搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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
PDF
HTML
导出引用
  • 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)
    [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]

    Yu X X, Thompson G B, Weinberger C R 2015 J. Eur. Ceram. Soc. 35 95Google Scholar

    [25]

    Yu X X, Weinberger C R, Thompson G B 2016 Comput. Mater. Sci. 112 318Google Scholar

    [26]

    Yu X X, Weinberger C R, Thompson G B 2014 Acta Mater. 80 341Google Scholar

    [27]

    Xie C, Liu N, Cheng X, Li D, Zeng Q 2016 J. Eur. Ceram. Soc. 36 3593Google Scholar

    [28]

    Xie C, Oganov A R, Li D, Debela T T, Liu N, Dong D, Zeng Q 2016 Phys. Chem. Chem. Phys. 18 12299Google Scholar

    [29]

    Zhang Y, Liu B, Wang J 2016 Sci. Rep. 5 18098Google Scholar

    [30]

    Gunda N S H, Van der Ven A 2018 Phys. Rev. Mater. 2 083602Google Scholar

    [31]

    Connolly J W D, Williams A R 1983 Phy. Rev. B 27 5169Google Scholar

    [32]

    Weinberger C R, Thompson G B 2018 J. Am. Ceram. Soc. 101 4401Google Scholar

    [33]

    Gusev A I, Rempel A A 1994 J. Phys. Chem. Solids 55 299Google Scholar

    [34]

    Yu S, Zeng Q, Oganov A R, Frapper G, Zhang L 2015 Phys. Chem. Chem. Phys. 17 11763Google Scholar

    [35]

    Yu S, Zeng Q, Oganov A R, Frapper G, Huang B, Niu H, Zhang L 2017 RSC Adv. 7 4697Google Scholar

    [36]

    樊涛, 曾庆丰, 于树印 2016 物理学报 65 118102Google Scholar

    Fan T, Zeng Q F, Yu S Y 2016 Acta Phys. Sin. 65 118102Google Scholar

    [37]

    Zhao Z L, Bao K, Tian F B, Duan D F, Liu B B, Cui T 2015 Phys. Chem. Chem. Phys. 17 22837Google Scholar

    [38]

    Li D, Tian F B, Duan D F, Bao K, Chu B, Sha X, Liu B B, Cui T 2014 RSC Adv. 4 10133Google Scholar

    [39]

    Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704Google Scholar

    [40]

    Lyakhov A O, Oganov A R, Stokes H T, Zhu Q 2013 Comput. Phys. Commun. 184 1172Google Scholar

    [41]

    Oganov A R, Lyakhov A O, Valle M 2011 Acc. Chem. Res. 44 227Google Scholar

    [42]

    Rudy E 1970 J. Less-Common Met. 20 49Google Scholar

    [43]

    Erniraliev A, Karimov I, Faizullaev F, Patiev M 1978 Kristallografiya 33 778

    [44]

    Karimov I, Em V T, Petrunin V F, Latergaus I S, Polishuk V S 1976 Materialy 12 1492

    [45]

    Em V T, Karimov I, Latergaus I S 1987 Metallofizika 9 113

    [46]

    Em V T, Tashmetov M Y 1996 Phys. Status Solidi B 198 571Google Scholar

    [47]

    Binder S, Lengauer W, Ettmayer P, Bauer J, Debuigne J, Bohn M 1995 J. Alloys Compd. 217 128Google Scholar

    [48]

    Hong Q J, van de Walle A 2015 Phys. Rev. B 92 020104Google Scholar

    [49]

    Buinevich V S, Nepapushev A A, Moskovskikh D O, Trusov G V, Kuskov K V, Vadchenko S G, Rogachev A S, Mukasyan A S 2020 Ceram. Int. 46 16068Google Scholar

    [50]

    Oganov A R 2011 Modern methods of crystal structure prediction (Weinheim: Wiley-VCR)

    [51]

    Kresse G, Furthmüller J 1996 Phys. Rev. B:Condens. Matter 54 11169Google Scholar

    [52]

    Blöchl P E 1994 Phys. Rev. B:Condens. Matter 50 17953Google Scholar

    [53]

    Perdew J P, Ruzsinszky A, Csonka G I, Vydrov O A, Scuseria G E, Constantin L A, Zhou X, Burke K 2008 Phys. Rev. Lett. 100 136406Google Scholar

    [54]

    Voigt W 1928 Lehrbuch der Kristallphysik (Leipzig, Germany: B. G. Teubner)

    [55]

    Reuss A 1929 Z. Angew. Math. Mech. 9 49Google Scholar

    [56]

    Hill R W 1952 Proc. Phys. Soc. London, Sect. A 65 349Google Scholar

    [57]

    Chen X Q, Niu H, Li D, Li Y 2011 Intermetallics 19 1275Google Scholar

    [58]

    Pugh S F 1954 Philos. Mag. 45 823Google Scholar

    [59]

    Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106Google Scholar

    [60]

    Momma K, Izumi F 2011 J. Appl. Crystallogr. 44 1272Google Scholar

    [61]

    Dronskowski R, Bloechl P E 1993 J. Phys. Chem. 97 8617Google Scholar

    [62]

    Hinuma Y, Pizzi G, Kumagai Y, Oba F, Tanaka I 2017 Comput. Mater. Sci. 128 140Google Scholar

    [63]

    Cowley R A 1976 Phys. Rev. B 13 4877Google Scholar

  • 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]

    Yu X X, Thompson G B, Weinberger C R 2015 J. Eur. Ceram. Soc. 35 95Google Scholar

    [25]

    Yu X X, Weinberger C R, Thompson G B 2016 Comput. Mater. Sci. 112 318Google Scholar

    [26]

    Yu X X, Weinberger C R, Thompson G B 2014 Acta Mater. 80 341Google Scholar

    [27]

    Xie C, Liu N, Cheng X, Li D, Zeng Q 2016 J. Eur. Ceram. Soc. 36 3593Google Scholar

    [28]

    Xie C, Oganov A R, Li D, Debela T T, Liu N, Dong D, Zeng Q 2016 Phys. Chem. Chem. Phys. 18 12299Google Scholar

    [29]

    Zhang Y, Liu B, Wang J 2016 Sci. Rep. 5 18098Google Scholar

    [30]

    Gunda N S H, Van der Ven A 2018 Phys. Rev. Mater. 2 083602Google Scholar

    [31]

    Connolly J W D, Williams A R 1983 Phy. Rev. B 27 5169Google Scholar

    [32]

    Weinberger C R, Thompson G B 2018 J. Am. Ceram. Soc. 101 4401Google Scholar

    [33]

    Gusev A I, Rempel A A 1994 J. Phys. Chem. Solids 55 299Google Scholar

    [34]

    Yu S, Zeng Q, Oganov A R, Frapper G, Zhang L 2015 Phys. Chem. Chem. Phys. 17 11763Google Scholar

    [35]

    Yu S, Zeng Q, Oganov A R, Frapper G, Huang B, Niu H, Zhang L 2017 RSC Adv. 7 4697Google Scholar

    [36]

    樊涛, 曾庆丰, 于树印 2016 物理学报 65 118102Google Scholar

    Fan T, Zeng Q F, Yu S Y 2016 Acta Phys. Sin. 65 118102Google Scholar

    [37]

    Zhao Z L, Bao K, Tian F B, Duan D F, Liu B B, Cui T 2015 Phys. Chem. Chem. Phys. 17 22837Google Scholar

    [38]

    Li D, Tian F B, Duan D F, Bao K, Chu B, Sha X, Liu B B, Cui T 2014 RSC Adv. 4 10133Google Scholar

    [39]

    Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704Google Scholar

    [40]

    Lyakhov A O, Oganov A R, Stokes H T, Zhu Q 2013 Comput. Phys. Commun. 184 1172Google Scholar

    [41]

    Oganov A R, Lyakhov A O, Valle M 2011 Acc. Chem. Res. 44 227Google Scholar

    [42]

    Rudy E 1970 J. Less-Common Met. 20 49Google Scholar

    [43]

    Erniraliev A, Karimov I, Faizullaev F, Patiev M 1978 Kristallografiya 33 778

    [44]

    Karimov I, Em V T, Petrunin V F, Latergaus I S, Polishuk V S 1976 Materialy 12 1492

    [45]

    Em V T, Karimov I, Latergaus I S 1987 Metallofizika 9 113

    [46]

    Em V T, Tashmetov M Y 1996 Phys. Status Solidi B 198 571Google Scholar

    [47]

    Binder S, Lengauer W, Ettmayer P, Bauer J, Debuigne J, Bohn M 1995 J. Alloys Compd. 217 128Google Scholar

    [48]

    Hong Q J, van de Walle A 2015 Phys. Rev. B 92 020104Google Scholar

    [49]

    Buinevich V S, Nepapushev A A, Moskovskikh D O, Trusov G V, Kuskov K V, Vadchenko S G, Rogachev A S, Mukasyan A S 2020 Ceram. Int. 46 16068Google Scholar

    [50]

    Oganov A R 2011 Modern methods of crystal structure prediction (Weinheim: Wiley-VCR)

    [51]

    Kresse G, Furthmüller J 1996 Phys. Rev. B:Condens. Matter 54 11169Google Scholar

    [52]

    Blöchl P E 1994 Phys. Rev. B:Condens. Matter 50 17953Google Scholar

    [53]

    Perdew J P, Ruzsinszky A, Csonka G I, Vydrov O A, Scuseria G E, Constantin L A, Zhou X, Burke K 2008 Phys. Rev. Lett. 100 136406Google Scholar

    [54]

    Voigt W 1928 Lehrbuch der Kristallphysik (Leipzig, Germany: B. G. Teubner)

    [55]

    Reuss A 1929 Z. Angew. Math. Mech. 9 49Google Scholar

    [56]

    Hill R W 1952 Proc. Phys. Soc. London, Sect. A 65 349Google Scholar

    [57]

    Chen X Q, Niu H, Li D, Li Y 2011 Intermetallics 19 1275Google Scholar

    [58]

    Pugh S F 1954 Philos. Mag. 45 823Google Scholar

    [59]

    Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106Google Scholar

    [60]

    Momma K, Izumi F 2011 J. Appl. Crystallogr. 44 1272Google Scholar

    [61]

    Dronskowski R, Bloechl P E 1993 J. Phys. Chem. 97 8617Google Scholar

    [62]

    Hinuma Y, Pizzi G, Kumagai Y, Oba F, Tanaka I 2017 Comput. Mater. Sci. 128 140Google Scholar

    [63]

    Cowley R A 1976 Phys. Rev. B 13 4877Google Scholar

  • [1] 计晨. 原子兰姆位移与超精细结构中的核结构效应. 物理学报, 2024, 73(20): 202101. doi: 10.7498/aps.73.20241063
    [2] 崔子纯, 杨莫涵, 阮晓鹏, 范晓丽, 周峰, 刘维民. 高通量计算二维材料界面摩擦. 物理学报, 2023, 72(2): 026801. doi: 10.7498/aps.72.20221676
    [3] 李君, 刘立胜, 徐爽, 张金咏. 单轴压缩下Ti3B4的力学、电学性能及变形机制的第一性原理研究. 物理学报, 2020, 69(4): 043102. doi: 10.7498/aps.69.20191194
    [4] 黄瑞, 李春, 金蔚, GeorgiosLefkidis, WolfgangHübner. 双磁性中心内嵌富勒烯Y2C2@C82-C2(1)中的超快自旋动力学行为. 物理学报, 2019, 68(2): 023101. doi: 10.7498/aps.68.20181887
    [5] 付宝勤, 侯氢, 汪俊, 丘明杰, 崔节超. 钨空位捕获氢及其解离过程的分子动力学. 物理学报, 2019, 68(24): 240201. doi: 10.7498/aps.68.20190701
    [6] 沙莎, 王伟丽, 吴宇昊, 魏炳波. 深过冷条件下Co7Mo6金属间化合物的枝晶生长和维氏硬度研究. 物理学报, 2018, 67(4): 046402. doi: 10.7498/aps.67.20172156
    [7] 王欣欣, 张颖, 周洪波, 王金龙. 铌对钨中氦行为影响的第一性原理研究. 物理学报, 2014, 63(4): 046103. doi: 10.7498/aps.63.046103
    [8] 牛海波, 陈光德, 伍叶龙, 耶红刚. 空位对纤锌矿型AlN自发极化影响的最大局域化Wannier函数方法研究. 物理学报, 2014, 63(16): 167701. doi: 10.7498/aps.63.167701
    [9] 黎军军, 赵学坪, 陶强, 黄晓庆, 朱品文, 崔田, 王欣. 二硼化钛的高温高压制备及其物性. 物理学报, 2013, 62(2): 026202. doi: 10.7498/aps.62.026202
    [10] 徐爽, 郭雅芳. 纳米铜薄膜塑性变形中空位型缺陷形核与演化的分子动力学研究. 物理学报, 2013, 62(19): 196201. doi: 10.7498/aps.62.196201
    [11] 魏哲, 袁健美, 李顺辉, 廖建, 毛宇亮. 含空位二维六角氮化硼电子和磁性质的密度泛函研究. 物理学报, 2013, 62(20): 203101. doi: 10.7498/aps.62.203101
    [12] 李宇波, 王骁, 戴庭舸, 袁广中, 杨杭生. 第一性原理计算研究立方氮化硼空位的电学和光学特性. 物理学报, 2013, 62(7): 074201. doi: 10.7498/aps.62.074201
    [13] 金硕, 孙璐. 带有碳杂质的钨中氢稳定性的第一性原理研究. 物理学报, 2012, 61(4): 046104. doi: 10.7498/aps.61.046104
    [14] 原鹏飞, 祝文军, 徐济安, 刘绍军, 经福谦. BeO高压相变和声子谱的第一性原理计算. 物理学报, 2010, 59(12): 8755-8761. doi: 10.7498/aps.59.8755
    [15] 李金, 桂贵, 孙立忠, 钟建新. 单轴大应变下二维六角氮化硼的结构变化. 物理学报, 2010, 59(12): 8820-8828. doi: 10.7498/aps.59.8820
    [16] 王超营, 王振清, 孟庆元. 空位的第一性原理及经验势函数的对比研究. 物理学报, 2010, 59(5): 3370-3376. doi: 10.7498/aps.59.3370
    [17] 顾娟, 王山鹰, 苟秉聪. Au和3d过渡金属元素混合团簇结构、电子结构和磁性的研究. 物理学报, 2009, 58(5): 3338-3351. doi: 10.7498/aps.58.3338
    [18] 宋庆功, 姜恩永, 裴海林, 康建海, 郭 英. 插层化合物LixTiS2中Li离子-空位二维有序结构稳定性的第一性原理研究. 物理学报, 2007, 56(8): 4817-4822. doi: 10.7498/aps.56.4817
    [19] 张 超, 王永亮, 颜 超, 张庆瑜. 替位杂质对低能Pt原子与Pt(111)表面相互作用影响的分子动力学模拟. 物理学报, 2006, 55(6): 2882-2891. doi: 10.7498/aps.55.2882
    [20] 胡晓君, 戴永兵, 何贤昶, 沈荷生, 李荣斌. 空位在金刚石近(001)表面扩散的分子动力学模拟. 物理学报, 2002, 51(6): 1388-1392. doi: 10.7498/aps.51.1388
计量
  • 文章访问数:  6222
  • PDF下载量:  120
  • 被引次数: 0
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

/

返回文章
返回