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First principles calculations of lattice dynamics and thermal transport properties of alpha uranium under high pressure

HU Ke SUN Qianhui WANG Yan HU Cuie ZENG Zhaoyi CHEN Jun

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First principles calculations of lattice dynamics and thermal transport properties of alpha uranium under high pressure

HU Ke, SUN Qianhui, WANG Yan, HU Cuie, ZENG Zhaoyi, CHEN Jun
cstr: 32037.14.aps.74.20250619
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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.
      Corresponding author: ZENG Zhaoyi, zhaoyizeng@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12072044).
    [1]

    Jacob C W, Warren B E 1937 J. Am. Chem. Soc. 59 2588Google Scholar

    [2]

    Tucker C W 1951 Acta Crystallogr. 4 425Google Scholar

    [3]

    Lawson A C, Olsen C E, Richardson J W 1988 Acta Crystallogr. B 44 89Google 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 134102Google 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 176104Google 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 176104Google Scholar

    [7]

    Wills J M, Eriksson O 1992 Phys. Rev. B 45 13879Google Scholar

    [8]

    Söderlind P 2002 Phys. Rev. B 66 085113Google Scholar

    [9]

    张其黎, 赵艳红, 马桂存. 2014 高压物理学报 30 32Google Scholar

    Zhang Q L, Zhao Y H, Ma G C 2014 J. High Press. Phys. 30 32Google 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 450Google Scholar

    Yin W Q, Bo T, Zhao Y B, Zhang L, Chai Z F, Shi W Q 2024 J. Nucl. Chem. Radiochem. 46 450Google Scholar

    [11]

    Fisher E S, McSkimin H J 1958 J. Appl. Phys. 29 1473Google Scholar

    [12]

    Bouchet J, Albers R C 2011 J. Phys.: Condens. Matter 23 215402Google Scholar

    [13]

    Yang J W, Gao T, Liu B Q, Sun G A, Chen B 2014 Eur. Phys. J. B 87 130Google Scholar

    [14]

    Söderlind P, Yang L H, Landa A, Wu A 2021 Appl. Sci. 11 5643Google Scholar

    [15]

    Crummett W P, Morris J A, Baker A R 1979 Phys. Rev. B 19 6028Google Scholar

    [16]

    Manley M E, Jarman T L, Cooper R A 2003 Phys. Rev. B 67 052302Google Scholar

    [17]

    Yang J W, Gao T,Liu B Q,Sun G A,Chen B 2015 J. Nucl. Mater. 252 521Google Scholar

    [18]

    Bouchet J, Bottin F J 2017 Phys. Rev. B 95 054113Google 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 141Google Scholar

    [22]

    Kaity S, Banerjee J, Nair MR, Ravi K, Dash S, Kutty TRG, Singh RP 2012 J. Nucl. Mater. 427 1Google Scholar

    [23]

    Zhou S X, Jacobs R, Xie W, Tea E, Hin C, Morgan D 2018 Phys. Rev. Mater. 2 083401Google Scholar

    [24]

    Peng J, Deskins W. R, Malakkal L, El-Azab A 2021 J. Appl. Phys. 130 185101Google 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 235112Google Scholar

    [27]

    Söderlind P, Zhang Z, Anderson O 1994 Phys. Rev. B 50 7291Google 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 1747Google Scholar

    [30]

    Madsen G K H, Singh D J 2006 Comput. Phys. Commun. 175 67Google Scholar

    [31]

    Bardeen J, Shockley W 1950 Phys. Rev. 80 72Google Scholar

    [32]

    Xi J Y, Long M Q, Tang L, Wang D, Shuai Z G 2012 Nanoscale 4 4348Google Scholar

    [33]

    Ziman J M 2001 Electrons and Phonons (Oxford University Press

    [34]

    Hashin Z, Shtrikman S 1963 Phys. Rev. 130 129Google Scholar

    [35]

    Kruglov I A, Yanilkin A, Oganov AR, Korotaev P 2019 Phys. Rev. B 100 174104Google Scholar

    [36]

    Dewaele A, Loubeyre P, Sato H 2013 Phys. Rev. B 88 134202Google Scholar

    [37]

    Akella J, Gupta Y, Luthra G 1990 High Press. Res. 2 295Google Scholar

    [38]

    Birch F 1952 J. Geophys. Res. 57 227Google Scholar

    [39]

    Bouchet J 2008 Phys. Rev. B 77 024113Google Scholar

    [40]

    Ren Z Y, Liu L, Zhang Q 2016 J. Nucl. Mater. 480 80Google Scholar

    [41]

    Yoo C S, Cynn H, Söderlind P 1998 Phys. Rev. B 57 10359Google Scholar

    [42]

    Raetsky V M 1967 J. Nucl. Mater. 21 105Google Scholar

    [43]

    Pascal J, Morin J, Lacombe P 1964 J. Nucl. Mater. 13 28Google 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 415Google Scholar

    [46]

    Howl D A 1966 J. Nucl. Mater. 19 9Google Scholar

  • 图 1  α-U的归一化晶格常数随压强的变化关系

    Figure 1.  Normalized lattice constant of α-U as a function of pressure.

    图 2  (a) α-U在0 GPa下的声子色散关系曲线, 实心球是实验数据[15]; (b) 在不同压强下的声子色散关系曲线

    Figure 2.  (a) Phonon dispersion relationship curve of α-U at 0 GPa, solid sphere is experimental data[15]; (b) phonon dispersion relationship curve at different pressures.

    图 3  不同压强下α-U的物态方程

    Figure 3.  Equation of state of α-U at different pressures.

    图 4  α-U在不同方向的晶格热导率, 五角星、圆形、三角形是Peng等[24]的计算值

    Figure 4.  The lattice thermal conductivity of α-U in different directions, with pentagrams, circles, and triangles being the calculated values by Peng et al[24].

    图 5  α-U在不同方向上, 20 GPa (a), 40 GPa (b), 60 GPa (c)和80 GPa (d)的晶格热导率

    Figure 5.  Lattice thermal conductivity of α-U in different directions at 20 GPa (a), 40 GPa (b), 60 GPa (c), and 80 GPa (d).

    图 6  α-U在不同压强下格林艾森参数随频率的变化

    Figure 6.  Frequency dependent Grüneisen parameters of α-U under different pressures.

    图 7  α-U在不同压强下沿着(a) [100]方向、(b) [010]方向、(c) [001]方向的声子群速度

    Figure 7.  Phonon group velocities of α-U along the (a) [100] direction, (b) [010] direction, and (c) [001] direction at different pressures.

    图 8  α-U在不同压强下的声子寿命

    Figure 8.  Phonon lifetime of α-U under different pressure.

    图 9  α-U沿不同方向的弛豫时间与温度的关系

    Figure 9.  Relationship between relaxation time and temperature of α-U along different directions.

    图 10  α-U电阻率与温度的关系, 阴影表示Zhou等[23]的结果, 散点表示实验值[42,43]

    Figure 10.  Relationship between resistivity and temperature of α-U, the shaded part represents the results of Zhou et al.[23], and the scattered point represents the experimental value[42,43]

    图 11  α-U在(a) 0 GPa下的电子热导率和(b) 不同压强的电子热导率

    Figure 11.  Electronic thermal conductivity of α-U at (a) 0 GPa and (b) at different pressures.

    图 12  α-U在0 GPa下的总热导率, 点线和划线表示计算值[23,24], 散点表示实验值[1922,4446]

    Figure 12.  Total thermal conductivity of α-U at 0 GPa, dotted lines and dashes represent calculated values[23,24], and scattered points represent experimental values[1922,4446].

    图 13  α-U在不同压强下的热导率

    Figure 13.  Total thermal conductivity of α-U at different pressures.

    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.

    方法 a b c V/(Å3·atom–1) B0/GPa $ B_0' $
    本文 2.809 5.798 4.909 19.99 146.2 4.97
    计算值[6] 2.803 5.872 4.905 20.18 141.6 4.83
    实验值[38] 2.836 5.866 4.935 20.52 135.5 3.80
    DownLoad: CSV

    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
    DownLoad: CSV
  • [1]

    Jacob C W, Warren B E 1937 J. Am. Chem. Soc. 59 2588Google Scholar

    [2]

    Tucker C W 1951 Acta Crystallogr. 4 425Google Scholar

    [3]

    Lawson A C, Olsen C E, Richardson J W 1988 Acta Crystallogr. B 44 89Google 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 134102Google 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 176104Google 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 176104Google Scholar

    [7]

    Wills J M, Eriksson O 1992 Phys. Rev. B 45 13879Google Scholar

    [8]

    Söderlind P 2002 Phys. Rev. B 66 085113Google Scholar

    [9]

    张其黎, 赵艳红, 马桂存. 2014 高压物理学报 30 32Google Scholar

    Zhang Q L, Zhao Y H, Ma G C 2014 J. High Press. Phys. 30 32Google 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 450Google Scholar

    Yin W Q, Bo T, Zhao Y B, Zhang L, Chai Z F, Shi W Q 2024 J. Nucl. Chem. Radiochem. 46 450Google Scholar

    [11]

    Fisher E S, McSkimin H J 1958 J. Appl. Phys. 29 1473Google Scholar

    [12]

    Bouchet J, Albers R C 2011 J. Phys.: Condens. Matter 23 215402Google Scholar

    [13]

    Yang J W, Gao T, Liu B Q, Sun G A, Chen B 2014 Eur. Phys. J. B 87 130Google Scholar

    [14]

    Söderlind P, Yang L H, Landa A, Wu A 2021 Appl. Sci. 11 5643Google Scholar

    [15]

    Crummett W P, Morris J A, Baker A R 1979 Phys. Rev. B 19 6028Google Scholar

    [16]

    Manley M E, Jarman T L, Cooper R A 2003 Phys. Rev. B 67 052302Google Scholar

    [17]

    Yang J W, Gao T,Liu B Q,Sun G A,Chen B 2015 J. Nucl. Mater. 252 521Google Scholar

    [18]

    Bouchet J, Bottin F J 2017 Phys. Rev. B 95 054113Google 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 141Google Scholar

    [22]

    Kaity S, Banerjee J, Nair MR, Ravi K, Dash S, Kutty TRG, Singh RP 2012 J. Nucl. Mater. 427 1Google Scholar

    [23]

    Zhou S X, Jacobs R, Xie W, Tea E, Hin C, Morgan D 2018 Phys. Rev. Mater. 2 083401Google Scholar

    [24]

    Peng J, Deskins W. R, Malakkal L, El-Azab A 2021 J. Appl. Phys. 130 185101Google 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 235112Google Scholar

    [27]

    Söderlind P, Zhang Z, Anderson O 1994 Phys. Rev. B 50 7291Google 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 1747Google Scholar

    [30]

    Madsen G K H, Singh D J 2006 Comput. Phys. Commun. 175 67Google Scholar

    [31]

    Bardeen J, Shockley W 1950 Phys. Rev. 80 72Google Scholar

    [32]

    Xi J Y, Long M Q, Tang L, Wang D, Shuai Z G 2012 Nanoscale 4 4348Google Scholar

    [33]

    Ziman J M 2001 Electrons and Phonons (Oxford University Press

    [34]

    Hashin Z, Shtrikman S 1963 Phys. Rev. 130 129Google Scholar

    [35]

    Kruglov I A, Yanilkin A, Oganov AR, Korotaev P 2019 Phys. Rev. B 100 174104Google Scholar

    [36]

    Dewaele A, Loubeyre P, Sato H 2013 Phys. Rev. B 88 134202Google Scholar

    [37]

    Akella J, Gupta Y, Luthra G 1990 High Press. Res. 2 295Google Scholar

    [38]

    Birch F 1952 J. Geophys. Res. 57 227Google Scholar

    [39]

    Bouchet J 2008 Phys. Rev. B 77 024113Google Scholar

    [40]

    Ren Z Y, Liu L, Zhang Q 2016 J. Nucl. Mater. 480 80Google Scholar

    [41]

    Yoo C S, Cynn H, Söderlind P 1998 Phys. Rev. B 57 10359Google Scholar

    [42]

    Raetsky V M 1967 J. Nucl. Mater. 21 105Google Scholar

    [43]

    Pascal J, Morin J, Lacombe P 1964 J. Nucl. Mater. 13 28Google 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 415Google Scholar

    [46]

    Howl D A 1966 J. Nucl. Mater. 19 9Google Scholar

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  • Received Date:  12 May 2025
  • Accepted Date:  02 July 2025
  • Available Online:  15 July 2025
  • Published Online:  05 September 2025
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