服役条件下方钴矿基热电元件的界面应力分析

doi:10.15541/jim20190112

无机材料学报 ›› 2020, Vol. 35 ›› Issue (2): 224-230.DOI: 10.15541/jim20190112

所属专题： 2020年能源材料论文精选(三) :太阳能电池、热电材料及其他

服役条件下方钴矿基热电元件的界面应力分析

邵笑^1,²,刘睿恒^1,³(),王亮¹,初靖^1,²,白光辉⁴,柏胜强^1,³,顾明¹,张丽娜⁴,马伟⁴,陈立东^1,³

1. 中国科学院上海硅酸盐研究所, 高性能陶瓷和超微结构国家重点实验室, 上海 201899
2. 中国科学院大学, 北京 100049
3. 中国科学院大学材料科学与光电技术学院, 北京 100049
4. 空间物理重点实验室, 北京, 100076

收稿日期:2019-03-18 修回日期:2019-04-30 出版日期:2020-02-20 网络出版日期:2019-05-29
作者简介:邵笑(1995-), 男, 硕士研究生. E-mail: shaoxiao@student.sic.ac.cn

Interfacial Stress Analysis on Skutterudite-based Thermoelectric Joints under Service Conditions

SHAO Xiao^1,²,LIU Rui-Heng^1,³(),WANG Liang¹,CHU Jing^1,²,BAI Guang-Hui⁴,BAI Sheng-Qiang^1,³,GU Ming¹,ZHANG Li-Na⁴,MA Wei⁴,CHEN Li-Dong^1,³

1. The State Key Lab of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 201899, China
2. University of Chinese Academy of Sciences, Beijing 100049, China
3. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
4. Science and Technology on Space Physics Laboratory, Beijing 100076, China

Received:2019-03-18 Revised:2019-04-30 Published:2020-02-20 Online:2019-05-29
Supported by:
National Key Research and Development Program of China(2018YFB0703600);National Natural Science Foundation of China(51572282);National Natural Science Foundation of China(51632010);National Natural Science Foundation of China(11572050);Youth Innovation Promotion Association CAS

摘要/Abstract

摘要：

热电器件中, 界面可靠性是影响整体稳定和功率输出的关键因素。对于方钴矿(SKD)器件, 热电臂和电极通过扩散阻挡层(DBL)连接。在高温下, DBL与SKD、电极之间会发生反应并生成复杂的界面结构, 导致界面附近的热、电、力学性能发生变化。本研究根据实际界面结构建立了包含微观结构的有限元模型, 并将其用于分析方钴矿基元件的界面应力状态。采用单层模型对DBL材料参数进行了筛选, 发现热膨胀系数(CTE)和弹性模量(E)对第一主应力有显著影响。采用包含界面微结构的多层模型定量模拟了不同老化温度、时间下元件内部的应力分布, 结果表明在SKD/Zr和SKD/Nb中, CoSb₂反应层最为薄弱, 随着老化时间的延长, 反应层的厚度增加, 界面应力变大。同时, 元件的拉伸试验结果与计算结果吻合较好, 验证了模型的准确性与可行性。本研究为提升SKD/DBL元件的结构稳定性提供了指导, 同时也为精确模拟多层结构中的应力状态提供了研究思路。

关键词: 热电元件, 扩散阻挡层, 有限元模型, 拉伸强度

Abstract:

In thermoelectric (TE) devices, the interfacial reliability greatly influenced devices’ durability and power output. For skutterudites (SKD) devices, TE legs and electrodes are bonded together with diffusion barrier layer (DBL). At elevated temperatures, DBL react with SKD matrix or electrode to generate complex interfacial microstructures, which often accompanies evolutions of the thermal, electrical and mechanical properties at the interfaces. In this work, a finite element model containing the interfacial microstructure characteristics based on the experimental results was built to analyze the interfacial stress state in the skutterudite-based TE joints. A single-layer model was applied to screen out the most important parameters of the coefficient of thermal expansion (CTE) and the modulus of DBL on the first principle stress. The multilayer model considering the interfacial microstructures evolution was built to quantitively simulate the stress state of the TE joints at different aging temperatures and time. The simulation results show that the reactive CoSb₂ layer is the weakest layer in both SKD/Nb and SKD/Zr joints. And by prolonging the aging time, the thickness of the reaction layer continuously increased, leading to a significant raising of the interfacial stress. The tensile testing results of the SKD/Nb joints match the simulation results well, consolidating accuracy and feasibility of this multilayer model. This study provides an important guidance on the design of DBL to improve the TE joints’ mechanical reliability, and a common method to precisely simulate the stress condition in other coating systems.

Key words: thermoelectric joints, diffusion barrier layer, finite element model, tensile strength

中图分类号:

TQ174

邵笑,刘睿恒,王亮,初靖,白光辉,柏胜强,顾明,张丽娜,马伟,陈立东. 服役条件下方钴矿基热电元件的界面应力分析[J]. 无机材料学报, 2020, 35(2): 224-230.

SHAO Xiao,LIU Rui-Heng,WANG Liang,CHU Jing,BAI Guang-Hui,BAI Sheng-Qiang,GU Ming,ZHANG Li-Na,MA Wei,CHEN Li-Dong. Interfacial Stress Analysis on Skutterudite-based Thermoelectric Joints under Service Conditions[J]. Journal of Inorganic Materials, 2020, 35(2): 224-230.

图/表 11

Fig. 1 (a) CTE, (b) Young’s modulus (E), and (c) variations of average first principle stresses with thicknesses of different DBL candidates (purple lines: CTE and E of SKD)

Fig. 2 σ1 distributions for (a) n=0, (b) n=1, (c) n=3, and (d) n=7 (initial thickness of Nb: 25 μm)

Table 1 Relative volume changes for one interface (SKD/Nb and SKD/Zr joints)

Layer	SKD	Nb/Zr	CoSb₂	NbSb₂/ ZrSb₂	Difference
Relative volume change (SKD/Nb)	-2.75	-0.27	+1.78	+1	-0.24
Relative volume change (SKD/Zr)	-2.48	-0.32	+1.65	+1	-0.15

Fig. 3 Variations of average σ1 on each interface with thicknesses of NbSb2 and Nb

Table 2 Thicknesses of NbSb2 layer dNbSb2, average sizes of micropores c, tensile strengths σt, maximum calculated stresses Ave-σ1 and the location interfaces, compositions of tensile fracture surface for series of aging SKD/Nb joints。。

Joints	d_NbSb2/μm	c/μm	n	Ave-σ₁/GPa	σ_t/MPa	Fracture position	Fracture composition
0 d	0	0	0	1.46	(9.68±1.70)	Nb/ SKD	(Nb+ NbSb₂)/(3%CoSb₂+97% SKD)
600-5 d	2	2.02	3	2.72	(4.63±2.12)	CoSb₂/NbSb₂	NbSb₂/(36%CoSb₂+64% SKD)
600-10 d	3	2.21	3	2.80	(3.39±1.44)	CoSb₂/NbSb₂	NbSb₂/(47%CoSb₂+53% SKD)
650-5 d	7	4.13	1	3.07	(4.44±1.50)	CoSb₂/NbSb₂	NbSb₂/(80%CoSb₂+20% SKD)
650-10 d	12	5.20	1	3.42	(1.46±0.38)	CoSb₂/NbSb₂	NbSb₂/(97%CoSb₂+3% SKD)

Fig. 4 EDS mappings of (a, d) interfaces and (b, e) fracture surfaces of (a-b) unaged joint and (d-e) sample 650-10d (White line indicating the fracture surface, and white arrow indicating direction of observation in (b) or (d)); Total element data were shown in table (c) for figure (b) and in table (f) for figure (e)

Table A1 Basic properties including molar mass, density, Young’s modulus, Poisson’s ratio, thermal conductivity, thermal expansions and heat capacity for series of materials

Material	SKD	CoSb₂	NbSb₂^[1]	ZrSb₂^[2]	Nb	Zr
Molar Mass/(g·mol^-1)	424.21	302.45	336.43	334.82	92.91	91.22
Density/(g·cm^-3)	7.80*	8.36	8.29	7.62	8.57-8.45	6.5-6.4
Young’s modulus/GPa	120*	160	186.1	135.7	104.8-105.7	97-57
Poisson’s ratio	0.21^[3]	0.23	0.21	0.243	0.382-0.394	0.34
Thermal conductivity/(W·m^-1·K^-1)	3.04-4.05*	6.8-12.5^[4]	24	10	55-65	20-25
Thermal expansion/(×10^-6, K^-1)	10-11^[5]	14-23^[6]	8.4	9.7	7-7.8	5.9-6.9
Heat capacity/(J·g^-1·K^-1)	0.22-0.23*	0.247	0.222	0.223	0.27-0.45	0.28-0.34

Fig. A1 (a) Finite element model of SKD/Nb joint with pores, detailed meshes of (b) NbSb2 layer and (c) CoSb2 layer

Fig. A2 Interface structures and line scans of joints (a) As-prepared; (b) Aged at 600 ℃ for 5 d; (c) Aged at 600 ℃ for 10 d; (d) Aged at 650 ℃ for 5 d; (e) Aged at 650 ℃ for 10 d

Fig. A3 Relationships between interface stresses and pores major axis ratios

Fig. A4 (a) Calculated stress state of SKD/Zr joint with the Zr layer of 25 μm and the micropores number n of 3; (b) Variation of average σ1 on SKD/CoSb2 interface with thickness of ZrSb2 and Zr (n=3); (c) Variation of average σ1 on CoSb2/ZrSb2 interface with thickness of ZrSb2 and Zr (n=3); (d) Variation of average σ1 on ZrSb2/Zr interface with thickness of ZrSb2 and Zr (n=3)

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服役条件下方钴矿基热电元件的界面应力分析

Interfacial Stress Analysis on Skutterudite-based Thermoelectric Joints under Service Conditions

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