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本论文中, 采用晶体结构预测软件USPEX结合第一性原理方法全面地搜索了Hf-C体系在高压下的晶体结构, 预测得到了两种新的化合物及HfC在高压下的相变路径. 压力低于100 GPa 时, 除了常压下的结构HfC, Hf3C2, Hf6C5, 并没有得到新的热力学稳定结构. 在200 GPa时, 预测得到了一种新化合物Hf2C, 空间群为I4/m; 且HfC的结构发生了相变, 空间群由Fm3m变为C2/m. 在300 GPa时, 预测得到了另一种新化合物HfC2, 空间群为Immm. 而在400 GPa时, HfC的结构再次发生相变, 空间群为Pnma. 通过能量计算, 得到了Hf-C体系的组分-压力相图: 在压力分别低于15.5 GPa和37.7 GPa时, Hf3C2和Hf6C5是稳定的; 压力分别大于102.5 GPa和215.5 GPa时, Hf2C和HfC2变成稳定化合物; HfC的相变路径为Fm3mC2/mPnma, 相变压力分别为185.5 GPa 和322 GPa. 经结构优化后, 得到了这四种高压新结构的晶体学数据, 如晶格常数、原子位置等, 并分析了其结构特点. 对于Hf-C 体系中的高压热力学稳定结构, 分别计算了其弹性性质和声子谱曲线, 证明是力学稳定和晶格动力学稳定的. 采用第一性原理软件VASP模拟高压结构的能带结构、态密度、电子局域函数和Bader 电荷分析, 发现HfC(C2/m, Pnma结构), Hf2C 和HfC2 中Hf-C 键具有强共价性、弱金属性和离子性, 且C-C 间存在共价作用.Hafnium carbides (Hf-C system), known as ultra-high temperature ceramics, have attracted growing attention because of their unique features. In this paper, we carry out researches on the stable crystal structures in the Hf-C system at high pressures, using a variable-composition ab initio evolutionary algorithm implemented in the USPEX code. In addition to the ambient-pressure structures HfC (Fm3m), there are two new compounds Hf3C2 and Hf6C5 and two high-pressure structures of HfC. When pressures are lower than 100 GPa, no new structures are found other than those at ambient pressure, and Hf3C2 and Hf6C5 become metastable at 20 GPa and 100 GPa, respectively. At 200 GPa, a new compound Hf2C is found, and the stable structure HfC has changed from Fm3m to C2/m. At 300 GPa, another new compound HfC2 is found. At 400 GPa, the stable structure of HfC has changed again to the space group Pnma. And at 500 GPa, the stable structures are Hf2C, HfC2 and HfC (Pnma), no new structures are found except those at 400 GPa. The composition-pressure phase diagram that shows the pressure range of stable structures in Hf-C system is simulated by calculation of their enthalpies. When the pressures are lower than 15.5 GPa and 37.7 GPa, Hf3C2 and Hf6C5 are stable, respectively, and their space groups are both of C2/m. And Hf2C and HfC2, with space group I4/m and Immm, respectively become stable structures when the pressure is higher than 102.5 GPa and 215.5 GPa, respectively. The phase-transition route of HfC is Fm3mC2/mPnma, and the two phase-transition pressures are 185.5 GPa and 322 GPa, respectively, which are different from the conclusion of Zhao. Then we will show and discuss the newly predicted high-pressure structures and their crystallographic data, such as volume, lattice constants and atom positions. The crystal structures of HfC are described in the literature. The structure of Hf2C contains 12 atoms in the conventional cell, and carbon atoms lie at the center of decahedron consisting of 8 hafnium atoms. In the structure of HfC2, carbon atoms form the quasi-graphite sheets and hafnium atoms lie betweent the two sheets. The dynamical and mechanical stabilities of the high-pressure structures have been verified by calculations of their phonon dispersion curves and elastic constants. And the bulk modulus and shear modulus of HfC2 are larger than those of the other three high-pressure structures. Finally we will study their electronic properties, band structures, density of states (DOS), electron localization functions (ELFs), and the Bader charge analyses of these structures are simulated based on the first-principle. The band structure and density of states show that these four high-pressure structures have weak metallic and strong Hf-C covalent bond. The Bader charge analysis further proves the strong Hf-C covalent bond and weak ionic bond. And ELF shows the existence of CC covalent bond. In summary, the HfC bond shows strong covalence, weak metallicity and ionicity, and the CC bond is covalent.
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Keywords:
- Hf-C system /
- crystal structure prediction /
- electronic properties /
- first-principle simulation
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[1] Levine S R, Opila E J, Halbig M C, Kiser J D, Singh M, Salem J A 2002 J. Eur. Ceram. Soc. 22 2757
[2] Savino R, Fumo M D S, Paterna D, Sperpico M 2005 Aerosp. Sci. Technol. 9 151
[3] Wuchina E, Opeka M, Causey S, Buesking K, Spain J, Cull A, Routbort J, Guitierrez-Mora F 2004 J. Mater. Sci. 39 5939
[4] Silvestroni L, Bellosi A, Melandri C, Sciti D, Liu J X, Zhang G J 2011 J. Eur. Ceram. Soc. 31 619
[5] Wu C G, Wu W Y, Gong Y C, Dai B F, He S H, Huang Y H 2015 Acta Phys. Sin. 64 114213 (in Chinese) [吴成国, 武文远, 龚艳春, 戴斌飞, 何苏红, 黄雁华 2015 64 114213]
[6] Shi Y, Bai Y, Mou L F, Xiang Q T, Huang Y L, Cao J L 2015 Acta Phys. Sin. 64 116301 (in Chinese) [石瑜, 白洋, 莫丽玢, 向青云, 黄亚丽, 曹江利 2015 64 116301]
[7] Li H, Zhang L, Zeng Q, Guan K, Li K, Ren H, Liu S, Cheng L 2011 Solid State Commun. 151 602
[8] Li H, Zhang L, Zeng Q, Ren H, Guan K, Liu Q, Cheng L 2011 Solid State Commun. 151 61
[9] Brown H L, Armstrong P E, Kempter C P 1966 J. Chem. Phys. 45 547
[10] Smith H G, Gläser W 1970 Phys. Rev. Lett. 25 1611
[11] Zeng Q, Peng J, Oganov A R, Zhu Q, Xie C, Zhang X, Dong D, Zhang L, Cheng L 2013 Phys. Rev. B 88 214107
[12] Zhao Z, Zhou X F, Wang L M, Xu B, He J, Liu Z, Wang H T, Tian Y 2011 Inorg. Chem. 50 9266
[13] Maddox J 1988 Nature 335 201
[14] Hawthorne F C 1990 Nature 345 297
[15] Gavezzotti A 1994 Accounts Chem. Res. 27 309
[16] Ball P 1996 Nature 381 648
[17] Oganov A R, Ma Y, Lyakhov A O, Valle M, Gatti C 2010 Rev. Mineral. Geochem. 71 271
[18] Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704
[19] Lyakhov A O, Oganov A R, Stokes H T, Zhu Q 2013 Comput. Phys. Commun. 184 1172
[20] Zhu Q, Oganov A R, Salvadó M A, Pertierra P, Lyakhov A O 2011 Phys. Rev. B 83 193410
[21] Oganov A R, Chen J, Gatti C, Ma Y, Glass C W, Liu Z, Yu T., Kurakevych O O, Solozhenko V L 2009 Nature 457 863
[22] Ma Y, Eremets M, Oganov A R, Xie Y, Trojan I, Medvedev S, Lyakhov A O, Valle M, Prakapenka V 2009 Nature 458 182
[23] Oganov A R 2010 Modern methods of crystal prediction (New York: Wiley-VCR) pp148-164
[24] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[25] Blöchl P E 1994 Phys. Rev. B 50 17953
[26] Parlinski K, Li Z Q, Kawazoe Y 1997 Phys. Rev. Lett. 78 4063
[27] Li Y L, Luo W, Zeng Z, Kin H Q, Mao H K, Ahuja R 2013 PNAS 110 9289
[28] Cowley R A 1976 Phys. Rev. B 13 4877
[29] Reuss A 1929 Z. Angew. Math. Mech. 9 49
[30] Voigt W 1928 Lehrbuch der Kristallphysik (Leipzig, Germany: B G. Teubner)
[31] Hill R 1952 Proc. Phys. Soc. A 65 349
[32] Becke A D, Edgecombe K E 1990 J. Chem. Phys. 92 5397
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