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First-principles calculations of stabilities and physical properties of ternary niobium borocarbides and tantalum borocarbides

Hu Qian-Ku Qin Shuang-Hong Wu Qing-Hua Li Dan-Dan Zhang Bin Yuan Wen-Feng Wang Li-Bo Zhou Ai-Guo

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First-principles calculations of stabilities and physical properties of ternary niobium borocarbides and tantalum borocarbides

Hu Qian-Ku, Qin Shuang-Hong, Wu Qing-Hua, Li Dan-Dan, Zhang Bin, Yuan Wen-Feng, Wang Li-Bo, Zhou Ai-Guo
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  • Transition-metal light-element compounds are potential candidates for hard materials. In the past, most of studies focused on the binary transition metal borides, carbides and nitrides, while the researches of ternary phases are relatively rare. In this paper, the structure units of the known Nb3B3C and Nb4B3C2 phases are first analyzed to be Nb6C octahedron and Nb6B triangular prism, respectively. By stacking the Nb6C octahedron and Nb6B triangular prism, twenty ternary Nb-B-C and twenty ternary Ta-B-C configurations with different compositions are constructed. The chemical formula of these Nb-B-C and Ta-B-C configurations can be defined to be Nb(m + n + 2)B(2m + 2)Cn and Ta(m + n + 2)B(2m + 2)Cn, respectively. Using first-principles density functional calculations, thermodynamical, dynamical and mechanical stabilities of the constructed ternary Nb-B-C and Ta-B-C configurations are investigated through calculating their enthalpies of formation, phonon dispersions and elastic constants. Five Nb-B-C (Nb3B3C, Nb4B3C2, Nb6B4C3, Nb7B4C4 and Nb7B6C3) phases and six Ta-B-C (Ta3B3C, Ta4B3C2, Ta6B4C3, Ta7B4C4, Ta7B6C3 and Ta3BC2) phases are predicted to be stable by analyzing the constructed ternary Nb-B-C and Ta-B-C phase diagrams, in which the seven phases (Nb6B4C3, Ta3B3C, Ta4B3C2, Ta6B4C3, Ta7B4C4, Ta7B6C3 and Ta3BC2) are first predicted to be stable. The Nb6B4C3, Ta6B4C3, Ta4B3C2 and Ta3B3C phases are stable when temperature is higher than 1730, 210, 360 and 1100 K, respectively. And the Ta3BC2 phase is stable only when temperature is lower than 130 K. The calculated results about mechanical and electric properties show that these Nb-B-C and Ta-B-C phases are conductive materials with a high hardness in a range of 23.8–27.4 GPa.
      Corresponding author: Zhou Ai-Guo, zhouag@hpu.edu.cn
    [1]

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

    [2]

    包括, 马帅领, 徐春红, 崔田 2017 物理学报 66 036104Google Scholar

    Bao K, Ma S L, Xu C H, Cui T 2017 Acta Phys. Sin. 66 036104Google Scholar

    [3]

    Zhou X F, Sun J, Fan Y X, Chen J, Wang H T, Guo X J, He J L, Tian Y J 2007 Phys. Rev. B 76 100101Google Scholar

    [4]

    Wu Q H, Hu Q K, Hou Y M, Wang H Y, Zhou A G, Wang L B 2018 J. Phys. Condens. Matter 30 385402Google Scholar

    [5]

    Tian Y J, Xu B, Yu D L, Ma Y M, Wang Y B, Jiang Y B, Hu W T, Tang C C, Gao Y F, Luo K, Zhao Z S, Wang L M, Wen B, He J L, Liu Z Y 2013 Nature 493 385Google Scholar

    [6]

    Huang Q, Yu D L, Xu B, Hu W T, Ma Y M, Wang Y B, Zhao Z S, Wen B, He J L, Liu Z Y, Tian Y J 2014 Nature 510 250Google Scholar

    [7]

    徐波, 田永君 2017 物理学报 66 036201Google Scholar

    Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201Google Scholar

    [8]

    Wu Q H, Hu Q K, Hou Y M, Wang H Y, Zhou A G, Wang L B, Cao G H 2018 Mater. Des. 140 45Google Scholar

    [9]

    Cumberland R W, Weinberger M B, Gilman J J, Clark S M, Tolbert S H, Kaner R B 2005 J. Am. Chem. Soc. 127 7264Google Scholar

    [10]

    Chung H Y, Weinberger M B, Levine J B, Kavner A, Yang J M, Tolbert S H, Kaner R B 2007 Science 316 436Google Scholar

    [11]

    Gregoryanz E, Sanloup C, Somayazulu M, Badro J, Fiquet G, Mao H K, Hemley R J 2004 Nat. Mater. 3 294Google Scholar

    [12]

    Young A F, Sanloup C, Gregoryanz E, Scandolo S, Hemley R J, Mao H K 2006 Phys. Rev. Lett. 96 155501Google Scholar

    [13]

    Ivanovskii A L 2012 Prog. Mater. Sci. 57 184Google Scholar

    [14]

    陶强, 马帅领, 崔田, 朱品文 2017 物理学报 66 036103Google Scholar

    Tao Q, Ma S L, Cui T, Zhu P W 2017 Acta Phys. Sin. 66 036103Google Scholar

    [15]

    Hillebrecht H, Gebhardt K 2001 Angew. Chem. Int. Ed. 40 1445Google Scholar

    [16]

    胡前库, 侯一鸣, 吴庆华, 秦双红, 王李波, 周爱国 2019 物理学报 68 096201Google Scholar

    Hu Q K, Hou Y M, Wu Q H, Qin S H, Wang L B, Zhou A G 2019 Acta Phys. Sin. 68 096201Google Scholar

    [17]

    Wang P F, Weng M Y, Xiao Y, Hu Z X, Li Q H, Li M, Wang Y D, Chen X, Yang X N, Wen Y R, Yin Y X, Yu X Q, Xiao Y G, Zheng J X, Wan L J, Pan F, Guo Y G 2019 Adv. Mater. 31 1903483Google Scholar

    [18]

    Xiao W J, Xin C, Li S B, Jie J S, Gu Y, Zheng J X, Pan F 2018 J. Mater. Chem. A 6 9893Google Scholar

    [19]

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

    [20]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [21]

    Le Page Y, Saxe P 2002 Phys. Rev. B 65 104104Google Scholar

    [22]

    Togo A, Tanaka I 2015 Scr. Mater. 108 1Google Scholar

    [23]

    Togo A, Chaput L, Tanaka I, Hug G 2010 Phys. Rev. B 81 174301Google Scholar

    [24]

    Mouhat F, Coudert F X 2014 Phys. Rev. B 90 224104Google Scholar

    [25]

    Wu Z J, Zhao E J, Xiang H P, Hao X F, Liu X J, Meng J 2007 Phys. Rev. B 76 054115Google Scholar

    [26]

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

    [27]

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

  • 图 1  (a), (b) Ta3B3C; (c) Ta4B3C2; (d) Ta3BC2; (e) Ta6B4C3; (f) Ta7B4C4; (g) Ta7B6C3的晶体结构. 棕球: Ta原子; 蓝球: B原子; 粉球: C原子. Ta6B三棱柱和Ta6C八面体分别用绿色和褐色表示

    Figure 1.  The crystal structures of (a), (b) Ta3B3C; (c) Ta4B3C2; (d) Ta3BC2; (e) Ta6B4C3; (f) Ta7B4C4; (g) Ta7B6C3. The light brown, blue and pink spheres represent Ta, B, and C atoms, respectively. The Ta6B triangular prisms and Ta6C octahedrons are painted green and dark brown.

    图 2  (a) Nb-B-C和(b) Ta-B-C三元相图. 红色, 稳定相; 蓝色, 亚稳相; 绿色, 不稳定相

    Figure 2.  Ternary phase diagrams of (a) Nb-B-C and (b) Ta-B-C. Red, stable; blue, metastable; green, unstable.

    图 3  不同温度下 (a) Nb-B-C和(b) Ta-B-C三元相分别和其相应最稳定竞争组合相的自由能之差

    Figure 3.  Energy differences of (a) Nb-B-C and (b) Ta-B-C ternary phases with respect to their most competing phases as a function of temperature.

    图 4  Nb-B-C和Ta-B-C三元相的声子色散曲线

    Figure 4.  Phonon dispersion curves of Nb-B-C and Ta-B-C ternary phases.

    图 5  Nb-B-C和Ta-B-C三元相的态密度图

    Figure 5.  Density of states of Nb-B-C and Ta-B-C ternary phases.

    表 1  不同成分Nb(m + n + 2)B(2m + 2)Cn和Ta(m + n + 2)B(2m + 2)Cn晶体的结构参数

    Table 1.  Structural parameters of Nb(m + n + 2)B(2m + 2)Cn and Ta(m + n + 2)B(2m + 2)Cn crystals.

    mn空间群模型晶格参数/Å模型晶格参数/Å
    abcabc
    01CmmmNb3B2C3.25413.8083.141Ta3B2C3.24013.6973.127
    02CmcmNb2BC3.23518.3303.153Ta2BC3.22018.1653.140
    03CmmmNb5B2C33.22522.9033.153Ta5B2C33.19922.6593.138
    04CmcmNb3BC23.21427.3763.156Ta3BC23.19827.1323.150
    11PmmmNb4B4C3.29018.9943.145Ta4B4C3.27718.8783.127
    12ImmmNb5B4C23.26723.6003.150Ta5B4C23.24823.3773.138
    13PmmmNb6B4C33.24328.0283.154Ta6B4C33.22527.8723.141
    14ImmmNb7B4C43.24232.5453.158Ta7B4C43.22432.3153.147
    21CmmmNb5B6C3.30224.4143.134Ta5B6C3.28924.2083.122
    22CmcmNb3B3C3.28428.8773.144Ta3B3C3.26728.6883.133
    23CmmmNb7B6C33.26433.3643.148Ta7B6C33.24633.1643.136
    24CmcmNb4B3C23.25737.8743.153Ta4B3C23.24337.6093.141
    31PmmmNb6B8C3.30914.8893.137Ta6B8C3.29814.7883.122
    32ImmmNb7B8C23.29034.2473.144Ta7B8C23.27634.0073.131
    33PmmmNb8B8C33.27619.3503.148Ta8B8C33.25819.2353.135
    34ImmmNb9B8C43.26843.2553.151Ta9B8C43.25242.9773.138
    41CmmmNb7B10C3.31235.1923.131Ta7B10C3.29934.9903.116
    42CmcmNb4B5C3.29639.6943.139Ta4B5C3.28039.4413.125
    43CmmmNb9B10C33.28144.2063.142Ta9B10C33.26343.9243.130
    44CmcmNb5B5C23.27348.7293.145Ta5B5C23.25748.4003.134
    DownLoad: CSV

    表 2  不同成分Nb-B-C相和Ta-B-C相的形成焓 (单位: eV/atom), $ \Delta{H}_{\rm{elements}} $表示单质为反应物, $ \Delta{H}_{\rm{comp}} $表示最稳定竞争组合为反应物

    Table 2.  Calculated formation enthalpies of different Nb-B-C and Ta-B-C phases (in eV/atom).$ \Delta{H}_{\rm{elements}} $ represents the elements as the reactants, and $\Delta{H}_{\rm{comp}}$ indicates the most stable composite as the reactants.

    Phases$ \Delta{H}_{\rm{elements}} $$ \Delta{H}_{\rm{comp}} $最稳定竞争组合Phases$ \Delta{H}_{\rm{elements}} $$ \Delta{H}_{\rm{comp}} $最稳定竞争组合
    Nb3B2C–0.6200.070Nb3B4 + 6NbB + Nb6C5 = 5Nb3B2CTa3B2C–0.6510.086Ta3BC2 + 3TaB = 2Ta3B2C
    Nb2BC–0.6190.029Nb3B4 + NbB + Nb6C5 = 5Nb2BCTa2BC–0.6640.035Ta3BC2 + TaB = 2Ta2BC
    Nb5B2C3–0.5860.0363Nb3B4 + Nb7B4C4 + 4Nb6C5 = 8Nb5B2C3Ta5B2C3–0.6550.0213Ta3BC2 + TaB = 2Ta5B2C3
    Nb3BC2–0.5860.019Nb3B4 + 3Nb7B4C4 + 4Nb6C5 = 16Nb3BC2Ta3BC2–0.660–0.002TaB + 2TaC = Ta3BC2
    Nb4B4C–0.6790.0303Nb3B4 + Nb7B4C4 = 4Nb4B4CTa4B4C–0.6910.044Ta7B4C4 + 3Ta3B4 = 4Ta4B4C
    Nb5B4C2–0.6680.006Nb3B4 + Nb7B4C4 = 2Nb5B4C2Ta5B4C2–0.6940.019Ta7B4C4 + Ta3B4 = 2Ta5B4C2
    Nb6B4C3–0.6450.005Nb3B4 + 3Nb7B4C4 = 4Nb6B4C3Ta6B4C3–0.6930.0043Ta7B4C4 + Ta3B4 = 4Ta6B4C3
    Nb7B4C4–0.632–0.0063Nb3B4 + 2C + 2Nb6C5 = 3Nb7B4C4Ta7B4C4–0.685–0.0173Ta3B4 + 4TaC = Ta7B4C4
    Nb5B6C–0.6970.0153Nb3B4 + C + 2Nb3B3C = 3Nb5B6CTa5B6C–0.6970.024C + Ta5B6 = Ta5B6C
    Nb3B3C–0.685–0.0013Nb3B4 + C + 3Nb4B3C2 = 7Nb3B3CTa3B3C–0.6990.0103Ta7B4C4 + 9Ta3B4 + 4C = 16Ta3B3C
    Nb7B6C3–0.6640.0005Nb3B3C + Nb4B3C2 = Nb7B6C3Ta7B6C3–0.6950.00085Ta7B4C4 + 7Ta3B4 + 4C = 8Ta7B6C3
    Nb4B3C2–0.648–0.0015Nb3B4 + 4C + 7Nb7B4C4 = 16Nb4B3C2Ta4B3C2–0.6840.0027Ta7B4C4 + 5Ta3B4 + 4C = 16Ta4B3C2
    Nb6B8C–0.6950.0192Nb3B4 + C = Nb6B8CTa6B8C–0.6850.0342Ta3B4 + C = Ta6B8C
    Nb7B8C2–0.6830.0083Nb3B4 + 2C + 4Nb3B3C = 3Nb7B8C2Ta7B8C2–0.6860.020Ta7B4C4 + 7Ta3B4 + 4C = 4Ta7B8C2
    Nb8B8C3–0.6650.008C + 8Nb3B3C = 3Nb8B8C3Ta8B8C3–0.6840.012Ta7B4C4 + 3Ta3B4 + 2C = 2Ta8B8C3
    Nb9B8C4–0.6510.008C + 5Nb3B3C + 3Nb4B3C2 = 3Nb9B8C4Ta9B8C4–0.6750.0133Ta7B4C4 + 5Ta3B4 + 4C = 4Ta9B8C4
    Nb7B10C–0.6930.021C + 2Nb2B3 + Nb3B4 = Nb7B10CTa7B10C–0.6770.030TaB2 + 2Ta3B4 + C = Ta7B10C
    Nb4B5C–0.6840.0112C + Nb3B3C + 3Nb3B4 = 3Nb4B5CTa4B5C–0.6790.026Ta7B4C4 + 19Ta3B4 + 12C = 16Ta4B5C
    Nb9B10C3–0.6680.012C + 2Nb3B3C + Nb3B4 = Nb9B10C3Ta9B10C3–0.6770.0193Ta7B4C4 + 17Ta3B4 + 12C = 8Ta9B10C3
    Nb5B5C2–0.6550.011C + 5Nb3B3C = 3Nb5B5C2Ta5B5C2–0.6700.0185Ta7B4C4 + 15Ta3B4 + 12C = 16Ta5B5C2
    DownLoad: CSV

    表 3  Nb-B-C和Ta-B-C三元相的弹性常数Cij、体模量B、剪切模量 G和维氏硬度Hv (单位: GPa)

    Table 3.  Elastic constants Cij, bulk modulus B, shear modulus G, Vickers hardness Hv of Nb-B-C and Ta-B-C ternary phases (in GPa).

    结构弹性常数力学性能a硬度
    C11C22C33C44C55C66C12C13C23BGB/GHChenHTian
    Nb3B3C544.3479.8522.8181.5171.9245.3170.9132.9162.2275.3189.71.4524.824.7
    Nb4B3C2551.5499.2548.5184.0175.1257.1183.2132.7157.8282.9195.81.4425.525.4
    Nb6B4C3533.3493.8548.1174.9161.3255.2175.4138.9151.7278.5189.51.4724.424.3
    Nb7B4C4535.9505.9526.4172.2161.3259.1184.0142.8152.6280.6188.31.4923.923.8
    Nb7B6C3553.1494.5563.2188.7179.6255.6176.4132.1157.7282.5198.91.4226.326.2
    Ta3B3C569.6514.4563.5194.1180.0261.8187.1147.3173.9295.9200.81.4725.325.3
    Ta4B3C2581.1535.3602.1197.3185.1275.8200.3146.0170.2305.7209.01.4626.226.2
    Ta3BC2550.0547.7550.0159.8159.5292.1216.7160.0149.2299.6191.81.5622.722.9
    Ta6B4C3584.7539.6614.2203.0189.9279.9195.5168.0144.1305.9213.91.4327.427.3
    Ta7B4C4563.1547.5571.5183.6170.4281.4200.2162.0164.3303.9200.81.5124.424.5
    Ta7B6C3584.7540.0614.2203.0190.0280.0195.5168.0144.1305.9213.91.4327.427.3
    TaB23022001.5124.424.5
    NbB22871951.4724.824.8
    TaC3242151.5125.625.9
    NbC2391611.4821.621.4
    SiC2131871.1433.632.2
    Al2O32321471.5818.718.7
    TiN2591801.4424.324.0
    注: a二元相力学性能数据来自Materials Project网站.
    DownLoad: CSV
  • [1]

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

    [2]

    包括, 马帅领, 徐春红, 崔田 2017 物理学报 66 036104Google Scholar

    Bao K, Ma S L, Xu C H, Cui T 2017 Acta Phys. Sin. 66 036104Google Scholar

    [3]

    Zhou X F, Sun J, Fan Y X, Chen J, Wang H T, Guo X J, He J L, Tian Y J 2007 Phys. Rev. B 76 100101Google Scholar

    [4]

    Wu Q H, Hu Q K, Hou Y M, Wang H Y, Zhou A G, Wang L B 2018 J. Phys. Condens. Matter 30 385402Google Scholar

    [5]

    Tian Y J, Xu B, Yu D L, Ma Y M, Wang Y B, Jiang Y B, Hu W T, Tang C C, Gao Y F, Luo K, Zhao Z S, Wang L M, Wen B, He J L, Liu Z Y 2013 Nature 493 385Google Scholar

    [6]

    Huang Q, Yu D L, Xu B, Hu W T, Ma Y M, Wang Y B, Zhao Z S, Wen B, He J L, Liu Z Y, Tian Y J 2014 Nature 510 250Google Scholar

    [7]

    徐波, 田永君 2017 物理学报 66 036201Google Scholar

    Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201Google Scholar

    [8]

    Wu Q H, Hu Q K, Hou Y M, Wang H Y, Zhou A G, Wang L B, Cao G H 2018 Mater. Des. 140 45Google Scholar

    [9]

    Cumberland R W, Weinberger M B, Gilman J J, Clark S M, Tolbert S H, Kaner R B 2005 J. Am. Chem. Soc. 127 7264Google Scholar

    [10]

    Chung H Y, Weinberger M B, Levine J B, Kavner A, Yang J M, Tolbert S H, Kaner R B 2007 Science 316 436Google Scholar

    [11]

    Gregoryanz E, Sanloup C, Somayazulu M, Badro J, Fiquet G, Mao H K, Hemley R J 2004 Nat. Mater. 3 294Google Scholar

    [12]

    Young A F, Sanloup C, Gregoryanz E, Scandolo S, Hemley R J, Mao H K 2006 Phys. Rev. Lett. 96 155501Google Scholar

    [13]

    Ivanovskii A L 2012 Prog. Mater. Sci. 57 184Google Scholar

    [14]

    陶强, 马帅领, 崔田, 朱品文 2017 物理学报 66 036103Google Scholar

    Tao Q, Ma S L, Cui T, Zhu P W 2017 Acta Phys. Sin. 66 036103Google Scholar

    [15]

    Hillebrecht H, Gebhardt K 2001 Angew. Chem. Int. Ed. 40 1445Google Scholar

    [16]

    胡前库, 侯一鸣, 吴庆华, 秦双红, 王李波, 周爱国 2019 物理学报 68 096201Google Scholar

    Hu Q K, Hou Y M, Wu Q H, Qin S H, Wang L B, Zhou A G 2019 Acta Phys. Sin. 68 096201Google Scholar

    [17]

    Wang P F, Weng M Y, Xiao Y, Hu Z X, Li Q H, Li M, Wang Y D, Chen X, Yang X N, Wen Y R, Yin Y X, Yu X Q, Xiao Y G, Zheng J X, Wan L J, Pan F, Guo Y G 2019 Adv. Mater. 31 1903483Google Scholar

    [18]

    Xiao W J, Xin C, Li S B, Jie J S, Gu Y, Zheng J X, Pan F 2018 J. Mater. Chem. A 6 9893Google Scholar

    [19]

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

    [20]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [21]

    Le Page Y, Saxe P 2002 Phys. Rev. B 65 104104Google Scholar

    [22]

    Togo A, Tanaka I 2015 Scr. Mater. 108 1Google Scholar

    [23]

    Togo A, Chaput L, Tanaka I, Hug G 2010 Phys. Rev. B 81 174301Google Scholar

    [24]

    Mouhat F, Coudert F X 2014 Phys. Rev. B 90 224104Google Scholar

    [25]

    Wu Z J, Zhao E J, Xiang H P, Hao X F, Liu X J, Meng J 2007 Phys. Rev. B 76 054115Google Scholar

    [26]

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

    [27]

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

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Metrics
  • Abstract views:  7091
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  • Cited By: 0
Publishing process
  • Received Date:  18 February 2020
  • Accepted Date:  01 April 2020
  • Published Online:  05 June 2020

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