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First principles investigations of the structural stability and thermal dynamical properties of metal Ba under high pressure

Zhou Da-Wei Lu Cheng Li Gen-Quan Song Jin-Fan Song Yu-Ling Bao Gang

First principles investigations of the structural stability and thermal dynamical properties of metal Ba under high pressure

Zhou Da-Wei, Lu Cheng, Li Gen-Quan, Song Jin-Fan, Song Yu-Ling, Bao Gang
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  • The stabilities and the thermal dynamical properties of the three high-pressure phases of Ba (Ba-I, Ba-Ⅱ and Ba-V ) are investigated systemically by first principles method. Our results show that all the three phase meet the criteria of mechanical and dynamical stabilities at 0 K. With pressure increasing, the phonon frequencies in Ba-I and Ba-Ⅱ phases become softened, whereas the Ba-V phase exhibits the hardening of phonon frequencies. Although both Ba-Ⅱ and Ba-V phase are the same hcp structures, they show different elastic anisotropies under high pressure. We also find that Ba-Ⅱ phase at higher pressure still meets the mechanical stability criterion, but does not meet the dynamical stability criterion. The absence of dynamical stability may be the reason for the transition from Ba-Ⅱ phase to Ba-I!V phase. We also calculate and make comparisons of sound velocity, Debye temperature, bulk modulus and shear modulus etc between Ba-Ⅱ and Ba-V phases, showing that Ba possesses the thermal dynamical properties under high pressure.
    • Funds: Projected supported by the National Natural Science Foundation of China (Grant No. 11164020), China Postdoctoral Science Foundation Funded Project (Grant No. 20110491317), Natural Science Foundation of Science and Technology Department of Henan Province, China (Grant Nos. 102300410209, 112300410112, 112300410121, 112300410187), Natural Science Foundation of Education Department of Henan Province, China (Grant Nos. 2011B140015, 2010B140012), the Higher Education Reform of Henan Province, China (Grant No. 2012SJGLX233), and the Nanyang Normal University Science Foundation, China (Grant Nos. ZX20100011, ZX2012018).
    [1]

    Zeng W X, Heinez V, Jepseny O 1997 J. Phys.: Condens. Matter 9 3489

    [2]

    Skriver H L 1982 Phys. Rev. Lett. 49 1768

    [3]

    Skriver H L 1985 Phys. Rev. B 31 1909

    [4]

    Moriarty J A 1986 Phys. Rev. B 34 6738

    [5]

    Olijnyk H, Holzapfel W B 1984 Phys. Lett. A 100 191

    [6]

    Kenichi T 1994 Phys. Rev. B 50 16238

    [7]

    Buzea C, Robbie K 2005 Supercond. Sci. Technol. 18 R1

    [8]

    Tian F B, Wang J H, He Z, Ma Y M, Wang L C, Cui T, Chen C B, Liu B B, Zou G T 2008 Phys. Rev. B 78 235431

    [9]

    Jin X L, Meng X, He Z, Ma Y M, Liu B B, Cui T, Zou G T, Mao H K 2010 Proc. Natl. Acad. Sci. USA 107 9969

    [10]

    Xu Y, Tse J S, Oganov A R, Cui T, Wang H, Ma Y M, Zou G T 2009 Phys. Rev. B 79 144110

    [11]

    Gao G Y, Oganov A R, Bergara A, Martinez-Canales M, Cui T, Iitaka T, Ma Y M, Zou G T 2008 Phys. Rev. Lett. 101 107002

    [12]

    Gao G Y, Oganov A R, Li P F, Li Z W, Wang H, Cui T, Ma Y M, Bergara A, Lyakhov A O, Iitaka T, Zou G T 2010 Proc. Natl. Acad. Sci. USA 107 1317

    [13]

    Li Y W, Gao G Y, Xie Y, Ma Y M, Cui T, Zou G T 2010 Proc. Natl. Acad. Sci. USA 107 15708

    [14]

    Moodenbaugh A R, Wittig J 1973 J. Low Temperat. Phys. 10 203

    [15]

    Dunn K J, Bundy F P 1982 Phys. Rev. B 25 194

    [16]

    Witting J, Matthias B T 1969 Phys. Rev. Lett. 22 634

    [17]

    Dunn K J, Bundy F P 1981 Phys. Rev. B 24 1643

    [18]

    Sakata M, Nakamoto Y, Shimizu K, Matsuoka T, Ohishi Y 2011 Phys. Rev. B 83 220512(R)

    [19]

    Zheng H F 2002 J. Phys.: Condens. Matter 14 5129

    [20]

    Jona F, Marcus P M 2006 J. Phys.: Condens. Matter 18 4623

    [21]

    Belger D, Hüsges Z, Voloshina E, Paulus B 2010 J. Phys.: Condens. Matter 22 275504

    [22]

    Jona F, Marcus P M 2008 Europhys. Lett. 74 83

    [23]

    Baroni S, Dal Corso A, de Gironcoli S, Giannozzi P, Cavazzoni C, Ballabio G, Scandolo S, Chiarotti G, Focher P, Pasquarello A, Laasonen K, Trave A, Car R, Marzari N, Kokalj A 2011 http: // www. pwscf. org/ [2011. 11. 19]

    [24]

    Troullier N, Martins J L 1991 Phys. Rev. B 43 1993

    [25]

    Perdew P J, Chevary A J , Vosko H S, Jackson A K, Pedersen R M, Singh J D, Fiolhais 1992 Phys. Rev. B 46 6671

    [26]

    Monnkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [27]

    Nielsen O H, Martin R M 1985 Phys. Rev. B 32 3792

    [28]

    Milman V, Warren M C 2001 J. Phys.: Condens. Matter 13 241

    [29]

    Sinpko G V, Smirnow N A 2002 J. Phys.: Condens. Matter 14 6989

    [30]

    Nelmes R J, Allan D R, McMahon M I, Belmonte S A 1999 Phys. Rev. Lett. 83 4081

    [31]

    Reed S K, Ackland G 2000 J. Phys. Rev. Lett. 84 5580

    [32]

    Liu Z M, Cui T, Ma Y M, Liu B B, Zou G T 2007 Acta Phys. Sin. 56 4877 (in Chinese) [刘志明, 崔田, 马琰铭, 刘冰冰, 邹广田 2005 物理学报 56 4877]

    [33]

    Yuan P F, Zhu W J, Xu J A, Liu S J, Jing F Q 2010 Acta Phys. Sin. 59 8755 (in Chinese) [原鹏飞, 祝文军, 徐济安, 刘绍军, 经福谦 2010 物理学报 59 8755]

    [34]

    Miao R D, Tian M, Huang G Q 2008 Acta Phys. Sin. 57 3709 (in Chinese) [苗仁德, 田苗, 黄桂芹 2008 物理学报 57 3709]

    [35]

    Xin X G, Chen X, Zhou J J, Shi S Q 2011 Acta Phys. Sin. 60 028201 (in Chinese) [忻晓桂, 陈香, 周晶晶, 施思齐 2008 物理学报 60 028201]

    [36]

    Sinko G V, Smirnow N A 2002 J. Phys.: Condens. Matter 14 6989

    [37]

    Anderson O L 1963 J. Phys. Chem. Solids 24 909

    [38]

    Schreiber E, Anderson O L, Soga N 1973 Elastic Constants and Their Measurements (NewYork: McGraw-Hill)

    [39]

    Hill R 1952 Phys. Soc. London 65 350

    [40]

    Deng X H, Lu W, Hu Y M, Gu H S 2009 Physica B 404 1218

    [41]

    Ravindran P, Fast L, Korzhavyi P A, Johansson B, Wills J, Eriksson O 1998 J. Appl. Phys. 84 4891

    [42]

    Lindemann F R 1910 Z. Phys. 11 609

  • [1]

    Zeng W X, Heinez V, Jepseny O 1997 J. Phys.: Condens. Matter 9 3489

    [2]

    Skriver H L 1982 Phys. Rev. Lett. 49 1768

    [3]

    Skriver H L 1985 Phys. Rev. B 31 1909

    [4]

    Moriarty J A 1986 Phys. Rev. B 34 6738

    [5]

    Olijnyk H, Holzapfel W B 1984 Phys. Lett. A 100 191

    [6]

    Kenichi T 1994 Phys. Rev. B 50 16238

    [7]

    Buzea C, Robbie K 2005 Supercond. Sci. Technol. 18 R1

    [8]

    Tian F B, Wang J H, He Z, Ma Y M, Wang L C, Cui T, Chen C B, Liu B B, Zou G T 2008 Phys. Rev. B 78 235431

    [9]

    Jin X L, Meng X, He Z, Ma Y M, Liu B B, Cui T, Zou G T, Mao H K 2010 Proc. Natl. Acad. Sci. USA 107 9969

    [10]

    Xu Y, Tse J S, Oganov A R, Cui T, Wang H, Ma Y M, Zou G T 2009 Phys. Rev. B 79 144110

    [11]

    Gao G Y, Oganov A R, Bergara A, Martinez-Canales M, Cui T, Iitaka T, Ma Y M, Zou G T 2008 Phys. Rev. Lett. 101 107002

    [12]

    Gao G Y, Oganov A R, Li P F, Li Z W, Wang H, Cui T, Ma Y M, Bergara A, Lyakhov A O, Iitaka T, Zou G T 2010 Proc. Natl. Acad. Sci. USA 107 1317

    [13]

    Li Y W, Gao G Y, Xie Y, Ma Y M, Cui T, Zou G T 2010 Proc. Natl. Acad. Sci. USA 107 15708

    [14]

    Moodenbaugh A R, Wittig J 1973 J. Low Temperat. Phys. 10 203

    [15]

    Dunn K J, Bundy F P 1982 Phys. Rev. B 25 194

    [16]

    Witting J, Matthias B T 1969 Phys. Rev. Lett. 22 634

    [17]

    Dunn K J, Bundy F P 1981 Phys. Rev. B 24 1643

    [18]

    Sakata M, Nakamoto Y, Shimizu K, Matsuoka T, Ohishi Y 2011 Phys. Rev. B 83 220512(R)

    [19]

    Zheng H F 2002 J. Phys.: Condens. Matter 14 5129

    [20]

    Jona F, Marcus P M 2006 J. Phys.: Condens. Matter 18 4623

    [21]

    Belger D, Hüsges Z, Voloshina E, Paulus B 2010 J. Phys.: Condens. Matter 22 275504

    [22]

    Jona F, Marcus P M 2008 Europhys. Lett. 74 83

    [23]

    Baroni S, Dal Corso A, de Gironcoli S, Giannozzi P, Cavazzoni C, Ballabio G, Scandolo S, Chiarotti G, Focher P, Pasquarello A, Laasonen K, Trave A, Car R, Marzari N, Kokalj A 2011 http: // www. pwscf. org/ [2011. 11. 19]

    [24]

    Troullier N, Martins J L 1991 Phys. Rev. B 43 1993

    [25]

    Perdew P J, Chevary A J , Vosko H S, Jackson A K, Pedersen R M, Singh J D, Fiolhais 1992 Phys. Rev. B 46 6671

    [26]

    Monnkhorst H J, Pack J D 1976 Phys. Rev. B 13 5188

    [27]

    Nielsen O H, Martin R M 1985 Phys. Rev. B 32 3792

    [28]

    Milman V, Warren M C 2001 J. Phys.: Condens. Matter 13 241

    [29]

    Sinpko G V, Smirnow N A 2002 J. Phys.: Condens. Matter 14 6989

    [30]

    Nelmes R J, Allan D R, McMahon M I, Belmonte S A 1999 Phys. Rev. Lett. 83 4081

    [31]

    Reed S K, Ackland G 2000 J. Phys. Rev. Lett. 84 5580

    [32]

    Liu Z M, Cui T, Ma Y M, Liu B B, Zou G T 2007 Acta Phys. Sin. 56 4877 (in Chinese) [刘志明, 崔田, 马琰铭, 刘冰冰, 邹广田 2005 物理学报 56 4877]

    [33]

    Yuan P F, Zhu W J, Xu J A, Liu S J, Jing F Q 2010 Acta Phys. Sin. 59 8755 (in Chinese) [原鹏飞, 祝文军, 徐济安, 刘绍军, 经福谦 2010 物理学报 59 8755]

    [34]

    Miao R D, Tian M, Huang G Q 2008 Acta Phys. Sin. 57 3709 (in Chinese) [苗仁德, 田苗, 黄桂芹 2008 物理学报 57 3709]

    [35]

    Xin X G, Chen X, Zhou J J, Shi S Q 2011 Acta Phys. Sin. 60 028201 (in Chinese) [忻晓桂, 陈香, 周晶晶, 施思齐 2008 物理学报 60 028201]

    [36]

    Sinko G V, Smirnow N A 2002 J. Phys.: Condens. Matter 14 6989

    [37]

    Anderson O L 1963 J. Phys. Chem. Solids 24 909

    [38]

    Schreiber E, Anderson O L, Soga N 1973 Elastic Constants and Their Measurements (NewYork: McGraw-Hill)

    [39]

    Hill R 1952 Phys. Soc. London 65 350

    [40]

    Deng X H, Lu W, Hu Y M, Gu H S 2009 Physica B 404 1218

    [41]

    Ravindran P, Fast L, Korzhavyi P A, Johansson B, Wills J, Eriksson O 1998 J. Appl. Phys. 84 4891

    [42]

    Lindemann F R 1910 Z. Phys. 11 609

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  • Received Date:  19 November 2011
  • Accepted Date:  26 December 2011
  • Published Online:  05 July 2012

First principles investigations of the structural stability and thermal dynamical properties of metal Ba under high pressure

  • 1. College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China;
  • 2. College of Physics and Electronic Information, Inner Mongolia University for Nationalities, Tongliao 028043, China
Fund Project:  Projected supported by the National Natural Science Foundation of China (Grant No. 11164020), China Postdoctoral Science Foundation Funded Project (Grant No. 20110491317), Natural Science Foundation of Science and Technology Department of Henan Province, China (Grant Nos. 102300410209, 112300410112, 112300410121, 112300410187), Natural Science Foundation of Education Department of Henan Province, China (Grant Nos. 2011B140015, 2010B140012), the Higher Education Reform of Henan Province, China (Grant No. 2012SJGLX233), and the Nanyang Normal University Science Foundation, China (Grant Nos. ZX20100011, ZX2012018).

Abstract: The stabilities and the thermal dynamical properties of the three high-pressure phases of Ba (Ba-I, Ba-Ⅱ and Ba-V ) are investigated systemically by first principles method. Our results show that all the three phase meet the criteria of mechanical and dynamical stabilities at 0 K. With pressure increasing, the phonon frequencies in Ba-I and Ba-Ⅱ phases become softened, whereas the Ba-V phase exhibits the hardening of phonon frequencies. Although both Ba-Ⅱ and Ba-V phase are the same hcp structures, they show different elastic anisotropies under high pressure. We also find that Ba-Ⅱ phase at higher pressure still meets the mechanical stability criterion, but does not meet the dynamical stability criterion. The absence of dynamical stability may be the reason for the transition from Ba-Ⅱ phase to Ba-I!V phase. We also calculate and make comparisons of sound velocity, Debye temperature, bulk modulus and shear modulus etc between Ba-Ⅱ and Ba-V phases, showing that Ba possesses the thermal dynamical properties under high pressure.

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