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

doi:10.7498/aps.70.20210191

Abstract

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 Ta_1–xHf_xC and Ta_1–xZr_xC 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 Ta_1–xHf_xC and Ta_1–xZr_xC solid solutions gradually increase. And the structure of Ta_1–xZr_xC solid solution is more stable than that of Ta_1–xHf_xC 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 Ta_1–xHf_xC and Ta_1–xZr_xC 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 Ta_1–xHf_xC and Ta_1–xZr_xC solid solution are brittle materials in the entire Hf/Zr content range and have mechanical stability. The bulk modulus of Ta_1–xHf_xC and Ta_1–xZr_xC 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 Ta_1–xHf_xC and Ta_1–xZr_xC 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 Ta_1–xHf_xC and Ta_1–xZr_xC solid solutions decrease, which also indicates that the solid solution structure becomes more and more stable.

Keywords:

Authors and contacts

1.
College of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China
2.
Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Nankai University, Tianjin 300071, China

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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References

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[2]	Liu J X, Huang X, Zhang G J 2013 J. Am. Ceram. Soc. 96 1751 Google Scholar
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[9]	Jiang D Y, Wang Q L, Hu W, Wei Z Q, Tong J B, Wan H Q 2016 J. Mater. Res. 31 3401 Google Scholar
[10]	Adjaoud O, Steinle-Neumann G, Burton B P, Walle A 2009 Phys. Rev. B 80 134112 Google Scholar
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[38]	Reuss A 1929 Z. Angew. Math. Mech. 9 49 Google Scholar
[39]	Hill R 1952 Proc. Phys. Soc. A 65 349 Google Scholar
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[42]	Niu H Y, Niu S W, Oganov A R 2019 J. Appl. Phys. 125 065105 Google 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 4486 Google Scholar
[45]	Yu X X, Thompson G B, Weinberger C R 2015 J. Eur. Ceram. Soc. 35 95 Google 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 19247 Google 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. 778 480 Google Scholar
[49]	Huang B, Duan Y H, Sun Y, Peng M J, Chen S 2015 J. Alloys Compd. 635 213 Google Scholar
[50]	Weber W 1973 Phys. Rev. B 8 5082 Google 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. 151 602 Google Scholar
[52]	Gautam G S, Hari Kumar K C 2014 J. Alloys. Compd. 587 380 Google Scholar
[53]	Fine M E, Brown L D, Marcus H L 1984 Scr. Metall. 18 951 Google Scholar
[54]	Huang H M, Jiang Z Y and Luo S J 2017 Chin. Phys. B 26 096301 Google Scholar
[55]	Fahrenholtz W G, Hilmas G E, Talmy I G, Zaykoski J A 2007 J. Am. Ceram. Soc. 90 1347 Google Scholar
[56]	Ionescu E I, Bernard S, Lucas R, Kroll P, Ushakov S, Navrotsky A, Riedel R 2019 Adv. Eng. Mater. 21 1900269 Google Scholar
[57]	Pugh S F 1954 Phiosl. Mag.J. Sci. 45 823 Google Scholar
[58]	Liu Y Z, Jiang Y H, Zhou R, Feng J 2014 J. Alloys Compd. 582 500 Google Scholar
[59]	Jiang X, Zhao J J, Jiang X 2011 Comput. Mater Sci. 50 2287 Google Scholar
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[61]	Yadav D S, Verma J, Singh D P 2016 J. Pure Appl. Ind. Phys. 6 212
[62]	Brown H L, Kempter C P 1966 Phys. Stat. Sol. 18 K21 Google Scholar
[63]	Zhang J, McMahon J M 2021 J. Mater Sci. 56 4266 Google Scholar
[64]	Feng L, Fahrenholtz W G, Hilmas G E, Watts J, Zhou Y 2019 J. Am. Ceram. Soc. 102 5786 Google Scholar
[65]	Valenccia D P, Yate L, Aperador W, Li Y G, Coy E 2018 J. Phys. Chem. C 122 25433 Google Scholar
[66]	Silvestroni L, Pienti L, Guicciardi S, Sciti D 2015 Compos. Part B Eng. 72 10 Google Scholar
[67]	He L F, Bao Y W, Wang J Y, Li M S, Zhou Y C 2009 Acta. Mater. 57 2765 Google Scholar
[68]	Leyland A, Matthews A 2000 Wear 246 1 Google Scholar
[69]	Carlsson A E 1990 Advances in Research and Applications (New York: Academic Press)
[70]	Zhou J, Fu C L, Yoo M H, 1995 Phil. Mag. Lett. 71 45 Google Scholar
[71]	李荣, 罗小玲, 梁国明, 付文升 2011 60 117105 Google Scholar Li R, Luo X L, Liang G M, Fu W S 2011 Acta Phys. Sin. 60 117105 Google Scholar
[72]	Laverntyev A A, Gabrelian B V, Vorzhev V B, Nikiforov I Y, Khyzhun O Y, Rehr J J 2008 J. Alloys Compd. 462 4 Google Scholar

Cited By

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Ta_1–xHf_xC/Ta_1–xZr_xC的晶体结构

Figure 1. (a) The crystal structure of pure TaC; and the crystal structure Ta_1–xHf_xC or Ta_1–xZr_xC with doping content x of (b) 0.25, (c) 0.5, (d) 0.75, (e) 1.

DownLoad: Full-Size Img PowerPoint

图 2 Ta_1–xHf_xC和Ta_1–xZr_xC固溶体的(a)形成能(E_form)和杂质形成能(E_imp)及(b)混合能(∆E_mix)随着Hf或Zr含量x的变化图

Figure 2. (a) The formation energy (E_form) and impurity formation energy (E_imp), and (b) mixing energy (∆E_mix) of Ta_1–xHf_xC and Ta_1–xZr_xC solid solutions as a function of Hf or Zr content x.

DownLoad: Full-Size Img PowerPoint

图 3 通过超胞(SC)方法和虚晶近似(VCA)方法比较Ta_1–xHf_xC和Ta_1–xZr_xC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

Figure 3. Comparison of the (a) lattice constants and (b) volumes of the Ta_1–xHf_xC and Ta_1–xZr_xC solid solutions as a function of the Hf/Zr content by the supercell (SC) and virtual crystal approximation (VCA) methods.

DownLoad: Full-Size Img PowerPoint

图 4 Ta_1–xHf_xC和Ta_1–xZr_xC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

Figure 4. (a) The elastic constants and (b) melting points for the Ta_1–xHf_xC and Ta_1–xZr_xC solid solutions as functions of the Hf or Zr content.

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图 5 Ta_1–xHf_xC和Ta_1–xZr_xC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

Figure 5. The mechanical properties of Ta_1–xHf_xC and Ta_1–xZr_xC 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.

DownLoad: Full-Size Img PowerPoint

图 6 Ta_1–xHf_xC和Ta_1–xZr_xC固溶体的耐磨性随Hf或Zr含量x的变化图:　(a) H_V/E; (b) $ H_{\rm V}^3 $/E²

Figure 6. The wear resistance of Ta_1–_xHf_xC and Ta_1–_xZr_xC solid solutions as a function of Hf or Zr content: (a) H_V/E; (b) $ H_{\rm V}^3 $/E².

DownLoad: Full-Size Img PowerPoint

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

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

DownLoad: Full-Size Img PowerPoint

map

[1]	Kurbatkina V V, Patsrea E I, Vorotilo S A, Levashov E A, Timofeev A N 2016 Ceram. Int. 42 16491 Google Scholar
[2]	Liu J X, Huang X, Zhang G J 2013 J. Am. Ceram. Soc. 96 1751 Google Scholar
[3]	Patsrea E I, Levashov E A, Kurbatkina V V, Kovalev D Y 2015 Ceram. Int. 41 8885 Google Scholar
[4]	Ghaffari S A, Faghihi-Sani M A, Golestani-Fard F, Mandal H 2013 J. Eur. Ceram. Soc. 33 1479 Google Scholar
[5]	Hao W, Ni N, Guo F W, Cao F C, Jiang J, Zhao X F, Xiao P 2019 J. Am. Ceram. Soc. 102 997 Google 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 2056 Google Scholar
[9]	Jiang D Y, Wang Q L, Hu W, Wei Z Q, Tong J B, Wan H Q 2016 J. Mater. Res. 31 3401 Google Scholar
[10]	Adjaoud O, Steinle-Neumann G, Burton B P, Walle A 2009 Phys. Rev. B 80 134112 Google Scholar
[11]	Wang X G, Liu J X, Kan Y M, Zhang G J 2012 J. Eur. Ceram. Soc. 32 1795 Google 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 1681 Google 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 1539 Google Scholar
[15]	Smith C J, Yu X, Guo Q, Weinberger C R 2018 Acta. Mater. 145 142 Google 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 3080 Google 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 2717 Google 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. 77 895 Google Scholar
[22]	Li X, Chen X, Han L, Ruan C, Lu P, Guan P 2016 J. Mater. Res. 31 2956 Google Scholar
[23]	Sun S, Fu H, Lin J, Guo G, Lei Y, Wang R 2018 J. Mater. Res. 33 495 Google 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 7743 Google Scholar
[25]	Hamann D R 1989 Phys. Rev. B 40 2980 Google 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 4019 Google 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 3336 Google 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 1221 Google 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 22190 Google Scholar
[30]	Liu S Y, Chen Q Y, Liu S, Li D J, Li Y, Liu Y, Wang S 2018 J. Alloys Compd. 764 869 Google Scholar
[31]	Liu S Y, Yu D S, Lv Y K, Li D J, Li Y, Cao M S 2013 Chin. Phys. B 22 017702 Google Scholar
[32]	邵庆生, 刘士余, 赵辉, 余大书, 曹茂盛 2012 61 047103 Google Scholar Shao Q S, Liu S Y, Zhao H, Yu D S, Cao M S 2012 Acta Phys. Sin. 61 047103 Google Scholar
[33]	刘士余, 余大书, 吕跃凯, 李德军, 曹茂盛 2013 62 177102 Google Scholar Liu S Y, Yu D S, Lv Y K, Li D J, Cao M S 2013 Acta Phys. Sin. 62 177102 Google Scholar
[34]	Liu S Y, Shang J X, Wang F H, Zhang Y 2009 J. Phys. Condens. Matter. 21 225005 Google Scholar
[35]	尚家香, 喻显扬 2008 57 2380 Google Scholar Shang J X, Yu X Y 2008 Acta Phys. Sin. 57 2380 Google Scholar
[36]	尚家香, 于潭波 2009 58 1179 Google Scholar Shang J X, Yu X Y 2009 Acta Phys. Sin. 58 1179 Google Scholar
[37]	Voigt W 1928 Lehrbuch der Kristallophysik Teuber-Leipzig (New York: Macmillan Publishers)
[38]	Reuss A 1929 Z. Angew. Math. Mech. 9 49 Google Scholar
[39]	Hill R 1952 Proc. Phys. Soc. A 65 349 Google Scholar
[40]	Yang J, Gao F M 2012 Physica B: Condens. Matter 407 3527 Google Scholar
[41]	Tian Y J, Xu B, Zhao Z H 2012 Int. J. Refract. Met. Hard. Mater 33 93 Google Scholar
[42]	Niu H Y, Niu S W, Oganov A R 2019 J. Appl. Phys. 125 065105 Google 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 4486 Google Scholar
[45]	Yu X X, Thompson G B, Weinberger C R 2015 J. Eur. Ceram. Soc. 35 95 Google 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 19247 Google 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. 778 480 Google Scholar
[49]	Huang B, Duan Y H, Sun Y, Peng M J, Chen S 2015 J. Alloys Compd. 635 213 Google Scholar
[50]	Weber W 1973 Phys. Rev. B 8 5082 Google 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. 151 602 Google Scholar
[52]	Gautam G S, Hari Kumar K C 2014 J. Alloys. Compd. 587 380 Google Scholar
[53]	Fine M E, Brown L D, Marcus H L 1984 Scr. Metall. 18 951 Google Scholar
[54]	Huang H M, Jiang Z Y and Luo S J 2017 Chin. Phys. B 26 096301 Google Scholar
[55]	Fahrenholtz W G, Hilmas G E, Talmy I G, Zaykoski J A 2007 J. Am. Ceram. Soc. 90 1347 Google Scholar
[56]	Ionescu E I, Bernard S, Lucas R, Kroll P, Ushakov S, Navrotsky A, Riedel R 2019 Adv. Eng. Mater. 21 1900269 Google Scholar
[57]	Pugh S F 1954 Phiosl. Mag.J. Sci. 45 823 Google Scholar
[58]	Liu Y Z, Jiang Y H, Zhou R, Feng J 2014 J. Alloys Compd. 582 500 Google Scholar
[59]	Jiang X, Zhao J J, Jiang X 2011 Comput. Mater Sci. 50 2287 Google Scholar
[60]	Frantsevich I N, Voronov F F, Bokuta S A 1983 Elastic Constants and Elastic Moduli of Metals and Insulators (Kiev: Naukova Dumka) pp60−180
[61]	Yadav D S, Verma J, Singh D P 2016 J. Pure Appl. Ind. Phys. 6 212
[62]	Brown H L, Kempter C P 1966 Phys. Stat. Sol. 18 K21 Google Scholar
[63]	Zhang J, McMahon J M 2021 J. Mater Sci. 56 4266 Google Scholar
[64]	Feng L, Fahrenholtz W G, Hilmas G E, Watts J, Zhou Y 2019 J. Am. Ceram. Soc. 102 5786 Google Scholar
[65]	Valenccia D P, Yate L, Aperador W, Li Y G, Coy E 2018 J. Phys. Chem. C 122 25433 Google Scholar
[66]	Silvestroni L, Pienti L, Guicciardi S, Sciti D 2015 Compos. Part B Eng. 72 10 Google Scholar
[67]	He L F, Bao Y W, Wang J Y, Li M S, Zhou Y C 2009 Acta. Mater. 57 2765 Google Scholar
[68]	Leyland A, Matthews A 2000 Wear 246 1 Google Scholar
[69]	Carlsson A E 1990 Advances in Research and Applications (New York: Academic Press)
[70]	Zhou J, Fu C L, Yoo M H, 1995 Phil. Mag. Lett. 71 45 Google Scholar
[71]	李荣, 罗小玲, 梁国明, 付文升 2011 60 117105 Google Scholar Li R, Luo X L, Liang G M, Fu W S 2011 Acta Phys. Sin. 60 117105 Google Scholar
[72]	Laverntyev A A, Gabrelian B V, Vorzhev V B, Nikiforov I Y, Khyzhun O Y, Rehr J J 2008 J. Alloys Compd. 462 4 Google Scholar

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Vol. 70, Issue 11 - 2021-06-05

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