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

doi:10.15541/jim20190112

Abstract

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

CLC Number:

TQ174

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.

Figures/Tables 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)

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

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)

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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