Ihm J, Louie S G, Cohen M L 1999 Nature 399 132Google Scholar

    [17]

    Feng W, Cui S, Hu H, Zhang G, Lü Z 2011 Physica B 406 3631Google Scholar

    [18]

    Balasubramanian K, Khare S V, Gall D 2018 Acta Mater. 152 175Google Scholar

    [19]

    Peng J, Tikhonov E 2021 Comput. Mater. Sci. 195 110464Google Scholar

    [20]

    Gusev A I, Rempel A A, Magerl A J 2001 Disorder and Order in Strongly Nonstoichiometric Compounds (Berlin Heidelberg: Springer) pp179−243

    [21]

    Gusev A I 1991 Physical Chemistry of Non stoichiometric Refractory Compounds (Moscow: Nauka) (in Russian)

    [22]

    Rudy E 1965 Ternary Phase Equilibria in Transition Metal-boron-carbon-silicon Systems. Part II. Ternary Systems. Vol. I. Ta-Hf-C system (Air Force Materials Laboratory, Wright-Patterson Air Force Base) pp38−60

    [23]

    Lipatnikov V N, Lengauer W, Ettmayer P, Keil E, Groboth G, Kny E 1997 J. Alloys Compd. 261 192Google Scholar

    [24]

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出版历程
  • 收稿日期:  2021-02-01
  • 修回日期:  2021-06-28
  • 上网日期:  2021-08-15
  • 刊出日期:  2021-11-05

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