Geometric design of Cu2Se-based thermoelectric device for enhancing power generation

doi:10.21203/rs.3.rs-3247845/v1

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Geometric design of Cu₂Se-based thermoelectric device for enhancing power generation

https://doi.org/10.21203/rs.3.rs-3247845/v1

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published 19 Jul, 2024

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Waste heat, an abundant energy source generated by both industries and nature, has the potential to be harnessed into electricity via thermoelectric power generation. The performance of thermoelectric modules, typically composed of cuboid-shaped materials, depends on both the materials’ intrinsic properties and the temperature difference created. Despite significant advancements in the development of efficient materials, macroscopic thermal designs capable of accommodating larger temperature differences have been largely underexplored because of the challenges associated with processing bulk thermoelectric materials. Herein, we present the design strategy for Cu₂Se thermoelectric materials for high-temperature power generation using a combination of finite element modelling and 3D printing. The macroscopic geometries and microscopic defects in Cu₂Se materials are precisely engineered by optimising the 3D printing and post-treatment processes, leading to significant enhancements in the material efficiency and temperature difference within devices, where the hourglass geometry exhibits maximised output powers. The proposed approach paves the way for designing efficient thermoelectric power generators.

Physical sciences/Energy science and technology/Thermoelectric devices and materials

Physical sciences/Materials science/Materials for energy and catalysis/Thermoelectrics

Physical sciences/Materials science/Techniques and instrumentation/Design, synthesis and processing

Global energy consumption is growing rapidly and there is an urgent need for sustainable and renewable energy sources to address fossil fuel depletion and environmental pollution^1-3. Waste heat is one of the most relevant renewable sources because it is generated by numerous systems, including automobiles, ships, power plants, and industrial plants of oil refineries and steelmaking^4-6. Recovering even a fraction of the waste heat enhances the overall process efficiency without any additional costs. Thermoelectric (TE) power generation offers a unique solution for the reliable and sustainable recovery of dissipated waste heat because it enables the direct conversion of heat to electricity without environmental pollution^7-10. The energy-conversion efficiency of TE devices depends on the efficiency of the TE material and the temperature difference across the TE devices, both of which should be high to achieve the optimal performance^9-12. Achieving a large temperature gradient across the TE device and ultimately maximising energy conversion efficiency requires the device-level design of TE generator^13,14. Traditional TE devices consist of coupled standard cuboid-shaped n- and p-type TE legs. The key design parameters in these conventional devices include the length and aspect ratio of the cuboid legs and their fill factor which is the relative occupation of TE legs in a device^15-20. Another important design strategy can involve the optimisation of non-cuboid geometries for individual TE legs, which offers an additional level of control over thermal transport and enables the creation of larger temperature differences compared with cuboid-shaped legs^21-27. Although several simulation studies on non-cuboid geometries of TE legs have been reported in some specific conditions, there has been a scarcity of the experimental validation combined with a comprehensive design for power generation in non-cuboid TE legs. This limitation is attributed to the challenge of fabricating materials with complex geometries. The conventional manufacturing process for TE legs, which involves the top–down dicing of ingots, restricts the production to cube-shaped structures, making it technically unfeasible to produce anything beyond that.

Recently, 3D printing has emerged as a promising manufacturing process for TE materials and offers the potential to customise TE legs into specific geometries^28-35. However, this technology is still in the development phase and further advancements are necessary to meet the manufacturing criteria for TE materials. These criteria include ensuring structural fidelity and achieving a high -TE figure of merit (ZT) in the printed products. The reported efficiencies (measured by ZT values) of 3D-printed TE materials have generally been lower than those achieved through traditional fabrication methods, such as hot pressing or melting^28,36. Enhancing the TE properties of materials requires the precise engineering of atomic defects and microstructures during the fabrication stage^37,38. However, this presents a challenge in the 3D printing process because the incorporation of additives or modifications to the microstructure can adversely affect the rheological properties of the particle-based inks and compromise the printability of the resulting 3D structures.

Among the various candidates, liquid-like materials of copper chalcogenides have attracted significant attention owing to their high efficiencies resulting from their extremely low thermal conductivities at high temperatures^39-43. These materials have a distinctive structural feature, in which one immobile ion forms a rigid sublattice framework for the free transport of electrons, and other mobile ions form a liquid-like sublattice to disrupt thermal transport⁴⁴. Moreover, the nontoxic and abundant elements in Cu₂Se-based compounds, which represent this class of materials, result in a substantial cost reduction of at least one order of magnitude compared with state-of-the-art TE materials^41,42. Here, we present a design strategy for determining the best geometry of TE legs for high-temperature power generation of Cu₂Se through 3D finite element model (FEM) simulations and experimental validation of the design using an extrusion-based 3D printing process (Fig. 1a). We conducted numerical simulations to evaluate the power generation of eight different geometries of the TE legs and further optimised the geometric parameters of the best-performing hourglass geometry. Moreover, the controlled liquid-phase sintering and Se evaporation of the printed Cu₂Se products allowed the defect formation of high-density stacking faults (SFs) and the resulting dislocations, which reduced the thermal conductivity of Cu₂Se and consequently enhanced the ZT values up to 2.0 at 950 K (Fig. 1b). To validate our designs, we fabricated and comparatively evaluated the power-generating power performances of TE generators (TEGs) with the 3D-printed hourglass, inverse hourglass, and cuboid. The hourglass-shaped TEG generated approximately 2.7 times higher power compared with that of the conventional cuboid-shaped TEG (Fig. 1c), experimentally validating our approach towards the maximization of power-generating performances of TEGs.

Geometric design of TE legs

The maximum output power (P_max) of TEGs is defined using Eq. (1).

$${P}_{max}=\frac{{S}^{2}{Δ T}^{2}}{4{R}_{el}}=\frac{(S{Q{R}_{th})}^{2}}{4{R}_{el}},$$

where S is the Seebeck coefficient, ΔT = QR_th is the created temperature difference, where Q is the heat flowing through a TE leg, R_th is the thermal resistance, and R_el is the electrical resistance of a TE leg. To maximise P_max in this simple relation, the optimisation of R_el and R_th is generally conducted with the parameter of the aspect ratio of a cuboid TE leg because they have a trade-off relationship with respect to the length and cross-sectional area of the TE leg. In the TE leg, R_el and R_th can be defined using Eq. (2).

$${R}_{el}={\int }_{0}^{L}\frac{dl}{\sigma A},$$

$${R}_{th}={\int }_{0}^{L}\frac{dl}{kA},$$

where L is the vertical length, σ is the electrical conductivity, k is the thermal conductivity, and A is the cross-sectional area of the TE leg⁴⁵. The geometric parameter of ${\int }_{0}^{L}\frac{dl}{A}$of the TE leg is present in Eq. (2). Because several factors affect the overall output power of a device, such as the temperature dependencies of σ and k, convection areas, and conduction path, this geometric parameter could be more flexible and effective for maximising P_max than the aspect ratio of a cuboid leg. For example, LeBlanc and coworkers investigated the influence of TE leg shapes by simulations, finding that the hourglass- and trapezoid-shaped TE legs generate more power than twice as much as the cuboid²⁷. To design geometry of Cu₂Se TE leg, we developed a 3D FEM model for the eight different geometries of the TE legs and comparatively computed their R_el, ΔT, output voltage, and P_max (Fig. 1a). We chose these geometries by considering the geometric parameters of ${\int }_{0}^{L}\frac{dl}{A}$, for which the selected geometries were varied (Supplementary Table 1), the conduction path (Y-shape and reverse Y-shape) or holes in it (multi-hollow rectangle). Also, we set a fixed temperature of 873 K on the hot side, while the cold side was subjected to forced convective conditions.

As shown in Fig. 2a the truncated pyramid and hourglass with higher R_th and larger geometric parameter than those of the cuboid are expected to produce the higher ΔT and resulting P_max compared with the cuboid (Supplementary Figs. 1 and 2), though they have a higher R_el. The Y-shaped leg with the same geometric parameter as the cuboid exhibited a slightly higher ΔT owing to a longer thermal conduction path. However, its P_max decreased with an increase in the R_el. The multi-hollow rectangular leg exhibited properties identical to those of the cuboid because of the same cross-sectional area profile. Another important parameter, namely the cooling surface, was identified by comparing the reverse structures with the primary designs, showing the opposite trends of ΔT and the resulting P_max to their primary designs. For example, the reverse truncated pyramid and inverse hourglass that have smaller convection areas exhibited considerably lower ΔT and P_max values. Owing to expansive cooling surface and high geometric parameter value, the truncated pyramid and hourglass are recognized as the best geometries, generating 35% and 31% higher P_max values, respectively, of that of the cuboid.

In addition, we extended our simulation to a TE device consisting of a single leg of a truncated pyramid, hourglass, and cuboid (Fig. 2b–d, Supplementary Fig. 3), where the TE leg was sandwiched between the top and bottom Cu electrodes and Ag paste solder layers, including the measured contact resistance (R_c) (Supplementary Fig. 4).⁴⁶ The hourglass, which has the highest power due to its lower R_c than those of the cuboid and truncated pyramid, was expected to generate 87% more power than that of the cuboid.

Finally, the area ratio (β/α) optimisation was performed on the hourglass, where β represents the areas of the top and bottom surfaces and α represents the area at the centre (Fig. 2f). With an increase in the area ratio to approximately 10, the ΔT, and resulting output voltage values abruptly increased, while the electrical resistance decreased (Supplementary Figs. 5 and 6). Above an area ratio of 12, all values were nearly saturated or changed slowly, but the output power decreased owing to the increase in the electrical resistance. Overall, the output power was maximised at an area ratio of 11.7, at which the predicted output voltage and power were 24% and 131% higher than those of the cuboid.

3D printing of the geometrically designed Cu₂Se

To achieve ink-extrusion-based 3D printing of Cu₂Se, we formulated a Cu₂Se particle-based colloid ink with the desired viscoelasticity. Such rheological properties of inks are crucial for ensuring consistent ink flow throughout the deposition and retainability of printed structures after deposition. Our group has previously reported the extrusion-based 3D printing of Cu₂Se inks whose rheological properties were tailored by the addition of Se₈²⁻ polyanions³³. In the current study, we further increased the concentration of solutes in the glycerol solvent medium, resulting in a higher viscosity (Supplementary Fig. 7). This rheological modification improved the 3D printability of our inks to make them directly writable, which enabled us to build complex architectures, including hourglass, arch, and lattice structures constructed by directly written filaments (Fig. 3a and Supplementary Movies 1–3). Optical microscopy and scanning electron microscopy (SEM) images of the printed filaments (Fig. 3b–f) show their smooth surface and uniform thickness. Moreover, after heat treatment at 1233 K, the primary shape of the filament was preserved perfectly without structural distortion. Additionally, the as-printed filament had a diameter of approximately 210 µm while the sintered filament uniformly shrank to a diameter of approximately 160 µm after the heat treatment, indicating densification of the printed filament.

TE properties of the 3D-printed Cu₂Se

The use of Se₈²⁻ polyanions as rheology-modifying additives also promotes the sintering of Cu₂Se. Upon heat treatment, Se₈²⁻ polyanions are decomposed into the Se phase at ~ 140 ºC among Cu₂Se particles (Supplementary Fig. 8) and induce the liquid-phase sintering of Cu₂Se particles due to the relatively low melting point of Se (~ 220 ºC). We investigated the effect of sintering temperatures on the TE properties of samples (873, 1053, and 1233 K). The SEM images show that all samples sintered at 873, 1053, and 1233 K have well-fused grains with multiple pores in their microstructures, suggesting a sintering effect of the Se₈²⁻ polyanions (Supplementary Fig. 9) ^28–33. Also, excess Se polyanions allowed us to control the composition of Cu_2 − xSe because elemental Se gradually evaporates during sintering. X-ray diffraction (XRD) patterns of the samples sintered at 873, 1053, and 1233 K revealed that the Cu_1.8Se phase mixed with the Cu₂Se phase was observed in the sample sintered at 873 K, and the peaks of the Cu_1.8Se phase progressively disappeared with increasing sintering temperature (Fig. 4a). At 1233 K, the XRD pattern shows only the peaks corresponding to the Cu₂Se bulk phase without any peaks related to the Cu_1.8Se phase.

We measured the temperature-dependent TE properties of the 3D-printed, heat-treated samples at 873, 1053, and 1233 K from room temperature to 1000 K. The formation of the Se-rich Cu_2 − xSe phase in our samples enabled control of the hole concentration of the samples because the Cu vacancies in Cu_2 − xSe are known to act as hole donors (Fig. 4b). Hall measurement results reveal that the hole concentration decreased from 2.39 × 10²⁰ to 8.09 × 10¹⁹ cm^− 3 as the heat treatment temperature increased, indicating the controlled formation of the Cu vacancy depending on the sintering temperatures. The hole mobilities of the samples also decrease with increasing sintering temperature. This trend can be understood by considering the defect formation in the sintered samples at higher temperatures.

Room-temperature electrical conductivity gradually decreased with increasing the sintering temperature (Fig. 4c). Meanwhile, the Seebeck coefficient at room temperature increased with increasing the sintering temperature from 873 K to 1233 K (Fig. 4d). This trend indicated that the Seebeck coefficient were inversely proportional to the carrier concentration^47,48. The electrical conductivity decreased as a function of temperature for all the samples over the entire temperature range, whereas the Seebeck coefficients were positive. These dependencies agree with the reported trends for Cu₂Se materials and indicate the behaviour of typical heavily doped semiconductors^41,42,49. The highest power factor of 9.38 µW∙cm^− 1∙K^− 2 was achieved by the 873 K-sintered sample at 1000 K (Supplementary Fig. 10).

Over the entire temperature range, the samples sintered at higher temperatures exhibited lower thermal conductivities (Fig. 4e and Supplementary Fig. 11). The 1233 K-sintered sample exhibited the lowest thermal conductivity of 0.33 W∙m^− 1∙K^− 1 at 950 K, which was lower than the reported values of bulk polycrystalline Cu₂Se materials and similar to those of the recently reported state-of-the-art Cu₂Se TE materials. In previous reports, the remarkably low thermal conductivity of Cu₂Se was achieved by strategies to create unique microstructures, such as mosaic nanostructuring^50,51, the fabrication of nanocomposites^52,53, incorporation of carbon allotropes^54–56, and atomic defect engineering⁵⁷.

To understand the extremely low thermal conductivity of the 3D-printed Cu₂Se, the sample sintered at 1233 K was analysed using transmission electron microscopy (TEM). The TEM images (Fig. 4f and Supplementary Figs. 12) clearly show dense array textures in the microstructures. These textures originate from the formation of SFs (Fig. 4g), which is further confirmed by the selected-area electron diffraction pattern (Fig. 4h) that possesses a (004) slip plane. The presence of diffuse streaks surrounding each diffraction pattern provides clear evidence that the microstructure corresponds to an SF in the planar defect^58–60. Moreover, we observed the formation of dislocation defects surrounded by SFs (Supplementary Figs. 13). In the sample sintered at 873 K, arrays of SFs were partially detected just near the grain boundary. Moreover, the Se-rich Cu_1.8Se phase was clearly detected, as confirmed by the fast Fourier transform image obtained from the TEM image of the surface (Supplementary Fig. 14).

The formation of SFs has been widely studied in materials with mixed phases, where a dislocation is created at the phase boundary between the two phases owing to lattice strain, which consequently creates an SF by dislocation propagation^61–64. The interaction between Cu₂Se particles and Se additive resulted in the formation of Se-rich Cu_1.8Se alongside the Cu₂Se matrix phase in our samples as evidenced by XRD patterns (Supplementary Fig. 15). This intermediate phase can be attributed to lattice strain caused by the lattice mismatch between orthorhombic Cu₂Se and cubic Cu_1.8Se, leading to the creation of dislocations and dense stacking faults (SFs) within the 3D-printed Cu₂Se samples. Notably, at elevated sintering temperatures, the diffusivity of Se ions escalated⁶⁵, facilitating their migration into Cu₂Se grains and promoting the development of Cu_1.8Se phases in larger regions during the intermediate state. Consequently, this process contributed to the widespread presence of SFs throughout the Cu₂Se grain during subsequent heat treatment. This scenario is supported by the observation of SF arrays in all the grains of the sample sintered at 1233 K, whereas SFs were observed only at the grain boundary of the sample sintered at 873 K. The enlarged XRD patterns (Supplementary Fig. 15) and TEM results affirmed these observations, revealing peak shifts and heightened lattice strains as sintering temperatures or holding times increased. Remarkably, particle surface of the 873 K-sintered sample predominantly exhibited the Cu_1.8Se phase.

Utilizing the Debye–Callaway model encompassing phonon scattering mechanisms such as Umklapp processes, grain boundary scattering, point defects, dislocations, pores, and SF scattering, we quantified the attained minimum lattice thermal conductivity (κ_l). Figure 4i represented the frequency (ω)-dependent κ_l for distinct scattering models, uncovering variations. Contrary to Umklapp processes, point defects, dislocations, and pores primarily impacted low- and high-frequency phonons, showing minimal effect on middle-frequency phonons. Conversely, SFs exhibited substantial phonon scattering reduction across all frequencies, including middle-frequency phonons. Figure 4j demonstrates the accordance between experimental and theoretical data, solidifying the existence of SF-mediated phonon scattering. Remarkably, κ_l decreases at higher sintering temperatures alongside increased SF density, affirming SFs' role in modifying thermal conductivity.

Because of such unique microstructures and the resulting low thermal conductivity, the calculated ZT values from the measured electrical and thermal properties reached 2.0 at 950 K for the sample sintered at 1233 K. This sample exhibited higher ZT values than those of the samples sintered at lower temperatures over the entire temperature range. Moreover, this maximum is higher than the values reported for polycrystalline bulk Cu₂Se⁴³. Although this value is slightly lower than the recently reported state-of-the-art Cu₂Se with carbon-introduced materials^54–56, doping⁵³, and nano-size compositing effect⁵² to the best of our knowledge, this is the first demonstration of the achievement of higher ZT values in printed TE materials compared to their bulk values (Supplementary Table 2).

Evaluation of 3D-printed Cu₂Se TEGs

To experimentally validate the design obtained by the FEM simulations, devices were chipped with three different TE legs using cuboid, reverse hourglass, and hourglass geometries fabricated by 3D printing (Fig. 5a–c) and the Cu plate electrodes using Ag paste as the solder. Additionally, we maintained identical hot-side temperatures during the measurement of the power-generating performance using a ceramic heater to heat the tops of the modules while cooling the bottoms using a water-circulating cooler with a constant water flow rate and temperature. As the temperature increased, all modules exhibited nearly linear increases in the output voltages and quadratic increases in the output power, indicating the reliability of the measurements (Fig. 5d–f). At the hot side temperature of 873 K, the hourglass-TEG exhibited a cold-side temperature of 354 K, which was significantly cooler than the temperatures of 549 and 463 K observed in the reverse hourglass- and cuboid-TEGs, respectively (Fig. 5g). The temperatures on the cold sides are in good agreement with the simulation results. Moreover, the resulting output voltages of the three designs were in accordance with the temperature difference trends. Consequently, the hourglass-TEG showed an output power and power density of 242 mW/cm² under a temperature difference of 518 K (Fig. 1c and 5h), which was approximately 2.7 times higher than those exhibited by the cuboid-TEG. These results demonstrate the feasibility of our design strategy for enhancing the power-generation performance of TEGs.

We demonstrated the feasibility of the design and 3D printing strategy for non-cuboid geometries of Cu₂Se TE materials and devices for more efficient thermal energy harvesters. We developed 3D FEMs for the library of geometries of TE legs that allowed us to comparatively optimise the geometries of the TE legs with respect to the shape parameter for creating a larger thermal resistance, resulting in a higher output power. Moreover, we demonstrated the controlled formation of atomic defects in 3D-printed Cu₂Se by induced lattice strain in the Cu₂Se grains, where a high density of SF arrays was created in the entire grain. Such defect engineering allowed us to significantly reduce the thermal conductivity and enhance the ZT values up to 2.0. The experimental validation of the FEM design by 3D printing fabrication and evaluation of the TEGs showed excellent agreement with the predicted power-generating performances, where the hourglass TEG exhibited a 2–7 times higher output power than the other geometries. Our design strategy for the non-cuboid geometry of a TE leg provides a way to overcome the trade-off between the electrical and thermal resistances of a device. In addition, this strategy can be easily applied to other TE materials and functional properties of materials, such as mechanical, optical, and catalytic properties. Moreover, this study demonstrates the applicability of the defect engineering strategy to materials synthesised by ink-based 3D printing, which has been actively studied in the recent decade in materials synthesised by traditional bulk synthesis. The approach presented here will unveil a new way to enhance the efficiency of TEGs, which ultimately contributes to future electricity supplies.

Materials

Chemicals used in this research were purchased from the following suppliers: ethylenediamine (> 99.5% pure), glycerol (> 99.5% pure), ethanethiol (> 97% pure) from Aldrich Chemical Co., Cu (99.9%) powder and Se (99.999%) powder for high-energy ball milling from Alfa Aesar and 5N Plus, respectively. Isopropanol (99.5%) and Se (99.999%) powder for the synthesis of Se polyanion from Samchun Chemicals and Alfa Aesar, respectively. The chemicals and elements were used as received without further purification.

Synthesis of 3D printable all-inorganic Cu_2-xSe-based ink

The entire procedure was conducted under N₂ atmosphere. To synthesize Cu₂Se powder, Cu and Se powder with the stoichiometric ratio of Cu₂Se were high-energy ball-milled (SPEX, 8000M Mixer/Mill) for 200 min. The resulting powder was sieved to eliminate particles larger than 45 µm. The Se polyanion additive was prepared with the following process: dissolving 0.5 g of Se powder in cosolvent of 0.5 mL of ethanethiol and 4.5 mL of ethylenediamine at room temperature with vigorous stirring. After 72 h, 5 mL of Se dissolved solution was mixed with 37.5 mL of isopropanol and centrifugated for 10 min at 7830 rpm to precipitate the Se polyanion from the dissolved solution. The precipitate was vacuum-dried for 1 h after discarding the supernatant. Cu₂Se-based ink was prepared by dispersing 2 or 3 g of ball-milled Cu₂Se powder, 1 or 1.5 g of dried Se polyanion, and 2.5 g of glycerol for 2 h in a planetary centrifugal mixer (ARM-100, Thinky). To ensure successful homogenization, 5 to 7 zirconium oxide grinding balls with a 5 mm diameter were introduced into the mixing process.

Rheological characterisations of Cu_2 − xSe-based inorganic ink

The rheological properties of the Cu₂Se inorganic ink were assessed at room temperature using a rotational rheometer (Haake MARS III, Thermo Scientific) with a coaxial cylinder geometry. Frequency sweep tests were performed at a constant stress of 1 Pa, while stress sweep tests were conducted at frequencies of 1 rad/s and stress values ranging from 0.005 to 300 Pa.

3D printing and heat treatment process of Cu₂Se

Three-dimensional printing was conducted using a home-built extrusion-based 3D printer with programmable temperature and pressure control. The synthesised ink was loaded into a 5 mL syringe (Saejong), which was fitted with a metal nozzle having an inner diameter of 340 µm. The design software was used to print the ink in layers of parallel lines, with each layer developed perpendicular to the previous one. The printing process was carried out at room temperature, with a 1-second interval between each layer deposition. The as-printed sample was dried at 423 K for 5 h and subsequently annealed under a nitrogen atmosphere at 873, 1053, and 1233 K for 1–13 h.

Microstructure characterization of 3D-printed Cu₂Se

The Olympus BX51M was used to capture the optical microscopy image. The field-effect SEM (Nova-NanoSEM230, FEI and S-4800 Hitachi High-Technologies) operated at 30 kV was used to obtain the scanning electron microscope images. The XRD patterns were obtained by the Rigaku D/Max2500 V diffractometer with a Cu-rotating anode X‐ray source (λ = 0.15418 nm) operating at 40 kV and 30 mA. The reference peaks of Cu_2 − xSe and Cu_1.8Se were determined by comparison with the references of JCPDS: 00-047-1448 and 01-073-8642, respectively. The TEM specimens were prepared using focused ion beam milling (NX5000, Hitachi), and the FE-TEM characterization was performed using the Titan G2 ChemiSTEM Cs Probe from FEI company.

Measurement of TE properties

The temperature-dependent electrical conductivity and Seebeck coefficient were measured using a commercial equipment (SBA 458 Nemesis, Netzsch) under argon atmosphere in the temperature range of 300 K to 1000 K. The thermal conductivity of the 3D-printed samples was estimated using the formula κ = ρC_pD, where κ is the thermal conductivity, ρ is the density, C_p is the specific heat capacity, and D is the thermal diffusivity, which was measured using laser flash analysis (LFA 467HT, Netzsch) in the same temperature range as the electrical conductivity. The maximum equipment error range for thermal diffusivity, considering radiation heat loss, is limited to 0.35%. The density of the samples was obtained by measuring their weight and volume. The specific heat capacity was calculated using the Dulong-Petit equation. The maximum equipment error range for thermal diffusivity measurement due to radiation heat loss was 0.35%. All the measurements were conducted with the 3D-printed Cu₂Se made from Cu₂Se ink containing 5 g of glycerol medium, 4 g of ball-milled Cu₂Se powder, and 2 g of Se polyanion additive. Room temperature carrier concentrations and mobilities were determined using a Hall measurement system (HMS-5000, ECOPIA) with a magnetic field strength of 0.55 T. TE properties are slightly changed during the process of optimising the heat treatment duration at the sintering temperature of 1233 K. (Supplementary Fig. 16, Supplementary Fig. 17, Supplementary Fig. 18, and Supplementary Fig. 19). The TE characterization of the 3D-printed Cu₂Se involved the use of an ink with low concentration during the fabrication process.

Optmising TE generator design

A three-dimensional finite element method (FEM) was developed using the commercial software COMSOL Multiphysics to calculate the temperature difference, output voltage, and power of the TEG. The dimensions of the shapes used in the TE leg are shown in Fig. 1a, and the volume of the TE material used is 64 mm³ with a height of 4 mm. The material properties of the used TE material are depicted in Fig. 4b-e. To assess the performance enhancement resulting from the change in geometry within an appropriate temperature range, the boundary conditions were set as follows: a hot side temperature of 873 K, a convection coefficient of 200 W/m²K on the cold side, and an ambient temperature of 25°C. Adiabatic conditions were applied to the exterior sides. In the TEG, the electrical potential (V_oc) was calculated by applying electrical ground to the top surface at open circuit and the current (I_sc) was calculated at short circuit to obtain the electrical resistance (R = V_oc/I_sc). The maximum output power (P_max) was calculated using P_max=V_oc²/4R. The cross-sectional area of the electrodes, which has thickness of 1 mm, is the same as those of the boundary surface of the TE leg, except for the narrow side of the truncated pyramid which uses electrode of the same size as the wider side. The solder layer between the electrodes and the TE leg was modelled with a thickness of 0.1 mm, and the properties of Ag paste were applied: electrical conductivity (σ) of 5×10⁵ S/m, Seebeck coefficient (S) of 0 V/K, thermal conductivity (κ) of 9.1 W/mK, and specific heat capacity (C_p) of 167 J/kg∙K.

Fabrication and power measurement of Cu₂Se TEGs

Copper electrodes were prepared in suitable dimensions and thickness of 0.3 mm for three distinct geometries of Cu₂Se legs presented in Fig. 5a-c. The samples were then electrically and mechanically attached to the Cu electrodes using Ag paste (Pyro-Duct 597-A, Aremco). The output power was measured under a temperature difference using a 70 mm by 15 mm ceramic heater as the heat source and a water-circulating chiller. To prevent thermal convection and radiation, glass fabric was wrapped around the hot plate and 3D-printed TEGs. Temperature changes were monitored with K-type thermocouples connected to a Keithley 2000 multimeter. To avoid unintended oxidation and air convection, the entire evaluation was performed in a vacuum chamber.

Data availability

The data that support the findings of this study are available within the article and its Supplementary Information. Source data are provided with this paper.

Code availability

The COMSOL Multiphysics codes are openly available at.

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2022R1A2C3009129; NRF-2022M3H4A1A04076667). B.Ş. and S.L. acknowledge the United States National Science Foundation (Award Number CMMI-1943104).

Author contributions

S.C. and J.L. contributed equally to this work. S.C., J.L., B.Ş., S.L., and J.S.S. designed the experiments, analyzed the data, and wrote the paper. S.C., J.L., S.E.Y., and S.J. carried out the synthesis and basic characterization of materials. S.-J.J. and S.K.K. carried out calculation of modelled lattice thermal conductivities. K.K. and H.G.C. performed the characterization of rheological properties. C.N. and S.A. performed the characterization of thermal conductivities. H.L. performed the characterization of TEM analysis. S.C. carried out the fabrication and measurement of TEGs. J.L., B.Ş., and S.L. performed the simulation studies. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing interests.

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Geometric design of Cu₂Se-based thermoelectric device for enhancing power generation

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Results

Geometric design of TE legs

Discussion

Methods

Materials

Rheological characterisations of Cu_2 − xSe-based inorganic ink

3D printing and heat treatment process of Cu₂Se

Microstructure characterization of 3D-printed Cu₂Se

Measurement of TE properties

Optmising TE generator design

Fabrication and power measurement of Cu₂Se TEGs

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Geometric design of Cu2Se-based thermoelectric device for enhancing power generation

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Results

Geometric design of TE legs

Discussion

Methods

Materials

Rheological characterisations of Cu2 − xSe-based inorganic ink

3D printing and heat treatment process of Cu2Se

Microstructure characterization of 3D-printed Cu2Se

Measurement of TE properties

Optmising TE generator design

Fabrication and power measurement of Cu2Se TEGs

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Geometric design of Cu₂Se-based thermoelectric device for enhancing power generation

Rheological characterisations of Cu_2 − xSe-based inorganic ink

3D printing and heat treatment process of Cu₂Se

Microstructure characterization of 3D-printed Cu₂Se

Fabrication and power measurement of Cu₂Se TEGs