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The phase transitions and structure stabilities of materials have always attracted much attention of the experimental and theoretical investigators. When calculating the phonon dispersion of the cubic structure of the transition metal Zr (β -Zr), the traditional methods always give the negative phonon frequencies. So the quasi-harmonic approximation cannot solve this kind of problem. We obtain the phonon dispersion of β -Zr at high pressure and high temperature by using the newly developed self-consistent ab initio lattice dynamics method, which can well consider the phonon-phonon interactions. And then the stable region of β -Zr in the high pressure and high temperature phase diagram is predicted. The full phase diagram of Zr is also predicted. We also obtain the high temperature equation of state (EOS) and thermal expansion of β -Zr, which can help to construct the EOS data base of Zr.
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Keywords:
- transition metals /
- high pressure and high temperature /
- lattice dynamics /
- first-principles
[1] Akahama Y, Kobayashi M, Kawamura H 1991 J. Phys. Soc. Jpn. 60 3211
[2] Olinger B, Jamieson J C 1973 High Temp. -High Press. 5 123
[3] Xia H, Duclos S J, Ruoff A L, Vohra Y K 1990 Phys. Rev. Lett. 64 204
[4] Young D A 1991 Phase Diagrams of the Elements (Berkeley: University of California Press) p171
[5] Trubitsin V Y 2006 Phys. Rev. B 73 214302
[6] Vohra Y K, Sikka S K, Chidambaram R 1979 J. Phys. F 9 1771
[7] Zhang J, Zhao Y, Pantea C, Qian J, Daemen L L, Rigg P A, Hixson R S, Greeff C W, Gray G T, Yang Y, Wang L, Wang Y, Uchida T 2005 J. Phys. Chem. Solids 66 1213
[8] Zhao Y, Zhang J, Pantea C, Qian J, Daemen L L, Rigg P A, Hixson R S, Gray G T, Yang Y, Wang L, Wang Y, Uchida T 2005 Phys. Rev. B 71 184119
[9] Hao Y J, Zhang L, Chen X R, Cai L C, Wu Q, Alfè D 2008 Phys. Rev. B 78 134101
[10] Hu C E, Zeng Z Y, Zhang L, Chen X R, Cai L C 2011 Comp. Mater. Sci. 50 835
[11] Yuan P F, Zhu W J, Xu J A, Jing F Q 2010 Acta Phys. Sin. 59 8755 (in Chinese) [原鹏飞, 祝文军, 徐济安, 经福谦 2010 59 8755]
[12] Zhou D W, Lu C, Li G Q, Song J F, Song Y L, Bao G 2012 Acta Phys. Sin. 61 146301 (in Chinese) [周大伟, 卢成, 李根全, 宋金璠, 宋玉玲, 包刚 2012 61 146301]
[13] Chen D 2013 Chin. Phys. B 22 126301
[14] Liu X K, Liu C, Zheng Z, Lan X H 2013 Chin. Phys. B 22 087102
[15] Souvatzis P, Eriksson O, Katsnelson M I, Rudin S P 2008 Phys. Rev. Lett. 100 095901
[16] Souvatzis P, Legut D, Eriksson O, Katsnelson M I 2010 Phys. Rev. B 81 092201
[17] Parlinski K, Li Z Q, Kawazoe Y 1997 Phys. Rev. Lett. 78 4063
[18] Birch F 1986 J. Geophys. Res. 91 4949
[19] Ostanin S A, Trubitsin V Y 1997 Phys. Solid State 39 1727
[20] Stassis C, Zarestky J, Arch D, McMasters O D, Harmon B N 1978 Phys. Rev. B 18 2632
[21] Heiming A, Petry W, Trampenau J, Alba M, Herzig C, Schober H R, Vogl G 1991 Phys. Rev. B 43 10948
[22] Heiming A, Petry W, Trampenau J, Alba M, Herzig C, Vogl G 1989 Phys. Rev. B 40 11425
[23] Greeff C W 2005 Model. Simul. Mater. Sci. Eng. 13 1015
[24] Rigg P A, Saavedra R A, Schar R J 2014 J. Phys.: Conf. Ser. 500 032014
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[1] Akahama Y, Kobayashi M, Kawamura H 1991 J. Phys. Soc. Jpn. 60 3211
[2] Olinger B, Jamieson J C 1973 High Temp. -High Press. 5 123
[3] Xia H, Duclos S J, Ruoff A L, Vohra Y K 1990 Phys. Rev. Lett. 64 204
[4] Young D A 1991 Phase Diagrams of the Elements (Berkeley: University of California Press) p171
[5] Trubitsin V Y 2006 Phys. Rev. B 73 214302
[6] Vohra Y K, Sikka S K, Chidambaram R 1979 J. Phys. F 9 1771
[7] Zhang J, Zhao Y, Pantea C, Qian J, Daemen L L, Rigg P A, Hixson R S, Greeff C W, Gray G T, Yang Y, Wang L, Wang Y, Uchida T 2005 J. Phys. Chem. Solids 66 1213
[8] Zhao Y, Zhang J, Pantea C, Qian J, Daemen L L, Rigg P A, Hixson R S, Gray G T, Yang Y, Wang L, Wang Y, Uchida T 2005 Phys. Rev. B 71 184119
[9] Hao Y J, Zhang L, Chen X R, Cai L C, Wu Q, Alfè D 2008 Phys. Rev. B 78 134101
[10] Hu C E, Zeng Z Y, Zhang L, Chen X R, Cai L C 2011 Comp. Mater. Sci. 50 835
[11] Yuan P F, Zhu W J, Xu J A, Jing F Q 2010 Acta Phys. Sin. 59 8755 (in Chinese) [原鹏飞, 祝文军, 徐济安, 经福谦 2010 59 8755]
[12] Zhou D W, Lu C, Li G Q, Song J F, Song Y L, Bao G 2012 Acta Phys. Sin. 61 146301 (in Chinese) [周大伟, 卢成, 李根全, 宋金璠, 宋玉玲, 包刚 2012 61 146301]
[13] Chen D 2013 Chin. Phys. B 22 126301
[14] Liu X K, Liu C, Zheng Z, Lan X H 2013 Chin. Phys. B 22 087102
[15] Souvatzis P, Eriksson O, Katsnelson M I, Rudin S P 2008 Phys. Rev. Lett. 100 095901
[16] Souvatzis P, Legut D, Eriksson O, Katsnelson M I 2010 Phys. Rev. B 81 092201
[17] Parlinski K, Li Z Q, Kawazoe Y 1997 Phys. Rev. Lett. 78 4063
[18] Birch F 1986 J. Geophys. Res. 91 4949
[19] Ostanin S A, Trubitsin V Y 1997 Phys. Solid State 39 1727
[20] Stassis C, Zarestky J, Arch D, McMasters O D, Harmon B N 1978 Phys. Rev. B 18 2632
[21] Heiming A, Petry W, Trampenau J, Alba M, Herzig C, Schober H R, Vogl G 1991 Phys. Rev. B 43 10948
[22] Heiming A, Petry W, Trampenau J, Alba M, Herzig C, Vogl G 1989 Phys. Rev. B 40 11425
[23] Greeff C W 2005 Model. Simul. Mater. Sci. Eng. 13 1015
[24] Rigg P A, Saavedra R A, Schar R J 2014 J. Phys.: Conf. Ser. 500 032014
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