Transient Liquid Induced Hierarchical Structure Contributes to High Thermoelectric Performance in Ag₂Se

Abstract

Owing to the intrinsic high thermoelectric performance, Ag₂Se is a promising alternative for traditional near‐room temperature Bi₂Te₃‐based materials. In this study, a Na₂SO₃ solution has been used as the transient liquid during the modified cold sintering process to induce a hierarchical structure, including micropores, nanopores, sub‐nanopores, and additional nanoscale Na₂SO₃ residuals. Such a hierarchical structure contributes to an ultralow lattice thermal conductivity of 0.18 W m⁻¹ K⁻¹ at ≈300 K in the Ag₂Se‐30%Na₂SO₃. Additionally, extra Se vacancies further optimize the carrier concentration to ≈5.6 × 10¹⁸ cm⁻³, leading to a high power factor of ≈25 µW cm⁻¹ K⁻² at ≈300 K in the Ag₂Se‐30%NS. Consequently, due to the synergistic effects of high power factor and low lattice thermal conductivity, an ultrahigh room‐temperature figure of merit of 1.04 in the Ag₂Se‐30%Na₂SO₃. The study demonstrates that introducing transient liquid solutions in the modified cold sintering process can effectively achieve specific structural engineering and high thermoelectric performance.

Na₂SO₃ solution has been used as the transient liquid during the modified cold sintering process to induce a hierarchical structure, including micropores, nanopores, sub‐nanopores, and additional nanoscale Na₂SO₃ residuals. Such a hierarchical structure contributes to an ultralow lattice thermal conductivity of 0.18 W m⁻¹ K⁻¹ and an ultrahigh figure of merit of 1.04 at ≈300 K in the Ag₂Se‐30%Na₂SO₃.

1. Introduction

Owing to the ability to directly convert heat into electricity, thermoelectric technology emerges as a promising sustainable energy technology.^{[ 1 ]} Such a thermoelectric technology has unique characteristics, including being noise‐free, emission‐free, and maintenance‐free, which make it suitable for a wide range of applications, such as microelectronics,^{[ 2} , ^{3 ]} medical sensors,^{[ 4} , ⁵ , ^{6 ]} and wearable devices.^{[ 7} , ⁸ , ^{9 ]} Thermoelectric performance is commonly assessed by the dimensionless figure of merit, ZT = (S²σT)/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, κ is total thermal conductivity, and T is the absolute temperature. The κ is comprised of the electronic thermal conductivity (κ _e) and the lattice thermal conductivity (κ _l). As can be seen, achieving a high ZT requires both maximizing the power factor (S²σ) and minimizing κ.

Generally, thermoelectric materials can be categorized into three types based on their operating temperature range: high‐temperature (>873 K), mid‐temperature (473–873 K), and near‐room‐temperature (<473 K) ones.^{[ 10 ]} For near‐room‐temperature applications, Bi₂Te₃‐based materials are highly attractive due to their outstanding thermoelectric performance at this temperature range.^{[ 11} , ^{12 ]} However, the scarcity of tellurium^{[ 13 ]} and the unsatisfactory mechanical properties of Bi₂Te₃ have limited their applications.^{[ 14 ]} As an alternative, silver selenide (Ag₂Se) is a promising high‐performance near‐room‐temperature thermoelectric material. Ag₂Se is an n‐type thermoelectric material with a narrow band gap of 0.04–0.2 eV.^{[ 15 ]} Ag₂Se is orthorhombic structured with a P2₁2₁2₁ space group at room temperature,^{[ 16 ]} which undergoes a phase transition into a superconducting cubic phase at ≈407 K.^{[ 17} , ^{18 ]} Pristine Ag₂Se exhibits high σ ^{[ 19 ]} and low κ,^{[ 20} , ^{21 ]} having an impressively high ZT of ≈0.7 at room temperature.^{[ 22 ]} In addition, due to its tunable ductility, Ag₂Se can be exploited as efficient flexible thermoelectric applications.^{[ 23} , ^{24 ]}

Currently, various strategies have been investigated to enhance the thermoelectric performance of Ag₂Se‐based materials, including compositing,^{[ 25} , ^{26 ]} introducing nano‐inclusions,^{[ 19} , ^{27 ]} creating point defects,^{[ 28 ]} densifying grain boundaries,^{[ 29} , ³⁰ , ³¹ , ³² , ^{33 ]} and incorporating nanopores.^{[ 34} , ^{35 ]} For instance, Nan et al.^{[ 36 ]} composited Ag₂Se with 1.0 wt.% Bi₂S₃, which decreased the Hall carrier concentration (n _H) and enhanced the S to −178.5 µV K⁻¹ at 300 K, leading to a high ZT of 0.96 at 370 K. Tee et al.^{[ 37 ]} developed ternary Cu_0.021Ag_1.979Se alloys, where Cu doping increased the n _H and induced a high σ of 1216 S cm⁻¹ at room temperature, leading to an enhanced ZT from 0.9 to 1.2. Wang et al.^{[ 16 ]} optimized the n _H and the Hall carrier mobility (µ _H) in Ag₂Se by introducing excess Se, which increased S to −136 µV K⁻¹ at 375 K. The reduced n _H also decreased κ _e, resulting in a high ZT value of 1.02 at 375 K of Ag₂Se_1.015. Chen et al.^{[ 38 ]} synthesized Ag₂Se with a hierarchical porous structure, achieving a ZT of ≈0.7 at 300 K due to its effective multi‐wavelength phonon scattering and ultralow κ _l.

Currently, high‐temperature sintering techniques easily induce grain growth and diminish various phonon scattering centers. To address this challenge, low‐temperature sintering methods that preserve nanostructures are essential. The cold sintering process (CSP), featured with the assistance of liquid phase, external pressure, and relatively low sintering temperature, has been applied for the fabrication of thermoelectric materials.^{[ 39} , ^{40 ]} Lu et al.^{[ 41 ]} compared PbTe_0.94Se_0.06 materials prepared by CSP and spark plasma sintering (SPS), and found that the CSP prepared PbTe_0.94Se_0.06 exhibits significantly less grain growth compared with that prepared by SPS. Zhu et al.^{[ 42 ]} developed Bi₂Te₃‐based bulk materials using CSP at a temperature of <423 K and observed refrained grain growth and small grain sizes.

Herein, we introduce a sodium sulfite (Na₂SO₃) solution (up to 40 wt.%) as a transient liquid during the modified cold sintering process (mCSP)^{[ 43 ]} of Ag₂Se, as illustrated in Figure 1a. Schematical mechanisms for Ag₂Se sintering during mCSPs with and without Na₂SO₃ solution are shown in Figure 1b. For mCSP‐ed Ag₂Se without Na₂SO₃ solution, deionized water was used as a reference. The water evaporation during mCSP can facilitate particle diffusion, resulting in a high density of 98.5%. In contrast, using Na₂SO₃ solution as the transient liquid can create a hierarchical structure, including micropores, nanopores, sub‐nanopores, and additional nanoscale Na₂SO₃ residuals, that can effectively scatter multi‐wavelength phonons and suppress κ _l. Simultaneously, additional Se vacancies induce optimized n _H and enhanced S ² σ. As a result, the thermoelectric performance of bulk Ag₂Se with 30 wt.% Na₂SO₃ (Ag₂Se‐30%NS) achieves a low κ _l of ≈0.18 W m⁻¹ K⁻¹ at room temperature with an outstanding ZT value of 1.04. Figure 1c compares the room‐temperature ZT of our study with other state‐of‐the‐art Ag₂Se‐based materials,^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]} which demonstrates the feasibility of the transient liquid‐assisted mCSP in enhancing thermoelectric properties of Ag₂Se‐based materials. And a more detailed comparison is shown in Table S1 (Supporting Information).

Figure 1.

a) A schematic diagram illustrating the modified cold sintering process (mCSP) using Na₂SO₃ solution to prepare bulk Ag₂Se. b) Schematic diagrams explaining the mechanism for the densification of bulk Ag₂Se during mCSP without and with Na₂SO₃ solution. c) Comparison of the room‐temperature (T) dimensionless figure of merit (ZT) in this study and other state‐of‐the‐art values.^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]}

2. Results and Discussion

Figure 2a shows the X‐ray diffraction (XRD) patterns of the mCSP‐ed Ag₂Se using different amounts of Na₂SO₃ solution. All observed peaks are well aligned with the standard pattern for orthorhombic Ag₂Se (PDF 00‐024‐1041), without obvious secondary phases and peak shifts. This indicates that our mCSP method with Na₂SO₃ solvent as the transient liquid has no significant influence on the phase. Scanning electron microscope (SEM) images of as mCSP‐ed Ag₂Se samples with increasing Na₂SO₃ content are shown in Figure S1 (Supporting Information). As can be seen, when only water is employed as the transit liquid, the Ag₂Se sample is densely sintered with high relative density (Figure 2d). Increasing Na₂SO₃ content leads to the formation of a hierarchical porous structure (Figure S1, Supporting Information), and dramatically reduced relative density (Figure 2d), with enriched Na, S, and O at the pore surface (Figure 2b). Therefore, the decomposition of Na₂SO₃ should be the main reason for the formation of the hierarchical porous structure. Simultaneously, some Na₂SO₃ residuals can be observed in the pores (Figure 2c1; Figure S2, Supporting Information) further suggesting partial decomposition of Na₂SO₃ during the mCSP.

Figure 2.

a) X‐ray diffraction (XRD) patterns of modified cold sintering processed (mCSP) Ag₂Se samples with varying quantities of Na₂SO₃ solution (0 – 40 wt.%). b) Scanning electron microscope (SEM) images with corresponding energy‐dispersive X‐ray spectroscopy (EDS) maps of the Ag₂Se‐30%NS sample containing a porous region. c) Transmission electron microscope (TEM) images of the Ag₂Se‐30%NS sample. d) The relative density of bulk Ag₂Se samples with different Na₂SO₃ quantities.

The porous structure is hierarchical, comprised of micropore (sub‐micron size), nanopore (≈100 nm), and sub‐nanopore (<10 nm) with some nanoscale Na₂SO₃ residuals as shown in the transmission electron microscope (TEM) image of Figure 2c. With increasing Na₂SO₃ solution content, such a hierarchical porous structure induces reduced densities for the mCSP‐ed Ag₂Se (Figure 2d), indicating that the formation of the hierarchical porous structure is dominated by Na₂SO₃ solution, which is possibly due to partial decomposition of Na₂SO₃ solution and the release of SO₂ gas during the mCSP process as shown below:

$$\mathrm{N}{\mathrm{a}}_2\mathrm{S}{\mathrm{O}}_3+2{\mathrm{H}}_2\mathrm{O}\rightleftharpoons {\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_3+2\mathrm{NaOH}$$ (1)

$${\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_3\rightleftharpoons {\mathrm{H}}_2\mathrm{O}+\mathrm{S}{\mathrm{O}}_2\left(g\right)$$ (2)

NaOH is fully dissoluble in water as depicted by Equations (1) and (2) forming a basic solution, which can facilitate the merging of particles during the mCSP process. It is then squeezed out without further affecting the thermoelectric performance. Therefore, the mCSP mainly influence the sintering process by facilitating the merging of particles, which does not influence the phase transition processes.

Figure 3 presents the thermoelectric properties of the mCSP‐ed Ag₂Se. Figure 3a illustrates the temperature‐dependent σ of the mCSP‐ed Ag₂Se. All samples display typical semiconducting behavior, as demonstrated by increasing σ with increasing temperature. The sample without Na₂SO₃ (Ag₂Se‐0%NS) exhibits the highest σ value of 1.95 × 10³ S cm⁻¹ at ≈300 K. Introducing Na₂SO₃ during mCSP results in reduced σ, reaching the lowest σ of 1.10 × 10³ S cm⁻¹ at ≈300 K for Ag₂Se‐40%NS. To understand the influence of Na₂SO₃ addition on σ, Hall measurement was conducted to measure the n _H and the µ _H, as shown in Figure 3b. The n _H decreases with increasing the amount of Na₂SO₃, from 13.5 × 10¹⁸ cm⁻³ for Ag₂Se‐0%NS to ≈5.6 × 10¹⁸ cm⁻³ for Ag₂Se‐30%NS. Therefore, the reduced n _H can be attributed to additional Se vacancies as indicated by the reduced Ag:Se ratios (Table S2, Supporting Information).^{[ 38} , ^{49 ]} To better understand the influence of Se vacancies on n _H, we perform first‐principal density functional theory (DFT) calculations of orthorhombic Ag₂Se. Figure 3c,d compares the calculated electronic band structures and density of states (DOS) of Ag₃₂Se₁₆ (pristine Ag₂Se) and Ag₃₂Se₁₅ (with additional Se vacancies), with corresponding crystal structures shown as insets. As can be seen, introducing Se vacancy expands the band gap of Ag₂Se‐based materials, which should be the main reason for reduced n _H. In contrast, the influence of nanoscale Na₂SO₃ residuals on electrical properties is minor. On the other hand, the µ _H tends to increase with increasing the amount of Na₂SO₃ addition, reaching a maximum of 1324 cm² V⁻¹ s⁻¹ for Ag₂Se‐30%NS. The increase in µ _H can be mainly attributed to significantly reduced n _H. Further increasing the Na₂SO₃ content from 30% to 40% leads to reduced µ _H (from 1324 to 1129 cm² V⁻¹ s⁻¹, respectively), which should be attributed to increased n _H (from 5.63 × 10¹⁸ to 6.08 × 10¹⁸ cm⁻³, respectively).

Figure 3.

Temperature (T)‐dependent (a) electrical conductivity (σ) and (b) Hall carrier concentration (n _H) and Hall carrier mobility (µ _H) at 300 K of Ag₂Se samples prepared by modified cold sintering process (mCSP) with varying quantities of Na₂SO₃ solution (0 – 40 wt.%). Density functional theory (DFT) calculated electronic band structures and density of states (DOS) with schematic crystal structures of (c) Ag₃₂Se₁₆ and (d) Ag₃₂Se₁₅. e) Temperature‐Seebeck coefficient (S), and (f) power factor (S²σ) as‐prepared Ag₂Se samples.

Figure 3e plots the temperature‐dependent S, all of which exhibit negative values, indicating n‐type semiconducting behavior. When Ag₂Se powders are mCSP‐ed without Na₂SO₃ solution, the absolute Seebeck coefficient (|S|) value is as small as ≈110 µV K⁻¹ at ≈300 K. However, with the addition of Na₂SO₃ solution during mCSP, the |S| values significantly increase to ≈136 – 144 µV K⁻¹ at ≈300 K. The increase in |S| with the additional Na₂SO₃ solution can be mainly attributed to the reduced n _H, according to Equation (3) as shown below:

$$\mathrm{S}=\frac{8{\pi }^2{\mathrm{k}}_{\mathrm{B}}^2{\mathrm{m}}^{\ast }\mathrm{T}}{3\mathrm{e}{\mathrm{h}}^2}{\left(\frac{\pi }{3{\mathrm{n}}_{\mathrm{H}}}\right)}^{2/3}$$ (3)

where k _B is the Boltzmann constant, h is the Planck constant, m^* is the effective mass, and e is the electron charge. Additionally, the temperature‐dependent n _H is shown in Figure S3 (Supporting Information). Decrease in |S| values with increasing temperature of as mCSP‐ed samples, should be attributed to the increased n _H with increasing temperature. Moreover, introducing an additional hierarchical porous structure with Na₂SO₃ residuals successfully changed the carrier scattering mechanism to acoustic phonon scattering (µ≈T ^−1.5) as shown in Figure S4 (Supporting Information). Using the measured values of |S| and n _H, we estimated the DOS effective mass (m*) of Ag₂Se‐30%NS at room temperature and compared with other studies^{[ 15} , ²⁴ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ^{46 ]} as shown in Figure S5 (Supporting Information). The m* of our study is 0.23m _e, which is closely comparable to other state‐of‐the‐art Ag₂Se‐based materials.^{[ 15} , ²⁴ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ^{46 ]}

Figure 3f plots the calculated S²σ. Without Na₂SO₃, the Ag₂Se‐0%NS sample exhibits a S²σ of 23.8 µW cm⁻¹ K⁻² at ≈300 K, which increases to 27.0 µW cm⁻¹ K⁻² at 356 K. Utilizing Na₂SO₃ solution as the transient liquid in the mCSP enhances the overall S²σ, which approaches the maximum value of 26.5 and 33.8 µW cm⁻¹ K⁻² at ≈300 K and 356 K, respectively, for the Ag₂Se‐10%NS sample. This can be attributed to better‐optimized n _H closer to the optimal level of ≈1.0 × 10¹⁸ cm⁻³ of Ag₂Se‐based materials.^{[ 38 ]} The cycling test of thermoelectric performance and carrier transport of the reproduced Ag₂Se‐30%NS sample is shown in Figures S6 and S7 (Supporting Information), respectively, which shows the performance is reliable and reproducible. Figure S8 (Supporting Information) shows the n _H‐dependent room‐temperature S ² σ of Ag₂Se in this study compared with other state‐of‐the‐art studies.^{[ 15} , ²⁴ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ^{46 ]} As can be seen, the optimized n _H for high S ² σ is from ≈3 × 10¹⁸ cm⁻³ to ≈1 × 10¹⁹ cm⁻³. And the n _H of our Ag₂Se‐30%NS sample is ≈5.6 × 10¹⁸ cm⁻³, which is closely within the optimal level, contributing to high S ² σ.

Figure 4 displays the thermal properties of the mCSP‐ed samples. Figure 4a plots the temperature‐dependent κ, which increases linearly with increasing temperature for all mCSP‐ed samples. Ag₂Se‐0%NS exhibits the highest κ from 1.77 to 2.45 W m⁻¹ K⁻¹ in the temperature range from ≈300 to 356 K. Employing Na₂SO₃ solution as the transient liquid during mCSP results in decreased κ. With increasing the amount of Na₂SO₃ solution from 10 to 40 wt.%, the κ substantially reduces from 1.32 to 0.73 m⁻¹ K⁻¹ at ≈300 K. In addition, the differential scanning calorimetry (DSC) curves, as shown in Figure S9 (Supporting Information), indicate that the Na₂SO₃ residual does not affect the thermal stability of as mCSP‐ed Ag₂Se samples.

Figure 4.

Temperature (T)‐dependent (a) total thermal conductivity (κ), b) electronic thermal conductivity (κ _e), and (c) lattice thermal conductivity (κ _l) of Ag₂Se samples prepared via modified cold sintering process (mCSP) with varying quantities of Na₂SO₃ solution (0 – 40 wt.%). d) Room‐temperature κ _l versus relative density of as mCSP‐ed Ag₂Se samples at ≈300 K.

To understand the underlying mechanism for such low κ values, the κ _e was calculated by using the Wiedemann–Franz law, κ _e = LσT, where L is the Lorenz number.^{[ 34 ]} Temperature‐dependent κ _e is plotted in Figure 4b. As can be seen, increasing the quantity of Na₂SO₃ results in significantly reduced κ _e, which has approached as low as 0.51 W m⁻¹ K⁻¹ at ≈300 K for the Ag₂Se‐40%NS sample. The κ _l values were calculated by subtracting of κ _e from κ, and plotted against temperature as shown in Figure 4c. Generally, with increasing Na₂SO₃ from 0 to 40 wt.%, the κ _l reduces. An ultralow κ _l is observed in the Ag₂Se‐30%NS sample, which approaches as low as 0.18 W m⁻¹ K⁻¹ at ≈300 K.

To understand the low κ _l, the influence of porosity was evaluated on room‐temperature κ _l based on the gray medium model^{[ 50 ]} (more details of the gray medium model are provided in the supporting information), as shown in Figure 4d. As can be seen, the κ _l values are significantly reduced with increasing porosity, induced by employing Na₂SO₃ as the transient liquid for mCSP. However, the increased porosity can only explain around half of the reduced κ _l, whereas the additional reduction of κ _l should be attributed to the presence of nanoscale Na₂SO₃ residuals. With the hierarchical porous structure and nanoscale Na₂SO₃ residuals functioning together as effective scattering centers for multi‐wavelength phonons,^{[ 51} , ⁵² , ^{53 ]} exceptionally low κ _l values can be realized in the mCSP‐ed Ag₂Se samples.

The temperature‐dependent ZT values of the mCSP‐ed Ag₂Se were calculated and presented in Figure 5a. The Ag₂Se‐0%NS sample exhibits the lowest ZT of ≈0.4 across the entire temperature range. Introducing Na₂SO₃ solution during mCSP significantly improves the ZT values, leading to the peak ZT of 1.04 at ≈300 K in the Ag₂Se‐30%NS sample. Additionally, the average ZT (ZT _ave) was calculated following the equation $Z{T}_{\mathrm{ave}}=\frac{1}{\mathrm{\Delta }T}{\int }_{T_c}^{T_{\mathrm{h}}}ZTdT$ ^{[ 16 ]} where T _h and T _c are the highest and lowest temperature values in the range, and compared with other literature, as shown in Figure 5b. A high ZT _ave of 0.97 can be observed across the temperature range from ≈300 to 356 K, which is higher than most literature and comparable with the state‐of‐the‐art values.^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]} Figure 5c illustrates the temperature‐dependent ZT values of this study compared to other literature.^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]} Different from other studies where the peak ZT values are generally observed at ≈330 – 380 K, our study presents a peak ZT of 1.04 at near room temperature, which is comparable with other state‐of‐the‐art Ag₂Se‐based materials, and the key reason for a high ZT _ave in our study. The decrease in ZT of the Ag₂Se‐30%NS sample with increasing temperature can be attributed to high n _H (as shown in Figure S3, Supporting Information), corresponding σ and κ _e. Correspondingly, at a higher temperature range, the κ _e plays a more significant role compared to κ _l, resulting in an overall increase in κ. Figure S10 (Supporting Information) compares the n _H‐dependent ZT of Ag₂Se at room temperature in this study with other state‐of‐the‐art studies.^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]} The predicted n _H‐dependent ZT curves, with differenced κ _l values, were reproduced based on previous literature.^{[ 43 ]} The optimized n _H for high ZT is from ≈2 × 10¹⁸ cm⁻³. Through Se vacancy engineering, the reduced n _H is getting closer to the optimal level and comparable with other state‐of‐the‐art studies,^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]} which contributes to a high ZT together with the reduced κ _l.

Figure 5.

a) Temperature (T)‐dependent dimensionless figure of merit (ZT) of Ag₂Se samples prepared via modified cols sintering process (mCSP) with varying quantities of Na₂SO₃ solution (0 – 40 wt.%). Comparison of (b) average ZT (ZT _ave), and c) temperature‐dependent ZT between this study and other state‐of‐the‐art values.^{[ 15} , ²⁴ , ³⁷ , ³⁸ , ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ^{48 ]}

3. Conclusion 

In this study, by introducing Na₂SO₃ solution as the transient liquid during mCSP, a hierarchical structure, including micropores, nanopores, sub‐nanopores, and additional nanoscale Na₂SO₃ residuals, can be achieved in Ag₂Se, which is attributed to the partial decomposition of Na₂SO₃ solution during the mCSP. Such a hierarchical structure contributes to an ultralow κ _l of 0.18 W m⁻¹ K⁻¹ at ≈300 K in the Ag₂Se‐30%NS. Simultaneously, additional Se vacancies have been observed, contributing to reduced n _H from 13.5 × 10¹⁸ cm⁻³ of Ag₂Se‐0%NS to ≈5.6 × 10¹⁸ cm⁻³ of Ag₂Se‐30%NS at 300 K, which is closer to the optimal level of ≈1.0 × 10¹⁸ cm⁻³.^{[ 38 ]} The optimized n _H results in a high S ² σ of ≈25 µW cm⁻¹ K⁻² at ≈300 K in Ag₂Se‐30%NS. Consequently, an untrahigh room‐temperature ZT of 1.04 at ≈300 K and a high ZT _ave of 0.97 from ≈300 to 356 K can be achieved in Ag₂Se‐30%NS. This study demonstrates that introducing additional transient liquid solutions in mCSP can effectively realize hierarchical structure features, contributing to ultralow κ _l and high thermoelectric performance.

4. Experimental Section

Synthesis of Ag₂Se Powder

Silver nitrate (AgNO₃, AR, RCI‐Labscan), selenium (Se) powder (100 mesh, 99.5%, Aldrich), and sodium sulfite (Na₂SO₃, AR, QRec) were purchased and used as raw materials without additional purification. Ag₂Se powders were synthesized via a chemical reaction route.^{[ 54 ]} Initially, 1.5125 g of Na₂SO₃ was dissolved in 60 mL of deionized (DI) water, and then 0.4739 g of Se powder was added to the solution. The mixture was continuously stirred using a magnetic stirrer at 100 °C for 30 min, followed by natural cooling to room temperature. The resulting clear yellow solution indicated the formation of the Na₂SeSO₃ compound. Subsequently, in another beaker, 2.0386 g of AgNO₃ was dissolved in 120 mL of DI water. The Na₂SeSO₃ solution was gradually added into the AgNO₃ solution and stirred steadily at room temperature for 2 h. Ag₂Se precipitate was formed following the chemical reaction described by Equation (4).^{[ 55 ]} The resulting dark gray Ag₂Se precipitate underwent several washes with DI water and ethanol before being dried in an oven at 80 °C overnight.

$$2\mathrm{AgN}{\mathrm{O}}_3+\mathrm{N}{\mathrm{a}}_2\mathrm{SeS}{\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{O}\to \mathrm{N}{\mathrm{g}}_2\mathrm{Se}+2\mathrm{NaN}{\mathrm{O}}_3+{\mathrm{H}}_2\mathrm{S}{\mathrm{O}}_4$$ (4)

Modified Cold Sintering Process of Bulk Ag₂Se

Ag₂Se bulk samples were prepared using the mCSP method using a 1 M Na₂SO₃ solution as the transient liquid. In a typical procedure, 1.2 g of as‐synthesized Ag₂Se powder was manually blended with the Na₂SO₃ solution in a mortar. The mixture was then placed into a 12.7 mm inner diameter die, which was subsequently heated to 170 °C at a rate of 5 °C min⁻¹ without applying external pressure. Once the desired temperature was reached, a uniaxial pressure of 620 MPa was applied and maintained for 1 h to consolidate the Ag₂Se powders. Afterward, the pressure was released, and the sample was allowed to cool naturally to room temperature. To investigate the effect of the amount of Na₂SO₃ solution on the microstructure and properties of the fabricated Ag₂Se pellets, Na₂SO₃ solutions were comprised of 10, 20, 30, and 40 wt.% of Na₂SO₃, relative to the total mass of Na₂SO₃ and Ag₂Se. These samples were designated as Ag₂Se‐10%NS, Ag₂Se‐20%NS, Ag₂Se‐30%NS, and Ag₂Se‐40%NS, respectively. For reference, another Ag₂Se pellet was prepared via mCSP without the Na₂SO₃ solution, namely Ag₂Se‐0%NS, using DI water equivalent to 30 wt.% of the total mass of DI water and Ag₂Se.

Material Characterizations

The phase and crystalline structure of the as‐synthesized Ag₂Se powder and the mCSP bulk Ag₂Se samples were determined using X‐ray diffraction (XRD, Panalytical, Empyrean). Field emission scanning electron microscopy (FE‐SEM) and energy‐dispersive X‐ray spectroscopy (EDS, FEI, Helios NanoLab G3 CX) were employed to observe the morphologies and elemental composition of the Ag₂Se powder and mCSP bulk pellets. Furthermore, a focused ion beam (FIB) equipped in the SEM instrument, was utilized to prepare a thin lamella for detailed microstructural investigation using a transmission electron microscope (TEM, Thermo Scientific, Talos F200X).

Measurements of Thermoelectric Properties

Electrical conductivity (σ) and Seebeck coefficient (S) were measured simultaneously using the LSR‐3 instrument (Linseis) under a He atmosphere from ≈300 to 383 K. The Hall coefficient (R _H) was measured using the van der Pauw method under a magnetic field of 0 ‐1 T, employing the electron transport option (ETO) in the VersaLab instrument (Quantum Design). The Hall carrier concentration (n _H) and Hall carrier mobility (µ _H) were calculated using the relationships: n _H = 1/(eR _H) and µ _H = σ/(en _H), respectively. Thermal conductivity (κ) was calculated using the equation κ = αρc _p, where α is thermal diffusivity measured using the laser flash method in Ar atmosphere (LFA‐500, Linseis). ρ is density determined through an Archimedes’ method in water following the relationship: ρ = W _a ρ _w /(W _{a –} W _w), where W _a, W _w, and ρ _w represent the weight in air, the weight in water, and the density of water, respectively. The error range of relative density in the study was determined by three repeated measurements under identical conditions. C _p is a specific heat capacity of as mCSP‐ed samples (Figure S11, Supporting Information) measured by a differential scanning calorimeter (DSC, Rigaku, Thermo plus evo2).

5. Computational Details

Density‐functional theory (DFT) calculations were performed using the all electron projected augmented wave (PAW) method, as implemented in the Vienna Ab initio Simulation Package (VASP).^{[ 56} , ⁵⁷ , ⁵⁸ , ⁵⁹ , ⁶⁰ , ^{61 ]} The generalized gradient approximation (GGA) with the fully relativistic Perdew‐Burke‐Ernzerhof (PBE) functional was employed to treat the exchange correlations.^{[ 62 ]} The valence wave functions were expanded in a plan‐wave basis with a cut‐off energy of 400 eV. All atoms were allowed to relax in their geometric optimizations until the Hellmann–Feynman force is less than 1 × 10⁻² eV·Å⁻¹. The convergence criterion and the Monkhorst‐Pack k‐mesh adopted for ionic relaxation are 1 × 10⁻⁷ eV per electron and 0.03π per Å, respectively. A denser 0.02π Å⁻¹ Monkhorst‐Pack k‐mesh was adopted for calculating density‐of‐state (DOS), and a line‐mode k‐path based on Brillouin path features indicated by the AFLOW framework was adopted for calculating band structures.^{[ 63} , ^{64 ]} To precisely predict bandgap, the Hubbard U model was considered, with the on‐site coulombic (U) and the exchange (J) terms combined in a single effective U parameter of 5.8 eV for Ag_4d orbitals, determined using the linear corresponding method. To eliminate the influence of the superpositions of wavefunctions, the band unfolding method was also used to reflect the band structure in the first Brillouin zone.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Kitthonbancha P., Liu W.‐D., Li M., Pinitsoontorn S., Chen Z.‐G., Transient Liquid Induced Hierarchical Structure Contributes to High Thermoelectric Performance in Ag₂Se. Small 2025, 21, 2411798. 10.1002/smll.202411798

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.