Isostructural phase transition of fcc Ce: Molecular dynamics simulations

Diwu Min-Jie; Hu Xiao-Mian

doi:10.7498/aps.68.20190884

Abstract

Ce is a rare earth element in the periodic table. In the range of low temperature and low pressure, there are two face-centered-cubic (FCC) phases (α-Ce and γ-Ce) and a double-hexagonal-close-packed phase (β-Ce) for metallic Ce. At ambient temperature and about 0.7 GPa pressure, Ce undergoes γ→α phase transition with a volume shrink of 14%–17% discontinuously. In this paper, an embedded-atom method (EAM) potential compatible for α-Ce and γ-Ce was developed. This EAM potential has been employed to study several basic properties of cerium in these two FCC phases, such as equilibrium lattice constants, cohesive energies, and elastic constants. These results showed good accordance with experiments and first principle calculations. The lattice defects have been studied with the formation energy calculations of vacancies, interstitials, surfaces, stacking faults, and twinning defects in α-Ce and γ-Ce lattice. The lattice dynamics of α-Ce and γ-Ce have been analyzed using our EAM potential. The lattice vibrational entropy was calculated and plotted as functions of temperature for each phases. The vibrational entropy change across the α-γ phase transition showed to be ~0.67 k_B per atom at ambient temperature. Using molecular dynamics simulation with our EAM potential, several isotherms and radial distribution functions were calculated. These isotherms and radial distribution functions demonstrate a first order phase transition between two FCC structures, corresponding to α-Ce and γ-Ce, with a critical point sets at T_c≈550 K and P_c≈1.21 GPa. Thus the newly developed EAM potential could provide a reasonable description of FCC Ce and its α-γ phase transition within the scale of classical molecular dynamics simulation.

Keywords:

Authors and contacts

Diwu Min-Jie¹,
Hu Xiao-Mian²

1.
Graduate School, China Academy of Engineering Physics, Beijing 100088, China
2.
National Laboratory of Computational Physics, Beijing Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Corresponding author: Hu Xiao-Mian, hu_xiaomian@iapcm.ac.cn

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References

[1]	郑海冰 2017 硕士学位论文 (哈尔滨: 哈尔滨工业大学 Zheng H B 2017 M. S. Thesis (Harbin: Harbin Institute of Technoloty) (in Chinese)
[2]	金铭 2018 硕士学位论文 (哈尔滨: 哈尔滨工业大学 Jin M 2018 M. S. Thesis (Harbin: Harbin Institute of Technoloty) (in Chinese)
[3]	林河成 2005 中国有色冶金 3 31 Google Scholar Lin H C 2005 China Nonferrous Metallurgy 3 31 Google Scholar
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[5]	潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 物理学报 61 206401 Google Scholar Pan H, Hu X M, Wu Z H, Dai C D, Wu Q 2012 Acta Phys. Sin. 61 206401 Google Scholar
[6]	Wang Y, Jr Hector L G, Zhang H, Shang S L, Chen L Q, Liu Z K 2008 Phys. Rev. B 78 104113 Google Scholar
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[12]	Amadon B, Biermann S, Georges A, Aryasetiawan F 2006 Phys. Rev. Lett. 96 066402 Google Scholar
[13]	Jeong I K, Darling T W, Graf M J, Proffen T, Heffner R H, Lee Y, Vogt T, Jorgensen J D 2004 Phys. Rev. Lett. 92 105702 Google Scholar
[14]	El'kin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Phys. Met. Metall. 101 208 Google Scholar
[15]	El'kin V M, Mikhaylov V N, Petrovtsev A V, Cherne F J 2011 Phys. Rev. B 84 094120 Google Scholar
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[18]	Huang L, Chen CA 2007 J. Phys.Condens. Matter 19 476206 Google Scholar
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[25]	Dupont V, Chen S P, Germann T C 2010 EPJ Web of Conferences Paris, France, May 24–28, 2010 p00009
[26]	Dupont V, Germann T C 2010 APS March Meeting Portland, Oregon, March 15–19, 2010 W30.00007
[27]	Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2963
[28]	Duff A I, Finnis M W, Maugis P, Thijsse B J, Sluiter M H F 2015 Comput. Phys. Commun. 196 439 Google Scholar
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[31]	Greiner J D, McMasters O D, Smith J F 1980 Scr. Metall. 14 989 Google Scholar
[32]	Staun Olsen J, Gerward L, Dancausse J P, Gering E 1993 Physica B 190 92 Google Scholar
[33]	Voronov F F, Goncharova V A, Stal'gorova O V 1979 Soviet Phys. JETP 49 687
[34]	Söderlind P, Eriksson O, Wills J M, Boring A M 1993 Phys. Rev. B 48 9306 Google Scholar
[35]	Korzhavyi P A, Abrikosov I A, Johansson B, Ruban A V, Skriver H L 1999 Phys. Rev. B 59 11693 Google Scholar
[36]	Press W H, Teukolsky S A, Vetterling W T, Flannery B P 2007 Numerical Recipes: The Art of Scientific Computing (3rd Ed.) (New York: Cambridge University Press) pp487–562
[37]	Östlin A, Di Marco I, Locht I L M, Lashley J C, Vitos L 2016 Phys. Rev. B 93 094103 Google Scholar
[38]	van Swygenhoven H, Derlet P M, Frøseth A G 2004 Nat. Mater. 3 399 Google Scholar
[39]	Hai S, Tadmor E B 2003 Acta Mater. 51 117 Google Scholar
[40]	Tadmor E, Hai S 2003 J. Mech. Phys. Solids 51 765 Google Scholar
[41]	Stassis C, Gould T, McMasters O D, Gschneidner K A, Nicklow R M 1979 Phys. Rev. B 19 5746 Google Scholar

Cited By

图 1 Ce的EAM势　(a)对势函数和电子密度分布函数; (b)嵌入能函数

Figure 1. EAM potential for Ce: (a) The pair function Φ(r_ij) and the density function f(r_ij); (b) the embedded function F(ρ).

DownLoad: Full-Size Img PowerPoint

图 2 由本文EAM势得出的面心立方Ce的冷能曲线

Figure 2. The cold energy of fcc Ce calculated with the newly developed EAM potential.

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图 3 面心立方Ce中的广义层错能和广义孪晶能　(a) α-Ce; (b) γ-Ce

Figure 3. Generalized stacking fault energy and generalized twining fault energy curve for (a) α-Ce and (b) γ-Ce.

DownLoad: Full-Size Img PowerPoint

图 4 面心立方Ce的声子态密度

Figure 4. Phonon density of states for FCC Ce.

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图 5 α-Ce和γ-Ce两相的晶格振动熵S_vib以及熵差ΔS_vib (右下插图)随温度T的变化

Figure 5. The vibrational entropy S_viband its change ΔS_vibbetween two phases (the inset) plotted as functions of temperature.

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图 6 面心立方Ce的声子色散谱

Figure 6. Phonon dispersion relations for FCC Ce.

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图 7 面心立方Ce的等温线　(a) NPT增压; (b) NPT减压; (c) NVT

Figure 7. Isotherms of FCC Ce: (a) NPT, pressure increased; (b) NPT, pressure decreased; (c) NVT.

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图 8 Ce的γ→α和α→γ相变路径

Figure 8. The path of Ce γ→α and α→γ phase transition.

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图 9 零压以及图7中A, B两点状态的径向分布函数

Figure 9. Radial distribution function for zero pressure (black), the A state (red), and the B state (blue) pointed in Fig.7.

DownLoad: Full-Size Img PowerPoint

表 1 面心立方Ce的基本性质的EAM计算值与实验和第一性原理结果的比较

Table 1. EAM predicted properties of Ce lattice in comparison with experimental and ab initiodata.

	γ-Ce			α-Ce
	实验	第一性原理	本文EAM	实验	第一性原理	本文EAM
a₀/Å	5.16^[4]	5.22^[11]	5.14	4.84^[4] 4.90^[30]	4.63^[11]	4.81
E_coh/eV	4.32^[4]	4.35^[11]	4.32	4.3^[11]	3.76^[11]	4.3255
体弹模量/GPa	18.18^[31]	28.3^[11]	16.78	35.0^[32], 16.94^[33]	37.0^[34]	37.00
c₁₁ /GPa	26.01^[31]		23.06		52.9^[34]	59.77
c₁₂ /GPa	14.26^[31]		13.64		29.1^[34]	25.62
c₄₄ /GPa	17.30^[31]		17.64		44.6^[34]	49.98
剪切模量/GPa	12.73^[31]		12.47	17.26^[33]		36.82

DownLoad: CSV

表 2 γ-Ce and α-Ce中晶体缺陷的形成能

Table 2. Calculated formation energy of lattice defectsin γ-Ce and α-Ce.

	γ-Ce		α-Ce
	之前的结果	本文EAM	之前的结果	本文EAM
Eⁱ_f/eV	3.3^[22]	1.93		2.97
E^v_f/eV	0.75^[22], 2.02^[23]	0.85		1.15
γ₍₁₀₀₎/mJ·m^–2	697^[22], 2140^[23]	391		308
γ₍₁₁₀₎/mJ·m^–2	797^[22], 2220^[23]	442		390
γ₍₁₁₁₎/mJ·m^–2	586^[22], 2190^[23]	297		195
γ_ssf/mJ·m^–2	486^[22],58^[37], 16^[37], –0.2^[37]	457	301^[37], 311^[37], 369^[37]	734
γ_usf/mJ·m^–2	501^[22]	543		822
γ_utf/mJ·m^–2	12^[22]	768		1167

DownLoad: CSV

[1]	郑海冰 2017 硕士学位论文 (哈尔滨: 哈尔滨工业大学 Zheng H B 2017 M. S. Thesis (Harbin: Harbin Institute of Technoloty) (in Chinese)
[2]	金铭 2018 硕士学位论文 (哈尔滨: 哈尔滨工业大学 Jin M 2018 M. S. Thesis (Harbin: Harbin Institute of Technoloty) (in Chinese)
[3]	林河成 2005 中国有色冶金 3 31 Google Scholar Lin H C 2005 China Nonferrous Metallurgy 3 31 Google Scholar
[4]	Koskenmaki D C, Gschneidner K A 1978 Handbook on the Physics and Chemistry of Rare Earths (Vol. 1) (Amsterdam: Elsevier North-Holland) pp337–377
[5]	潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 物理学报 61 206401 Google Scholar Pan H, Hu X M, Wu Z H, Dai C D, Wu Q 2012 Acta Phys. Sin. 61 206401 Google Scholar
[6]	Wang Y, Jr Hector L G, Zhang H, Shang S L, Chen L Q, Liu Z K 2008 Phys. Rev. B 78 104113 Google Scholar
[7]	Decremps F, Belhadi L, Farber D L, Moore K T, Occelli F, Gauthier M, Polian A, Antonangeli D, Aracne-Ruddle C M, Amadon B 2011 Phys. Rev. Lett. 106 065701
[8]	Lipp M J, Jackson D, Cynn H, Aracne C, Evans W J, McMahan A K 2008 Phys. Rev. Lett. 101 165703 Google Scholar
[9]	Johansson B 1974 Philos. Mag. 30 469 Google Scholar
[10]	Allen J W, Martin R M 1982 Phys. Rev. Lett. 49 1106 Google Scholar
[11]	Casadei M, Ren X, Rinke P, Rubio A, Scheffler M 2016 Phys. Rev. B 93 075153 Google Scholar
[12]	Amadon B, Biermann S, Georges A, Aryasetiawan F 2006 Phys. Rev. Lett. 96 066402 Google Scholar
[13]	Jeong I K, Darling T W, Graf M J, Proffen T, Heffner R H, Lee Y, Vogt T, Jorgensen J D 2004 Phys. Rev. Lett. 92 105702 Google Scholar
[14]	El'kin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Phys. Met. Metall. 101 208 Google Scholar
[15]	El'kin V M, Mikhaylov V N, Petrovtsev A V, Cherne F J 2011 Phys. Rev. B 84 094120 Google Scholar
[16]	Yelkin V M, Kozlov E A, Kakshina E V, Moreva Y S 2006 Shock Compression of Condensed Matter–2005 Baltimore, Maryland 31 July–5 August, 2005 pp77–80
[17]	Casadei M, Ren X, Rinke P, Rubio A, Scheffler M 2012 Phys. Rev. Lett. 109 146402 Google Scholar
[18]	Huang L, Chen CA 2007 J. Phys.Condens. Matter 19 476206 Google Scholar
[19]	Krisch M, Farber D L, Xu R, Antonangeli D, Aracne C M, Beraud A, Chiang T-C, Zarestky J, Kim D Y, Isaev E I, Ahuja R, Johansson B 2011 Proc. Natl. Acad. Sci. U.S.A. 108 9342 Google Scholar
[20]	Singh N, Singh S P 1990 Phys. Rev. B 42 1652 Google Scholar
[21]	Hachiya K, Ito Y 1999 J. Phys. Condens. Matter 11 6543 Google Scholar
[22]	Sheng H W, Kramer M J, Cadien A, Fujita T, Chen M W 2011 Phys. Rev. B 83 134118 Google Scholar
[23]	Fu J, Zhao J 2013 Modell. Simul. Mater. Sci. Eng. 21 065003 Google Scholar
[24]	Voter A F, Chen S P 1986 MRS Proceedings 82 175 Google Scholar
[25]	Dupont V, Chen S P, Germann T C 2010 EPJ Web of Conferences Paris, France, May 24–28, 2010 p00009
[26]	Dupont V, Germann T C 2010 APS March Meeting Portland, Oregon, March 15–19, 2010 W30.00007
[27]	Rose J H, Smith J R, Guinea F, Ferrante J 1984 Phys. Rev. B 29 2963
[28]	Duff A I, Finnis M W, Maugis P, Thijsse B J, Sluiter M H F 2015 Comput. Phys. Commun. 196 439 Google Scholar
[29]	Plimpton S 1995 J. Comput. Phys. 117 1 Google Scholar
[30]	Eriksson O, Brooks M S S, Johansson B 1990 Phys. Rev. B 41 7311 Google Scholar
[31]	Greiner J D, McMasters O D, Smith J F 1980 Scr. Metall. 14 989 Google Scholar
[32]	Staun Olsen J, Gerward L, Dancausse J P, Gering E 1993 Physica B 190 92 Google Scholar
[33]	Voronov F F, Goncharova V A, Stal'gorova O V 1979 Soviet Phys. JETP 49 687
[34]	Söderlind P, Eriksson O, Wills J M, Boring A M 1993 Phys. Rev. B 48 9306 Google Scholar
[35]	Korzhavyi P A, Abrikosov I A, Johansson B, Ruban A V, Skriver H L 1999 Phys. Rev. B 59 11693 Google Scholar
[36]	Press W H, Teukolsky S A, Vetterling W T, Flannery B P 2007 Numerical Recipes: The Art of Scientific Computing (3rd Ed.) (New York: Cambridge University Press) pp487–562
[37]	Östlin A, Di Marco I, Locht I L M, Lashley J C, Vitos L 2016 Phys. Rev. B 93 094103 Google Scholar
[38]	van Swygenhoven H, Derlet P M, Frøseth A G 2004 Nat. Mater. 3 399 Google Scholar
[39]	Hai S, Tadmor E B 2003 Acta Mater. 51 117 Google Scholar
[40]	Tadmor E, Hai S 2003 J. Mech. Phys. Solids 51 765 Google Scholar
[41]	Stassis C, Gould T, McMasters O D, Gschneidner K A, Nicklow R M 1979 Phys. Rev. B 19 5746 Google Scholar

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