First-principles study of high-pressure physical properties of α-Ti2Zr

Zhang Pin-Liang; Gong Zi-Zheng; Ji Guang-Fu; Liu Song

doi:10.7498/aps.62.046202

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:

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).

References

[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 物理学报 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 物理学报 61 186501]
[24]	Chen Z J 2012 Acta Phys. Sin. 61 177104 (in Chinese) [陈中钧 2012 物理学报 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

Cited By

[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 物理学报 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 物理学报 61 186501]
[24]	Chen Z J 2012 Acta Phys. Sin. 61 177104 (in Chinese) [陈中钧 2012 物理学报 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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Vol. 62, Issue 4 - 2013-02-20

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