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BaF 2高压相变行为的第一性原理研究

田城 蓝剑雄 王苍龙 翟鹏飞 刘杰

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BaF 2高压相变行为的第一性原理研究

田城, 蓝剑雄, 王苍龙, 翟鹏飞, 刘杰

First-principles study of phase transition of BaF 2 under high pressue

Tian Cheng, Lan Jian-Xiong, Wang Cang-Long, Zhai Peng-Fei, Liu Jie
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  • 通过理论计算研究了BaF 2在高压下的晶体结构及物理性质. 结果表明, 在3.5和18.3 GPa, BaF 2依次经历了 Fm $ \overline {3} $ m- Pnma- P6 3/ mmc两次结构相变, 相变过程伴随着体积的塌缩, 均为一级相变. 约15 GP时, Pnma相晶轴压缩性出现异常, 表现为随压强增大, 晶轴 b o轻微增加, a o略微减小. 对其电子态密度进行分析发现, 在16 GPa以后, 由于F1原子的p y + p z 与p x 轨道电子离域, 导致其带隙随压强增加而降低. 在约20 GPa时, Pnma相完全转变为 P6 3/ mmc相, 相变完成. 对BaF 2的拉曼峰位随压强变化进行了计算, 为其高压拉曼光谱行为提供了相应的理论依据. 计算了 P6 3/ mmc相在不同压强下的声子色散曲线, 揭示了其卸压过程中的滞后机制, 计算结果还预测该物相至少可以稳定到80 GPa.
    There have been some theoretical studies of high pressure phase transition behavior of BaF 2, while in most cases the attention is paid mainly to the optical and electrical properties of BaF 2 under increasing pressure. To date, there has been still a lack of theoretical explanation for the hysteresis phenomenon of high-pressure phase of BaF 2 when the pressure is released. In addition, the pressure-dependent behavior of the BaF 2 band gap is still under controversy, and there are few studies of its high-pressure Raman spectra. Therefore, first principle is used to make a supplementary calculation of the high pressure behavior of BaF 2. For a given pressure P and temperature T, the thermodynamic stable phase has the lowest Gibbs free energy. The calculations are performed at zero temperature and hence, the Gibbs free energy becomes equal to the enthalpy. Thus, the variation of enthalpy is calculated as a function of pressure to study the high-pressure phase stability of BaF 2 based on density functional theory as implemented in the Vienna ab initio simulation package (VASP). The results show that the BaF 2 undergoes two structural phase transitions from Fm3 m(cubic) to Pnma (orthorhombic) and then to P6 3/ mmc(hexagonal) with increasing pressure, and their corresponding transition pressures are 3.5 and 18.3 GPa, respectively. By calculating the evolution of lattice constant with pressure, it is found that at about 15 GPa (near the second phase transition pressure), the lattice constants of the Pnma structure show abnormal behavior (a slight increase in b o and a slight decrease in a o). We suggest that this behavior leads the band gap to decrease, indicated by analyzing the calculated results of Pnma structure of other materials. The Pnma structure completely transforms into P6 3/ mmc structure at about 20 GPa. By analyzing the phonon dispersion curves of BaF 2 as a function of pressure, the structural stability information of the material can also be obtained. Then the density functional perturbation theory (DFPT) is used to calculate the phonon dispersion curves of BaF 2 by VASP code and Phonopy code. The hysteresis phenomenon of the P6 3/ mmc structure, when the pressure is released, is explained by the kinetic stability. The results predict that the P6 3/ mmc structure can be stabilized at least to 80 GPa.
      通信作者: 翟鹏飞, zhaipengfei@impcas.ac.cn
    • 基金项目: 国家自然科学基金(批准号: 12075290, 12035019)、中国科学院青年创新促进会(批准号: 2020412)和中国科学院硅器件技术重点实验室开放基金(批准号: KLSDTJJ2019-06)资助的课题
      Corresponding author: Zhai Peng-Fei, zhaipengfei@impcas.ac.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 12075290, 12035019), the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No. 2020412), and the Opening Fund of Key Laboratory of Silicon Device and Technology, Chinese Academy of Sciences (Grant No. KLSDTJJ2019-06)
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    Snider E, Dasenbrock-Gammon N, McBride R, Debessai M, Vindana H, Vencatasamy K, Lawler K V, Salamat A, Dias R P 2020 Nature 586 373Google Scholar

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    Xia J, Yan J, Wang Z, He Y, Gong Y, Chen W, Sum T C, Liu Z, Ajayan P M, Shen Z 2021 Nat. Phys. 17 92Google Scholar

    [3]

    徐波, 田永君 2017 物理学报 66 036201Google Scholar

    Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201Google Scholar

    [4]

    Ayala A P 2001 J. Phys. Condens. Matter 13 11741Google Scholar

    [5]

    Kavner A 2008 Phys. Rev. B 77 224102Google Scholar

    [6]

    Leger J M, Haines J, Atouf A, Schulte O, Hull S 1995 Phys. Rev. B 52 13247Google Scholar

    [7]

    Wang J S, Ma C L, Zhou D, Xu Y S, Zhang M Z, Gao W, Zhu H Y, Cui Q L 2012 J. Solid State Chem. 186 231Google Scholar

    [8]

    Speziale S, Duffy T S 2002 Phys. Chem. Miner. 29 465Google Scholar

    [9]

    Dorfman S M, Jiang F M, Mao Z, Kubo A, Meng Y, Prakapenka V B, Duffy T S 2010 Phys. Rev. B 81 174121Google Scholar

    [10]

    Smith J S, Desgreniers S, Tse J S, Sun J, Klug D D, Ohishi Y 2009 Phys. Rev. B 79 134101Google Scholar

    [11]

    Kourouklis G A, Anastassakis E 1989 Phys. Status Solidi B 152 89Google Scholar

    [12]

    Kessler J R, Monberg E, Nicol M 1974 J. Chem. Phys. 60 5057Google Scholar

    [13]

    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. U. S. A. 107 1317Google Scholar

    [14]

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

    [15]

    Yang X C, Hao A M, Wang X M, Liu X, Zhu Y 2010 Comput. Mater. Sci. 49 530Google Scholar

    [16]

    Jiang H T, Pandey R, Darrigan C, Rerat M 2003 J. Phys. Condens. Matter 15 709Google Scholar

    [17]

    Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 J. Alloys Compd. 359 66Google Scholar

    [18]

    Blochl P E 1994 Phys. Rev. B 50 17953Google Scholar

    [19]

    Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 6 15Google Scholar

    [20]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [21]

    Dai J J, Feng Q G 2020 Phys. Status Solidi B 257 1900726Google Scholar

    [22]

    Xiao H Y, Jiang X D, Duan G, Gao F, Zu X T, Weber W J 2010 Comput. Mater. Sci. 48 768Google Scholar

    [23]

    Cui S X, Feng W X, Hua H Q, Feng Z B, Wang Y X 2009 Comput. Mater. Sci. 47 41Google Scholar

    [24]

    Kessair S, Arbouche O, Amara K, Benallou Y, Azzaz Y, Zemouli M, Bekki M, Ameri M, Bouazza B S 2016 Indian J. Phys. 90 1403Google Scholar

    [25]

    Boudjemline A, Louail L, Islam M M, Diawara B 2011 Comput. Mater. Sci. 50 2280Google Scholar

    [26]

    Guo Y, Fang Y M, Li J 2021 Chin. Phys. B 30 030502Google Scholar

    [27]

    Wu X, Qin S, Wu Z Y 2006 Phys. Rev. B 73 134103Google Scholar

    [28]

    Verma A K, Modak P, Sharma S M 2017 J. Alloys Compd. 710 460Google Scholar

    [29]

    Tse J S, Klug D D, Desgreniers S, Smith J S, Flacau R, Liu Z, Hu J, Chen N, Jiang D T 2007 Phys. Rev. B 75 134108Google Scholar

    [30]

    Song H X, Liu L, Geng H Y, Wu Q 2013 Phys. Rev. B 87 184103Google Scholar

    [31]

    Kunc K, Loa I, Syassen K 2008 Phys. Rev. B 77 094110Google Scholar

    [32]

    Ji D P, Chong X Y, Ge Z H, Feng J 2019 J. Alloys Compd. 773 988Google Scholar

    [33]

    Liu G, Wang H, Ma Y M, Ma Y M 2011 Solid State Commun. 151 1899Google Scholar

    [34]

    Gonze X, Lee C 1997 Phys. Rev. B 55 10355Google Scholar

    [35]

    Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106Google Scholar

    [36]

    Kroumova E, Aroyo M I, Perez-Mato J M, Kirov A, Capillas C, Ivantchev S, Wondratschek H 2003 Phase Transitions 76 155Google Scholar

    [37]

    Soni H R, Gupta S K, Talati M, Jha P K 2011 J. Phys. Chem. Solids 72 934Google Scholar

    [38]

    Kinoshita K, Nishimura M, Akahama Y, Kawamura H 2007 Solid State Commun. 141 69Google Scholar

    [39]

    Luo D B, Wang Y C, Yang G C, Ma Y M 2018 J. Phys. Chem. C 122 12448Google Scholar

    [40]

    Rubloff G W 1972 Phys. Rev. B 5 662Google Scholar

    [41]

    Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 Physica B 328 283Google Scholar

    [42]

    Shi H, Luo W, Johansson B, Ahujia R 2009 J. Phys. Condens. Matter 21 415501Google Scholar

    [43]

    Hao A M, Yang X C, Li J, Xin W, Zhang S H, Zhang X Y, Liu R P 2009 Chin. Phys. Lett. 26 077103Google Scholar

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    朱春野, 刘欢欢, 刘艳辉 2011 延边大学学报(自然科学版) 37 19Google Scholar

    Zhu C Y, Liu H H, Liu Y H 2011 J. Yanbian Univ. (Natural Science Edition) 37 19Google Scholar

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    吴成国, 武文远, 龚艳春, 戴斌飞, 何苏红, 黄雁华 2015 物理学报 64 114213Google Scholar

    Wu C G, Wu W Y, Gong Y C, Dai B F, He S H, Huang Y H 2015 Acta Phys. Sin. 64 114213Google Scholar

  • 图 1  BaF 2相对焓差随压强的变化

    Fig. 1.  Variation of enthalpy difference with pressure for BaF 2

    图 2  BaF 2的相对体积随压强的变化

    Fig. 2.  Relative volume ( V/ V 0) variation of BaF 2 as a function of pressure.

    图 3  BaF 23种物相晶格常数随压强的变化

    Fig. 3.  Evolution of the lattice constants of BaF 2 with three structures under pressure.

    图 4  BaF 2(a) Fm $ \overline {3} $ m结构T 2g模和(b) P6 3/ mmc结构2E 2g模拉曼峰位随压强的变化

    Fig. 4.  Raman shift as a function of pressure for (a) T 2g of Fm $ \overline {3} $ m and (b) 2E 2g of P6 3/ mmc.

    图 5  不同压强下BaF 2P6 3/ mmc相声子谱 (a) 12 GPa; (b) 14 GPa; (c) 40 GPa; (d) 80 GPa

    Fig. 5.  Phonon dispersion curves for P6 3/ mmc structure of BaF 2 at different pressures: (a) 12 GPa; (b) 14 GPa; (c) 40 GPa; (d) 80 GPa.

    图 6  P6 3/ mmc结构 M点声学支声子振动频率随压强的变化

    Fig. 6.  Phonon frequencies at M point as a function of pressure for P6 3/ mmc structure.

    图 7  GGA泛函计算BaF 23种物相带隙随压强的变化

    Fig. 7.  Band gap as a function of pressure for three structures with GGA of BaF 2.

    图 8  Pnma相电子态密度随压强的变化

    Fig. 8.  DOS of BaF 2 for Pnma structure at different pressure

    图 9  Pnma相F1原子投影电子态密度(PDOS)随压强的变化

    Fig. 9.  Projected DOS onto p y + p z and px orbitals of F1 atoms for Pnma and P6 3/ mmc structure.

    表 1  10 GPa压强下 Pnma结构BaF 2拉曼峰位计算结果

    Table 1.  Calculated Raman shift of Pnma structure BaF 2 under 10 GPa.

    Mode ω/cm –1 Mode ω/cm –1 Mode ω/cm –1
    A g 81.2 A g 190.6 B 2g 268.7
    B 3g 81.4 B 1g 203.3 A g 283.3
    B 1g 90.2 A g 211.2 B 1g 304.4
    A g 112.9 B 3g 218.7 B 3g 309.6
    B 2g 151.5 B 2g 224.0 A g 321.6
    B 2g 174.7 B 2g 251.2 B 2g 363.8
    下载: 导出CSV
  • [1]

    Snider E, Dasenbrock-Gammon N, McBride R, Debessai M, Vindana H, Vencatasamy K, Lawler K V, Salamat A, Dias R P 2020 Nature 586 373Google Scholar

    [2]

    Xia J, Yan J, Wang Z, He Y, Gong Y, Chen W, Sum T C, Liu Z, Ajayan P M, Shen Z 2021 Nat. Phys. 17 92Google Scholar

    [3]

    徐波, 田永君 2017 物理学报 66 036201Google Scholar

    Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201Google Scholar

    [4]

    Ayala A P 2001 J. Phys. Condens. Matter 13 11741Google Scholar

    [5]

    Kavner A 2008 Phys. Rev. B 77 224102Google Scholar

    [6]

    Leger J M, Haines J, Atouf A, Schulte O, Hull S 1995 Phys. Rev. B 52 13247Google Scholar

    [7]

    Wang J S, Ma C L, Zhou D, Xu Y S, Zhang M Z, Gao W, Zhu H Y, Cui Q L 2012 J. Solid State Chem. 186 231Google Scholar

    [8]

    Speziale S, Duffy T S 2002 Phys. Chem. Miner. 29 465Google Scholar

    [9]

    Dorfman S M, Jiang F M, Mao Z, Kubo A, Meng Y, Prakapenka V B, Duffy T S 2010 Phys. Rev. B 81 174121Google Scholar

    [10]

    Smith J S, Desgreniers S, Tse J S, Sun J, Klug D D, Ohishi Y 2009 Phys. Rev. B 79 134101Google Scholar

    [11]

    Kourouklis G A, Anastassakis E 1989 Phys. Status Solidi B 152 89Google Scholar

    [12]

    Kessler J R, Monberg E, Nicol M 1974 J. Chem. Phys. 60 5057Google Scholar

    [13]

    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. U. S. A. 107 1317Google Scholar

    [14]

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

    [15]

    Yang X C, Hao A M, Wang X M, Liu X, Zhu Y 2010 Comput. Mater. Sci. 49 530Google Scholar

    [16]

    Jiang H T, Pandey R, Darrigan C, Rerat M 2003 J. Phys. Condens. Matter 15 709Google Scholar

    [17]

    Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 J. Alloys Compd. 359 66Google Scholar

    [18]

    Blochl P E 1994 Phys. Rev. B 50 17953Google Scholar

    [19]

    Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 6 15Google Scholar

    [20]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [21]

    Dai J J, Feng Q G 2020 Phys. Status Solidi B 257 1900726Google Scholar

    [22]

    Xiao H Y, Jiang X D, Duan G, Gao F, Zu X T, Weber W J 2010 Comput. Mater. Sci. 48 768Google Scholar

    [23]

    Cui S X, Feng W X, Hua H Q, Feng Z B, Wang Y X 2009 Comput. Mater. Sci. 47 41Google Scholar

    [24]

    Kessair S, Arbouche O, Amara K, Benallou Y, Azzaz Y, Zemouli M, Bekki M, Ameri M, Bouazza B S 2016 Indian J. Phys. 90 1403Google Scholar

    [25]

    Boudjemline A, Louail L, Islam M M, Diawara B 2011 Comput. Mater. Sci. 50 2280Google Scholar

    [26]

    Guo Y, Fang Y M, Li J 2021 Chin. Phys. B 30 030502Google Scholar

    [27]

    Wu X, Qin S, Wu Z Y 2006 Phys. Rev. B 73 134103Google Scholar

    [28]

    Verma A K, Modak P, Sharma S M 2017 J. Alloys Compd. 710 460Google Scholar

    [29]

    Tse J S, Klug D D, Desgreniers S, Smith J S, Flacau R, Liu Z, Hu J, Chen N, Jiang D T 2007 Phys. Rev. B 75 134108Google Scholar

    [30]

    Song H X, Liu L, Geng H Y, Wu Q 2013 Phys. Rev. B 87 184103Google Scholar

    [31]

    Kunc K, Loa I, Syassen K 2008 Phys. Rev. B 77 094110Google Scholar

    [32]

    Ji D P, Chong X Y, Ge Z H, Feng J 2019 J. Alloys Compd. 773 988Google Scholar

    [33]

    Liu G, Wang H, Ma Y M, Ma Y M 2011 Solid State Commun. 151 1899Google Scholar

    [34]

    Gonze X, Lee C 1997 Phys. Rev. B 55 10355Google Scholar

    [35]

    Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106Google Scholar

    [36]

    Kroumova E, Aroyo M I, Perez-Mato J M, Kirov A, Capillas C, Ivantchev S, Wondratschek H 2003 Phase Transitions 76 155Google Scholar

    [37]

    Soni H R, Gupta S K, Talati M, Jha P K 2011 J. Phys. Chem. Solids 72 934Google Scholar

    [38]

    Kinoshita K, Nishimura M, Akahama Y, Kawamura H 2007 Solid State Commun. 141 69Google Scholar

    [39]

    Luo D B, Wang Y C, Yang G C, Ma Y M 2018 J. Phys. Chem. C 122 12448Google Scholar

    [40]

    Rubloff G W 1972 Phys. Rev. B 5 662Google Scholar

    [41]

    Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 Physica B 328 283Google Scholar

    [42]

    Shi H, Luo W, Johansson B, Ahujia R 2009 J. Phys. Condens. Matter 21 415501Google Scholar

    [43]

    Hao A M, Yang X C, Li J, Xin W, Zhang S H, Zhang X Y, Liu R P 2009 Chin. Phys. Lett. 26 077103Google Scholar

    [44]

    朱春野, 刘欢欢, 刘艳辉 2011 延边大学学报(自然科学版) 37 19Google Scholar

    Zhu C Y, Liu H H, Liu Y H 2011 J. Yanbian Univ. (Natural Science Edition) 37 19Google Scholar

    [45]

    吴成国, 武文远, 龚艳春, 戴斌飞, 何苏红, 黄雁华 2015 物理学报 64 114213Google Scholar

    Wu C G, Wu W Y, Gong Y C, Dai B F, He S H, Huang Y H 2015 Acta Phys. Sin. 64 114213Google Scholar

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出版历程
  • 收稿日期:  2021-06-21
  • 修回日期:  2021-09-29
  • 上网日期:  2021-12-25
  • 刊出日期:  2022-01-05

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