In situ nanostructure design leading to a high figure of merit in an eco-friendly stable Mg₂Si_0.30Sn_0.70 solid solution

Abstract

The relationship between the temperature and the composition as well as the microstructure of a Sb-doped Mg₂Si_0.30Sn_0.70 solid solution was systematically studied according to the Mg₂Si–Mg₂Sn pseudo-binary phase diagram. This work shows that the composition, distribution pattern, and fraction of in situ nanostructures can be controlled by the heat treatment carried out at a specific peritectic reaction temperature. A large number of in situ nanoprecipitates were observed when the sample was quenched at 900 K or 1130 K. However, quenching at 900 K resulted in the formation of agglomerates while quenching at 1130 K yielded a more even dispersion of nanoprecipitates. Monochromatic X-ray studies, back-scattering images and HRTEM results showed that the composition of the nanoprecipitates when quenched at 900 K was the Mg₂Si-rich phase, while the nanostructure was the Mg₂Sn-rich phase when quenched at 1130 K. The lattice thermal conductivity decreased dramatically due to the well distributed Mg₂Sn-rich nanoprecipitates, and the maximum ZT of about 1.2 was achieved at around 750 K. Moreover, the average value of the figure of merit ZT_average reached about 0.9 in the range of 300–800 K, about a 15% higher value than in the sample composed of Mg₂Si-rich nano-agglomerates. This study demonstrates that carrying out heat treatments at the phase transformation temperatures is a simple and controllable method to design and form in situ nanostructures, which is of vital importance in the fabrication of nanocomposites and optimization of the thermoelectric performance.

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Introduction

Thermoelectric (TE) power generation is a technology capable of directly converting waste industrial heat (such as from exhaust pipes of cars and trucks or industrial kilns and furnaces) into usable electricity, with the advantages of exceptionally high reliability, absence of any moving parts, and silent operation. Thus, TE power generation shows a great potential for large scale applications among other new green energy technologies.^1,2 The energy conversion efficiency of TE materials is characterized by the figure of merit which is defined as ZT = S²σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity. The state-of-the-art TE materials should have a high power factor (defined as S²σ) together with a low thermal conductivity (κ). The former is usually optimized by doping^3–6 and electronic band engineering,^7–12 while the latter is often achieved by forming solid solutions,^13,14 low dimensional structures^15–18 and nanocomposites.^19–22

Mg₂Si_1−xSn_x solid solutions are consist of earth abundant, inexpensive, and environmentally friendly raw elements and possess a relatively high volume power density. They are expected to be operated in the temperature range of 300–800 K.²³ So far, the electronic properties of Mg₂Si_1−xSn_x have been optimized by adjusting the Si/Sn ratio,^24,25 by doping with Sb or Bi,^26–29 and by varying the stoichiometry of Mg.^30,31 And the thermal properties have been tuned by altering the Si/Sn ratio or by introducing nanoinclusions.^19,32,33 However, tuning the thermal conductivity by changing the Si/Sn ratio has been hampered by the fact that there is a miscibility gap for compositions 0.4 ≤ x ≤ 0.6 (ref. 34) which precludes to use the most disordered structure with x = 0.5. Consequently, nanostructuring has been explored as an alternative strategy of reducing the thermal conductivity.³⁵

It is important to keep in mind that grain boundaries and interfaces scatter not only phonons but also charge carriers and thus decrease the mobility.^36–38 Benefits of nanostructuring are realized only if the mean-free path of phonons is reduced to a greater extent than the mean-free path of charge carriers. Consequently, it is desirable to have nanostructures that are coherent or at least semi-coherent with the matrix. Such nanostructures still scatter phonons very effectively but exert only a minor influence on the transport of charge carriers.^39–41

Several studies have shown that semi-coherent and coherent interfaces can be achieved in the Mg₂Si_1−xSn_x system via phase segregation, by making use of the miscibility gap. For instance, using the melt spinning technique, X. Zhang et al.⁴² synthesized Mg₂Si_0.4Sn_0.6 solid solution decorated with 10–20 nm homogeneously distributed nanoparticles, while W. Liu et al.⁴³ observed numerous Mg₂Sn-rich nanoprecipitates in Mg₂Si_0.4Sn_0.6, prepared by a two-step solid state reaction (SSR) method. However, different morphologies were obtained with Mg₂Si_0.3Sn_0.7, a solid solution containing a larger fraction of Mg₂Sn. In this case, a single phase structure with good homogeneity was achieved by melt spinning, while Mg₂Si-rich nanoinclusions were observed when the solid solution was prepared by the two-step SSR method.⁴⁴ The key point behind the inconsistent results is that the researchers have not clearly understood how the composition and the microstructure of Mg₂Si_1−xSn_x evolve and depend on the preparation methods due to a complicated and unclear phase diagram. According to the Mg₂Si–Mg₂Sn pseudo-binary phase diagram,^34,45,46 there are three peritectic reactions in the system taking place at 1130 K, 900 K, and 837 K, respectively (1130 K: Mg₂Si_0.2Sn_0.8(L) + Mg₂Si_0.4Sn_0.6(S) → Mg₂Si_0.3Sn_0.7(S); 900 K: 7Mg₂Si_0.28Sn_0.72(L) + 3Mg₂Si_0.86Sn_0.14(S) → 10Mg₂Si_0.45Sn_0.55(S) + 0.04Si(S); 837 K: Mg_0.9Si_0.03Sn_0.07(L) + Mg₂Si_0.88Sn_0.12(S) → Mg_0.98Sn_0.02(S) + Mg₂Si_0.43Sn_0.57(S)). The composition and the phase (solid or liquid) differ from one another depending on which peritectic reaction is involved, thus the composition and the microstructure of the resulting solid solutions are very sensitive to the synthesis process and its parameters.

In this study, Sb-doped Mg₂Si_0.30Sn_0.70 was chosen as an example with which to shed light on the inconsistency of results when guided by the existing Mg₂Si–Mg₂Sn pseudo-binary phase diagram and carrying out the synthesis using different peritectic reactions. The results showed that the microstructure and the composition depend strongly on the temperature at which the sample was quenched. Specifically, a single phase material was successfully obtained when quenching at 1080 K. In contrast, quenching at a lower temperature of 900 K, one obtained lots of Mg₂Si-rich nanoprecipitates which tend to agglomerate, while quenching at a higher temperature of 1130 K resulted in Mg₂Sn-rich nanoprecipitates which were uniformly distributed. This high-temperature quenched solid solution with Mg₂Sn-rich nanoprecipitates has an outstanding TE performance with the average value of the figure of merit ZT_average ∼ 0.9 in the temperature range of 300–800 K and the peak value ZT_max of ∼1.2 near 750 K. Moreover, this particular nanostructured solid solution showed an excellent thermal stability. After extended annealing at 773 K for no less than 15 days, the TE properties were essentially unchanged which is of critical importance for power generation applications. All in all, a high TE performance Mg₂Si_0.30Sn_0.70 solid solution was obtained by carefully designing the composition and the distribution pattern of in situ nanoinclusions according to the phase diagram.

Experimental

High purity powders of Mg (99%, 100–200 mesh), Si (99.99%, 200 mesh), Sn (99.9%, 200 mesh), and Sb (99.999%, 200 mesh) were used in the two-step solid state reaction (SSR) synthesis of Mg_2.16(Si_0.30Sn_0.70)_0.98Sb_0.02 solid solution, where the samples were situated in the pyrolytic boron nitride (PBN) crucibles and sealed in the silica ampoules.³¹ The first reaction step was carried out at 837 K for 6 h, and the reaction temperature of the second step was chosen according to the different peritectic reactions mentioned above (details are shown in Table 1). And all the samples were quenched in over-saturated salt water as soon as the last SSR step was completed. The final consolidation into an ingot was done by electron-discharge plasma activated sintering (Elenix, Ed-PAS III), with the uniaxial pressure of 35 MPa at 933 K and the holding time of 10 min. An 8% excess of Mg over the stoichiometric amount was applied to compensate for the evaporation loss of Mg during the synthesis. The resulting ingots were then cut into suitable sizes for different measurements as listed below.

Table 1 The reaction temperature, holding time of the solid state reaction (SSR) process, and the actual composition of the sintered ingots by EPMA

Sample	1st SSR	2nd SSR	Actual composition
1	837 K-6 h	—	Mg2.158(Si0.281Sn0.719)0.978Sb0.022
2	837 K-6 h	900 K-4 h	Mg2.148(Si0.289Sn0.711)0.979Sb0.021
3	837 K-6 h	1080 K-4 h	Mg2.139(Si0.306Sn0.694)0.982Sb0.018
4	837 K-6 h	1130 K-4 h	Mg2.082(Si0.346Sn0.654)0.981Sb0.019

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The phase composition of the solid solution at different steps of processing was characterized using a PANalytical X'Pert Empyrean type X-ray diffractometer with Cu K_α and K_α1 radiations, and the lattice parameters were calculated by the Rietveld method. For the regular X-ray diffraction, the ratio of K_α2/K_α1 was 0.5, with the generator voltage and the tube current to be 40 kV and 40 mA, respectively, and the scan range was 10–80 degrees with a scan step size of 0.02 degree and the divergence slit of 0.38 mm. Except the scan step size of 0.005 degree as well as the divergence slit of 0.5 mm, all parameters were the same as aforementioned for the monochromatic X-ray diffraction. The actual chemical composition and back-scattering images of the polished ingots were analyzed by electron probe microanalysis (EPMA) with the aid of JEOL JXA-8230 system. The microstructure of the fractured surface was characterized by field-emission scanning electron microscopy (FESEM) using a Hitachi SU8020 apparatus. And high resolution transmission electron microscopy (HRTEM) was carried out with a JEOL JEM-2100F equipment.

The electrical conductivity and the Seebeck coefficient in the range of 300–800 K were acquired on a commercial ZEM-3 system (Ulvac Sinku-Riko) in helium by a standard four-probe DC configuration. The Hall coefficient at 300 K was measured by the five probe method using a physical property measurement system (PPMS, Quantum Design). The carrier concentration and the carrier mobility were then calculated from the equation n_H = 1/eR_H and μ_H = σR_H, respectively. The thermal conductivity was determined by κ = λC_pρ, where λ is the thermal diffusivity acquired by the laser flash method (Netzsch LFA 457), C_p is the specific heat measured by a differential scanning calorimeter (TA DSC Q20) in argon, and ρ is the density determined by the Archimedes method in alcohol.

To explore the thermal stability of in situ formed nanostructures (solid solution quenched at 1130 K), the sintered ingot was coated with BN spray and annealed in air at 773 K for 15 days.⁴⁷ The microstructure and the transport properties of thus annealed sample were then characterized in detail.

Results and discussion

Fig. 1 shows the XRD patterns of samples at different steps of the synthesis process. Fig. 1(a) and (b) depict the patterns (Cu K_α) after the solid state reaction and after sintering, respectively, Fig. 1(c) is an expanded view of Fig. 1(b) within the angular range of 68–75 degrees, and Fig. 1(d) shows the monochromatic X-ray (Cu K_α1) results of the sintered ingots. All samples can be refined in the antifluorite structure, Fm3̄m group, and the reference pattern of Mg₂Si_0.30Sn_0.70 is derived from JCPDS # 01-089-4254 by modifying the Si/Sn ratio.⁴⁸ The major phase of the products after the first SSR step was Mg₂Si_1−xSn_x (x ≥ 0.7) and the Mg₂Si-rich phase together with a tiny amount of unreacted Mg and Sn. Almost the same composition (except for the absence of Sn) was obtained after the second SSR step carried out at 900 K and 1080 K. However, when the second reaction step was carried out at 1130 K, a very different outcome resulted with Mg₂Si_1−xSn_x (x ≤ 0.7) and Mg₂Sn-rich phase being detected. Though multiple phases still coexisted after the second SSR step, a single phase material was obtained upon subsequent sintering, see Fig. 1(b). This indicates that sintering is helpful in promoting the formation of single phase solid solution as it enhances the process of mass transfer.⁴⁹ However, a closer look, see Fig. 1(c), reveals that the XRD peaks of the sintered ingots have shifted to higher angles and the lattice parameters (shown in Fig. SI1, ESI†) decreased as the temperature of the second SSR step increased. We suspected that the powders prepared for X-ray investigations after sintering may have still contained traces of Mg₂Si-rich or Mg₂Sn-rich phases,⁵⁰ but these were too difficult to distinguish from the major phase due to the very similar lattice parameters and mixed wavelengths of K_α1 and K_α2 radiation. To verify this point, monochromatic X-ray diffraction was conducted on powders of the sintered ingots, Mg₂Si-rich second phase was detected in the sintered ingots quenched at 837 K and 900 K, while a single phase material was obtained when quenched at 1080 K. Increasing the quenching temperature to 1130 K, Mg₂Sn-rich phase was detected (presented in Fig. 1(d)). The results were also confirmed by the electron back-scattering (see Fig. 2) images, where the circled regions indicate the Mg₂Si-rich phase (it was the second phase in Fig. 2(a) and (b), while the major phase in Fig. 2(d)). Moreover, EPMA data (shown in Table 1) also confirm the difference in the phase composition of this solid solution subjected to different heat treatment conditions. To get a clear picture regarding the phase composition of the solid solution, an inquiry into the formation mechanism and microstructure during different peritectic reactions was made according to the Mg₂Si–Mg₂Sn pseudo-binary phase diagram.

Fig. 1 Powder XRD data of samples: (a) after solid state reactions (SSR); (b) after sintering; (c) enlarged XRD patterns of (b) within the angular range of 68–75 degrees; (d) powder monochromatic XRD data of the sintered samples. The inset shows the enlarged patterns within the angular range of 20–30 degrees.

Fig. 2 Back-scattering images of the sintered ingots. (a) Without 2nd SSR step; (b) with the 2nd SSR step quenched at 900 K; (c) with the 2nd SSR step quenched at 1080 K; (d) with the 2nd SSR step quenched at 1130 K.

Though researchers argued about the actual region of the miscibility gap, they agreed on the peritectic temperature, as E. N. Nikitin et al.³⁴ conducted the experiment with a longer annealing time and slower crystallization than that of Sh. F. Muntyanu et al.⁵¹ we take the diagram plotted by E. N. Nikitin et al. as a reference. Taking the Mg₂Si_0.30Sn_0.70 solid solution as an example (see Fig. SI2, ESI†), and starting with a liquid at high temperature, the liquidus will be reached upon cooling the melt at about 1200 K (the process 1 → 2). A solid phase with the composition of approximately Mg₂Si_0.75Sn_0.25 will appear together with the liquid phase of Mg₂Si_0.3Sn_0.7 expressed schematically as:

L → S_A(Mg₂Si_0.75Sn_0.25) + L_B(Mg₂Si_0.3Sn_0.7)

As the temperature decreases (the process 2 → 3), the composition of the solid changes along the AC line while that of the liquid changes along the BE line. At 1130 K, by a lever rule, the composition should be S_C(Mg₂Si_0.6Sn_0.4) : L_E(Mg₂Si_0.2Sn_0.8) = 1 : 3. However, the composition varies as there follows a peritectic reaction (the process 3 → 3′):

Mg₂Si_0.2Sn_0.8(L) + Mg₂Si_0.6Sn_0.4(S) → 2Mg₂Si_0.4Sn_0.6(S)

The resulting products are S_D(Mg₂Si_0.4Sn_0.6) : L_E(Mg₂Si_0.2Sn_0.8) = 1 : 1, and they will change along the DH line and EI line, respectively if keep cooling (the process 3′ → 4). Due to the heat loss by radiation, the actual temperature of the sample when quenched was a bit lower than 1130 K (in reality it was ∼1120 K when cooling down in the oversaturated salt water, measured by a chromel–constantan thermocouple), so the composition after quenching should have been S_F(Mg₂Si_0.35Sn_0.65) : L_G(Mg₂Si_0.18Sn_0.82) = 12 : 5. This was confirmed by the XRD, the back-scattering images and the EPMA results which indicate the Mg₂Si-rich matrix together with the Mg₂Sn-rich second phase.

Single phase was obtained when quenched at 1080 K, and this is due to the critical temperature at which liquid and solid phases coexist (the process 3′ → 4). The liquid phase speeds up the mass transfer which is helpful for forming a homogeneous solid solution. When the temperature drops a bit below 1080 K, the liquid phase disappears and Mg₂Si_0.30Sn_0.70 solid forms.

About 40 years later after the reports by E. N. Nikitin et al.³⁴ and Sh. F. Muntyanu et al.⁵¹ researchers found another two peritectic reactions happen at 900 K and 837 K, by calculations and experiments.^45,46 The phase transformation process at 900 K is almost the same as at 1130 K, as shown in Fig. SI3(a), ESI.† Liquid appears when the temperature goes to 900 K:

Mg₂Si_0.3Sn_0.7(S) → 0.97Mg₂Si_0.28Sn_0.72(L) + 0.03Mg₂Si_0.86Sn_0.14(S)

This is followed by the peritectic reaction:

7Mg₂Si_0.28Sn_0.72(L) + 3Mg₂Si_0.86Sn_0.14(S) → 10Mg₂Si_0.45Sn_0.55(S) + 0.04Si(S)

The products would have been Mg₂Si_0.28Sn_0.72(L) : Mg₂Si_0.45Sn_0.55(S) : Si(S) = 9 : 1 : 4 × 10⁻³. As the content of Si was rather small compared with others, only the Mg₂Sn-rich matrix and the Mg₂Si-rich second phase were observed.

A similar situation happens at 837 K, where the peritectic reaction (shown in Fig. SI3(b), ESI†) is:^45,46

Mg_0.9Si_0.03Sn_0.07(L) + Mg₂Si_0.88Sn_0.12(S) → Mg_0.98Sn_0.02(S) + Mg₂Si_0.43Sn_0.57(S)

The actual composition after quenching would have been Mg₂Si_0.27Sn_0.73 : Mg₂Si_0.43Sn_0.57 = 13 : 3, consistent with the data mentioned above. A minor Mg phase was observed, likely the result of intentionally added Mg to compensate for the evaporative loss.

Because liquid has appeared during the peritectic reaction, quenching at the phase transformation temperatures may result in the formation of unique nanostructures due to the non-equilibrium solidification.^52,53 Consequently, the microstructure of samples prepared using different heat treatments was characterized in detail. Since the phase composition and the state of the second phase before quenching (both were solids) were similar when heat treated at 837 K and 900 K, while very different when heat treated at 1130 K, the samples quenched at 900 K and 1130 K were selected as representatives to explore the size and distribution of different nanostructures (shown in Fig. 3). Thermal stability of the nanostructures was also characterized by annealing at 773 K for 15 days. Fig. 3(a) and (b) are the FESEM images of powders after the second SSR step, while Fig. 3(c) and (d) are those of the sintered ingots, and Fig. 3(e)–(h) provide the size distribution of nanoparticles appearing in Fig. 3(a)–(d), respectively. The microstructure and the nanoparticle size distribution of the annealed bulk structures (773 K for 15 days) are shown in Fig. SI4, ESI.† Nanoprecipitates with the size around 25 nm were observed after heat treatment at 900 K as well as at 1130 K, and they grew up to about 45 nm after sintering. Moreover, the most striking difference concerns the distribution pattern. When quenched at 900 K, the nanoprecipitates tend to agglomerate while they were well-dispersed when quenched at 1130 K. The morphological difference is induced primarily by the state of the second phase during different peritectic reactions. The second phase, composed of Mg₂Si_0.45Sn_0.55, was a solid before quenching at 900 K (similarly when quenched at 837 K). In contrast, the second phase comprising Mg₂Si_0.18Sn_0.82 was a liquid before quenching at 1130 K, and the Mg₂Sn-rich nanoprecipitates were evenly dispersed without any tendency to agglomerate due to the much faster mass transfer in the liquid phase. After annealing at 773 K over an extended period of time for no less than 15 days, the size of the nanoprecipitates was essentially unchanged, boding well for high temperature applications of Mg₂Si_1−xSn_x solid solutions containing in situ grown nanoinclusions. HRTEM analysis, shown in Fig. 4, was conducted to reveal the composition and microstructure of nanoprecipitates, beyond the information gained from monochromatic X-ray diffraction data mentioned above. Fig. 4(a) and (b) are low magnification images of the sintered ingots with the second SSR step quenched at 900 K and 1130 K, respectively, while Fig. 4(c) and (d) are the same images at higher magnification. As clearly shown in Fig. 4(a), the nanoprecipitates agglomerated when the second reaction step was quenched at 900 K, while well-dispersed nanoparticles were observed when quenching is done at 1130 K, the results were consistent with the FESEM data. Such finely dispersed Mg₂Sn-rich nanoprecipitates facilitate a suppression of the lattice thermal conductivity, as we shall see later. Moreover, at least semi-coherent interfaces are observed between the matrix and the nanoprecipitates which is favorable for electronic transport properties. It is follows that the composition and the distribution pattern of in situ formed nanoprecipitates can be designed and tuned through a carefully selected and applied heat treatment at a specific temperature where the phase transformation takes place, and the fraction of nanoprecipitates can be properly adjusted according to a lever rule of the relevant phase diagram.

Fig. 3 SEM images of: (a) powders with the 2nd SSR step quenched at 900 K; (b) powders with the 2nd SSR step quenched at 1130 K; (c) sintered ingot from the powders in (a); (d) sintered ingot from the powders in (b); (e)–(h) nanoparticle size distribution of (a)–(d), respectively.

Fig. 4 (a) and (b) are low magnification HRTEM images of the ingot with the 2nd SSR step quenched at 900 K and 1130 K, respectively; (c) and (d) are high magnification HRTEM images of the ingot with the 2nd SSR step quenched at 900 K and 1130 K, respectively. The insets in (c) and (d) show the corresponding Fast Fourier Transform (FFT) patterns.

Transport properties

The key transport parameters, such as the carrier concentration n_H and the carrier mobility μ_H at 300 K, the temperature dependent electrical conductivity, Seebeck coefficient and the power factor, the Pisarenko plot (S–n_H), and the dependence of the mobility μ_H on the carrier concentration n_H at 300 K, are shown in Fig. 5. Also presented are data obtained on an ingot with the second SSR step quenched at 1130 K, which was subsequently annealed at 773 K for 15 days. As Fig. 5(a) indicates, the carrier concentration decreased with the increasing temperature of the second SSR step while the carrier mobility increased, but to a lesser degree. Consequently, the electrical conductivity somewhat decreased and the Seebeck coefficient marginally increased with the increasing temperature of the second SSR step. The combined influence of the electrical conductivity and the Seebeck coefficient on the power factor is shown in Fig. 5(d). The power factor increases up to temperatures of around 550 K and then turns around and rapidly falls. As the temperature of the second SSR step increases, the peak value of the power factor decreases and the temperature where the power factor attains its maximum value shifts to a lower temperature. The effective mass of charge carriers (electrons) is about 2.25m₀, independent of the carrier concentration. And the carrier mobility roughly follows the relationship μ_H ∝ n_H^−1/3 at 300 K, a characteristic variation of the transport in degenerate semiconductors.⁵⁵

Fig. 5 (a) The carrier concentration and the carrier mobility at 300 K; (b) the electrical conductivity; (c) the Seebeck coefficient; (d) the power factor; (e) the Pisarenko plot (S–n_H) at 300 K; (f) the μ_H–n_H plot at 300 K, of samples with different heat treatments. The reference data of W. Liu et al.⁵⁴ are noted in (e) and (f).

The temperature dependent thermal conductivity κ_Total, the sum of the lattice thermal conductivity κ_Lattice combined with the bipolar contribution κ_Bipolar, and the ZT value are shown in Fig. 6. The value of κ_Lattice + κ_Bipolar was calculated by subtracting the electronic part κ_electron = LσT from the total thermal conductivity κ_Total. The Lorenz number L was calculated based on the SPB model under the relaxation time approximation, and is shown in Fig. SI5, ESI.†^,54,56 As there was little difference between κ_electron of samples quenched at different temperatures, the different values of κ_Total were caused mainly by variations in the lattice thermal conductivity which behaved as κ_Lattice ∝ T^−0.7, indicating the mixed dominance of Umklapp scattering and alloy scattering.^57,58 The lattice thermal conductivity of the sample quenched at 1130 K is much lower than the value of other samples likely due to the presence of well distributed Mg₂Sn-rich nanoprecipitates.⁵⁹ However, the bipolar effect started to be important at a somewhat lower temperature (∼600 K) as a consequence of the lower carrier concentration. The theoretical minimum value of the lattice thermal conductivity of ∼0.7 W m⁻¹ K⁻¹ above 500 K was estimated using the Cahill model by taking the Debye temperature of θ_D = 247 K and the average phonon velocity of ν_average = 2375 m s⁻¹.^43,60 Comparing this value with the experimental data, it shows that there is still some room to reduce the lattice thermal conductivity further.

Fig. 6 (a) Thermal conductivity κ_Total; (b) sum of the lattice thermal conductivity κ_Lattice and the bipolar part κ_Bipolar; (c) the κ_Lattice + κ_Bipolar data of the sample quenched at 1130 K and the value predicted by different models, the minimum and the maximum value predicted by the H–S model are very close due to the small value of high-order terms; (d) ZT value as a function of temperature.

Since the value of κ_Lattice + κ_Bipolar of the sample quenched at 1130 K is notably smaller than that of other samples, simple calculations were made to give an insight into the effect of semi-coherent and coherent nanoprecipitates. The Hashin–Shtrikman (H–S) model describing the lattice thermal conductivity of a binary composite was applied to explain the changing trend before the bipolar effect becomes important at high temperature:^61,62

where x_i and κ_i are the volume fraction and the lattice thermal conductivity of phase i, respectively, and d is the dimension (d = 3 in this case). The composition in question was Mg₂Si_0.35Sn_0.65 : Mg₂Si_0.18Sn_0.82 = 12 : 5 (mole fraction), with the second SSR step quenched at 1130 K, according to the phase analysis mentioned above. In terms of the volume fraction, it should be Mg₂Si_0.35Sn_0.65 : Mg₂Si_0.18Sn_0.82 = 2.85 : 1, i.e., x₁ = 74% and x₂ = 26%. The lattice thermal conductivity of the composite under the H–S model was obtained by interpolation according to the inequations mentioned above. Judging from Fig. 6(c), the actual value of the lattice thermal conductivity of this sample was significantly lower than what calculations predict, suggesting that the decrease of the lattice thermal conductivity cannot be explained simply by the formation of binary composite, nanoprecipitates and newly grown grain boundaries/interfaces should also be taken into consideration. Thus, the calculation was revised^33,63 by assuming that all Mg₂Si_0.18Sn_0.82 nanoprecipitates are of the 45 nm size and dispersed homogeneously, as observed in the FESEM image. The resulting value (solid curve in Fig. 6(c)) is much closer to the actual experimental value than that predicted by the H–S model, even though the temperature dependence is not perfect.

Due to its lower lattice thermal conductivity, the value of ZT_average observed on the sample quenched at 1130 K reached ∼0.9 over the temperature interval 330–800 K. This is about 15% higher than that of the sample quenched at 837 K. The maximum figure of merit of the sample quenched at 1130 K reached ∼1.2 near 750 K. Annealing this sample at 773 K for 15 days had essentially no effect on the transport properties, demonstrating a bright prospect for the TE power generation.

Conclusions

The composition and the microstructure of Sb-doped Mg₂Si_0.30Sn_0.70 solid solution under different heat treatment conditions were explored according to the Mg₂Si–Mg₂Sn pseudo-binary phase diagram. We found that the composition, the fraction of in situ formed nanoprecipitates, and their distribution can be controlled and tuned by heat treatments carried out at temperatures where phase transformations take place. Thus, by quenching the second reaction step in the synthesis at a lower temperature of 900 K, the in situ formed second phase are Mg₂Si-rich nanoprecipitates with the size of about 40 nm which tend to agglomerate. By raising the temperature of the second reaction step to 1130 K, the in situ formed second phase is now Mg₂Sn-rich phase with almost the same size but well dispersed. The presence of such uniformly dispersed nanoprecipitates leads to about 10% decrease in the lattice thermal conductivity. The average value of the figure of merit ZT_average of this sample increased by about 15% in the range of 300–800 K as compared with the sample including Mg₂Si-rich nano-agglomerates, as well as keeping the peak value ZT_max ∼ 1.2 at about 750 K. The highlight of this research work is a finding that carrying out heat treatment at temperatures where phase transformations take place is a simple and convenient knob with which to control the composition, the content, and the distribution of in situ formed nanoprecipitates which, in turn, benefit the thermoelectric properties. Moreover, thus formed nanoprecipitates showed good thermal stability which is an important aspect of any thermoelectric device intended to operate at elevated temperatures.

Acknowledgements

This work is financially supported by the National Basic Research Program of China under project 2013CB632502, the Natural Science Foundation of China (Grant No. 51402222, 51172174, 51521001), the 111 Project of China (Grant No. B07040), the Fundamental Research Funds for the Central Universities (WUT 2013-YB-013, 2015III061), and the CERC-CVC joint U.S.-China Program supported by the U.S. Department of Energy. We would like to thank Tingting Luo and Rong Jiang for their HRTEM analysis in the Materials Research and Test Center of WUT.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra27171a

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