Hf-N体系的晶体结构预测和性质的第一性原理研究

樊涛; 曾庆丰; 于树印

doi:10.7498/aps.65.118102

摘要

为了寻找具有优异力学性能的新型超高温陶瓷材料, 结合进化算法和第一性原理, 系统研究了Hf-N二元体系所有稳定存在的化合物及其晶体结构. 除了实验已知的岩盐结构的HfN之外, 本文还找到了Hf6N(R-3), Hf3N(P6322), Hf3N2(R-3m), Hf5N6(C2/m)和Hf3N4(C2/m)五种新结构, 基于准简谐近似原理计算了这些稳定结构的声子谱以验证其动力学稳定性, 常温甚至更高温度下的吉布斯自由能以验证其高温热力学稳定性. 结果表明, 这些结构是动力学稳定的, 且在1500 K以下都是热力学稳定的. 同时, 本文还列出了在搜索过程中出现的空间对称性较高、能量较低的亚稳态结构, 包括Hf2N(P42/mnm), Hf4N3(C2/m), Hf6N5(C2/m), Hf4N5(I4/m), Hf3N4(I-43d)和Hf3N4(Pnma). 之后计算了上述所有结构的力学性质(弹性常数、体模量、剪切模量、杨氏模量、硬度), 随着N 所占比例的增加, 硬度呈现的整体趋势是先增大后下降, 在Hf5N6处取得最大值, 为21 GPa. 其中Hf3N2和Hf4N5也展现出了较高的硬度, 都为19 GPa. 最后, 计算了这些结构的电子态密度和晶体轨道汉密尔顿分布, 从电子结构的角度分析了力学性能的成因. 研究结果显示, 较强的Hf-N共价键和较低的结构空位率是Hf5N6具有优异力学性能的主要原因.

关键词:

Abstract

Motivated by exploring new high temperature ceramics which have excellent mechanical properties, we systematically search for all the stable compounds and their crystal structures in the binary Hf-N system by combining the evolutionary algorithm with first principle calculation. In addition to the well-known rock-salt HfN, we find five other novel compounds, i.e., Hf6N(R-3), Hf3N(P6322), Hf3N2(R-3m), Hf5N6(C2/m), and Hf3N4(C2/m). Then, their phonon frequencies are calculated so that the dynamical stabilities are known. Their high temperature thermodynamic stabilities are further confirmed and the Gibbs free energies are calculated in thequasi-harmonic approximation. All of these structures are thermodynamic stable when the temperature is lower than 1500 K. However, as temperature increases, the structuresHf5N6(C2/m) and Hf3N4(C2/m) become meta-stable. Meanwhile, some meta-stable structures, including Hf2N (P42/mnm), Hf4N3 (C2/m), Hf6N5(C2/m), Hf4N5(I4/m), Hf3N4 (I-43d), and Hf3N4 (Pnma), each of which has higher symmetry and lower formation enthalpy, are all listed. At the same time, our results of Hf3N4 testify that C2/m structure is stabler than Pnma and I-43d structures when the temperature is lower than 2000 K, which is different from the conclusion given by Bazhanov [Bazhanov D I, Knizhnik A A, Safonov A A, Bagatur'yants A A, Stoker M W, Korkin A A 2005 J. Appl. Phys. 97 044108]. The results also show that the difference in Gibbs free energy between C2/m and Pnma Hf3N4 structure decreases with temperature increasing. Thus, we speculate that the C2/m Hf3N4 transforms into Pnma Hf3N4 when the temperature is above 2000 K. The mechanical properties, including the elastic constant, bulk modulus, shear modulus, Young's modulus and hardness, are systematically investigated. The hardness first increases, reaching a maximum at Hf5N6 (21 GPa), and then decreases with increasing nitrogen content. Besides, Hf3N2 and Hf4N5 both exhibit relatively high hardness value of 19 GPa, while the hardness of HfN is 15 GPa. Finally, the electron densities of states and crystal orbital Hamilton populations are calculated so that the mechanic origins can be analyzed from the electronic structures of these phases. The crystal orbital Hamilton populations show that the strength of Hf-N covalent bonding increases with increasing nitrogen content, however, it has an exceptional peak for Hf3N2, which can be used to explain the relatively high hardness of this structure. Beside covalent bonding strength, structural vacancy can also affect their mechanical properties. It is concluded that the strong covalent bonding and low structural vacancy both can explain the good mechanical performance of Hf5N6.

Keywords:

作者及机构信息

1.
西北工业大学, 材料基因组国际合作研究中心, 西安 710072;

2.
西北工业大学, 超高温结构复合材料重点实验室, 西安 710072

通信作者: 曾庆丰, qfzeng@nwpu.edu.cn

基金项目: 国家自然科学基金(批准号: 51372203, 51332004)和中央高校基本科研业务费专项资金(批准号: 3102015BJ(II) JGZ005)资助的课题.

Authors and contacts

1.
The International Center of Materials Design, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China;

2.
Science and Technology on Thermostructural Composite Materials Laboratory, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Corresponding author: Zeng Qing-Feng, qfzeng@nwpu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51372203, 51332004) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 3102015BJ(II) JGZ005).

参考文献

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[16]	Patsalas P, Kalfagiannis N, Kassavetis S 2015 Materials 8 3128
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[26]	Seo H S, Lee T Y, Wen J G, Petrov I, Greene J E, Gall D 2004 J. Appl. Phys. 96 878
[27]	Zerr A, Gerhard M, Ralf R 2003 Nat. Mater. 2 185
[28]	Bazhanov D I, Knizhnik A A, Safonov A A, Bagatur'yants A A, Stoker M W, Korkin A A 2005 J. Appl. Phys. 97 044108
[29]	Lyakhov A O, Oganov A R, Valle M 2010 Comput. Phys. Commun. 181 1623
[30]	Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704
[31]	Oganov A R, Lyakhov A O, Mario V 2011 Acc. Chem. Res. 44 227
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[34]	Kohn W, Sham L J 1965 Phys. Rev. 140 1133
[35]	Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[36]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[37]	Blchl P E 1994 Phys. Rev. B 50 17953
[38]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[39]	Wang S Q, Ye H Q 2003 J. Phys. Condens. Mat. 15 5307
[40]	Hill R 1952 Proc. Phys. Soc. London, Sect. A 65 349
[41]	Voigt W 1910 Lehrbuch der kristallphysik (Leipzig: B.G. Teubner) pp100
[42]	Reuss A 1929 Z. Angew. Math. Mech. 9 49
[43]	Chen X Q, Niu H, Li D, Li Y 2011 Intermetallics 19 1275
[44]	Ohodnicki Jr P, Cates N, Laughlin D, Mchenry M, Widom M 2008 Phys. Rev. B 78 144414
[45]	Morris A J, Grey C P, Needs R J, Pickard C J {2012 Phys. Rev. B 84 1894
[46]	Christensen A 1990 Acta Chem. Scand. 44 851
[47]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
[48]	Shankar A R, Mudali U K, Chawla V, Chandra R 2013 Ceram. Int. 39 5175
[49]	Zaoui A, Bouhafs B, Ruterana P 2005 Mater. Chem. Phys. 91 108
[50]	Nagao S, Nordlund K, Nowak R {2006 Phys. Rev. B 73 144113
[51]	Patil S K R, Mangale N S, Khare S V, Marsillac S 2008 Thin Solid Films 517 824
[52]	Chen Z Q, Wang J, Li C M 2013 J. Alloys Compd. 575 137
[53]	Peter K 2003 Phys. Rev. Lett. 90 125501
[54]	Cowley R 1976 Phys. Rev. B 13 4877
[55]	Liu A Y, Wentzcovitch R M 1994 Phys. Rev. B 50 10362
[56]	Karki B B, Ackland G J, Crain J 1997 J. Phys. Condens. Mat. 9 8579
[57]	Yang Q, Lengauer W, Koch T, Scheerer M, Smid I 2000 J. Alloys Compd. 309 L5
[58]	Gupta D C, Chauhan M, Bhat I H {2014 J. Appl. Phys. 1591 36
[59]	Chung H Y, Weinberger M B, Yang J M, Tolbert S H, Kaner R B 2008 Appl. Phys. Lett. 92 261904
[60]	Jacobson B E, Nimmagadda R, Bunshah R F 1979 Thin Solid Films 63 333
[61]	Deringer V L, Tchougreff A L, Richard D 2011 J. Phys. Chem. A 115 5461
[62]	Dronskowski R, Bloechl P E 1993 J. Phys. Chem. 97 8617

施引文献

[1]	Zhang L L, Fu Q G, Li H J {2015 Mater. Chin. 34 675 (in Chinese) [张磊磊, 付前刚, 李贺军 2015 中国材料进展 34 675]
[2]	Xie Y, Cheng L, Li L, Mei H, Zhang L 2013 J. Eur. Ceram. Soc. 33 1701
[3]	Li H, Zhang L, Cheng L, Wang Y, Yu Z, Huang M, Tu H, Xia H 2008 J. Mater. Sci. 43 2806
[4]	Huang S H, Liu J 2014 Chin. Phys. B 23 058105
[5]	Wang C L, Yu B H, Huo H L, Chen D, Sun H B 2009 Chin. Phys. B 18 1248
[6]	Zhao L K, Zhao E J, Wu Z J 2013 Acta Phys. Sin. 62 046201 (in Chinese) [赵立凯, 赵二俊, 武志坚 2013 62 046201]
[7]	Zhang G T, Bai T T, Yan H Y, Zhao Y R 2015 Chin. Phys. B 24 106104
[8]	Peng J H, Zeng Q F, Xie C W, Zhu K J, Tan J H {2015 Acta Phys. Sin. 64 236102 (in Chinese) [彭军辉, 曾庆丰, 谢聪伟, 朱开金, 谭俊华 2015 64 236102]
[9]	Zhang M G, Yan H Y, Zhang G T, Wang H 2012 Chin. Phys. B 21 076103
[10]	Pu C Y, Zhou D W, Bao D X, Lu C, Jin X L, Su T C, Zhang F W 2014 Chin. Phys. B 23 026201
[11]	Li X F, Zhai H C, Fu H Z, Liu Z L, Ji G F 2011 Chin. Phys. B 20 093101
[12]	Zhao W J, Wang Y X 2009 Chin. Phys. B 18 3934
[13]	Wang J, Li C M, Ao J, Li F, Chen Z Q 2013 Acta Phys. Sin. 62 087102 (in Chinese) [王瑨, 李春梅, 敖靖, 李凤, 陈志谦 2013 62 087102]
[14]	Xun X C 2008 M.S. Dissertation (Changchun: Jilin University) (in Chinese) [荀显超 2008 硕士学位论文 (长春: 吉林大学)]
[15]	Santecchia E, Hamouda A, Musharavati F, Zalnezhad E, Cabibbo M, Spigarelli S 2015 Ceram. Int. 41 10349
[16]	Patsalas P, Kalfagiannis N, Kassavetis S 2015 Materials 8 3128
[17]	Sue J, Chang T {1995 Surf. Coat. Technol. 76 61
[18]	Bringans R D, Hchst H 1984 Phys. Rev. B 30 5416
[19]	Benia H M, Guemmaz M, Schmerber G, Mosser A, Parlebas J C 2002 Appl. Surf. Sci. 200 231
[20]	Chen X J, Struzhkin V V, Wu Z, Somayazulu M, Qian J, Kung S, Christensen A N, Zhao Y, Cohen R E, Mao H K 2005 Proc. Natl. Acad. Sci. U.S.A. 102 3198
[21]	Zhao E, Wu Z 2008 J. Solid State Chem. 181 2814
[22]	Reza M, Lech A T, Miao X, Weaver B E, Yeung M T, Tolbert S H, Kaner R B 2011 Proc. Natl. Acad. Sci. U.S.A. 108 10958
[23]	Yamanaka S, Hotehama K I, Kawaji H 1998 Nature 392 580
[24]	Gasch M, Ellerby D, Irby E, Beckman S, Gusman M, Johnson S 2004 J. Mater. Sci. 39 5925
[25]	Johansson B O, Sundgren J E, Helmersson U, Hibbs M K 1984 Appl. Phys. Lett. 44 670
[26]	Seo H S, Lee T Y, Wen J G, Petrov I, Greene J E, Gall D 2004 J. Appl. Phys. 96 878
[27]	Zerr A, Gerhard M, Ralf R 2003 Nat. Mater. 2 185
[28]	Bazhanov D I, Knizhnik A A, Safonov A A, Bagatur'yants A A, Stoker M W, Korkin A A 2005 J. Appl. Phys. 97 044108
[29]	Lyakhov A O, Oganov A R, Valle M 2010 Comput. Phys. Commun. 181 1623
[30]	Oganov A R, Glass C W 2006 J. Chem. Phys. 124 244704
[31]	Oganov A R, Lyakhov A O, Mario V 2011 Acc. Chem. Res. 44 227
[32]	Oganov, Artem R 2011 Modern Methods of Crystal Structure Prediction (New York: Wiley-VCH) pp147
[33]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 864
[34]	Kohn W, Sham L J 1965 Phys. Rev. 140 1133
[35]	Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[36]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[37]	Blchl P E 1994 Phys. Rev. B 50 17953
[38]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[39]	Wang S Q, Ye H Q 2003 J. Phys. Condens. Mat. 15 5307
[40]	Hill R 1952 Proc. Phys. Soc. London, Sect. A 65 349
[41]	Voigt W 1910 Lehrbuch der kristallphysik (Leipzig: B.G. Teubner) pp100
[42]	Reuss A 1929 Z. Angew. Math. Mech. 9 49
[43]	Chen X Q, Niu H, Li D, Li Y 2011 Intermetallics 19 1275
[44]	Ohodnicki Jr P, Cates N, Laughlin D, Mchenry M, Widom M 2008 Phys. Rev. B 78 144414
[45]	Morris A J, Grey C P, Needs R J, Pickard C J {2012 Phys. Rev. B 84 1894
[46]	Christensen A 1990 Acta Chem. Scand. 44 851
[47]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106
[48]	Shankar A R, Mudali U K, Chawla V, Chandra R 2013 Ceram. Int. 39 5175
[49]	Zaoui A, Bouhafs B, Ruterana P 2005 Mater. Chem. Phys. 91 108
[50]	Nagao S, Nordlund K, Nowak R {2006 Phys. Rev. B 73 144113
[51]	Patil S K R, Mangale N S, Khare S V, Marsillac S 2008 Thin Solid Films 517 824
[52]	Chen Z Q, Wang J, Li C M 2013 J. Alloys Compd. 575 137
[53]	Peter K 2003 Phys. Rev. Lett. 90 125501
[54]	Cowley R 1976 Phys. Rev. B 13 4877
[55]	Liu A Y, Wentzcovitch R M 1994 Phys. Rev. B 50 10362
[56]	Karki B B, Ackland G J, Crain J 1997 J. Phys. Condens. Mat. 9 8579
[57]	Yang Q, Lengauer W, Koch T, Scheerer M, Smid I 2000 J. Alloys Compd. 309 L5
[58]	Gupta D C, Chauhan M, Bhat I H {2014 J. Appl. Phys. 1591 36
[59]	Chung H Y, Weinberger M B, Yang J M, Tolbert S H, Kaner R B 2008 Appl. Phys. Lett. 92 261904
[60]	Jacobson B E, Nimmagadda R, Bunshah R F 1979 Thin Solid Films 63 333
[61]	Deringer V L, Tchougreff A L, Richard D 2011 J. Phys. Chem. A 115 5461
[62]	Dronskowski R, Bloechl P E 1993 J. Phys. Chem. 97 8617

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[20]	魏仑, 梅芳华, 邵楠, 董云杉, 李戈扬. TiN/TiB2异结构纳米多层膜的共格生长与力学性能. , 2005, 54(10): 4846-4851. doi: 10.7498/aps.54.4846

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