First-principles study of phase transition of BaF
						<sub>2</sub> under high pressue

Tian Cheng; Lan Jian-Xiong; Wang Cang-Long; Zhai Peng-Fei; Liu Jie

doi:10.7498/aps.71.20211163

Abstract

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.

Keywords:

Authors and contacts

1.
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
2.
School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China

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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References

[1]	Snider E, Dasenbrock-Gammon N, McBride R, Debessai M, Vindana H, Vencatasamy K, Lawler K V, Salamat A, Dias R P 2020 Nature 586 373 Google 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 92 Google Scholar
[3]	徐波, 田永君 2017 物理学报 66 036201 Google Scholar Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201 Google Scholar
[4]	Ayala A P 2001 J. Phys. Condens. Matter 13 11741 Google Scholar
[5]	Kavner A 2008 Phys. Rev. B 77 224102 Google Scholar
[6]	Leger J M, Haines J, Atouf A, Schulte O, Hull S 1995 Phys. Rev. B 52 13247 Google 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. 186 231 Google Scholar
[8]	Speziale S, Duffy T S 2002 Phys. Chem. Miner. 29 465 Google 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 174121 Google Scholar
[10]	Smith J S, Desgreniers S, Tse J S, Sun J, Klug D D, Ohishi Y 2009 Phys. Rev. B 79 134101 Google Scholar
[11]	Kourouklis G A, Anastassakis E 1989 Phys. Status Solidi B 152 89 Google Scholar
[12]	Kessler J R, Monberg E, Nicol M 1974 J. Chem. Phys. 60 5057 Google 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 1317 Google Scholar
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[34]	Gonze X, Lee C 1997 Phys. Rev. B 55 10355 Google Scholar
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[37]	Soni H R, Gupta S K, Talati M, Jha P K 2011 J. Phys. Chem. Solids 72 934 Google Scholar
[38]	Kinoshita K, Nishimura M, Akahama Y, Kawamura H 2007 Solid State Commun. 141 69 Google Scholar
[39]	Luo D B, Wang Y C, Yang G C, Ma Y M 2018 J. Phys. Chem. C 122 12448 Google Scholar
[40]	Rubloff G W 1972 Phys. Rev. B 5 662 Google Scholar
[41]	Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 Physica B 328 283 Google Scholar
[42]	Shi H, Luo W, Johansson B, Ahujia R 2009 J. Phys. Condens. Matter 21 415501 Google 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 077103 Google Scholar
[44]	朱春野, 刘欢欢, 刘艳辉 2011 延边大学学报(自然科学版) 37 19 Google Scholar Zhu C Y, Liu H H, Liu Y H 2011 J. Yanbian Univ. (Natural Science Edition) 37 19 Google 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 114213 Google Scholar Wu C G, Wu W Y, Gong Y C, Dai B F, He S H, Huang Y H 2015 Acta Phys. Sin. 64 114213 Google Scholar

Cited By

图 1 BaF ₂相对焓差随压强的变化

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

DownLoad: Full-Size Img PowerPoint

图 2 BaF ₂的相对体积随压强的变化

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

DownLoad: Full-Size Img PowerPoint

图 3 BaF ₂3种物相晶格常数随压强的变化

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

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 6 P6 ₃/ mmc结构 M点声学支声子振动频率随压强的变化

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

DownLoad: Full-Size Img PowerPoint

图 7 GGA泛函计算BaF ₂3种物相带隙随压强的变化

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

DownLoad: Full-Size Img PowerPoint

图 8 Pnma相电子态密度随压强的变化

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

DownLoad: Full-Size Img PowerPoint

图 9 Pnma相F1原子投影电子态密度(PDOS)随压强的变化

Figure 9. Projected DOS onto p _y + p _z and px orbitals of F1 atoms for Pnma and P6 ₃/ mmc structure.

DownLoad: Full-Size Img PowerPoint

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

DownLoad: 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 586 373 Google 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 92 Google Scholar
[3]	徐波, 田永君 2017 物理学报 66 036201 Google Scholar Xu B, Tian Y J 2017 Acta Phys. Sin. 66 036201 Google Scholar
[4]	Ayala A P 2001 J. Phys. Condens. Matter 13 11741 Google Scholar
[5]	Kavner A 2008 Phys. Rev. B 77 224102 Google Scholar
[6]	Leger J M, Haines J, Atouf A, Schulte O, Hull S 1995 Phys. Rev. B 52 13247 Google 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. 186 231 Google Scholar
[8]	Speziale S, Duffy T S 2002 Phys. Chem. Miner. 29 465 Google 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 174121 Google Scholar
[10]	Smith J S, Desgreniers S, Tse J S, Sun J, Klug D D, Ohishi Y 2009 Phys. Rev. B 79 134101 Google Scholar
[11]	Kourouklis G A, Anastassakis E 1989 Phys. Status Solidi B 152 89 Google Scholar
[12]	Kessler J R, Monberg E, Nicol M 1974 J. Chem. Phys. 60 5057 Google 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 1317 Google 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 9969 Google Scholar
[15]	Yang X C, Hao A M, Wang X M, Liu X, Zhu Y 2010 Comput. Mater. Sci. 49 530 Google Scholar
[16]	Jiang H T, Pandey R, Darrigan C, Rerat M 2003 J. Phys. Condens. Matter 15 709 Google Scholar
[17]	Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 J. Alloys Compd. 359 66 Google Scholar
[18]	Blochl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[19]	Kresse G, Furthmuller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[20]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[21]	Dai J J, Feng Q G 2020 Phys. Status Solidi B 257 1900726 Google Scholar
[22]	Xiao H Y, Jiang X D, Duan G, Gao F, Zu X T, Weber W J 2010 Comput. Mater. Sci. 48 768 Google Scholar
[23]	Cui S X, Feng W X, Hua H Q, Feng Z B, Wang Y X 2009 Comput. Mater. Sci. 47 41 Google 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 1403 Google Scholar
[25]	Boudjemline A, Louail L, Islam M M, Diawara B 2011 Comput. Mater. Sci. 50 2280 Google Scholar
[26]	Guo Y, Fang Y M, Li J 2021 Chin. Phys. B 30 030502 Google Scholar
[27]	Wu X, Qin S, Wu Z Y 2006 Phys. Rev. B 73 134103 Google Scholar
[28]	Verma A K, Modak P, Sharma S M 2017 J. Alloys Compd. 710 460 Google 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 134108 Google Scholar
[30]	Song H X, Liu L, Geng H Y, Wu Q 2013 Phys. Rev. B 87 184103 Google Scholar
[31]	Kunc K, Loa I, Syassen K 2008 Phys. Rev. B 77 094110 Google Scholar
[32]	Ji D P, Chong X Y, Ge Z H, Feng J 2019 J. Alloys Compd. 773 988 Google Scholar
[33]	Liu G, Wang H, Ma Y M, Ma Y M 2011 Solid State Commun. 151 1899 Google Scholar
[34]	Gonze X, Lee C 1997 Phys. Rev. B 55 10355 Google Scholar
[35]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106 Google Scholar
[36]	Kroumova E, Aroyo M I, Perez-Mato J M, Kirov A, Capillas C, Ivantchev S, Wondratschek H 2003 Phase Transitions 76 155 Google Scholar
[37]	Soni H R, Gupta S K, Talati M, Jha P K 2011 J. Phys. Chem. Solids 72 934 Google Scholar
[38]	Kinoshita K, Nishimura M, Akahama Y, Kawamura H 2007 Solid State Commun. 141 69 Google Scholar
[39]	Luo D B, Wang Y C, Yang G C, Ma Y M 2018 J. Phys. Chem. C 122 12448 Google Scholar
[40]	Rubloff G W 1972 Phys. Rev. B 5 662 Google Scholar
[41]	Kanchana V, Vaitheeswaran G, Rajagopalan M 2003 Physica B 328 283 Google Scholar
[42]	Shi H, Luo W, Johansson B, Ahujia R 2009 J. Phys. Condens. Matter 21 415501 Google 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 077103 Google Scholar
[44]	朱春野, 刘欢欢, 刘艳辉 2011 延边大学学报(自然科学版) 37 19 Google Scholar Zhu C Y, Liu H H, Liu Y H 2011 J. Yanbian Univ. (Natural Science Edition) 37 19 Google 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 114213 Google Scholar Wu C G, Wu W Y, Gong Y C, Dai B F, He S H, Huang Y H 2015 Acta Phys. Sin. 64 114213 Google Scholar

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

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Corresponding author: Zhai Peng-Fei, zhaipengfei@impcas.ac.cn

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

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Corresponding author: Zhai Peng-Fei, zhaipengfei@impcas.ac.cn

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