Introduction

As a new kind of clean energy conversion technique, thermoelectric power generators (TEG) can directly convert waste heat into electric energy and improve the efficiency of energy usage based on Seebeck effect. They have been applied in a wide range of fields including the recovery and utilization of industrial waste heat and deep-space exploration.1,2 A large number of materials with zT > 1 have been reported, e.g., nanostructured PbTe, CoSb3 -based skutterudites, half-Heuslers, SnSe, Cu2Se-based materials, and Mg2Si-based solid solutions, which have potential prospect for use in the mid-temperature region between 500 K and 800 K.3

In recent years, the performance of thermoelectric materials has continued to make breakthroughs, which is determined by the dimensionless figure of merit,4 zT = S2σT/k,5,6,7 where σ is the electrical conductivity, S is the Seebeck coefficient, k is the thermal conductivity and T is the absolute temperature. When the temperature difference reaches 350 K, the theoretical value of thermoelectric conversion efficiency of thermoelectric materials with average zT between 1 and 2 is about 10%.8 However, these high values never translate adequately into the performance of devices, mainly due to challenges in making stable contact between thermoelectric material and electrodes. To realize a stable contact between thermoelectric material and electrodes, a barrier layer is usually applied. However, due to the inevitable mutual diffusion reaction at the interface of the barrier and thermoelectric material, there is still a long way to improve the interface contact by designing proper barrier materials. Furthermore, it must be pointed out that the interfacial reaction, usually accompanied by atomic diffusion across the interface, could be more critical for the magnesium-based TEG working in the mid-temperature region. It has been proved that a deficiency of Mg may deteriorate the performance of the thermoelectric materials4,9 and contact to the electrode10,11 as well. So, it is necessary to inhibit the diffusion of elements between thermoelectric material and electrodes by adjusting the chemical composition gradient across the interface.

For thermoelectric devices, in addition to the performance of the thermoelectric material itself, contact resistance and bonding strength of the interface between thermoelectric materials and electrodes also have great influence on the efficiency, stability and life of thermoelectric devices.12,13 In the cases of waste heat harvesting from the vehicle transport and furnace operation, the thermal interfacial resistance of the interface of the diffusion barrier materials and thermoelectric materials are not critical.14 So, as shown in Eq. 1,10 contact resistance is one of the main key factors that reduces the effective \(\left\langle {ZT} \right\rangle_{{\text{D}}}\) of thermoelectric devices.

$$ \left\langle {ZT} \right\rangle_{D} = \left( {L/\left( {L + 2R_{c} \sigma } \right)} \right)\left\langle {zT} \right\rangle_{M} $$
(1)

where L and \(\sigma\) are the length and electrical conductivity of the thermoelectric leg, respectively, Rc is the contact resistivity, and \(\left\langle {zT} \right\rangle_{M}\) is the average zT of the thermoelectric material between Th and Tc. Usually, the ratio of contact resistance to total leg resistance of less than 10% is acceptable. For a typical device, Rc should be much less than L/2 \(\sigma\) or 102 μΩ·cm2.10

Mg2Si-based thermoelectric material, as a very promising thermoelectric material with a zT up to 1.45,15,16,17 has been attracting more attention of scientists committing to its popularization and application as a medium-temperature TEG. As a defective compound, its transport behavior is determined by the concentration of intrinsic point defects, which is closely related to the stoichiometric ratio of elements.18,19 The mutual diffusion and reaction occurring across the interface destroys the balance of point defects and causes the increase of interface resistance and deterioration of efficiency and even failure due to mechanical damage.10 In our recent work, it has been shown that Mg2SiNi3 is an excellent diffusion barrier between Cu electrodes and Mg2Si, which not only effectively blocks the diffusion of Cu from the electrode to Mg2Si thermoelectric material, but also ensures the maximum shear strength (28.29 MPa).20 It is especially worth mentioning that the contact resistance between the intrinsic Mg2Si and Mg2SiNi3 is pretty low compared to that reported in the literature.20 However, the influence of the chemical potential of Mg in the interface of Mg2SiNi3/Mg2Si on the dynamic equilibrium of point defects and thermoelectric transport must be further discussed and clarified.

Figure 1 illustrates the complex crystal structure of the Mg2SiNi3 material. Mg2SiNi3 is a reaction product between Mg2Si and Ni, with \(R\overline{3}\) m space group structure, which belongs to the μ phase in the topologically densely packed intermetallic compound (TCP-IMC).21 In the space unit, the coordination numbers of Mg, Si, and Ni are 15,12,12, respectively, and the packing ratio is as high as 0.85. It is very dense and stable in air even at 300 °C.22 The introduction of Mg2SiNi3 to form TE/TCP-IMC interface is thought to improve the contact and stability of the interface by suppressing the chemical potential of diffusion and reaction in both thermodynamics and dynamics. Additionally, the dual-bond characteristics of metallic bond and covalent bond is helpful to decrease interface residual stress due to mismatch as well. In this work, Mg2SiNi3 is used as a barrier to prepare Mg2Si/MgxSi15Ni50 (x=36,50,150) thermoelectric joints to discover how the composition gradient affects the interface diffusion between Mg2Si and Mg2SiNi3. The contact resistance, strength and thermal stability of these joints were studied in detail.

Fig. 1
figure 1

The crystal structure of the Mg2SiNi3 material.

Experimental Procedure

Magnesium powder (≤50 μm, 99.5% pure, Aladdin, Shanghai), silicon powder (≤45 μm, 99.5% pure, Aladdin, Shanghai) and nickel powder (≤45 μm, 99.5% pure, Kermel, Tianjin) were ball mixed for 30 min in stoichiometric ratios of Mg:Si=1.8:1, Mg:Si=2:1 and Mg:Si:Ni=x:15:50 (x=36, 50, 130), respectively, in a high-speed ball mill (QM-3B) with a ball-to-powder mass ratio of 10:1 to obtain Mg1.8Si, Mg2Si and Mg2SiNi3.

The milled powders of thermoelectric materials were then cold-pressed inside a graphite die to obtain a green pellet (a diameter of 20 mm). The sample was sintered in a spark plasma sintering apparatus (SPS-630Lx) under sintering temperature 750 °C, uniaxial pressure of 40 MPa and vacuum of 20 Pa. The milled powders of thermoelectric and intermediate materials were then cold-pressed inside a graphite die to obtain a pellet (a diameter of 20 mm) with a symmetrical structure of MgxSi15Ni50/Mg2Si (x=36, 50, 130).

SPS is conducted in vacuum by heating to 630 °C at a speed of 100 °C/min under 10 MPa followed by a 2-min dwell, and then rapidly heating to 750 °C under 40 MPa and staying for another 15 min. During cooling, the temperature was first decreased to 400 °C at a speed of 12.5 °C/min, and then decreased to room temperature at a speed of 10 °C/min. All handling was performed under a protective argon atmosphere.

A thermomechanical analyzer (DIL 402SU, NETZSCH) was used to measure the CTEs of MgxSi15Ni50(x=36,50,150). The microstructure and chemical composition of thermoelectric joints before and after aging were determined with scanning electron microscopy (SEM, JEOL JSM 6300) and energy dispersive spectroscopy (EDS, HKL). Contact resistance of samples was measured with the four-probe method and the samples for this evaluation were 3×3×δ mm in dimension, with δ being the thickness of the sample, typically 4-5 mm. The phase purity of the thermoelectric materials was confirmed by X-ray diffraction (DX-2700). The Seebeck coefficient and resistivity were performed in a Namicro3 system. A Hall effect test system (CH-100) was used to measure the carrier concentration. The shear strength of samples was tested by a microcomputer-controlled electronic universal testing machine (DNS200) with a head movement rate of 0.5 mm min−1. The samples used for this evaluation were 7×7×δ mm in dimension (δ = 4-5 mm). The joints samples were heat-treated at 400 °C for 120, 240, 360 and 480 h under vacuum of 10−4 Pa to evaluate the thermal stability.

Results and Discussion

The Presence and the Influence of Mg-Depletion Layer

As shown in Fig. 2a, the interface of the Mg36Si15Ni50/Mg2Si thermoelectric joint is a sandwich-like structure. The gray part on the right is the diffusion barrier Mg2SiNi3 phase, and the dark layer on the left is the Mg2Si thermoelectric material. No voids or cracks were observed in the joints. Figure 2b shows a uniform and dense diffusion layer formed in the Mg2Si/Mg36Si15Ni50 interface with a thickness of about 15 μm. There are two different phases in the diffusion layer: dark phase and dispersed particles. Combined with EDS analysis (see Fig. 2c) and Mg-Ni-Si ternary phase diagram,23 it is shown that the atomic ratios of Mg, Si, and Ni at different site are very different, the phase component of matrix of the diffusion layer is basically a mixture of Mg2Si and Mg, and the second phase particles is NiSi2 phase.24 EDS analysis result (see Fig. 2d) indicates that a Mg-depletion region (MDR) exists next to the thermoelectric material with a thickness of 7 μm, which is detrimental to the thermoelectric properties of Mg2Si (discussed below). The formation of MDR is mainly due to faster diffusion velocity of Mg than Si. It is generally accepted that substitutional migration of atoms in intermetallic compounds occurs by virtue of vacancy-type defects. In such an antifluorite-type structure (\(Fm\overline{3}m\)), sublattice of Si in Mg2Si can also be viewed as simple cubic with one Si atom of every two missing, so Mg diffuses faster than Si element and is easier to lose.25 So it would be helpful to suppress the migration of Mg by increasing the percentage of Mg in the barrier and decreasing its ingredient gradient as well. Figure 3a shows the variation of lattice parameters of MgxSi15Ni50 (36≤x≤130). Linear variation follows the Vegard’s law up to x=45, subsequently saturating between x=45 and x=50. Partially squeezed out liquid from the interface may be observed when x≥55, which is Mg (see Fig. 3b).

Fig. 2
figure 2

Mg36Si15Ni50/Mg2Si thermoelectric joint interface micromorphology (a), (b) micromorphology (c) EDS point analysis results (d) EDS line analysis results of line ab in (b).

Fig. 3
figure 3

(a) lattice constant of MgxSi15Ni50 (36 ≤ x ≤ 130) sample (b) sample with Mg squeezed out during sintering.

Influence of Mg Defect

Because of the high vapor pressure of Mg and high sintering temperature of Mg2Si, it is difficult to accurately control the stoichiometry of Mg.26 The excess or lack of magnesium in Mg2Si affects the balance of the intrinsic defects (IMg,27 VMg 28 and anti-defects), thus affecting the electrical properties. In order to study the influence of Mg content on the electrical properties of the material, Mg1.8Si and Mg2Si were made by SPS. As shown in Fig. 4a, all of diffraction peaks can be indexed to the antifluorite structure (PDF#35-0773; a = b = c = 6.351 Å), with a small amount of MgO. The study on the stability and electronic properties of point defects and multivacancies in Mg2Si shows that the stability of the defects is strongly dependent on the stoichiometric conditions.29 The VMgSi, VMg2Si and IMg are the most stable defects when Mg is rich, while the antisite SiMg becomes more stable, and IMg becomes less stable when Mg is poor. Mg2Si is always n-type in experiments, so the most stable defect is IMg, which acts as a donor. In stoichiometric conditions, the IMg defect becomes less favorable, whereas the VMg defect becomes more stable and the multivacancies are still very favorable.4 The temperature-dependent electrical properties of Mg1.8Si and Mg2Si indicate a non-degenerate feature, as shown in Fig. 4b and c. The higher resistivity of the Mg1.8Si sample can be ascribed to the formation of VMg and loss of the IMg due to lack of Mg.30 VMg has a significant effect on the electric properties of Mg2Si. In stoichiometric conditions, the formation energy of VMg is as low as 1.54 eV.29 This is one of the reasons that the magnesium atoms diffuse very easily. Our recent work shows that the use of intermetallic compounds as a barrier may block the diffusion of Mg effectively.20

Fig. 4
figure 4

(a) Room-temperature XRD patterns, (b) Resistivity and (c) Carrier concentration of Mg1.8Si and Mg2Si.

Suppressing Mg Deletion Through Ingredient Gradient Design

Suppression of the excessive diffusion of Mg atoms in thermoelectric materials can alleviate the generation of Mg vacancies and improve the interface performance. In order to study the effect of the percentage Mg content in the barrier on the net diffusion of interface elements, thermoelectric joints with different concentration gradients (MgxSi15Ni50/Mg2Si; x=36,50,130) were designed.

Figure 5a and c presents the microstructures of Mg130Si15Ni50/Mg2Si and Mg50Si15Ni50/Mg2Si joints. A dense and uniform intermediate layer is formed between the thermoelectric material and the barrier layer with a thickness of 10 μm and 15 μm, respectively. The chemical composition of the diffusion layer is Mg:Si:Ni≈1:1:1, which is close to ω-(Mg0.52Ni0.48)7Si4 phase according to the phase diagram and literature.28 The EDS results show a diffusion layer next to thermoelectric material as thin as 2 to 3 μm, and no MDR is observed, as shown in Fig. 5b and d, which proves that increasing Mg concentration gradient across the interface by increase of Mg content in Mg2SiNi3 side can effectively suppress the Mg loss in the Mg2Si effectively. Furthermore, when x increases from 50 to 130, no obvious effect is observed in either interface but excess squeezed-out liquid Mg is present in the former sample.

Fig. 5
figure 5

Interface micromorphology and element distribution across the interface of (a), (b) Mg130Si15Ni50/Mg2Si and (c) (d) Mg50Si15Ni50/Mg2Si.

According to Fick's first law of diffusion, the flux of Mg atom from Mg2Si to Mg36Si15Ni50 is given by:

$$ J = ( - D_{0} \Delta C)/\Delta x $$
(2)

where D0 is the diffusion coefficient of Mg in the reaction layer, \(\Delta c\) is concentration difference of \(c_{{{\text{Mg}}_{2} {\text{Si}}}}\)-\(c_{{{\text{Mg}}_{36} {\text{Si}}_{15} {\text{Ni}}_{50} }}\), \(\Delta x\) is the thickness of reaction layer (15 μm). The per second total number of Mg atom diffusion from Mg2Si to Mg36Si15Ni50 is calculated by

$$ J_{{{\text{total}}}} = J \cdot S $$
(3)

where S is the cross-section of the interface. The per second amount of Mg atoms diffused from the Mg36Si15Ni50/Mg2Si interface is calculated by

$$ J_{\sec } = J_{{{\text{total}}}} /C_{{\left( {{\text{Mg}}_{2} {\text{Si}}} \right)}} $$
(4)

where \( c_{{{\text{Mg}}_{2} {\text{Si}}}}\) is concentration of Mg in Mg2Si (3.1 × 1022 at./cm3). In Mg2Si, the thickness increase per second of the Mg-poor layer is calculated by

$$ \Delta l_{{{\text{Sec}}}} = J_{{{\text{sec}}}} /S $$
(5)

Therefore, the thickness of the Mg-poor layer in Mg2Si is calculated by

$$ \Delta l = \left( { - D_{0} \Delta c \cdot t} \right)/\left( {\Delta xC_{{\left( {{\text{Mg}}_{2} {\text{Si}}} \right)}} } \right) $$
(6)

\(c_{{{\text{Mg}}_{36} {\text{Si}}_{15} {\text{Ni}}_{50} }}\) is the concentration of Mg in Mg36Si15Ni50 (3 × 1022 at./cm3), t is aging time. According to the Mg-poor layer thickness from Figs. 2 and 7, \(\Delta l\) is 4 μm. So, the diffusion coefficient of Mg from Mg2Si to Mg36Si15Ni50 at 400 ℃ is 2.15×10−12 cm2/s. Compared with that25 (2.0 × 10-10 cm2/s) of Mg in the Mg2Si at 500 °C , the diffusion coefficient of Mg from Mg2Si to Mg36Si15Ni50 at 400 ℃ was lower. For the interface of Mg2Si/Mg50Si15Ni50, \(c_{{{\text{Mg}}_{36} {\text{Si}}_{15} {\text{Ni}}_{50} }}\) in Mg50Si15Ni50(4.2 × 1022 at./cm3). The direction of Mg concentration difference is from Mg50Si15Ni50 to Mg2Si. The results above indicate that increasing of Mg content of Mg2SiNi3 side can effectively suppress the Mg diffusion from Mg2Si to Mg2SiNi3.

Interface Performance is Improved by Gradient Design

Contact resistivity has a significant effect on conversion efficiency and power output for thermoelectric modules,33 which mainly depends on the interface microstructure as well as the electrical properties of the interfacial materials.34,35,36,37,38,39,40 Lower contact resistivity (RC<< L/2σ) for thermoelectric joints is expected in long-term service.

Figure 6a shows the change of electrical resistance across the section of MgxSi15Ni50/Mg2Si (x=36,50,130) joints. The linearly increasing resistance on the Mg2Si side indicates a semiconductor while that in the Mg2SiNi3 side indicates metallic property. An abrupt change between Mg2SiNi3 and intrinsic Mg2Si can be observed, as summarized in Fig. 6a. The intrinsic contact resistance is 275.4 μΩ cm2, 171.9 μΩ cm2, 141.3 μΩ cm2 for Mg36Si15Ni50/Mg2Si, Mg50Si15Ni50/Mg2Si, and Mg130Si15Ni50/Mg2Si, respectively, which are smaller than 320 μΩ cm2 for the Mg2Si/Ni joint measured by Sakamoto et al.41 Compared with the Mg36Si15Ni50/Mg2Si joint, the contact resistance of MgxSi15Ni50/Mg2Si joints (x=50, 130) is reduced by 50%. The higher contact resistivity of the Mg36Si15Ni50/Mg2Si joint may be ascribed to the formation of MDR due to Mg diffusion.

Fig. 6
figure 6

(a) Testing curve of contact resistance of the joints (b) Variation of contact resistivity with different aging time for MgxSi15Ni50/Mg2Si (x = 36, 50, 130) joints.

To evaluate the interfacial reliability of the thermoelectric joints at high temperatures, aging tests of MgxSi15Ni50/Mg2Si (x=36, 50, 130) joints at 400 °C for 480 h are carried out. Figure 6b shows the change of contact resistance of MgxSi15Ni50/Mg2Si (x=36, 50, 130) joints after aging. These values are smaller than 16.4 mΩ cm2 obtained for the Mg2Si/Cu joint by Cai et al.42 We conjecture that the increase in the contact resistivity with aging time might be ascribed to the loss vitalization of Mg of TE material during aging. Similar results have been reported in the literature.20,24,43 The contact resistance of Mg130Si15Ni50/Mg2Si and Mg50Si15Ni50/Mg2Si are smaller than that of Mg36Si15Ni50/Mg2Si, indicating that the Mg-rich diffusion barrier layer can suppress the loss of Mg, thereby increasing the stability of the joint.

As shown in Fig. 7a, compared with that before aging in Fig. 2b, the phase component of the aged interface Mg36Si15Ni50/Mg2Si after aging for 240 h is almost unchanged. But the thickness of the diffusion layer and MDR increases, where the thickness of the diffusion layer and MDR is around 20 μm and 11 μm, respectively (Fig. 7b). The increase in the MDR thickness may be ascribed to the diffusion layer which has inconspicuous inhibitory on the diffusion of Mg. Figure 7c and e shows the interface microstructure of Mg50Si15Ni50/Mg2Si and Mg130Si15Ni50/Mg2Si joints after aging at 400 °C for 240 h, respectively. Compared with that before aging, both the thickness and phase component remain unchanged.

Fig. 7
figure 7

Microstructure and EDS line scan analysis of MgxSi15Ni50/Mg2Si interface after annealing at 400 °C for 240 h (a), (b) Mg36Si15Ni50/Mg2Si joint (c), (d) Mg50Si15Ni50/Mg2Si joint (e) (f) Mg130Si15Ni50/Mg2Si joint.

The CTEs of Ni, MgxSi15Ni50(x=36, 50, 150) and Mg2Si within the temperature range of 150-400 °C are shown in Fig. 8a. The CTE of Ni ranges from 13.2×10-6 K-1 to 14.8×10-6 K-1 between 150 °C and 400 °C,20 that of Mg36Si15Ni50 ranges from 12.1×10-6 K-1 to 11.2×10-6 K-1 , and that of Mg50Si15Ni50 ranges from 11.3×10-6 K-1 to 13×10-6 K-1, which is very close to that of Mg130Si15Ni50.

Fig. 8
figure 8

(a) The CTE values of the MgxSi15Ni50(x = 36, 50, 150) (b) temperature dependence of resistivity of MgxSi15Ni50(36 ≤ x ≤ 130) within the temperature range.

Figure 8b shows that the resistivity decreases with increase of x. when x is greater than 50, it remains almost unchanged, and some liquid magnesium can be observed at the surface of the plunger (Fig. 3b), which indicates that no more magnesium may enter into the lattice. The Mg-Si-Ni ternary phase diagram23 indicates that the residual Mg in MgxSi15Ni50(x=50, 130) exists as a second phase of Mg2Ni at the grain boundary, with a CTE of 7.5×10-6 K-1 to 12.5×10-6 K-1 from 150 ℃ to 350 ℃,20 which is far lower than that of Mg36Si15Ni50.

Mg2Si has a CTE within the scope of 10.2×10-6 K-1 and 18.9×10-6 K-1 from 150 °C to 400 °C.20 The previous report showed that a CTE difference less than around 5-6 ×10-6 K-1 does not lead to failure of the joint of Mg2Si and Ni.20 CTE of the barrier may be modified by changing the content of magnesium, which is beneficial to reduce the residual interface stress and improve the bonding strength and stability.

The shearing tests were conducted to evaluate the mechanical properties, as shown in Fig. 9. All of them are about 23 MPa before aging. These values are higher than that of 16.2 MPa and 19 MPa obtained for Mg2Si/Cu and Mg2Si/Ni joints by Cai et al42 and Tohei et al.44 Furthermore, this work shows great advantage after aging. As can be seen from Fig. 9, the strength of the Mg36Si15Ni50/Mg2Si joint decreases more than the other two, which is mainly due to the phase component of the interface diffusion layer. The uniform and dense ω-phase diffusion layer at the interface of MgxSi15Ni50/Mg2Si (x=50, 130) can maintain high bonding strength during the aging. Additionally, the CTE difference (see Fig. 8) in interfaces is one of the reasons that the bonding strength decreases with aging time.24

Fig. 9
figure 9

The shear strength of MgxSi15Ni50/Mg2Si (x = 36, 50, 130) joints after aging.

Conclusions

In this work, Mg2SiNi3 (TCP-IMC) was selected as the barrier layer to bond with intrinsic Mg2Si by SPS in one step. Adjusting the proportion of Mg in the barrier to suppress the migration of Mg across the interface thereby alleviates the degradation of the thermoelectric properties of the Mg2Si thermoelectric material and increases the stability in service as well.

A diffusion layer was located between Mg2Si and Mg36Si15Ni50. The matrix is basically a mixture of Mg2Si and Mg, with NiSi2 precipitates as second phase. In the matrix of MgxSi15Ni50/Mg2Si (x=50, 130), a dense and uniform diffusion layer was observed, which was composed of an ω-phase (Mg:Si:Ni≈1:1:1) based on EDS and phase diagram. A higher chemical potential of Mg in the barrier is helpful to suppress the formation of the Mg-depletion layer in Mg2Si.

The barrier of MgxSi15Ni50 (x=50, 130) effectively improves the interface conductivity and the bonding strength. The contact resistivity in MgxSi15Ni50/Mg2Si (x=50, 130) joints are 171.9 μΩ cm2 and 141.3 μΩ cm2, which are about 50% of that of Mg36Si15Ni50/Mg2Si joint. The shear strength of all joints with different Mg content is around 23 MPa. Mg50Si15Ni50/Mg2Si and Mg130Si15Ni50/Mg2Si joints show better stability both in contact and shear strength after aging at 400 ℃ for different time.