α-Ti2Zr高压物性的第一性原理计算研究

张品亮; 龚自正; 姬广富; 刘崧

doi:10.7498/aps.62.046202

摘要

基于密度泛函理论的第一性原理计算获得了α-Ti2Zr的晶体结构、弹性常数、德拜温度和电子分布情况, 研究了它们与压力的关系. 计算得到的晶体结构参数与实验值一致. 运用有限应变方法计算得到了α-Ti2Zr的体积模量B、剪切模量G、杨氏模量E和泊松比σ. B和E的零压值分别为101.2和35.6 GPa. G/B的值较小, 并且随着压力的增加而减小, 表明α-Ti2Zr具有优异的延展性. 基于弹性常数得到平均声速, 从而获得了德拜温度Θ=321.7 K. 通过解Christoffel方程获得的压缩波和剪切波数据揭示α-Ti2Zr具有较强的各向异性. 此外, 压力诱导电子从s轨道到d轨道的转移说明在一定压力下α-Ti2Zr将转变为β相.

关键词:

第一性原理 /
α-Ti2Zr /
物性 /
高压

Abstract

The structure, elastic constant, Debey temperature and electron distribution of α-Ti2Zr under high pressure are presented by using first-principles pseudopotential method based on density functional theory in this paper. The calculated structural parameters at zero pressure are in agreement with experimental values. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We obtain the bulk modulus, Young’s modulus and Poisson’s ratio for α-Ti2Zr. The G and B at zero pressure are 101.2 and 35.6 GPa, respectively. The G/B value is relatively small and decreases with pressure increasing, showing that the α-Ti2Zr is rather ductile. The Debye temperature Θ=321.7 K is obtained by the average sound velocity based on elastic constants. We investigate anisotropies of the compressional wave and two shear waves. The acoustic velocities are obtained from elastic constants by solving Christoffel equation. The results indicate the strong anisotropy for α-Ti2Zr. Moreover, the pressure dependence of s→d electron transfer indicates that β-Ti2Zr will occur under high pressure.

Keywords:

作者及机构信息

1.
西南交通大学材料科学与工程学院, 材料先进技术教育部重点实验室, 成都 610031;

2.
北京卫星环境工程研究所, 可靠性与环境工程技术国防科技重点实验室, 北京 100094;

3.
中国工程物理研究院流体物理研究所, 冲击波物理与爆轰物理国防科技重点实验室, 绵阳 621900

基金项目: 国家重点基础研究发展计划(批准号:2010CB731600)和国家国防科工局空间碎片专项(批准号:KJSP06209,KJSP06210)资助的课题.

Authors and contacts

1.
Key Laboratory of Advanced Technologies of Materials of Ministry of Education, School of Material Science and Engineering, Southwest Jiaotong University, Chengdu 610031, China;

2.
National Key Laboratory of Science and Technology on Reliabilityand Environment Engineering, Beijing Institute of Spacecraft Environment Engineering, Beijing 100094, China;

3.
Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China

Funds: Project supported by the National Basic Research Program of China (Grant No. 2010CB731600) and the Specialized Research Project for the Protection Against Space Debris of China (Grant Nos. KJSP06209, KJSP06210).

参考文献

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[48]	Zhang P L, Gong Z Z, Ji G F 2012 Proceedings of 20th International Conference on Composites Engineering Beijing, China, July 22-28, 2012

施引文献

[1]	Vohra Y K, Spencer P T 2001 Phys. Rev. Lett. 86 3068
[2]	Murray J L 1981 Bulletin of Alloys Phase Diagrams 2 197
[3]	Chatterji D, Hepworth M T, Hruska S J 1971 Metall. Trans. 2 1271
[4]	Liu W, Li B S, Wang L P, Zhang J Z, Zhao Y S 2007 Phys. Rew. B 76 144107
[5]	Hao Y J, Zhang L, Chen X R, Li Y H, He H L 2008 Solid State Commun. 146 105
[6]	Mei Z G, Shang S L, Wang Y, Liu Z K 2009 Phys. Rev. B 79 134102
[7]	Errandonea D, Meng Y, Somayazulu M, Häusermann D 2005 Physica B 355 116
[8]	Kerley G I 2003 Sandia Report, Sand 2003-3785
[9]	Hao Y J, Zhu J, Zhang L, Qu J Y, Ren H S 2010 Solid State Commun. 12 1473
[10]	Wang B T, Zhang P, Liu H Y, Li W D, Zhang P 2011 J. Appl. Phys. 109 063514
[11]	Hao Y J, Zhang L, Chen X R, Li Y H, He H L 2008 J. Phys.: Condens. Mat. 20 235230
[12]	Liu W, Li B S, Wang L P, Zhang J Z, Zhao Y S 2008 J. Appl. Phys. 104 076102
[13]	Xia H, Duclos S J, Ruoff A L, Vohra Y K 1990 Phys. Rev. Lett. 64 204
[14]	Zhang S H, Zhu Y, Zhang X Y, Zhang S L, Qi L, Liu R P 2010 Comput. Mat. Sci. 50 179
[15]	Bashkin I O, Fedotov V K, Nefedova M V, Tissen V G, Ponyatovsky E G, Schiwek A, Holzapfel W B 2003 Phys. Rev. B 68 054401
[16]	Wang B T, Li W D, Zhang P 2012 J. Nucl. Mater. 420 501
[17]	Dolukhanyan S K, Aleksanyan A G, Ter-Galstyan O P, Shekhtman V S, Sakharov M K, Abrosimova G E 2007 Russ. J. Phys. Chem. B 1 563
[18]	Shekhtman V S, Dolukhanyan S K, Aleksanyan A G, Mayilyan D G, Ter-Galstyan O P, Sakharov M K, Khasanov S S 2010 Int. J. Self-Propag. High-Temp Synth. 19 40
[19]	Swainson I P, Dolukanyan S K, Aleksanyan A G, Shekhtman V S, Mayilyan D G, Yonkeu A L 2010 Can. J. Phys. 88 741
[20]	Xu G L, Chen J D, Chen D, Ma J Z, Yu B H, Shi D H 2009 Chin. Phys. B 18 0744
[21]	Hao A M, Zhou T J, Zhu Y, Zhang X Y, Liu R P 2011 Chin. Phys. B 20 047103
[22]	Li D H, Su W J, Zhu X L 2012 Acta Phys. Sin. 61 023103 (in Chinese) [李德华, 苏文晋, 朱晓玲 2012 61 023103]
[23]	Wang B, Liu Y, Ye J W 2012 Acta Phys. Sin. 61 186501 (in Chinese) [王斌, 刘颖, 叶金文 2012 61 186501]
[24]	Chen Z J 2012 Acta Phys. Sin. 61 177104 (in Chinese) [陈中钧 2012 61 177104]
[25]	Zhu J, Yu J X, Wang Y J, Chen X R, Jing F Q 2008 Chin. Phys. B 17 2216
[26]	Segall M D, Lindan P J D, Probert M J, Pickard C J, Hasnip P J, Clark S J, Payne M C 2002 J. Phys.: Condens. Mat. 14 2717
[27]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[28]	Vanderbilt D 1990 Phys. Rev. B 41 7892
[29]	Nye J F 1957 Physical Properties of Crystals (London: Oxford University Press)
[30]	Watt J P, Peselnick L 1980 J. Appl. Phys. 51 1525
[31]	Hill R 1952 Proc. Phys. Soc. 65 350
[32]	Long R, Dai Y, Jin H, Huang B B 2008 Res. Lett. Phys. 2008 293517
[33]	Murnaghan F D 1944 Proc. Natl. Acad. Sci. USA 30 244
[34]	Antonov V, Iordanova I 2009 AIP Conf. Proc. 1203 1149
[35]	Accelrys Software Inc. 2010 Materials Studio Release Notes (Release 5.5) (Scan Diego: Accelrys Software Inc.)
[36]	Born M 1940 Proc. Cambridge Philos. Soc. 36 160
[37]	Sin’ko G V, Smirnov N A 2002 J. Phys.: Condens. Mat. 14 6989
[38]	Tang W H, Zhang R Q 1999 Equation of State Theory and Calculation Conspectus (Changsha: National University of Defense Technology Press) p321(in Chinese) [汤文辉, 张若棋 1999物态方程理论及计算概论 (长沙: 国防科技大学出版社) 第321页]
[39]	Pugh S F 1954 Philos. Mag. 45 823
[40]	Auld M A 1973 Acoustic Fields and Waves in Solids (Vol. I) (New York: Wiley)
[41]	Steinle-Neumann G, Stixrude L, Cohen R E 1999 Phys. Rev. B 60 791
[42]	Born M, Huang K 1954 Dynamical Theory of Crystal Lattices (Clarendon: Oxford)
[43]	Anderson O L 1963 J. Phys. Chem. Solids 24 909
[44]	Schreiber E, Anderson O L, Soga N 1973 Elastic Constants and Their Measurements (New York: McGraw-Hill)
[45]	Skriver H L 1985 Phys. Rev. B 31 909
[46]	Mulliken R S 1955 J. Chem. Phys. 23 1833
[47]	Vohra Y K, Sikka S K, Holzapfel W B 1983 J. Phys. F: Met. Phys. 13 L107
[48]	Zhang P L, Gong Z Z, Ji G F 2012 Proceedings of 20th International Conference on Composites Engineering Beijing, China, July 22-28, 2012

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