高温高压下镁及典型镁铝合金的电热导率

陈浩; 徐远骥; 咸家伟; 高兴誉; 田付阳; 宋海峰

doi:10.7498/aps.74.20250352

摘要

金属材料因其优异的电输运性能和良好的散热性能, 在工业领域应用广泛. 高温高压条件下, 实验测量金属的电热导率难度大且成本高, 数值模拟则是一种高效的方法. 本研究基于Kubo-Greenwood (KG) 公式结合第一性原理分子动力学开发了电导率和电子热导率计算软件TREX (TRansport at EXtremes). 采用该软件计算了镁及镁铝合金 AZ31B在300—1200 K和0—50 GPa温压范围内的电导率和电子热导率, 并与玻耳兹曼输运方程的计算结果进行了对比. 应用Slack方程计算其晶格热导率, 结合电子热导率得到了其总热导率. TREX 软件的计算结果与实验测试数据高度吻合, 充分验证了其计算电热导率的准确性, 并系统揭示了电热导率随温度与压强的变化规律. 本文数据集可在https://doi.org/10.57760/sciencedb.j00213.00128中访问获取.

关键词:

Abstract

Metallic materials are widely used in the industrial field due to their excellent electrical transport properties and superior thermal dissipation performance. However, experimental measurements of electrical and thermal conductivity under high-temperature and high-pressure conditions are challenging and costly. This makes numerical simulation an efficient alternative solution. In this study, we develop a computational software named TREX (TRansport at EXtremes). It is based on the Kubo-Greenwood (KG) formula combined with first-principles molecular dynamics. This software is used to calculate electrical conductivity and electronic thermal conductivity. Using magnesium and magnesium-aluminum alloy AZ31B as research subjects, we systematically investigate their electrical and thermal transport properties. The temperature and pressure are in a range of 300−1200 K and 0−50 GPa, respectively. The method involves using first-principles molecular dynamics simulations to obtain equilibrium configurations of high-temperature disordered structures. Electrical conductivity and electronic thermal conductivity are calculated using the KG formula. Lattice thermal conductivity is determined by the Slack equation. To validate the reliability of our approach, we perform comparative calculations by using the Boltzmann transport equation. The research results are cross-verified with experimental data from Sichuan University and the Aerospace Materials Test and Analysis Center. The findings demonstrate that the maximum relative error between computational and experimental results is within 20%. This confirms the accuracy of our method. Additionally, we elucidate the variation patterns of electrical and thermal conductivity in magnesium and AZ31B alloy with temperature and pressure. These patterns include the reduction in electrical conductivity due to aluminum doping, the significant enhancement of conductivity under high pressure, and the unique temperature-induced thermal conductivity enhancement in AZ31B alloy. The TREX program developed in this study and the established performance dataset provide essential tools and data support. They are useful for research on electrical and thermal transport mechanisms in metallic materials under extreme conditions, and also for engineering applications. All the data presented in this paper are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00128.

Keywords:

作者及机构信息

1.
北京科技大学应用物理研究所, 北京　100083

2.
北京应用物理与计算数学研究所, 计算物理全国重点实验室, 北京　100088

通信作者: 咸家伟, xian_jiawei@iapcm.ac.cn ; 田付阳, fuyang@ustb.edu.cn ;

基金项目: 计算物理全国重点实验室基金和国家自然科学基金(批准号: 52371174, 12204033)资助的课题.

Authors and contacts

1.
Institute of Applied Physics, University of Science and Technology Beijing, Beijing 100083, China

2.
National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Corresponding author: XIAN Jiawei, xian_jiawei@iapcm.ac.cn ; TIAN Fuyang, fuyang@ustb.edu.cn ;

Funds: Project supported by the Funding of National Key Laboratory of Computational Physics and the National Natural Science Foundation of China (Grant Nos. 52371174, 12204033).

文章全文

参考文献

[1]	王奥, 盛宇飞, 鲍华 2024 物理学报 73 037201 Google Scholar Wang A, Shen Y F, Bao H 2024 Acta Phys. Sin. 73 037201 Google Scholar
[2]	Ventura G, Perfetti M 2014 Electrical and Thermal Conductivity (Dordrecht: Springer Netherlands) pp131–168
[3]	Burger N, Laachachi A, Ferriol M, Lutz M, Toniazzo V, Ruch D 2016 Prog. Polym. Sci. 61 1 Google Scholar
[4]	Reif-Acherman S 2011 Revista Brasileira de Ensino de Física 33 4602 Google Scholar
[5]	Demyanov G S, Knyazev D V, Levashov P R 2022 Phys. Rev. E 105 035307 Google Scholar
[6]	Vlček V, De Koker N, Steinle-Neumann G 2012 Phys. Rev. B 85 184201 Google Scholar
[7]	Naumov I I, Hemley R J 2015 Phys. Rev. Lett. 114 156403 Google Scholar
[8]	Matsuoka T, Shimizu K 2009 Nature 458 186 Google Scholar
[9]	Kietzmann A, Redmer R, Desjarlais M P, Mattsson T R 2008 Phys. Rev. Lett. 101 070401 Google Scholar
[10]	崔洋, 李寿航, 应韬, 鲍华, 曾小勤 2021 金属学报 57 375 Google Scholar Yang C, Li S H, Ying T, Bao H, Zeng X Q 2021 Acta Metallurgica Sinica 57 375 Google Scholar
[11]	Reif F 2009 Fundamentals of Statistical and Thermal Physics (New York: McGraw-Hill) pp483–522
[12]	Bulusu A, Walker D 2008 Superlattices Microstruct. 44 1 Google Scholar
[13]	Migdal K, Zhakhovsky V, Yanilkin A, Petrov Y V, Inogamov N 2019 Appl. Surf. Sci. 478 818 Google Scholar
[14]	Calderín L, Karasiev V, Trickey S 2017 Comput. Phys. Commun. 221 118 Google Scholar
[15]	French M, Mattsson T R 2014 Phys. Rev. B 90 165113 Google Scholar
[16]	Kramer D A 2010 Springer Handbook of Materials Data (Cham: Springer International Publishing) pp151–159
[17]	Zhang Q, Fu J, Zhou J, Qi L, Li H 2024 Chem. Eng. J. 496 154023 Google Scholar
[18]	Xin W, Wang S, Yan Z 2025 Mater. Today Commun. 43 111584 Google Scholar
[19]	Madsen G K, Carrete J, Verstraete M J 2018 Comput. Phys. Commun. 231 140 Google Scholar
[20]	Slack G A 1973 J. Phys. Chem. Solids 34 321 Google Scholar
[21]	Moseley L, Lukes T 1978 Am. J. Phys 46 676 Google Scholar
[22]	Knyazev D V, Levashov P R 2019 Contrib. Plasma Phys. 59 345 Google Scholar
[23]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864 Google Scholar
[24]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133 Google Scholar
[25]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[26]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[27]	Blöchl P 1994 Phys. Rev. B 50 17953 Google Scholar
[28]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[29]	Kubo R, Yokota M, Nakajima S 1957 J. Phys. Soc. Jpn. 12 1203 Google Scholar
[30]	Tian F, Lin D Y, Gao X, Zhao Y F, Song H F 2020 J. Chem. Phys. 153 034101 Google Scholar
[31]	Desjarlais M, Kress J, Collins L 2002 Phys. Rev. E 66 025401 Google Scholar
[32]	Choi G, Kim H S, Lee K, Park S H, Cha J, Chung I, Lee W B 2017 J. Alloys Compd. 727 1237 Google Scholar
[33]	Ahmad S, Mahanti S D 2010 Phys. Rev. B 81 165203 Google Scholar
[34]	Lang H N D, van Kempen H, Wyder P 1978 J. Phys. F: Met. Phys. 8 L39 Google Scholar
[35]	Iida T, Guthrie R I L 1988 The Physical Properties of Liquid Metals (New York: Oxford Clarendon Press) pp266–253
[36]	Pan H, Pan F, Wang X, Peng J, Gou J, She J, Tang A 2013 Int. J. Thermophys. 34 1336 Google Scholar
[37]	Chen F, Huang Q, Jiang Z, Zhao J, Sun B, Li Y 2015 Vacuum 115 80 Google Scholar
[38]	Motta C, El-Mellouhi F, Sanvito S 2015 Sci. Rep. 5 12746 Google Scholar
[39]	Madsen G K, Singh D J 2006 Comput. Phys. Commun. 175 67 Google Scholar
[40]	Yue S Y, Zhang X, Stackhouse S, Qin G, Di Napoli E, Hu M 2016 Phys. Rev. B 94 075149 Google Scholar
[41]	Blakemore J S 1985 Solid State Physics (Cambridge: Cambridge University Press) pp149–292
[42]	Ho C Y, Powell R W, Liley P E 1972 J. Phys. Chem. Ref. Data 1 279 Google Scholar
[43]	Ying T, Zheng M, Li Z, Qiao X 2014 J. Alloys Compd. 608 19 Google Scholar

施引文献

图 2 512个原子的AZ31B合金超胞结构示意图(蓝色原子表示镁, 红色原子表示铝)

Fig. 2. Schematic diagram of the supercell structure of AZ31B alloy with 512 atoms. Blue atoms represent magnesium, and red atoms represent aluminum.

下载: 全尺寸图片幻灯片

图 1 TREX程序(基于KG公式与AIMD模拟) 计算电导率和电子热导率的流程示意图. 红色虚线框表示TREX程序的核心功能(包括平衡构型提取、电子输运性质计算等); 蓝色框表示与第一性原理计算软件相关的计算内容(如第一性原理分子动力学、电子结构、跃迁矩阵等)

Fig. 1. Schematic diagram of the workflow for calculating electrical conductivity and electronic thermal conductivity using the TREX code (based on the Kubo-Greenwood formula and AIMD simulations). The red dashed box indicates the core functions of the TREX code (including equilibrium configuration extraction, electronic transport property calculations, etc.). The blue boxes represent calculations related to first-principles software (such as ab initio molecular dynamics, electronic structure, and transition matrices).

下载: 全尺寸图片幻灯片

图 3 (a)镁单质电导率计算结果与实验值对比图, 竖点线表示镁在常压条件下的熔化温度; (b) AZ31B合金电导率计算结果与实验值对比图, 黑色(红色、蓝色) 图例表示0 GPa (40, 50 GPa)的实验和计算结果

Fig. 3. (a) Comparison between the calculated electrical conductivity of magnesium single crystal and the experimental values, with the vertical dotted line indicating the melting temperature of magnesium under ambient pressure; (b) the comparison between the calculated electrical conductivity of AZ31B alloy and the experimental values, where the black (red, blue) legend represents the experimental and calculated results at 0 GPa (40, 50 GPa).

下载: 全尺寸图片幻灯片

图 4 (a)镁的热导率各分项贡献的组成; (b) AZ31B合金的热导率各分项贡献的组成, 实线和实心(虚线和空心) 图例表示0 GPa (40 GPa) 的计算结果. ETC表示电子热导率, LTC表示晶格热导率, TTC表示总热导率

Fig. 4. (a) Composition of various contributions to the thermal conductivity of magnesium; (b) the composition of different contributions to the thermal conductivity of AZ31B alloy, where solid lines and solid symbols (dashed lines and hollow symbols) represent the calculated results at 0 GPa (40 GPa). Here, ETC denotes the electronic thermal conductivity, LTC represents the lattice thermal conductivity, and TTC stands for the total thermal conductivity.

下载: 全尺寸图片幻灯片

图 5 (a)镁单质热导率计算结果与实验值对比图, 竖点线表示镁在常压条件下的熔化温度; (b) AZ31B合金热导率计算结果与实验值对比图, 黑色(红色) 图例表示0 GPa (40 GPa) 的实验和计算结果, 红色虚线表示对40 GPa实验结果的线性拟合

Fig. 5. (a) A comparison between the calculated and experimental values of thermal conductivity for pure magnesium, with the vertical dotted line indicating the melting temperature of magnesium under ambient pressure; (b) a comparison between the calculated and experimental values of thermal conductivity for AZ31B alloy, where black (red) symbols represent the experimental and computational results at 0 GPa (40 GPa), and the red dashed line denotes the linear fit to the experimental data at 40 GPa.

下载: 全尺寸图片幻灯片

表 1 电子弛豫时间τ (单位: 10^–14 s) 随温度T变化的拟合公式$ \tau=AT^{-r} $

Table 1. Fitting formula for the electron relaxation time τ (unit: 10^–14 s) as a function of temperature T is given by $ \tau = A T^{-r} $.

材料	压强/GPa	参数A	参数r	R²
Mg	0	1306.36	1.12	0.9999
AZ31B	0	52.54	0.58	0.9976
AZ31B	40	230.74	0.76	0.9953
AZ31B	50	182.05	0.73	0.9993

下载: 导出CSV

[1]	王奥, 盛宇飞, 鲍华 2024 物理学报 73 037201 Google Scholar Wang A, Shen Y F, Bao H 2024 Acta Phys. Sin. 73 037201 Google Scholar
[2]	Ventura G, Perfetti M 2014 Electrical and Thermal Conductivity (Dordrecht: Springer Netherlands) pp131–168
[3]	Burger N, Laachachi A, Ferriol M, Lutz M, Toniazzo V, Ruch D 2016 Prog. Polym. Sci. 61 1 Google Scholar
[4]	Reif-Acherman S 2011 Revista Brasileira de Ensino de Física 33 4602 Google Scholar
[5]	Demyanov G S, Knyazev D V, Levashov P R 2022 Phys. Rev. E 105 035307 Google Scholar
[6]	Vlček V, De Koker N, Steinle-Neumann G 2012 Phys. Rev. B 85 184201 Google Scholar
[7]	Naumov I I, Hemley R J 2015 Phys. Rev. Lett. 114 156403 Google Scholar
[8]	Matsuoka T, Shimizu K 2009 Nature 458 186 Google Scholar
[9]	Kietzmann A, Redmer R, Desjarlais M P, Mattsson T R 2008 Phys. Rev. Lett. 101 070401 Google Scholar
[10]	崔洋, 李寿航, 应韬, 鲍华, 曾小勤 2021 金属学报 57 375 Google Scholar Yang C, Li S H, Ying T, Bao H, Zeng X Q 2021 Acta Metallurgica Sinica 57 375 Google Scholar
[11]	Reif F 2009 Fundamentals of Statistical and Thermal Physics (New York: McGraw-Hill) pp483–522
[12]	Bulusu A, Walker D 2008 Superlattices Microstruct. 44 1 Google Scholar
[13]	Migdal K, Zhakhovsky V, Yanilkin A, Petrov Y V, Inogamov N 2019 Appl. Surf. Sci. 478 818 Google Scholar
[14]	Calderín L, Karasiev V, Trickey S 2017 Comput. Phys. Commun. 221 118 Google Scholar
[15]	French M, Mattsson T R 2014 Phys. Rev. B 90 165113 Google Scholar
[16]	Kramer D A 2010 Springer Handbook of Materials Data (Cham: Springer International Publishing) pp151–159
[17]	Zhang Q, Fu J, Zhou J, Qi L, Li H 2024 Chem. Eng. J. 496 154023 Google Scholar
[18]	Xin W, Wang S, Yan Z 2025 Mater. Today Commun. 43 111584 Google Scholar
[19]	Madsen G K, Carrete J, Verstraete M J 2018 Comput. Phys. Commun. 231 140 Google Scholar
[20]	Slack G A 1973 J. Phys. Chem. Solids 34 321 Google Scholar
[21]	Moseley L, Lukes T 1978 Am. J. Phys 46 676 Google Scholar
[22]	Knyazev D V, Levashov P R 2019 Contrib. Plasma Phys. 59 345 Google Scholar
[23]	Hohenberg P, Kohn W 1964 Phys. Rev. 136 B864 Google Scholar
[24]	Kohn W, Sham L J 1965 Phys. Rev. 140 A1133 Google Scholar
[25]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[26]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[27]	Blöchl P 1994 Phys. Rev. B 50 17953 Google Scholar
[28]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[29]	Kubo R, Yokota M, Nakajima S 1957 J. Phys. Soc. Jpn. 12 1203 Google Scholar
[30]	Tian F, Lin D Y, Gao X, Zhao Y F, Song H F 2020 J. Chem. Phys. 153 034101 Google Scholar
[31]	Desjarlais M, Kress J, Collins L 2002 Phys. Rev. E 66 025401 Google Scholar
[32]	Choi G, Kim H S, Lee K, Park S H, Cha J, Chung I, Lee W B 2017 J. Alloys Compd. 727 1237 Google Scholar
[33]	Ahmad S, Mahanti S D 2010 Phys. Rev. B 81 165203 Google Scholar
[34]	Lang H N D, van Kempen H, Wyder P 1978 J. Phys. F: Met. Phys. 8 L39 Google Scholar
[35]	Iida T, Guthrie R I L 1988 The Physical Properties of Liquid Metals (New York: Oxford Clarendon Press) pp266–253
[36]	Pan H, Pan F, Wang X, Peng J, Gou J, She J, Tang A 2013 Int. J. Thermophys. 34 1336 Google Scholar
[37]	Chen F, Huang Q, Jiang Z, Zhao J, Sun B, Li Y 2015 Vacuum 115 80 Google Scholar
[38]	Motta C, El-Mellouhi F, Sanvito S 2015 Sci. Rep. 5 12746 Google Scholar
[39]	Madsen G K, Singh D J 2006 Comput. Phys. Commun. 175 67 Google Scholar
[40]	Yue S Y, Zhang X, Stackhouse S, Qin G, Di Napoli E, Hu M 2016 Phys. Rev. B 94 075149 Google Scholar
[41]	Blakemore J S 1985 Solid State Physics (Cambridge: Cambridge University Press) pp149–292
[42]	Ho C Y, Powell R W, Liley P E 1972 J. Phys. Chem. Ref. Data 1 279 Google Scholar
[43]	Ying T, Zheng M, Li Z, Qiao X 2014 J. Alloys Compd. 608 19 Google Scholar

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