Cr2MC(M=Al, Ga)的电子结构、弹性和热力学性质的第一性原理研究

杨则金; 令狐荣锋; 程新路; 杨向东

doi:10.7498/aps.61.046301

摘要

本文使用第一性原理的GGA/RPBE方法研究了Cr2MC(M=Al, Ga)的电子结构、弹性和热力学性质. 研究发现两个化合物的体积压缩性几乎相同, 并且证实了在050 GPa范围内c轴始终较a轴更难以压缩并且结构始终是稳定的. 通过对内坐标的研究发现了Cr2AlC中Cr离子的内坐标始终大于Cr2GaC中Cr离子的内坐标. 使用准谐德拜模型得到的体弹模量在0 GPa下随着温度的升高而减小, 而在300 GPa下则随着温度的升高而增大. 对德拜温度的研究发现Cr2GaC的值小于Cr2AlC的值, 而对热膨胀系数、Grneisen参数、熵和热容的计算发现Cr2GaC的值大于Cr2AlC的值. 对电子结构的分析发现Cr2GaC的s和p电子在费米能级处的值大于Cr2AlC的s和p电子的值, 而其他离子的电子分布几乎一致.

关键词:

Abstract

We investigate the electronic, elastic and thermodynamic properties of nanolaminate Cr2MC(M=Al, Ga) by using the ab initio pseudopotential total energy method. Our results show that they have shown almost identical volume compressibilities. The axial compressibility investigations show that the c axis is always stiffer than a axis. The internal coordinate calculations revealed that the values of Cr atoms in Cr2AlC are always larger than those in Cr2GaC. The elastic constants calculations demonstrated the structural stability within 050 GPa. The obtained bulk moduli by quasi-harmonic Debye model observed that the bulk moduli of Cr2MC(M=Al, Ga)decrease with temperature at 0 GPa, but increase at 300 GPa. We also found that the Debye temperatures of Cr2GaC are always smaller than those of Cr2AlC at any conditions. However, the opposite cases can be found in thermal expansion coefficients, Grneisen parameter, entropy and heat capacity when comparing their respective counterparts between Cr2GaC and Cr2AlC. The electronic density of states and energy band distribution demonstrated that the Cr2MC(M=Al, Ga) have shown similar profiles with the only exception of the more localized s and p electrons in Cr2GaC than their respective counterparts in Cr2AlC.

Keywords:

作者及机构信息

1.
浙江工业大学理学院, 杭州 310023;

2.
贵州师范学院物理与电子科学学院, 贵阳 550018;

3.
四川大学原子与分子物理研究所, 成都 610065

基金项目: 国家自然科学基金(批准号: 10974139, 10964002, 11104247, 11176020)、贵州省科学技术基金(批准号: 黔科合J字[2009]2066号和LKS[2009]07), 贵州省高层次人才科研条件特助项目(批准号: TZJF-2008年-42号)和浙江省教育厅科研项目(批准号: Y201121807)资助的课题.

Authors and contacts

1.
School of Science, Zhejiang University of Technology, Hangzhou 310023, China;

2.
School of Physics, Guizhou Normal College, Guiyang 550018, China;

3.
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China

Funds: Projects supported by the National Natural Science Foundation of China (Grant Nos. 10974139, 10964002, 11104247, 11176020), the Natural Science Foundation of Guizhou Province, China (Grant Nos. [2009]2066 and [2009]07), the Project of Aiding Elites Research Condition of Guizhou Province, China (Grant No. TZJF-2008-42), and the Science Foundation from Education Ministry of Zhejiang Province, China (Grant No. Y201121807).

参考文献

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[13]	Lin Z J, Zhou Y C, Li M S, Wang J Y 2005 Z. Metallkd 96 291
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[22]	Ying G B, He X D, Li M W, Du S Y, Han W B, He F 2011 J. Alloys Compd. 509 8022
[23]	Zhou W B, Mei B C, Zhu J Q 2009 Mater. Sci. Poland 27 973
[24]	Manoun B, Gulve R P, Saxena S K, Gupta S, Barsoum M W, Zha C S 2006 Phys. Rev. B 73 024110
[25]	Xiao L O, Li S B, Song GM, SloofWG 2011 J. Eur.Ceramic Soc. 31 1497
[26]	Etzkorn J, Ade M, Kotzott D, Kleczek M, Hillebrecht H 2009 J. Solid State Chem. 182 995
[27]	Manoun B, Kulkarni S, Pathak N, Saxena S K, Amini S, Barsoum M W 2010 J. Alloys Compd. 505 328
[28]	Cover M F, Warschkow O, Bilek M M M, Mckenzie D R 2009 J. Phys.: Condens. Matter 21 305403
[29]	Jia G Z, Yang L J 2010 Physica B 405 4561
[30]	Sun ZM, Li S, Ahuja R, Schneider JM2004 Solid State Commun. 129 589
[31]	Music D, Sun Z M, Ahuja R, Schneider J M 2006 Phys. Rev. B 73 134117
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[35]	Leaffer O D, Gupta S J, Barsoum MW, Spanier J E 2007 J. Mater. Res. 22 2651
[36]	Sun Z M 2011 Int. Mater. Rev. 56 143
[37]	Dahlqvist M, Alling B, Rosen J 2010 Phys. Rev. B 81 220102
[38]	Emmerlich J, Music D, Houben A, Dronskowski R, Schneider J M 2007 Phys. Rev. B 76 224111
[39]	Phatak N A, Kulkarni S R, Drozd V, Saxena S K, Deng L W, Fei Y W, Hu J Z, Luo W, Ahuja R 2008 J. Alloys Compd. 463 220
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[41]	Cheng Z M, Wang X Q, Wang F, Lu L Y, Liu G B, Duan Z F, Nie Z X 2011 Acta Phys. Sin. 60 096301 (in Chinese) [程志梅, 王新强, 王风, 卤丽娅, 刘高斌, 段壮芬, 聂招秀 2011 60 096301]
[42]	He J P, Lu W Z, Wang X H 2011 Acta Phys. Sin. 60 097102 (in Chinese) [何建平, 吕文中, 汪小红 2011 60 097102]
[43]	Jiang L, Wang P J, Zhang C W, Feng X Y, Lu Y, Zhang G L 2011 Acta Phys. Sin. 60 093101 (in Chinese) [蒋雷, 王培吉, 张昌文, 冯现徉, 逯瑶, 张国莲 2011 60 093101]
[44]	Li X F, Liu Z L, Peng W M, Zhao A K 2011 Acta Phys. Sin. 60 076501 (in Chinese) [李晓凤, 刘中利, 彭卫民, 赵阿可 2011 60 076501]
[45]	Li X M, Han H L, He G P 2011 Acta Phys. Sin. 60 087104 (in Chinese) [李雪梅, 韩会磊, 何光谱 2011 60 087104]
[46]	Liu C H, Ouyang C Y, Ji Y H 2011 Acta Phys. Sin. 60 077103 (in Chinese) [刘春华, 欧阳楚英, 嵇英华 2011 60 077103]
[47]	Yu B H, Liu M L, Chen D 2011 Acta Phys. Sin. 60 087105 (in Chinese) [余本海, 刘墨林, 陈东 2011 60 087105]
[48]	Yuang D, Luo H F, Huang D H, Wang F H 2011 Acta Phys. Sin. 60 077101 (in Chinese) [袁娣, 罗华锋, 黄多辉, 王藩侯 2011 60 077101]
[49]	Ma Y M, Eremets M, Oganov A R, Xie Y, Trojan I, Medvedev S, Lyakhov A O, Valle M, Prakapenka V 2009 Nature 458 182
[50]	Gao G Y, Oganov A R, Li P F, Li Z W, Wang H, Cui T, Ma Y M, Bergara A, Lyakhov A O, Litaka T, Zou G T 2010 Proc. Natl. Acad. Sci. USA 107 1317
[51]	Lv J, Wang Y C, Zhu L, Ma Y M 2011 Phys. Rev. Lett. 106 015503
[52]	Zhu L, Wang H, Wang Y C, Lv J, Ma Y M, Cui Q L, Ma Y M, Zou G T 2011 Phys. Rev. Lett. 106 145501
[53]	Li Q, Ma Y M 2011 Prog. Chem. 23 829 (in Chinese) [李全, 马琰铭 2011 化学进展 23 829]
[54]	Li Y W, Ma Y M 2010 SCIENTIA SINICA Phys, Mech & Astron 40 146 (in Chinese) [李印威, 马琰铭 2010 中国科学: 物理学力学天文学 40 146]
[55]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[56]	Hammer B, Hansen L B, Norskov J K 1999 Phys. Rev. B 59 7413
[57]	Vanderbilt D 1990 Phys. Rev. B 41 7892
[58]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[59]	Payne M C, Teter M P, Allen D C, Arias T A, Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045
[60]	Milman V, Winkler B, White A, Packard C J, Payne M C, Akhmatskaya E V, Nobes R H 2000 Int. J. Quantum. Chem. 77 895
[61]	Manoum B, Amini S, Gupta S, Saxena S K, Barsoum M W 2007 J. Phys.: Condensed Matter 19 456218
[62]	Sun Z, Ahjua R, Li S, Schneiger J M 2003 Appl. Phys. Lett. 83 899
[63]	Born M 1940 Proc. Cambridge Philos. Soc. 36 160
[64]	Pugh S F 1954 Philos. Mag. 45 833
[65]	Blanco M A, Francisco E, Luana V 2004 Comp. Phys. Comm. 158 57
[66]	Drulis M K, Drulis H, Hackemer A E, Ganguly A, EI-Raghy T, Barsoum M W 2007 J. Alloys Compd. 433 59
[67]	Loftland S E, Hettinger J D, Harell K, Finkel P, Gupta S, Barsoum M W, Hug G 2004 Appl. Phys. Lett. 84 508
[68]	Scabarozi T H, Amini S, Leaffer O, Ganguly A, Gupta S, Tambussi W, Clipper S, Spanier J E, Barsoum M W, Hettinger J D, Lofland S E 2009 J. Appl. Phys. 105 013543
[69]	Haines J, Leger J M, Boequillon G 2001 Ann. Rev. Mater. Res. 31 1
[70]	Jeitschko W, Nowotny H, Benesovsky F 1963 Monatsh. Chem. 94 672
[71]	Sun Z M, Music D, Ahuja R, Schneider J M 2005 Phys. Rev. B 71 193402
[72]	Wang J Y, Zhou Y C 2004 Phys. Rev. B 69 214111
[73]	Barsoum M W 2000 Prog. Solid State Chem. 28 201

施引文献

[1]	Nowotny H 1970 Prog. Solid State Chem. 2 27
[2]	Barsoum M W, Radovic M 2011 Annu. Rev. Mater. Res. 41 1
[3]	Barsoum M W, EI-Raghy T 1996 J. Am. Ceram. Soc. 79 1953
[4]	Schneider J M, Sun Z M,Mertens R, Uestel F, Ahuja R 2004 Solid State Commun. 130 445
[5]	Walter C, Sigumonrong D P, EI-Raghy T, Schneider JM2006 Thin Solid Films 515 389
[6]	Li J J, Hu L F, Li F Z, LiM S, Zhou Y C 2010 Surf. Coat. Technol. 204 3838
[7]	Panigrahi B B, Chu M C, Kim Y I, Cho S J, Gracio J J 2010 J. Am. Ceram. Soc. 93 1530
[8]	Tian W B,Wang P L, Kan Y M, Zhang G J 2008 J. Alloys Compd. 461 L5
[9]	Schuster J C, Nowotny H, Vaccaro C 1980 J. Solid State Chem. 32 213
[10]	Lin Z J, Li M S, Wang J Y, Zhou Y C 2007 J. Am. Ceram. Soc. 90 3930
[11]	TianWB,Wang P L, Zhang G J, Kan Y M, Li Y X, Yan D S 2006 Scripta Mater. 54 841
[12]	Lin Z J, Li M S, Wang J Y, Zhou Y C 2007 Acta Mater. 55 6182
[13]	Lin Z J, Zhou Y C, Li M S, Wang J Y 2005 Z. Metallkd 96 291
[14]	Tian F B, Wang P L, Zhang G J, Kan Y M, Li Y X 2007 J. Inorg. Mater. 22 189
[15]	Tian W B, Wang P L, Zhang G J, Kan Y M, Li Y X 2007 J. Am. Ceram. Soc. 90 1663
[16]	TianWB,Wang P L, Zhang G J, Kan Y M, Li Y X, Yan D S 2007 Mater. Sci. Eng. A 454 132
[17]	Ying G B, He X D, Li M W, Han W B, He F, Du S Y 2010 Mater. Sci. Eng. A 528 2635
[18]	Tian WB,Wang P L, Kan Y M, Zhang G J, Li Y X, Yan D S 2007 Mater. Sci. Eng. A 3 229
[19]	Sun Z M, Hashimoto H, Tian W, Zou Y 2010 Int. J. Appl. Ceram. Technol. 7 704
[20]	Tian W B, Sun Z M, Hashimoto H, Du Y L 2009 J. Mater. Sci. 44 102
[21]	Hettinger J D, Loflang S E, Finkel P, Meehan T, Palma J, Harrell K, Gupta S, Ganguly A, EI-Raghy T, Barsoum M W 2005 Phys. Rev. B 72 115120
[22]	Ying G B, He X D, Li M W, Du S Y, Han W B, He F 2011 J. Alloys Compd. 509 8022
[23]	Zhou W B, Mei B C, Zhu J Q 2009 Mater. Sci. Poland 27 973
[24]	Manoun B, Gulve R P, Saxena S K, Gupta S, Barsoum M W, Zha C S 2006 Phys. Rev. B 73 024110
[25]	Xiao L O, Li S B, Song GM, SloofWG 2011 J. Eur.Ceramic Soc. 31 1497
[26]	Etzkorn J, Ade M, Kotzott D, Kleczek M, Hillebrecht H 2009 J. Solid State Chem. 182 995
[27]	Manoun B, Kulkarni S, Pathak N, Saxena S K, Amini S, Barsoum M W 2010 J. Alloys Compd. 505 328
[28]	Cover M F, Warschkow O, Bilek M M M, Mckenzie D R 2009 J. Phys.: Condens. Matter 21 305403
[29]	Jia G Z, Yang L J 2010 Physica B 405 4561
[30]	Sun ZM, Li S, Ahuja R, Schneider JM2004 Solid State Commun. 129 589
[31]	Music D, Sun Z M, Ahuja R, Schneider J M 2006 Phys. Rev. B 73 134117
[32]	Schneider J M, Sigumonrong D P, Music D,Walter C, Emmerlich J, Iskandar R, Mayer J 2007 Scripta Mater. 57 1137
[33]	Sun Z M, Music D, Ahuja R, Schneider J M 2005 J. Phys.: Condens. Matter 17 7169
[34]	Music D, Sun ZM, Voevodin A A, Schneider JM2006 Solid State Commun. 139 139
[35]	Leaffer O D, Gupta S J, Barsoum MW, Spanier J E 2007 J. Mater. Res. 22 2651
[36]	Sun Z M 2011 Int. Mater. Rev. 56 143
[37]	Dahlqvist M, Alling B, Rosen J 2010 Phys. Rev. B 81 220102
[38]	Emmerlich J, Music D, Houben A, Dronskowski R, Schneider J M 2007 Phys. Rev. B 76 224111
[39]	Phatak N A, Kulkarni S R, Drozd V, Saxena S K, Deng L W, Fei Y W, Hu J Z, Luo W, Ahuja R 2008 J. Alloys Compd. 463 220
[40]	Chen Y H, Du R, Zhang Z L, Wang W C, Zhang C R, Kang L, Luo Y C 2011 Acta Phys. Sin. 60 086801 (in Chinese) [陈玉红, 杜瑞, 张致龙, 王伟超, 张材荣, 康龙, 罗永春 2011 60 086801]
[41]	Cheng Z M, Wang X Q, Wang F, Lu L Y, Liu G B, Duan Z F, Nie Z X 2011 Acta Phys. Sin. 60 096301 (in Chinese) [程志梅, 王新强, 王风, 卤丽娅, 刘高斌, 段壮芬, 聂招秀 2011 60 096301]
[42]	He J P, Lu W Z, Wang X H 2011 Acta Phys. Sin. 60 097102 (in Chinese) [何建平, 吕文中, 汪小红 2011 60 097102]
[43]	Jiang L, Wang P J, Zhang C W, Feng X Y, Lu Y, Zhang G L 2011 Acta Phys. Sin. 60 093101 (in Chinese) [蒋雷, 王培吉, 张昌文, 冯现徉, 逯瑶, 张国莲 2011 60 093101]
[44]	Li X F, Liu Z L, Peng W M, Zhao A K 2011 Acta Phys. Sin. 60 076501 (in Chinese) [李晓凤, 刘中利, 彭卫民, 赵阿可 2011 60 076501]
[45]	Li X M, Han H L, He G P 2011 Acta Phys. Sin. 60 087104 (in Chinese) [李雪梅, 韩会磊, 何光谱 2011 60 087104]
[46]	Liu C H, Ouyang C Y, Ji Y H 2011 Acta Phys. Sin. 60 077103 (in Chinese) [刘春华, 欧阳楚英, 嵇英华 2011 60 077103]
[47]	Yu B H, Liu M L, Chen D 2011 Acta Phys. Sin. 60 087105 (in Chinese) [余本海, 刘墨林, 陈东 2011 60 087105]
[48]	Yuang D, Luo H F, Huang D H, Wang F H 2011 Acta Phys. Sin. 60 077101 (in Chinese) [袁娣, 罗华锋, 黄多辉, 王藩侯 2011 60 077101]
[49]	Ma Y M, Eremets M, Oganov A R, Xie Y, Trojan I, Medvedev S, Lyakhov A O, Valle M, Prakapenka V 2009 Nature 458 182
[50]	Gao G Y, Oganov A R, Li P F, Li Z W, Wang H, Cui T, Ma Y M, Bergara A, Lyakhov A O, Litaka T, Zou G T 2010 Proc. Natl. Acad. Sci. USA 107 1317
[51]	Lv J, Wang Y C, Zhu L, Ma Y M 2011 Phys. Rev. Lett. 106 015503
[52]	Zhu L, Wang H, Wang Y C, Lv J, Ma Y M, Cui Q L, Ma Y M, Zou G T 2011 Phys. Rev. Lett. 106 145501
[53]	Li Q, Ma Y M 2011 Prog. Chem. 23 829 (in Chinese) [李全, 马琰铭 2011 化学进展 23 829]
[54]	Li Y W, Ma Y M 2010 SCIENTIA SINICA Phys, Mech & Astron 40 146 (in Chinese) [李印威, 马琰铭 2010 中国科学: 物理学力学天文学 40 146]
[55]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[56]	Hammer B, Hansen L B, Norskov J K 1999 Phys. Rev. B 59 7413
[57]	Vanderbilt D 1990 Phys. Rev. B 41 7892
[58]	Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[59]	Payne M C, Teter M P, Allen D C, Arias T A, Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045
[60]	Milman V, Winkler B, White A, Packard C J, Payne M C, Akhmatskaya E V, Nobes R H 2000 Int. J. Quantum. Chem. 77 895
[61]	Manoum B, Amini S, Gupta S, Saxena S K, Barsoum M W 2007 J. Phys.: Condensed Matter 19 456218
[62]	Sun Z, Ahjua R, Li S, Schneiger J M 2003 Appl. Phys. Lett. 83 899
[63]	Born M 1940 Proc. Cambridge Philos. Soc. 36 160
[64]	Pugh S F 1954 Philos. Mag. 45 833
[65]	Blanco M A, Francisco E, Luana V 2004 Comp. Phys. Comm. 158 57
[66]	Drulis M K, Drulis H, Hackemer A E, Ganguly A, EI-Raghy T, Barsoum M W 2007 J. Alloys Compd. 433 59
[67]	Loftland S E, Hettinger J D, Harell K, Finkel P, Gupta S, Barsoum M W, Hug G 2004 Appl. Phys. Lett. 84 508
[68]	Scabarozi T H, Amini S, Leaffer O, Ganguly A, Gupta S, Tambussi W, Clipper S, Spanier J E, Barsoum M W, Hettinger J D, Lofland S E 2009 J. Appl. Phys. 105 013543
[69]	Haines J, Leger J M, Boequillon G 2001 Ann. Rev. Mater. Res. 31 1
[70]	Jeitschko W, Nowotny H, Benesovsky F 1963 Monatsh. Chem. 94 672
[71]	Sun Z M, Music D, Ahuja R, Schneider J M 2005 Phys. Rev. B 71 193402
[72]	Wang J Y, Zhou Y C 2004 Phys. Rev. B 69 214111
[73]	Barsoum M W 2000 Prog. Solid State Chem. 28 201

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