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Through first-principles calculations based on density functional theory (DFT) and the Boltzmann transport equation (BTE), the thermal transport properties of α-uranium under high pressure are investigated. In order to investigate the effects of pressure on the phonon dispersion relations and thermal conductivity of α-U, the phonon dispersion relations and lattice thermal conductivity at different pressures are obtained using a 4×4×4 supercell. First, for the calculation of electronic thermal conductivity, the ratio of thermal conductivity to relaxation time is calculated from the Boltzmann transport equation. Then, the relaxation time is calculated using deformation potential energy theory, relaxation time approximation, and effective mass approximation method derived from DFT band structure. Finally, the electronic thermal conductivity is obtained through the Wiedemann-Franz law. The calculation results indicate that α-U remains dynamically stable under a pressure of 80 GPa. The thermal conductivity of α-U exhibits a typical “V”-shaped temperature dependence: at low temperatures, phonon thermal conductivity dominates and decreases with the increase of temperature; at high temperatures, the electronic thermal conductivity becomes more significant and increases with temperature increasing. The combined effect of phonon thermal conductivity and electron thermal conductivity results in the total thermal conductivity reaching its minimum value at a temperature of approximately 160 K. When the temperature is 300 K, the thermal conductivity of α-U at 0 GPa is 25.11 W/(m·K), and increases to 250.75 W/(m·K) at 80 GPa as pressure increases. This result clearly indicates that an increase in pressure significantly enhances thermal conductivity. The calculation results also highlight the influences of pressure on phonon group velocity, phonon lifetime, and electron phonon interactions, all of which promote an increase in thermal conductivity. These findings provide a comprehensive understanding of the thermal conductivity of α-U depending on temperature and pressure and offer valuable insights into potential applications in extreme environments.
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Keywords:
- uranium /
- phonon dispersion relation /
- lattice thermal conductivity /
- electronic thermal conductivity
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表 1 α-U的晶格常数、体积、体弹模量及其对压强的一阶导数
Table 1. Lattice constants, volume, bulk modulus, and its derivative with respect to pressure of α-U.
表 2 α-U在不同压强下沿着3个方向的声速(单位: km/s)
Table 2. The sound velocity of α-U along three directions at different pressures (in km/s).
0 GPa 20 GPa 40 GPa 60 GPa 80 GPa
[100]LA 27.117 31.438 35.331 39.011 43.929 TA1 17.936 19.167 21.691 22.338 22.826 TA2 17.471 17.942 19.273 20.341 20.529
[010]LA 20.052 22.916 26.307 26.954 29.422 TA1 16.761 17.295 19.731 20.636 21.069 TA2 12.026 13.935 17.402 18.338 19.317
[001]LA 23.129 29.177 34.213 37.737 42.609 TA1 17.239 18.526 20.391 21.735 22.445 TA2 12.102 15.813 17.534 18.767 19.462 -
[1] Jacob C W, Warren B E 1937 J. Am. Chem. Soc. 59 2588
Google Scholar
[2] Tucker C W 1951 Acta Crystallogr. 4 425
Google Scholar
[3] Lawson A C, Olsen C E, Richardson J W 1988 Acta Crystallogr. B 44 89
Google Scholar
[4] Wilson A S, Rundle R E 1949 Acta Crystallogr. 2 126.
Google Scholar
[5] Le Bihan T, Heathman S, Idiri M 2003 Phys. Rev. B 67 134102
Google Scholar
[6] 刘本琼, 谢雷, 段晓溪, 孙光爱, 陈波, 宋建明, 刘耀光, 汪小琳 2013 物理学报 62 176104
Google Scholar
Liu B Q, Xie L, Duan X X, Sun G A, Chen B, Song J M, Liu Y G, Wang X L 2013 Acta Phys. Sin. 62 176104
Google Scholar
[7] Wills J M, Eriksson O 1992 Phys. Rev. B 45 13879
Google Scholar
[8] Söderlind P 2002 Phys. Rev. B 66 085113
Google Scholar
[9] 张其黎, 赵艳红, 马桂存. 2014 高压物理学报 30 32
Google Scholar
Zhang Q L, Zhao Y H, Ma G C 2014 J. High Press. Phys. 30 32
Google Scholar
[10] 尹晚秋, 薄涛, 赵玉宝, 张蕾, 柴之芳, 石伟群 2024 核化学与放射化学 46 450
Google Scholar
Yin W Q, Bo T, Zhao Y B, Zhang L, Chai Z F, Shi W Q 2024 J. Nucl. Chem. Radiochem. 46 450
Google Scholar
[11] Fisher E S, McSkimin H J 1958 J. Appl. Phys. 29 1473
Google Scholar
[12] Bouchet J, Albers R C 2011 J. Phys.: Condens. Matter 23 215402
Google Scholar
[13] Yang J W, Gao T, Liu B Q, Sun G A, Chen B 2014 Eur. Phys. J. B 87 130
Google Scholar
[14] Söderlind P, Yang L H, Landa A, Wu A 2021 Appl. Sci. 11 5643
Google Scholar
[15] Crummett W P, Morris J A, Baker A R 1979 Phys. Rev. B 19 6028
Google Scholar
[16] Manley M E, Jarman T L, Cooper R A 2003 Phys. Rev. B 67 052302
Google Scholar
[17] Yang J W, Gao T,Liu B Q,Sun G A,Chen B 2015 J. Nucl. Mater. 252 521
Google Scholar
[18] Bouchet J, Bottin F J 2017 Phys. Rev. B 95 054113
Google Scholar
[19] Eriksen V O, Halg W 1955 J. Nucl. Mater. 1 232
[20] Pearson G J D, Danielson G C 1957 Proc. Iowa Acad. Sci. 64 461
[21] Takahashi Y, Yamawaki M, Yamamoto K 1988 J. Nucl. Mater. 154 141
Google Scholar
[22] Kaity S, Banerjee J, Nair MR, Ravi K, Dash S, Kutty TRG, Singh RP 2012 J. Nucl. Mater. 427 1
Google Scholar
[23] Zhou S X, Jacobs R, Xie W, Tea E, Hin C, Morgan D 2018 Phys. Rev. Mater. 2 083401
Google Scholar
[24] Peng J, Deskins W. R, Malakkal L, El-Azab A 2021 J. Appl. Phys. 130 185101
Google Scholar
[25] 简单 2020 硕士学位论文(绵阳: 中国工程物理研究院)
Jian D 2020 M. S. Thesis (Mianyang: China Academy of Engineering Physics
[26] Richard N, Hall R O, Lee J A 2002 Phys. Rev. B 66 235112
Google Scholar
[27] Söderlind P, Zhang Z, Anderson O 1994 Phys. Rev. B 50 7291
Google Scholar
[28] Lan G Q, Yang B O, Xu Y S, Song J, Jiang Y 2016 J. Appl. Phys. 119 235103.
Google Scholar
[29] Li W, Carrete J, Katcho N A, Mingo N 2014 Comput. Phys. Commun. 185 1747
Google Scholar
[30] Madsen G K H, Singh D J 2006 Comput. Phys. Commun. 175 67
Google Scholar
[31] Bardeen J, Shockley W 1950 Phys. Rev. 80 72
Google Scholar
[32] Xi J Y, Long M Q, Tang L, Wang D, Shuai Z G 2012 Nanoscale 4 4348
Google Scholar
[33] Ziman J M 2001 Electrons and Phonons (Oxford University Press
[34] Hashin Z, Shtrikman S 1963 Phys. Rev. 130 129
Google Scholar
[35] Kruglov I A, Yanilkin A, Oganov AR, Korotaev P 2019 Phys. Rev. B 100 174104
Google Scholar
[36] Dewaele A, Loubeyre P, Sato H 2013 Phys. Rev. B 88 134202
Google Scholar
[37] Akella J, Gupta Y, Luthra G 1990 High Press. Res. 2 295
Google Scholar
[38] Birch F 1952 J. Geophys. Res. 57 227
Google Scholar
[39] Bouchet J 2008 Phys. Rev. B 77 024113
Google Scholar
[40] Ren Z Y, Liu L, Zhang Q 2016 J. Nucl. Mater. 480 80
Google Scholar
[41] Yoo C S, Cynn H, Söderlind P 1998 Phys. Rev. B 57 10359
Google Scholar
[42] Raetsky V M 1967 J. Nucl. Mater. 21 105
Google Scholar
[43] Pascal J, Morin J, Lacombe P 1964 J. Nucl. Mater. 13 28
Google Scholar
[44] Touloukian Y S, Bass R L, Shapiro S M 1970 Thermophysical Properties of Matter (TPRC Data Series) (Vol. 1) (New York: IFI/Plenum
[45] Hall R O A, Lee J A 1971 J. Low Temp. Phys. 4 415
Google Scholar
[46] Howl D A 1966 J. Nucl. Mater. 19 9
Google Scholar
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