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

doi:10.7498/aps.74.20250619

Abstract

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.

Keywords:

Authors and contacts

1.
College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
2.
School of Science, Southern University of Science and Technology, Shenzhen 518055, China
3.
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Corresponding author: ZENG Zhaoyi, zhaoyizeng@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12072044).

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References

[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
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Cited By

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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].

DownLoad: Full-Size Img PowerPoint

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).

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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]

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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^{[19–22,44–46]}

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^{[19–22,44–46]}.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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/Å	b/Å	c/Å	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 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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