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The magnetism, stabilities and phase transition of Ru in hcp, fcc, bct and bcc structures are investigated with detailed first-principles calculations based on density-functional theory and quasiharmonic lattice dynamics approximation. Magnetic ground states and stability ranges of various phases are obtained. Calculated results indicate that the non-magnetic (NM)-hcp structure is the most stable in the entire pressure range at zero temperature, and the structural transition cannot be induced by pressure alone. NM-fcc structure is a metastable phase of bulk Ru, while both the NM-bcc and ferromagnetic (FM)-bct structures are dynamically unstable. At high pressure and temperature, a transformation from NM-hcp to NM-fcc structure will occur. Finally, the pressure-temperature phase diagram of Ru is presented.
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Keywords:
- phase transition /
- structrual stability /
- magnetism /
- first-principles
[1] Cazorla C, Alfé D, Gillan M J 2008 Phys. Rev. B 77 224103
[2] Duthie J C, Pettifor D G 1977 Phys. Rev. Lett. 38 564
[3] Friedel J 1969 The Physics of Metals (London: Cambridge University)
[4] Heine V 1967 Phys. Rev. 153 673
[5] Pettifor D G 1972 Metallurgical Chemistry (London: Her Majesty’s Stationery Office)
[6] Souvatzis P, Eriksson O 2008 Phys. Rev. B 77 024110
[7] Zheng-Johansson J X, Eriksson O, Johansson B 1999 Phys. Rev. B 69 6131
[8] Cazorla C, Gillan M J, Taioli S, Alfé D 2007 J. Chem. Phys. 126 194502
[9] Taioli S, Cazorla C, Gillan M J, Alfé D 2007 Phys. Rev. B 75 214103
[10] Ross M, Errandonea D, Boehler R 2007 Phys. Rev. B 76 184118
[11] Errandonea D 2005 Physica B (Amsterdam) 357 356
[12] Belonoshko A B, Simak S I, Kochetov A E, Johansson B, Burakovsky L, Preston D L 2004 Phys. Rev. Lett. 92 195701
[13] Ding Y, Ahuja R, Shu J, Chow P, Luo W, Mao H K 2007 Phys. Rev. Lett. 98 085502
[14] Hebbache M, Zemzemi M 2004 Phys. Rev. B 70 224107
[15] Liu C M, Cheng Y, Zhu B, Ji G F 2011 Physica B 406 2110
[16] Occelli F, Farber D L, Badro J, Aracne C M, Teter D M, Hanfland M, Canny B, Couzinet B 2004 Phys. Rev. Lett. 93 095502
[17] Shiiki K, Hio O 1997 Jpn. J. Appl. Phys. 36 7360
[18] Watanabe S, Komine T, Kai T, Shiiki K 2000 J. Magn. Magn. Mater. 220 277
[19] Schönecker S, Richter M, Koepernik K, Eschrig H 2012 Phys. Rev. B 85 024407
[20] Wang W C, Shen Y X, Li J H, Liu B X 2006 J. Phys.: Condens. Matter 18 9911
[21] Wang W C, Kong Y, He X, Liu B X 2006 Appl. Phys. Lett. 89 262511
[22] Herper H C, Hoffmann E, Entel P 1999 Phys. Rev. B 60 3839
[23] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[24] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[25] Blöchl P E 1994 Phys. Rev. B 50 17953
[26] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[27] Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B 49 16223
[28] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[29] Alfé D 2009 Comput. Phys. Commun 180 2622
[30] Methfessel M, Paxton A T 1989 Phys. Rev. B 40 3616
[31] Mermin N D 1965 Phys. Rev. 137 A1441
[32] Cazorla C, Gillan M J 2007 J. Chem. Phys. 126 194502
[33] Gunnarsson O 1976 J. Phys. F 6 587
[34] Janak J F 1977 Phys. Rev. B 16 255
[35] Cynn H, Klepeis J E, Yoo C, Young D A 2002 Phys. Rev. Lett. 88 135701
[36] Kittel C 1996 Introduction to solid state physics (New York: Wiley)
[37] Vinet P, Ferrante J, Smith J R, Rose J H 1986 J. Phys. C: Solid State Phys. 19 L467
[38] Vinet P, Rose J H, Ferrante J, Smith J R 1989 J. Phys.: Condens. Matter 1 1941
[39] Bain E C 1924 Am. Inst. Min. Metall. Eng. 70 25
[40] Heid R, Pintschovius L, Reichardt W, Bohnen K P 2000 Phys. Rev. B 61 12059
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[1] Cazorla C, Alfé D, Gillan M J 2008 Phys. Rev. B 77 224103
[2] Duthie J C, Pettifor D G 1977 Phys. Rev. Lett. 38 564
[3] Friedel J 1969 The Physics of Metals (London: Cambridge University)
[4] Heine V 1967 Phys. Rev. 153 673
[5] Pettifor D G 1972 Metallurgical Chemistry (London: Her Majesty’s Stationery Office)
[6] Souvatzis P, Eriksson O 2008 Phys. Rev. B 77 024110
[7] Zheng-Johansson J X, Eriksson O, Johansson B 1999 Phys. Rev. B 69 6131
[8] Cazorla C, Gillan M J, Taioli S, Alfé D 2007 J. Chem. Phys. 126 194502
[9] Taioli S, Cazorla C, Gillan M J, Alfé D 2007 Phys. Rev. B 75 214103
[10] Ross M, Errandonea D, Boehler R 2007 Phys. Rev. B 76 184118
[11] Errandonea D 2005 Physica B (Amsterdam) 357 356
[12] Belonoshko A B, Simak S I, Kochetov A E, Johansson B, Burakovsky L, Preston D L 2004 Phys. Rev. Lett. 92 195701
[13] Ding Y, Ahuja R, Shu J, Chow P, Luo W, Mao H K 2007 Phys. Rev. Lett. 98 085502
[14] Hebbache M, Zemzemi M 2004 Phys. Rev. B 70 224107
[15] Liu C M, Cheng Y, Zhu B, Ji G F 2011 Physica B 406 2110
[16] Occelli F, Farber D L, Badro J, Aracne C M, Teter D M, Hanfland M, Canny B, Couzinet B 2004 Phys. Rev. Lett. 93 095502
[17] Shiiki K, Hio O 1997 Jpn. J. Appl. Phys. 36 7360
[18] Watanabe S, Komine T, Kai T, Shiiki K 2000 J. Magn. Magn. Mater. 220 277
[19] Schönecker S, Richter M, Koepernik K, Eschrig H 2012 Phys. Rev. B 85 024407
[20] Wang W C, Shen Y X, Li J H, Liu B X 2006 J. Phys.: Condens. Matter 18 9911
[21] Wang W C, Kong Y, He X, Liu B X 2006 Appl. Phys. Lett. 89 262511
[22] Herper H C, Hoffmann E, Entel P 1999 Phys. Rev. B 60 3839
[23] Kresse G, Furthmller J 1996 Phys. Rev. B 54 11169
[24] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[25] Blöchl P E 1994 Phys. Rev. B 50 17953
[26] Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[27] Blöchl P E, Jepsen O, Andersen O K 1994 Phys. Rev. B 49 16223
[28] Monkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188
[29] Alfé D 2009 Comput. Phys. Commun 180 2622
[30] Methfessel M, Paxton A T 1989 Phys. Rev. B 40 3616
[31] Mermin N D 1965 Phys. Rev. 137 A1441
[32] Cazorla C, Gillan M J 2007 J. Chem. Phys. 126 194502
[33] Gunnarsson O 1976 J. Phys. F 6 587
[34] Janak J F 1977 Phys. Rev. B 16 255
[35] Cynn H, Klepeis J E, Yoo C, Young D A 2002 Phys. Rev. Lett. 88 135701
[36] Kittel C 1996 Introduction to solid state physics (New York: Wiley)
[37] Vinet P, Ferrante J, Smith J R, Rose J H 1986 J. Phys. C: Solid State Phys. 19 L467
[38] Vinet P, Rose J H, Ferrante J, Smith J R 1989 J. Phys.: Condens. Matter 1 1941
[39] Bain E C 1924 Am. Inst. Min. Metall. Eng. 70 25
[40] Heid R, Pintschovius L, Reichardt W, Bohnen K P 2000 Phys. Rev. B 61 12059
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