过渡金属硼碳化物TM_3B_3C和TM_4B_3C_2稳定性和性能的理论计算
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摘要
在过渡金属轻元素化合物中,寻找新的硬质或者超硬材料是当前的一个研究热点.目前寻找范围多集中在过渡金属硼化物、碳化物和氮化物等二元体系,三元相的研究则相对较少.本文以已知Nb_3B_3C和Nb_4B_3C_2结构为模板,采用元素替代法构建了29种TM_3B_3C (TM为过渡金属元素)结构和29种TM_4B_3C_2结构,采用基于密度泛函理论的第一性原理计算方法,成功找到了热力学、动力学以及力学都稳定的Ta_3B_3C和Ta4B_3C2两种新相.结构搜索计算确认了这两相为全局能量最优结构.能带结构和态密度的计算显示这两相均为导体,导电性主要源于Ta原子的d电子.这两种新相的硬度大约为26 GPa,说明Ta_3B_3C和Ta_4B_3C_2属于高硬度材料,但不是超硬材料.
To search new hard or superhard materials in transition-metal light-element compounds is a current research focus. Most of the past researches focused on binary phases such as transition metal borides, carbides and nitrides, while the researches on ternary phases were relatively rare. The single crystals Nb_3B_3C and Nb4B_3C_2 were synthesized recently by using Al-Cu alloys as auxiliary metals and their structures were determined by Hillebrechtand Gebhardt. In the present paper, 29 TM_3B_3C and 29 TM_4B_3C_2 configurations are constructed by TM atoms(TM = Sc to Zn, Y to Cd, Hf to Hg) replacing Nb atoms in the known Nb3B_3C and Nb4B_3C_2 configuration. By calculating the formation energy from first-principles density functional theories,only 13 TM_3B_3C and 11 TM_4B_3C_2 phases are stable compared with the three elemental substances of TM, boron and carbon. However compared with the most competing phases, only Ta_3B_3C, Nb_3B_3C and Nb_4B_3C_2 phases are stable thermodynamically. The metastable Ta4B_3C_2 phase at 0 K becomes stable when temperature is higher than 250 K. Thus two new phases of Ta_3B_3C and Ta_4B_3C_2 are uncovered to be stable thermodynamically.Global structure searches conducted by the popular USPEX and CALYPSO softwares prove the Ta_3B_3C and Ta_4B_3C_2 phases to be the most favorable energetically. By calculating the phonon dispersion curves of the Ta_3B_3C and Ta_4B_3C_2 phase, no imaginary phonon frequencies are observed in the whole Brillouin zone, which demonstrates the dynamical stability of the Ta_3B_3C and Ta_4B_3C_2 phase. The calculated elastic constant of the Ta_3B_3C and Ta_4B_3C_2 phases satisfy the criteria of mechanical stability, showing that the Ta_3B_3C and Ta_4B_3C_2 phase are stable mechanically. The calculations of band structure and density of state show that the Ta_3B_3C and Ta_4B_3C_2 phases are both conducting, which mainly arises from the d electrons of Ta atoms. The calculated bulk modulus and shear modulus of the Ta_3B_3C and T_a4B_3C_2 phases show their brittle nature. The hardness of Ta_3B_3C and Ta_4B_3C_2 phase are nearly the same and calculated to be about 26 GPa by Chen' s and Tian' s models, which illuminates that the two phases are hard but not superhard.
To search new hard or superhard materials in transition-metal light-element compounds is a current research focus. Most of the past researches focused on binary phases such as transition metal borides, carbides and nitrides, while the researches on ternary phases were relatively rare. The single crystals Nb_3B_3C and Nb4B_3C_2 were synthesized recently by using Al-Cu alloys as auxiliary metals and their structures were determined by Hillebrechtand Gebhardt. In the present paper, 29 TM_3B_3C and 29 TM_4B_3C_2 configurations are constructed by TM atoms(TM = Sc to Zn, Y to Cd, Hf to Hg) replacing Nb atoms in the known Nb3B_3C and Nb4B_3C_2 configuration. By calculating the formation energy from first-principles density functional theories,only 13 TM_3B_3C and 11 TM_4B_3C_2 phases are stable compared with the three elemental substances of TM, boron and carbon. However compared with the most competing phases, only Ta_3B_3C, Nb_3B_3C and Nb_4B_3C_2 phases are stable thermodynamically. The metastable Ta4B_3C_2 phase at 0 K becomes stable when temperature is higher than 250 K. Thus two new phases of Ta_3B_3C and Ta_4B_3C_2 are uncovered to be stable thermodynamically.Global structure searches conducted by the popular USPEX and CALYPSO softwares prove the Ta_3B_3C and Ta_4B_3C_2 phases to be the most favorable energetically. By calculating the phonon dispersion curves of the Ta_3B_3C and Ta_4B_3C_2 phase, no imaginary phonon frequencies are observed in the whole Brillouin zone, which demonstrates the dynamical stability of the Ta_3B_3C and Ta_4B_3C_2 phase. The calculated elastic constant of the Ta_3B_3C and Ta_4B_3C_2 phases satisfy the criteria of mechanical stability, showing that the Ta_3B_3C and Ta_4B_3C_2 phase are stable mechanically. The calculations of band structure and density of state show that the Ta_3B_3C and Ta_4B_3C_2 phases are both conducting, which mainly arises from the d electrons of Ta atoms. The calculated bulk modulus and shear modulus of the Ta_3B_3C and T_a4B_3C_2 phases show their brittle nature. The hardness of Ta_3B_3C and Ta_4B_3C_2 phase are nearly the same and calculated to be about 26 GPa by Chen' s and Tian' s models, which illuminates that the two phases are hard but not superhard.
引文
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[2] Bao K, Ma S L, Xu C H, Cui T 2017 Acta Phys. Sin. 66036104(in Chinese)[包括,马帅领,徐春红,崔田2017物理学报66 036104]
[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 100101
[4] Dong H F,Oganov A R,Wang Q G, Wang S N,Wang Z H,Zhang J, Esfahani M M D, Zhou X F, Wu F G, Zhu Q 2016Sci. Rep. 6 31288
[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 493 385
[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 Nature510 250
[7] Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201(in Chinese)[徐波,田永君2017物理学报66 036201]
[8] Kaner R B, Gilman J J, Tolbert S H 2005 Science 308 1268
[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 7264
[10] Chung H Y, Weinberger M B, Levine J B, Kavner A, Yang J M, Tolbert S H, Kaner R B 2007 Science 316 436
[11] Li Q, Zhou D, Zheng W T, Ma Y M, Chen C F 2013 Phys.Rev. Lett. 110 136403
[12] Zhao C M, Duan Y F, Gao J, Liu W J, Dong H M, Dong H F, Zhang D K, Oganov A R 2018 Phys. Chem. Chem. Phys.20 24665
[13] Gregoryanz E, Sanloup C, Somayazulu M, Badro J, Fiquet G,Mao H K, Hemley R J 2004 Nat. Mater. 3 294
[14] Young A F, Sanloup C, Gregoryanz E, Scandolo S, Hemley R J, Mao H K 2006 Phys. Rev. Lett. 96 155501
[15] Ivanovskii A L 2012 Prog. Mater. Sci. 57 184
[16] Tao Q, Ma S L, Cui T, Zhu P W 2017 Acta Phys. Sin. 66036103(in Chinese)[陶强,马帅领,崔田,朱品文2017物理学报66 036103]
[17] Hillebrecht H, Gebhardt K 2001 Angewandte Chemie(Int.Ed. in English)40 1445
[18] Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704
[19] Wang Y C, Lii J A, Zhu L, Ma Y M 2010 Phys. Rev. B 82094116
[20] Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169
[21] Le Page Y, Saxe P 2002 Phys. Rev. B 65 104104
[22] Togo A, Tanaka I 2015 Scr. Mater. 108 1
[23] Jain A, Ong S P, Hautier G, Chen W, Richards W D, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G, Persson K A2013 APL Mater. 1 011002
[24] Togo A, Chaput L, Tanaka I, Hug G 2010 Phys. Rev. B 81174301
[25] Mouhat F, Coudert F X 2014 Phys. Rev. B 90 224104
[26] Wu Z J, Zhao E J, Xiang H P, Hao X F, Liu X J, Meng J2007 Phys. Rev. B 76 054115
[27] Pugh S F 1954 Philos. Mag. 45 823
[28] Chen X Q, Niu H Y, Li D Z, Li Y Y 2011 Intermetallics 191275