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The lanthanide and actinide metals and alloys are of great interest in experimental and theoretical high-pressure research, because of the unique behavior of the f electrons under pressure and their delocalization and participation in bonding. Cerium (Ce) metal is the first lanthanide element with a 4f electron. It has a very complex phase diagram and displays intriguing physical and chemical properties. In addition, it is expected to be an excellent surrogate candidate for plutonium (Pu), one of the radioactive transuranic actinides with a 5f electron. The bulk properties and phase transformation characteristics of Ce-based alloys are similar to those of Pu and its compounds. Thus, the investigations of Ce-based alloys are necessary and can potentially advance the understanding of the behavior of Pu. In this work, the equation of state, phase transition, elastic and thermodynamic properties of Ce0.8La0.1Th0.1 alloy at high pressure are investigated by using first-principles calculations based on the density-functional theory. The structural properties of the Ce0.8La0.1Th0.1 alloy are in good agreement with the available experimental and theoretical data. The lattice constant a decreases with pressure increasing, while c shows an opposite variation. It is found that the lattice parameter c shows abnormal jump. And the critical volume is located at 20.1 Å3. The axial ratio jumps from a value of about
$\sqrt 2 $ (corresponding to the fcc structure) to a higher value, which indicates that the fcc-bct transition occurs. And the corresponding transition pressure is located at ~31.6 GPa. When the pressure rises to 34.9 GPa, the bct structure displays a saturated c/a axial ratio close to about 1.67. The Young's modulus E, shear modulus G and the Debye temperature of the fcc phase tend to be " softened” around the phase transition pressure. The vibrational free energy is obtained by using the quasi-harmonic Debye model. And then the thermodynamic properties including the thermal equation of state, heat capacity and entropy under high pressure and high temperature are also predicted successfully. The results show that the heat capacity and entropy increase rapidly with temperature increasing, and decrease with pressure increasing. The high pressure can suppress part of the anharmonicity caused by temperature.-
Keywords:
- Ce-based alloy /
- density functional theory /
- phase transformation /
- high pressure
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图 1 体积随压强变化的规律(黑色实点为直接加压结构优化后的结果, 黑色实线为状态方程拟合结果), 并与已有的Ce[20], Th[19], Ce0.875La0.125[12]的计算值及Ce0.76Th0.24[21]实验值进行比较
Figure 1. The EOS of fcc and bct Ce-La-Th together with the experimental data (the black solid point is the result of the structure optimization, the black solid line is the fitting result of the EOS), together with the experimental data for Ce0.76Th0.24[21] and the calculated results for Ce[20], Th[19], Ce0.875La0.125[12].
图 3 Ce-La-Th合金fcc相及bct相弹性常量随压强的变化
Figure 3. Elastic constants as functions of pressure.
图 4 剪切模量G、体模量B和杨氏模量E随压强的变化
Figure 4. Shear modulus G, bulk modulus B and Young′s modulus E as functions of pressure.
图 5 德拜温度随压强的变化
Figure 5. The Debye temperature as a function of pressure.
图 6 不同温度下的等温线, 其中V0为零温零压下的体积, 小图为零压下体积随温度的变化
Figure 6. Isotherms at different temperatures, where V0 is the volume at zero temperature and zero pressure; the volumes at zero pressure as functions of temperature (the insert) .
图 7 定容热容CV随温度(a)和压强(b)的变化, 以及熵S随温度(c)和压强(d)的变化; 图中阴影区域包含fcc和bct两相的数据
Figure 7. The constant volume heat capacity CV versus temperature (a) and pressure (b), and the entropy S versus temperature (c) and pressure (d).
表 1 零温零压下fcc相Ce-La-Th合金的平衡体积(V0)及体积模量(B0)
Table 1. Equilibrium volume (V0) and bulk modulus (B0) of Ce-La-Th of fcc phase at 0 GPa and 0 K.
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[1] Bridgman P W 1927 Proc. Am. Acad.Arts Sci. 62 207
Google Scholar
[2] Bridgman P W 1951 Proc. Am. Acad. Arts Sci. 79 149
Google Scholar
[3] Bridgman P W 1954 Proc. Am. Acad. Arts Sci. 83 1
[4] Lanson A W, Tang T Y 1949 Phys. Rev. 76 301
Google Scholar
[5] 潘昊, 胡晓棉, 吴子辉, 戴诚达, 吴强 2012 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] Hu C E, Zeng Z Y, Zhang L, Chen X T, Cai L C 2011 Physica B 406 669
Google Scholar
[7] Lawson A C, Williams A, Wire M S 1988 J. Less-common Met. 142 177
Google Scholar
[8] Lawrence J M, Thompson J D, Fisk Z, Smith J L, Batlogg B 1984 Phys. Rev. B 29 4017
Google Scholar
[9] Drymiotis F, Singleton J, Harrison N, Lashley J C, Bangura A, Mielke C H, Balicas L, Fisk Z, Migliori A, Smith J L 2005 J. Phys.: Condens. Matter 17 L77
Google Scholar
[10] Ruff J P C, Islam Z, Das R K, Nojiri H, Cooley J C, Mielke C H 2012 Phys. Rev. B 85 024104
Google Scholar
[11] Hu C E, Zeng Z Y, Zhang L, Chen X R, Cai L C 2010 Solid State Commun. 150 2362
Google Scholar
[12] Zeng Z Y, Hu C E, Li Z G, Zhang W, Cai L C 2015 J. Alloys Compd. 640 201
Google Scholar
[13] Blanco M A, Francisco E, Luaña V 2004 Comput. Phys. Commun. 158 57
Google Scholar
[14] Blanco M A, MartínPendás A, Francisco E, Recio J M, Franco R 1996 J. Mol. Struct.: Theochem 368 245
Google Scholar
[15] Francisco E, Recio J M, Blanco M A, Pendás A M 1998 J. Phys. Chem. 102 1595
Google Scholar
[16] Francisco E, Sanjurjo G, Blanco M A 2001 Phys. Rev. B 63 094107
Google Scholar
[17] Flórez M, Recio J M, Francisco E, Blanco M A, Pendás A M 2002 Phys. Rev. B 66 144112
Google Scholar
[18] 邓世杰, 赵宇宏, 侯华, 文志勤, 韩培德 2017 66 146101
Google Scholar
Deng S J, Zhao H Y, Hou H, Wen Z Q, Han P D 2017 Acta Phys. Sin. 66 146101
Google Scholar
[19] Vohra Y K, Holzapfel W B 1993 High Pressure Res. 11 223
Google Scholar
[20] Olsen J S, Gerward L, Benedict U, Itié J P 1985 Physica B+C (Amsterdam)
133 129 Google Scholar
[21] Gu G, Vohra Y K, Winand J M, Spirlet J C 1995 Scr. Metall. Mater. 32 2081
Google Scholar
[22] Svane A 1996 Phys. Rev. B 53 4275
[23] Soderlind P, Eriksson O, Wills J M, Boring A M 1993 Phys. Rev. B 48 9306
Google Scholar
[24] Koskenmaki D C, Gschneidner K A 1978 Handb. Phys. Chem. Rare Earths 1 337
Google Scholar
[25] Gerward L, Olsen J S, Diffr P 1993 Powder Diffr. 8 127
Google Scholar
[26] Decremps F, Antonangeli D, Amadon B, Schmerber G 2009 Phys. Rev. B 80 132103
Google Scholar
[27] Lipp M J, Kono Y, Jenei Z, Cynn H, Aracne-Ruddle C, Park C, Kenney-Benson C, Evans W J 2013 J. Phys: Condens. Matter 25 34
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