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Ta1–xHfxC和Ta1–xZrxC固溶体的结构稳定性和力学性质的第一性原理研究

张硕鑫 刘士余 严达利 余浅 任海涛 于彬 李德军

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Ta1–xHfxC和Ta1–xZrxC固溶体的结构稳定性和力学性质的第一性原理研究

张硕鑫, 刘士余, 严达利, 余浅, 任海涛, 于彬, 李德军

First-principles study of structural stability and mechanical properties of Ta1–xHfxC and Ta1–xZrxC solid solutions

Zhang Shuo-Xin, Liu Shi-Yu, Yan Da-Li, Yu Qian, Ren Hai-Tao, Yu Bin, Li De-Jun
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  • 随着航空航天领域的飞速发展, 极端的环境要求超高温陶瓷材料具有更好的力学性能和超高熔点. 目前, 单金属碳化物的超高温陶瓷材料承受的压力日渐增大. 为了解决过渡金属单碳化物性能不足的问题, 我们基于密度泛函理论系统地研究了Ta1–xHfxC和Ta1–xZrxC (0 ≤ x ≤ 1)固溶体的物理性质. 通过调节Hf和Zr的浓度来研究它们的结构稳定性、晶格参数、力学性能、熔点和电子结构. 我们的计算结果表明碳化物固溶体的稳定性随Hf/Zr含量的增加而增加, 并且当Hf/Zr含量相同时, Ta1–xZrxC比Ta1–xHfxC的结构更稳定. 我们还发现随着Hf/Zr含量的增加, 固溶体的晶格常数和体积会膨胀. Ta1–xHfxC和Ta1–xZrxC固溶体的体积模量随着Hf/Zr含量的增加而减小, 而固溶体的熔点、杨氏模量、剪切模量、维氏硬度和断裂韧性在掺杂含量x = 0.2处会出现峰值. 而且, 添加Hf和Zr可以提高TaC的耐磨性. 电子态密度结果显示随着Hf/Zr含量的增加, 固溶体费米能级处的态密度值逐渐降低, 这表明固溶体的结构稳定性逐渐增强.
    With the rapid development of the aerospace field, the harsh environment requires ultra-high temperature ceramic materials with better mechanical properties and ultra-high melting points. At present, the ultra-high temperature ceramic materials of single metal carbides are required more and more urgently. In order to solve the problem about the insufficient performance of transition metal single carbides, we systematically study the various physical properties of Ta1–xHfxC and Ta1–xZrxC solid solutions in an entire content range (0 ≤ x ≤ 1) based on density functional theory, including the formation energy, impurity formation energy, mixing energy, lattice parameters, elastic constants, elastic modulus, Vickers hardness, fracture toughness, wear resistance, melting point and electronic density of states. The results of formation energy show that with the increase of Hf and Zr doping concentration, the structural stability of Ta1–xHfxC and Ta1–xZrxC solid solutions gradually increase. And the structure of Ta1–xZrxC solid solution is more stable than that of Ta1–xHfxC solid solution when the doping content of Hf and Zr are the same. The results of mixing energy indicate that the formation of binary metal carbides from single metal carbides is an exothermic process. Furthermore, we also find that with the increase of Hf and Zr doping content, the lattice constant and volume of Ta1–xHfxC and Ta1–xZrxC solid solutions can expand, which is mainly attributed to the atomic radii of Hf and Zr being larger than the radius of Ta. The results of mechanical properties show that the Ta1–xHfxC and Ta1–xZrxC solid solution are brittle materials in the entire Hf/Zr content range and have mechanical stability. The bulk modulus of Ta1–xHfxC and Ta1–xZrxC solid solutions decrease with the increase of Hf and Zr content, while the melting point, Young's modulus, shear modulus, Vickers hardness and fracture toughness of Ta1–xHfxC and Ta1–xZrxC solid solutions have peaks with the doping content x = 0.2. Moreover, the addition of Hf/Zr can enhance the wear resistance of TaC. The results of the electronic density of states show that as the doping content increases, the density of states at the Fermi level of Ta1–xHfxC and Ta1–xZrxC solid solutions decrease, which also indicates that the solid solution structure becomes more and more stable.
      通信作者: 刘士余, buaasyliu@sohu.com
    • 基金项目: 国家自然科学基金(批准号: 61601327, 51772209, 11604244)和天津市自然科学基金(批准号: 17JCQNJC01000)资助的课题
      Corresponding author: Liu Shi-Yu, buaasyliu@sohu.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61601327, 51772209, 11604244) and the Natural Science Foundation of Tianjin, China (Grant No. 17JCQNJC01000)
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  • 图 1  (a)纯TaC的晶体结构; 掺杂含量x为(b) 0.25, (c) 0.5, (d) 0.75, (e) 1的Ta1–xHfxC/Ta1–xZrxC的晶体结构

    Fig. 1.  (a) The crystal structure of pure TaC; and the crystal structure Ta1–xHfxC or Ta1–xZrxC with doping content x of (b) 0.25, (c) 0.5, (d) 0.75, (e) 1.

    图 2  Ta1–xHfxC和Ta1–xZrxC固溶体的(a)形成能(Eform)和杂质形成能(Eimp)及(b)混合能(∆Emix)随着Hf或Zr含量x的变化图

    Fig. 2.  (a) The formation energy (Eform) and impurity formation energy (Eimp), and (b) mixing energy (∆Emix) of Ta1–xHfxC and Ta1–xZrxC solid solutions as a function of Hf or Zr content x.

    图 3  通过超胞(SC)方法和虚晶近似(VCA)方法比较Ta1–xHfxC和Ta1–xZrxC固溶体的(a)晶格常数和(b)体积随着Hf或Zr含量x的变化图

    Fig. 3.  Comparison of the (a) lattice constants and (b) volumes of the Ta1–xHfxC and Ta1–xZrxC solid solutions as a function of the Hf/Zr content by the supercell (SC) and virtual crystal approximation (VCA) methods.

    图 4  Ta1–xHfxC和Ta1–xZrxC固溶体的(a)弹性常数和(b)熔点随着Hf或Zr含量x的变化图

    Fig. 4.  (a) The elastic constants and (b) melting points for the Ta1–xHfxC and Ta1–xZrxC solid solutions as functions of the Hf or Zr content.

    图 5  Ta1–xHfxC和Ta1–xZrxC固溶体的力学性质随Hf或Zr含量x的变化 (a) B/G比; (b)泊松比; (c) 杨氏模量; (d) 体积模量; (e) 剪切模量; (f) 维氏硬度; (g) 断裂韧性; (h) 临界能量释放率

    Fig. 5.  The mechanical properties of Ta1–xHfxC and Ta1–xZrxC solid solutions as a function of the Hf/Zr content: (a) B/G ratio; (b) Poisson’s ratio; (c) Young’s modulus; (d) bulk modulus; (e) shear modulus; (f) Vickers hardness; (g) fracture toughness; (h) critical energy release rate.

    图 6  Ta1–xHfxC和Ta1–xZrxC固溶体的耐磨性随Hf或Zr含量x的变化图: (a) HV/E; (b) $ H_{\rm V}^3 $/E2

    Fig. 6.  The wear resistance of Ta1–xHfxC and Ta1–xZrxC solid solutions as a function of Hf or Zr content: (a) HV/E; (b) $ H_{\rm V}^3 $/E2.

    图 7  不同浓度的(a) Hf掺杂和(b) Zr掺杂TaC电子态密度(DOS)

    Fig. 7.  The electronic density of states (DOS) of (a) Hf-doped and (b) Zr-doped TaC with various doping contents.

  • [1]

    Kurbatkina V V, Patsrea E I, Vorotilo S A, Levashov E A, Timofeev A N 2016 Ceram. Int. 42 16491Google Scholar

    [2]

    Liu J X, Huang X, Zhang G J 2013 J. Am. Ceram. Soc. 96 1751Google Scholar

    [3]

    Patsrea E I, Levashov E A, Kurbatkina V V, Kovalev D Y 2015 Ceram. Int. 41 8885Google Scholar

    [4]

    Ghaffari S A, Faghihi-Sani M A, Golestani-Fard F, Mandal H 2013 J. Eur. Ceram. Soc. 33 1479Google Scholar

    [5]

    Hao W, Ni N, Guo F W, Cao F C, Jiang J, Zhao X F, Xiao P 2019 J. Am. Ceram. Soc. 102 997Google Scholar

    [6]

    Oyama S T 1996 The Chemistry of Transition Metal Carbides and Nitrides (Glasgow: Blackie Academic and Professional) pp1−27

    [7]

    Pierson H O 1996 Handbook of Refractory Carbides and Nitrides (New Jersey: Noyes Publications) pp5−16

    [8]

    Sciti D, Silvestroni L, Guicciardi S, Fabbriche D D, Bellosi A 2009 J. Mater. Res. 24 2056Google Scholar

    [9]

    Jiang D Y, Wang Q L, Hu W, Wei Z Q, Tong J B, Wan H Q 2016 J. Mater. Res. 31 3401Google Scholar

    [10]

    Adjaoud O, Steinle-Neumann G, Burton B P, Walle A 2009 Phys. Rev. B 80 134112Google Scholar

    [11]

    Wang X G, Liu J X, Kan Y M, Zhang G J 2012 J. Eur. Ceram. Soc. 32 1795Google Scholar

    [12]

    Simonenko E P, Ignatov N A, Simonenko N P, Ezhov Y S, Sevastyanov V G, Kuznetsov N T 2011 Russ. J. Inorg. Chem. 56 1681Google Scholar

    [13]

    Agte C, Alterthum H 1930 Z. Tech. Physik 11 182

    [14]

    Barraza O C, Grasso S, Nasiri N A, Jayaseelan D D, Reece M J, Lee W E 2016 J. Eur. Ceram. Soc. 36 1539Google Scholar

    [15]

    Smith C J, Yu X, Guo Q, Weinberger C R 2018 Acta. Mater. 145 142Google Scholar

    [16]

    Gladyshevsky E I, Fedorov T F, Gorshkova L V 1964 Russ. J. Inorg. Chem. 9 639

    [17]

    Avgustinik A I, Ordan’yan S S 1966 Zh. Prikl. Kim. 39 318

    [18]

    Rudy E 1969 Techn. Rep. AFML-TR 65 334

    [19]

    Yate L, Coy L E, Aperador W 2017 Sci. Rep. 7 3080Google Scholar

    [20]

    Segall M D, Lindan P L D, Probert M J, Pickard C J, Hasnip P J, Clark S J 2002 J. Phys. Condens. Matter 14 2717Google Scholar

    [21]

    Milman V, Winkler B, White J A, Pickard C J, Payne M C, Akhmatskaya E V, Nobes R H 2000 Int. J. Quantum Chem. 77 895Google Scholar

    [22]

    Li X, Chen X, Han L, Ruan C, Lu P, Guan P 2016 J. Mater. Res. 31 2956Google Scholar

    [23]

    Sun S, Fu H, Lin J, Guo G, Lei Y, Wang R 2018 J. Mater. Res. 33 495Google Scholar

    [24]

    Sun X W, Zhang X Y, Zhu Y Z, Zhang S H, Qin J Q, Ma M Z, Liu R P 2013 J. Mater. Sci. 48 7743Google Scholar

    [25]

    Hamann D R 1989 Phys. Rev. B 40 2980Google Scholar

    [26]

    Liu S Y, Liu S, Li D, Shen Y, Dang H, Liu Y, Xue W, Wang S 2014 J. Am. Ceram. Soc. 97 4019Google Scholar

    [27]

    Liu S Y, Zhang E, Liu S, Li D J, Li Y, Liu Y, Shen Y, Wang S 2016 J. Am. Ceram. Soc. 99 3336Google Scholar

    [28]

    Liu S Y, Meng Y, Liu S, Li D J, Li Y, Liu Y, Shen Y, Wang S 2017 J. Am. Ceram. Soc. 100 1221Google Scholar

    [29]

    Liu S Y, Meng Y, Liu S, Li D J, Li Y, Liu Y, Shen Y, Wang S 2017 Phys. Chem. Chem. Phys. 19 22190Google Scholar

    [30]

    Liu S Y, Chen Q Y, Liu S, Li D J, Li Y, Liu Y, Wang S 2018 J. Alloys Compd. 764 869Google Scholar

    [31]

    Liu S Y, Yu D S, Lv Y K, Li D J, Li Y, Cao M S 2013 Chin. Phys. B 22 017702Google Scholar

    [32]

    邵庆生, 刘士余, 赵辉, 余大书, 曹茂盛 2012 物理学报 61 047103Google Scholar

    Shao Q S, Liu S Y, Zhao H, Yu D S, Cao M S 2012 Acta Phys. Sin. 61 047103Google Scholar

    [33]

    刘士余, 余大书, 吕跃凯, 李德军, 曹茂盛 2013 物理学报 62 177102Google Scholar

    Liu S Y, Yu D S, Lv Y K, Li D J, Cao M S 2013 Acta Phys. Sin. 62 177102Google Scholar

    [34]

    Liu S Y, Shang J X, Wang F H, Zhang Y 2009 J. Phys. Condens. Matter. 21 225005Google Scholar

    [35]

    尚家香, 喻显扬 2008 物理学报 57 2380Google Scholar

    Shang J X, Yu X Y 2008 Acta Phys. Sin. 57 2380Google Scholar

    [36]

    尚家香, 于潭波 2009 物理学报 58 1179Google Scholar

    Shang J X, Yu X Y 2009 Acta Phys. Sin. 58 1179Google Scholar

    [37]

    Voigt W 1928 Lehrbuch der Kristallophysik Teuber-Leipzig (New York: Macmillan Publishers)

    [38]

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

    [39]

    Hill R 1952 Proc. Phys. Soc. A 65 349Google Scholar

    [40]

    Yang J, Gao F M 2012 Physica B: Condens. Matter 407 3527Google Scholar

    [41]

    Tian Y J, Xu B, Zhao Z H 2012 Int. J. Refract. Met. Hard. Mater 33 93Google Scholar

    [42]

    Niu H Y, Niu S W, Oganov A R 2019 J. Appl. Phys. 125 065105Google Scholar

    [43]

    Broek D 1982 Elementary Engineering Fracture Mechanics (3rd Ed.) (Netherlands: Martinus Nijhoff Publishers)

    [44]

    Yan X L, Constantin L, Lu Y F, Silvain J F, Nastasi M, Cui B 2018 J. Am. Ceram. Soc. 101 4486Google Scholar

    [45]

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

    [46]

    Wehr M R, Richards J A, Adair T W 1978 Physics of the Atom (Boston: Addison-Wesley Publishing Company)

    [47]

    Ha D G, Kim J, Han J S, Kang S 2018 Ceram. Int. 44 19247Google Scholar

    [48]

    Vorotilo S, Sidnov K, Mosyagin I Y, Khvan A V, Levashov E A, Patsera E I, Abrikosov I A 2019 J. Alloys Compd. 778 480Google Scholar

    [49]

    Huang B, Duan Y H, Sun Y, Peng M J, Chen S 2015 J. Alloys Compd. 635 213Google Scholar

    [50]

    Weber W 1973 Phys. Rev. B 8 5082Google Scholar

    [51]

    Li H, Zhang L T, Zeng Q F, Guan K, Li K Y, Ren H T, Liu S H, Cheng L F 2011 Solid State Commun. 151 602Google Scholar

    [52]

    Gautam G S, Hari Kumar K C 2014 J. Alloys. Compd. 587 380Google Scholar

    [53]

    Fine M E, Brown L D, Marcus H L 1984 Scr. Metall. 18 951Google Scholar

    [54]

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出版历程
  • 收稿日期:  2021-01-26
  • 修回日期:  2021-03-01
  • 上网日期:  2021-05-29
  • 刊出日期:  2021-06-05

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