基于第一性原理的金属导热性能研究

doi:10.11900/0412.1961.2020.00250

金属学报

2021, Vol. 57

Issue (3): 375-384 DOI: 10.11900/0412.1961.2020.00250

研究论文

本期目录 | 过刊浏览

基于第一性原理的金属导热性能研究

崔洋¹, 李寿航², 应韬¹(

), 鲍华², 曾小勤¹

^1.上海交通大学材料科学与工程学院上海 200240
^2.上海交通大学上海交大密西根学院上海 200240

Research on the Thermal Conductivity of Metals Based on First Principles

CUI Yang¹, LI Shouhang², YING Tao¹(

), BAO Hua², ZENG Xiaoqin¹

^1.School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
^2.University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China

引用本文:

崔洋, 李寿航, 应韬, 鲍华, 曾小勤. 基于第一性原理的金属导热性能研究[J]. 金属学报, 2021, 57(3): 375-384.
Yang CUI, Shouhang LI, Tao YING, Hua BAO, Xiaoqin ZENG. Research on the Thermal Conductivity of Metals Based on First Principles[J]. Acta Metall Sin, 2021, 57(3): 375-384.

全文: PDF(1928 KB) HTML

摘要:

基于第一性原理提出了一种纯金属热导率的高效计算方法。引入常弛豫时间近似，应用密度泛函理论(DFT)与最大局域化Wannier函数(MLWFs)方法求解金属材料的电子热导率，简化了电子热导率的计算流程；在计算声子热导率时，将Birch-Murnaghan状态方程与Debye模型引入Slack方程，提高了声子热导率的计算效率。采用本方法计算了Al、Mg、Zn 3种材料在300~700 K温度范围内的电导率和热导率，计算值与实测值吻合良好，验证了计算方法的准确性。结果表明，材料的电子和声子的结构是影响热导率的关键因素，在金属材料的导热过程中，电子始终发挥着主要的输运作用，并且随着温度的升高，电子热导率占总热导率的比率也逐渐上升。

关键词 ：第一性原理, 纯金属, 电导率, 热导率

Abstract：

Metals are widely used for heat sink and thermal management products, and their thermal conductivities are critical in determining the cooling performance. An efficient method to calculate the thermal conductivity of pure metal is proposed based on the first principles. By introducing the constant relaxation time approximation, density functional theory (DFT) and maximum localized Wannier function (MLWFs) are used to solve the electronic thermal conductivity of metal materials, the calculation procedure of electronic thermal conductivity can be simplified. Regarding the phonon thermal conductivity calculation part, the combination of Slack equation, Birch-Murnaghan equation and Debye model is capable of improving the calculation efficiency. The electrical and thermal conductivities of Al, Mg and Zn in the temperature range of 300-700 K are calculated by the up-mentioned new method. The calculated thermal conductivity was consistent with the measured values, which confirmed the accuracy of the calculation method. The calculation results show that the electronic and phonon structures were essential parameters in thermal conduction of metals. With the increase of temperature, the ratio of the electronic thermal conductivity to the total thermal conductivity increased gradually.

Key words： first-principle pure metal electrical conductivity thermal conductivity

收稿日期: 2020-07-09

ZTFLH:

TG146

基金资助:国家自然科学基金项目(51601111);上海市科委科研计划项目(18511109302);装备预研航天科技联合基金项目;内蒙古自治区重大专项项目(ZDZX2016022)

作者简介: 崔洋，男，1997年生，硕士生

	服务

	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	崔洋
	李寿航
	应韬
	鲍华
	曾小勤
44.8K

链接本文:

https://www.ams.org.cn/CN/10.11900/0412.1961.2020.00250 或 https://www.ams.org.cn/CN/Y2021/V57/I3/375

Material	$t e ? / ? h$			$t p h ? / ? h$
	C.R.T	Quantum-Espresso	VASP	Slack	Phonon-Boltzmann
Mg	1	5	3	1	14
Mg₂Si	2	14	9	1	28
Mg₂Ca	2	13	8	1	24

表1 电子热导率与声子热导率常用计算方法的用时比较

图1 Al、Mg和Zn的原子结构示意图

Phase	Spacegroup	Lattice constant / nm				Unit cell volume / 10³ nm³
		Calculated		Ref.[25]		Calculated	Ref.[25]
		a₀	c₀	a₀	c₀
Al	$F m 3 ˉ m$	40.4	-	40.4	-	16.47	16.47
Mg	$P 63 / m m c$	32.1	52.2	31.8	52.2	46.62	45.63
Zn	$P 63 / m m c$	25.7	44.3	26.7	46.3	25.42	28.65

表2 Al、Mg和Zn的晶体结构与点阵常数

图2 基于DFT与MLWFs的Al、Mg和Zn的电子能带结构比较

Material	$σ 300 ? K$ / (MS·m^-1)		$σ 500 ? K$ / (MS·m^-1)		$σ 700 ? K$ / (MS·m^-1)		κ_e / (W·m^-1·K^-1)
	Cal.	Exp.	Cal.	Exp.	Cal.	Exp.	300 K	500 K	700 K
Al	32.07	35.38^[26]	19.48	19.66^[26]	14.06	13.61^[26]	242.15	247.39	249.90
Mg	18.87	20.82^[27]	12.22	11.57^[27]	8.99	8.01^[27]	143.54	143.25	143.27
Zn	15.58	16.69^[28]	9.21	9.59^[28]	6.52	6.73^[28]	110.07	107.89	111.72

表3 Al、Mg、Zn的电导率计算值与实测值[26~28]及电子热导率

图3 Al、Mg和Zn的电导率计算值与实测值[26~28]随温度变化关系

图4 Al、Mg和Zn的电子热导率随温度变化曲线

Material	B₀ / GPa		$θ D$ / K		$γ$	κ_ph / (W·m^-1·K^-1)
	Cal.	Exp.	Cal.	Exp.		300 K	500 K	700 K
Al	65.09	68^[30]	492.21	438^[7]	2.02	20.22	12.13	8.67
Mg	33.25	32^[31]	392.74	344^[32]	1.79	8.56	5.13	3.67
Zn	70.16	67^[33]	314.51	316^[28]	2.27	5.75	3.45	2.47

表4 Al、Mg和Zn的热力学参数计算值与实测值[7,28,30~33]与声子热导率

图5 Al、Mg和Zn的声子热导率随温度变化曲线

图6 Al、Mg和Zn的总热导率计算值与实测值[34]随温度变化关系

图7 Al、Mg和Zn的Lorenz数与温度的关系曲线

图8 不同温度下Al、Mg、Zn的电子热导率与声子热导率对比Color online

图9 不同温度下Al、Mg、Zn的电子与声子热导率占总热导率比值

1	Watanabe H, Fukusumi M, Somekawa H, et al. Texture and mechanical properties of superplastically deformed magnesium alloy rod [J]. Mater. Sci. Eng., 2010, A527: 6350
2	Shaeri M R, Yaghoubi M. Thermal enhancement from heat sinks by using perforated fins [J]. Energy Conv. Manag., 2009, 50: 1264
3	Liang X B, Jia C C, Chu K, et al. Predicted interfacial thermal conductance and thermal conductivity of diamond/Al composites with various interfacial coatings [J]. Rare Met., 2011, 30: 544
4	Wang R G. Research on the extrusion technology of magnesium alloy radiator [J]. China Met. Bull., 2009, (46): 42
4	王荣贵. 镁合金散热器挤压工艺研究 [J]. 中国金属通报, 2009, (46): 42
5	Klemens P G, Williams R K. Thermal conductivity of metals and alloys [J]. Int. Met. Rev., 1986, 31: 197
6	Liu J. First principal study of thermal conductivity of Cu/Fe/Al and their alloys [D]. Harbin: Harbin Institute of Technology, 2014
6	刘金. 关于金属Cu、Fe、Al及其合金热导率的第一性原理研究 [D]. 哈尔滨: 哈尔滨工业大学, 2014
7	Wen B, Feng X. Thermal conductivity of metal from first principles calculations and its application in aluminum [J]. J. Yanshan Univ., 2015, 39: 298
7	温斌, 冯幸. 金属热导率的第一性原理计算方法在铝中的应用 [J]. 燕山大学学报, 2015, 39: 298
8	Tong Z, Bao H. Decompose the electron and phonon thermal transport of intermetallic compounds NiAl and Ni₃Al by first-principles calculations [J]. Int. J. Heat Mass Trans., 2018, 117: 972
9	Ma H, Yang C L, Wang M S, et al. Effects of transport direction and carrier concentration on the thermoelectric properties of AgIn₅Te₈: A first-principles study [J]. Mater. Res. Bull., 2019, 113: 77
10	Den E V. Influence of the relaxation time approximation on first principle study of transport coefficients in thermoelectric material PbTe [D]. Louvain-la-Neuve: Université catholique de Louvain, 2016
11	Berman R. Thermal Conduction in Solids [M]. Oxford: Oxford University Press, 1976: 10
12	Tritt T M. Thermal Conductivity: Theory, Properties, and Applications [M]. New York: Kluwer Academic/Plenum Publishers, 2004: 21
13	Ziman J M. Electrons and Phonons [M]. Oxford: Oxford University Press, 1960: 12
14	Madsen G K H, Singh D J. BoltzTraP. A code for calculating band-structure dependent quantities [J]. Comput. Phys. Commun., 2006, 175: 67
15	Motta C, El-Mellouhi F, Sanvito S. Charge carrier mobility in hybrid halide perovskites [J]. Sci. Rep., 2015, 5: 12746
16	Souza I, Marzari N, Vanderbilt D. Maximally localized Wannier functions for entangled energy bands [J]. Phys. Rev., 2001, 65B: 035109
17	Nath P, Plata J J, Usanmaz D, et al. High throughput combinatorial method for fast and robust prediction of lattice thermal conductivity [J]. Scr. Mater., 2017, 129: 88
18	Slack G A. The thermal conductivity of nonmetallic crystals [J]. Solid State Phys., 1979, 34: 1
19	Poirier J P. Introduction to the Physics of the Earth's Interior [M]. Cambridge: Cambridge University Press, 1991: 66
20	Toher C, Plata J J, Levy O, et al. High-throughput computational screening of thermal conductivity, Debye temperature, and Grüneisen parameter using a quasiharmonic Debye model [J]. Phys. Rev., 2014, 90B: 174107
21	Birch F. Finite elastic strain of cubic crystals [J]. Phys. Rev., 1947, 71: 809
22	Murnaghan F D. The compressibility of media under extreme pressures [J]. Proc. Natl. Acad. Sci. USA, 1944, 30: 244
23	Wang Z, Wang S D, Obukhov S, et al. Thermoelectric transport properties of silicon: Toward an ab initio approach [J]. Phys. Rev., 2011, 83B: 205208
24	Deinzer G, Birner G, Strauch D. Ab initio calculation of the linewidth of various phonon modes in germanium and silicon [J]. Phys. Rev., 2003, 67B: 144304
25	Curtarolo S, Setyawan W, Wang S D, et al. AFLOWLIB.ORG: A distributed materials properties repository from high-throughput ab initio calculations [J]. Comput. Mater. Sci., 2012, 58: 227
26	Bai S J. Effect of Zr content on the structure and properties of commercial aluminum [D]. Shenyang: Northeastern University, 2015
26	白嗣俊. Zr含量对工业纯铝组织性能的影响 [D]. 沈阳: 东北大学, 2015
27	Tong X, You G Q, Ding Y H, et al. Effect of grain size on low-temperature electrical resistivity and thermal conductivity of pure magnesium [J]. Mater. Lett., 2018, 229: 261
28	Tyndall E P T, Hoyem A G. Resistivity of single crystal zinc [J]. Phys. Rev., 1931, 38: 820
29	Blakemore J S. Solid State Physics [M]. Cambridge: Cambridge University Press, 1985: 87
30	Wang Y, Liu Z K, Chen L Q. Thermodynamic properties of Al, Ni, NiAl, and Ni₃Al from first-principles calculations [J]. Acta Mater., 2004, 52: 2665
31	Yamagishi H, Fukuhara M, Chiba A. Determination of the mechanical properties of extruded pure magnesium during tension-tension low-cycle fatigue using ultrasonic testing [J]. Mater. Trans., 2010, 51: 2025
32	Weiss R J. The absolute X-ray scattering factor of magnesium [J]. Philos. Mag., 1967, 16: 141
33	Siebke W. Considerations on the bulk modulus of pure metals [J]. Phys. Status Solidi, 1981, 64: 577
34	Madelung O, White G K. Landolt-Bo¨rnstein—Group III Condensed Matter. Metals: Electronic Transport Phenomena•Thermal Conductivity of Pure Metals and Alloys[M]. Berlin: Springer, 1991: 12
35	Franz R, Wiedemann G. Ueber die Wärme-Leitungsfähigkeit der Metalle [J]. Ann. Phys., 1853, 165: 497
36	Ying T. Thermal behavior of pure magnesium and binary magnesium alloys [D]. Harbin: Harbin Institute of Technology, 2015
36	应韬. 纯镁和二元镁合金的导热行为研究 [D]. 哈尔滨: 哈尔滨工业大学, 2015
37	Seitz F, Turnbull D. Solid State Physics [M]. New York: Academic Press, 1958: 255
38	Yang J, Morelli D T, Meisner G P, et al. Influence of electron-phonon interaction on the lattice thermal conductivity of Co_1-_xNi_xSb₃ [J]. Phys. Rev., 2002, 65B: 094115

[1]	王福容, 张永梅, 柏国宁, 郭庆伟, 赵宇宏. Al掺杂Mg/Mg₂Sn合金界面的第一性原理计算[J]. 金属学报, 2023, 59(6): 812-820.
[2]	李昕, 江河, 姚志浩, 董建新. O原子对高温合金基体Ni、Co和NiCr晶界作用的理论计算分析[J]. 金属学报, 2023, 59(2): 309-318.
[3]	李斗, 徐长江, 李旭光, 李双明, 钟宏. La掺杂P型Ce_yFe₃CoSb₁₂ 热电材料及涂层的热电性能[J]. 金属学报, 2023, 59(2): 237-247.
[4]	任师浩, 刘永利, 孟凡顺, 祁阳. 应变工程中Bi(111)薄膜的半导体-半金属转变及其机理[J]. 金属学报, 2022, 58(7): 911-920.
[5]	曾小勤, 王杰, 应韬, 丁文江. 镁及其合金导热研究进展[J]. 金属学报, 2022, 58(4): 400-411.
[6]	李亚敏, 张瑶瑶, 赵旺, 周生睿, 刘洪军. Cu对Inconel 718合金Nb偏析影响机理的第一性原理研究[J]. 金属学报, 2022, 58(2): 241-249.
[7]	周丽君, 位松, 郭敬东, 孙方远, 王新伟, 唐大伟. 基于飞秒激光时域热反射法的微尺度Cu-Sn金属间化合物热导率研究[J]. 金属学报, 2022, 58(12): 1645-1654.
[8]	王硕, 王俊升. Al-Li合金中 δ′/θ′/δ′复合沉淀相结构演化及稳定性的第一性原理探究[J]. 金属学报, 2022, 58(10): 1325-1333.
[9]	赵立东, 王思宁, 肖钰. 热电材料的载流子迁移率优化[J]. 金属学报, 2021, 57(9): 1171-1183.
[10]	周洪宇, 冉珉瑞, 李亚强, 张卫冬, 刘俊友, 郑文跃. 颗粒尺寸对金刚石/Al封装基板热物性的影响[J]. 金属学报, 2021, 57(7): 937-947.
[11]	毛斐, 吕皓, 唐法威, 郭凯, 刘东, 宋晓艳. Mn和In添加对SmCo₇结构稳定性及磁矩影响的第一性原理计算[J]. 金属学报, 2021, 57(7): 948-958.
[12]	张海军, 邱实, 孙志梅, 胡青苗, 杨锐. 无序β-Ti₁_-_xNb_x合金自由能及弹性性质的第一性原理计算:特殊准无序结构和相干势近似的比较[J]. 金属学报, 2020, 56(9): 1304-1312.
[13]	盖逸冰, 唐法威, 侯超, 吕皓, 宋晓艳. 合金化元素对W-Cu体系多类界面特征影响的第一性原理计算[J]. 金属学报, 2020, 56(7): 1036-1046.
[14]	高翔, 张桂凯, 向鑫, 罗丽珠, 汪小琳. 合金元素对V(110)表面O吸附影响的第一性原理研究[J]. 金属学报, 2020, 56(6): 919-928.
[15]	白静, 石少锋, 王锦龙, 王帅, 赵骧. Ni-Mn-Ga-Ti铁磁形状记忆合金的相稳定性和磁性能的第一性原理计算[J]. 金属学报, 2019, 55(3): 369-375.

Viewed

Full text

Abstract

Cited

Shared

Discussed