Tuning amorphous-crystalline heterogeneity enables simultaneous optimization of thermoelectric performance and ductility in silver chalcogenides

Tuning amorphous-crystalline heterogeneity enables simultaneous optimization of thermoelectric performance and ductility in silver chalcogenides | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Tuning amorphous-crystalline heterogeneity enables simultaneous optimization of thermoelectric performance and ductility in silver chalcogenides Kyung Tae Kim, Jong Min Park, Jeong Min Lee, Seungki Jo, Soo-ho Jung, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9531103/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Ductile thermoelectric materials are key to enabling mechanically reliable, self-powered wearable electronics; however, achieving high thermoelectric performance near room temperature without sacrificing mechanical flexibility remains a persistent challenge. Silver chalcogenides have attracted considerable interest due to their intrinsic ductility. However, their propensity for amorphous-crystalline transformation introduces structural heterogeneity whose impact on transport properties remains unclear. Here, we demonstrate that amorphous-crystalline heterogeneity serves as an effective structural parameter to decouple charge and heat transport in Ag 2 S 0.4 Te 0.6 by integrating density functional theory calculations with the controlled synthesis of materials featuring tunable phase fractions. We show that decreasing the amorphous fraction reduces carrier concentration while enhancing carrier mobility, resulting in compensated electrical transport behavior. In parallel, the total thermal conductivity decreases primarily due to suppression of the electronic contribution, while the lattice thermal conductivity remains below the Cahill-Pohl minimum. As a result, an optimized composition with ~ 60% amorphous content achieves a room-temperature ZT of ~ 0.47 while maintaining a high bending strain exceeding 22%. These findings establish amorphous-crystalline heterogeneity as a design strategy for simultaneously controlling transport properties and mechanical compliance, offering a pathway toward high-performance ductile thermoelectric materials. Physical sciences/Energy science and technology/Thermoelectric devices and materials Physical sciences/Materials science/Materials for energy and catalysis/Thermoelectrics Amorphous-crystalline heterogeneity Thermoelectric materials Silver Chalcogenides mechanical ductility Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Ductile thermoelectric (TE) materials are essential for enabling mechanically compliant, on skin energy harvesting and thermal management devices; however, achieving high thermoelectric performance near room temperature while maintaining mechanical flexibility remains a fundamental challenge due to the intrinsic coupling between electronic and thermal transport 1 . Conventional inorganic TE materials such as Bi 2 Te 3 exhibit excellent performance at room temperature 2 , 3 , 4 , 5 , 6 but suffer from intrinsic brittleness 7 , whereas organic systems offer mechanical compliance 8 , 9 , 10 , 11 , 12 at the expense of low thermoelectric efficiency 13 . Bridging this performance-ductility trade-off remains a central challenge in the development of next-generation TE materials. Silver chalcogenides, particularly Ag 2 S-based systems 14 , 15 , 16 , 17 , 18 , have recently emerged as promising alternatives, combining moderate thermoelectric performance with intrinsic ductility. However, their relatively low carrier concentration ( n ) remains a key limitation for further performance enhancement 18 . Despite extensive efforts to optimize Ag₂S-based systems through alloying and compositional tuning, these approaches primarily focus on adjusting carrier concentration and phonon scattering, while lacking a generalizable structural design parameter that can simultaneously control electronic transport, thermal transport, and mechanical behavior. Therefore, establishing such a structural design parameter represents a critical unmet challenge in ductile thermoelectric materials. Alloying strategies, such as Te or Se incorporation, have been widely explored to optimize the electronic and thermal transport properties of Ag 2 S 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 . Among these, Ag 2 S 0.4 Te 0.6 has attracted considerable attention due to its intrinsically low thermal conductivity ( κ ), which has been attributed to nanoscale structural disorder 29 . While this material has often been described as amorphous-like, recent studies suggest that its structural state is highly sensitive to external perturbations and can readily transition between crystalline and amorphous configurations during processing 30 . This indicates that the material inherently exhibits a heterogeneous amorphous-crystalline structure, rather than a purely amorphous phase. The coexistence of amorphous and crystalline phases is expected to strongly influence thermoelectric transport. Amorphous regions introduce localized electronic states and band-tail features that can alter carrier concentration, while enhancing phonon scattering and suppressing thermal conductivity 31 , 32 . In contrast, crystalline domains provide ordered pathways that facilitate carrier transport and improve mobility ( µ ) 33 . This contrast suggests that armorphous-crystalline heterogeneity may provide a route to decouple electronic and thermal transport. However, a systematic understanding of how amorphous-crystalline phase fractions govern transport behavior and mechanical properties in ductile thermoelectric systems remains lacking. Here, we demonstrate that amorphous-crystalline structural heterogeneity serves as an effective structural design parameter to regulate both thermoelectric and mechanical behavior in Ag 2 S 0.4 Te 0.6 . Density functional theory calculations are first employed to elucidate how structural transitions influence electronic structure and carrier transport. Guided by these insights, samples with tunable amorphous-to-crystalline phase fractions are synthesized by controlling heat-treatment conditions while maintaining identical compositions. Additional low-temperature annealing is introduced to induce controlled crystallization of secondary phases. By correlating structural state with transport and mechanical properties, we demonstrate that phase-fraction engineering enables simultaneous optimization of thermoelectric performance and ductility. The optimized material achieves a room-temperature figure of merit ( ZT ) of ~ 0.47 together with a bending strain of ~ 22%, highlighting amorphous-crystalline heterogeneity as a design paradigm for high-performance, mechanically compliant thermoelectric materials. Results and Discussion Amorphous-Crystalline Structural heterogeneity of Ag 2 S 0.4 Te 0.6 Structural heterogeneity provides a versatile mechanism for reconfiguring electronic structures and tailoring the resultant physical properties. In Ag 2 S 0.4 Te 0.6 , which exhibits amorphous–crystalline coexistence, this effect is directly reflected in the evolution of its atomic and electronic structures. While the crystalline phase maintains a well-defined atomic arrangement, increasing structural heterogeneity introduces significant atomic disorder (Fig. 1 a). This structural variation leads to a clear modification of the electronic structure. The crystalline phase exhibits a bandgap of ~ 0.47 eV. Increasing structural heterogeneity reduces the bandgap to ~ 0.29 eV and introduces band-tail states extending into the gap region. These results indicate that structural heterogeneity broadens the electronic states near the band edges and reduces the effective bandgap (Fig. 1 b, c). Based on these changes in the electronic structure, structural heterogeneity was induced by external stimuli through reducing the heat-treatment time or varying applied strain to generate an amorphous–crystalline mixed structure. A subsequent low-temperature annealing step further promoted precipitate formation (Fig. S3). X-ray diffraction patterns of Ag 2 S 0.4 Te 0.6 show the coexistence of broad amorphous features and crystalline peaks, confirming the formation of structural heterogeneity (Fig. 1 d). Peaks near ~ 35° and ~ 43° are consistently located between the corresponding reflections of cubic Ag 2 S and Ag 2 Te, indicating S–Te substitution within a single lattice rather than a simple phase mixture. In addition, peaks in the 20–30° range emerge with decreasing amorphous fraction and are consistent with monoclinic Ag 2 Te- and Ag 2 S-related structures (Fig. S4). A peak near ~ 21° appears at an intermediate position between monoclinic Ag 2 S and Ag 2 Te reflections, consistent with substitutional mixing within the lattice. These diffraction results indicate a mixed amorphous–crystalline structure with substitutional effects and locally ordered domains. Consistent with the X-ray diffraction results, transmission electron microscopy reveals pronounced structural heterogeneity at the nanoscale (Fig. 1 e). Selected area electron diffraction (SAED) patterns from the matrix region show either cubic diffraction features or diffuse rings with discontinuous intensity, indicating the coexistence of locally ordered crystalline domains and disordered regions. In addition, precipitates with distinct contrast relative to the surrounding matrix are observed and can be primarily indexed to monoclinic Ag 2 Te. These precipitates are randomly dispersed and embedded within the disordered matrix, further contributing to the structural heterogeneity. Although Ag 2 S-related reflections are present in the X-ray diffraction patterns, corresponding precipitates are not directly observed in the TEM analysis. Their presence can be inferred from the diffraction results and from their relative thermodynamic stability compared to Ag 2 Te (Table S1 ). These observations indicate that Ag 2 S 0.4 Te 0.6 forms a hierarchical amorphous–crystalline heterostructure, in which crystalline domains and secondary precipitates are distributed within a disordered matrix. The amorphous-to-crystalline fraction was quantified using peak-area integration of the background-subtracted XRD patterns (Fig. 1 f) 34 , allowing the samples to be categorized as AM72, AM67, and AM60 according to their amorphous fractions of 72%, 67% and 60%. All samples are dominated by the disordered phase, with the crystalline fraction accounting for approximately one-third of the structure. Further separation of the crystalline contributions into matrix and precipitate components (Fig. S5) shows that both increase with overall crystallinity, with a more pronounced increase in the precipitate phase. However, these precipitates are not clearly resolved in scanning electron microscopy (SEM) images, indicating that they exist at the nanoscale beyond the spatial resolution of SEM. Energy-dispersive X-ray spectroscopy (EDS) analysis confirms that all ingots exhibit nearly identical overall compositions (Fig. S6, S7). These results indicate that the observed structural heterogeneity originates from differences in local phase distribution within the same nominal composition rather than from variations in bulk composition. Electrical Transport in Amorphous-Crystalline AgSTe The electrical transport behavior of Ag 2 S 0.4 Te 0.6 is governed by a competition between disorder-induced carrier generation and crystallinity-driven mobility enhancement. Structural disorder reduces the effective bandgap and introduces band-tail states, as indicated by the DFT results, thereby increasing the carrier concentration. At the same time, disorder introduces local potential fluctuations and structural irregularities that enhance carrier scattering, resulting in reduced mobility 35 . As the crystalline fraction increases, disorder-induced carrier generation is suppressed, leading to a decrease in carrier concentration 36 , 37 , 38 . In parallel, the formation of crystalline domains and precipitates establishes more continuous and ordered transport pathways, resulting in enhanced carrier mobility 33 . These effects are reflected in the measured electrical transport properties (Fig. 2 ). As the amorphous fraction decreases, the electrical conductivity decreases, whereas the Seebeck coefficient increases. This trend reflects systematic changes in carrier concentration and mobility. From AM72 to AM60, the carrier concentration decreases, while the mobility initially decreases and then increases. This behavior correlates with the formation of precipitates observed in the X-ray diffraction patterns. At intermediate crystallinity (AM67), the increased number of precipitates is accompanied by a higher density of interfaces. This can enhance carrier scattering and reduce mobility. With further increase in crystallinity (AM60), the connectivity between crystalline domains becomes more pronounced. This enables more continuous transport pathways and leads to enhanced mobility. The increase in mobility mitigates the effect of reduced carrier concentration, thereby suppressing the decrease in electrical conductivity. Although the Hall mobility partially recovers at higher crystallinity, the weighted mobility decreases with decreasing amorphous fraction (Fig. 2 d). This indicates that the intrinsic carrier transport quality does not continuously improve with increasing crystallinity. The Seebeck coefficient (S) exhibits an opposite trend, increasing as the carrier concentration decreases. This behavior is consistent with the single parabolic band (SPB) model, which describes the relationship between Seebeck coefficient, carrier concentration, and density-of-states effective mass ( m d * ). While strictly valid in the degenerate regime, the following expression provides an intuitive description of the S–n relationship 39 , 40 , 41 : $$\:S\:=\:\frac{8{\pi\:}^{2}{k}_{B}^{2}T}{3q{h}^{2}}{m}_{d}^{*}{\left(\frac{\pi\:}{3n}\right)}^{2/3}$$ where k B is the Boltzmann constant, q is the carrier charge, h is the Planck constant, and m d * is the density of states effective mass. Consistent with this trend, the Pisarenko plot (Fig. 2 e) shows that the experimental data follow the SPB trend with a nearly constant effective mass, confirming that the variation in the Seebeck coefficient is primarily driven by shifts in the Fermi level. In addition, the enhanced Seebeck coefficient may reflect an energy-dependent carrier filtering effect associated with bandgap variation and structural heterogeneity. This interpretation is supported by the reduced weighted mobility in AM60 (Fig. 2 d), indicating enhanced overall carrier scattering. Such enhanced scattering may preferentially affect low-energy carriers, contributing to the increase in the Seebeck coefficient. Consequently, the opposing trends of electrical conductivity and Seebeck coefficient lead to comparable power factor values among the samples at room temperature (Fig. 2 b inset). In particular, AM60 exhibits a carrier concentration closest to the optimal range, resulting in a balanced combination of electrical conductivity and Seebeck coefficient. Thermal Transport and Thermoelectric Performance in Amorphous-Crystalline AgSTe The thermal transport properties of Ag 2 S 0.4 Te 0.6 are strongly influenced by structural heterogeneity, which introduces multiple phonon scattering mechanisms. The coexistence of amorphous regions, crystalline domains, and nanoscale precipitates provides a hierarchical scattering environment that suppresses phonon transport. As the amorphous fraction increases, structural disorder becomes more pronounced, leading to enhanced phonon scattering due to lattice distortion and increased lattice disorder. In addition, nanoscale precipitates introduce interfacial scattering, further suppressing phonon propagation. These effects are reflected in the measured thermal transport properties (Fig. 3 a–c), where the total thermal conductivity decreases with increasing amorphous fraction. To further analyze the thermal transport behavior, the electronic contribution ( κ e ) was estimated using the Wiedemann–Franz law, \(\:{\kappa\:}_{e}=L{\sigma\:}T\) , where L is the Lorenz number. The lattice thermal conductivity ( κ L ) was then obtained by subtracting electronic thermal conductivity from the total thermal conductivity. The lattice thermal conductivity remains nearly unchanged across the samples, indicating that phonon transport is already strongly suppressed by structural disorder and exhibits limited sensitivity to the amorphous–crystalline fraction. To evaluate the lower bound of lattice thermal conductivity, the minimum value was estimated using the Cahill–Pohl model 42 . The calculated minimum (~ 0.38 Wm - 1 K - 1 ) is higher than the experimentally measured value (~ 0.2 Wm - 1 K - 1 ). This discrepancy can be attributed in part to the tendency of the Cahill–Pohl model to overestimate the minimum lattice thermal conductivity 43 . In addition, the model parameters were interpolated from crystalline Ag 2 S and Ag 2 Te 44 , whereas the present samples contain a substantial amorphous fraction and enhanced disorder-induced phonon scattering. These factors collectively contribute to the lower experimentally observed lattice thermal conductivity. These results indicate that the variation in total thermal conductivity is primarily governed by the electronic contribution, which scales with electrical conductivity. Based on the evaluated thermoelectric properties, the quality factor ( B ) and ZT were derived (Fig. 3 e, f). The quality factor exhibits the lowest value for AM60 (~ 0.22), whereas the room-temperature ZT reaches its maximum (~ 0.47) compared to those of AM67 and AM72. This contrasting behavior suggests that the enhancement in thermoelectric performance is not solely dictated by the intrinsic quality factor, but instead arises from the optimization of carrier transport conditions. This interpretation is consistent with the SPB analysis (Fig. 2 f), where AM60 is located closest to the optimal transport condition among the samples. Although AM67 and AM72 exhibit higher quality factors, their ZT could only be improved through carrier concentration tuning that inevitably alters the structural state. As a result, independent optimization of carrier concentration while preserving their structural characteristics is difficult, and AM60, which is closest to the optimal carrier concentration, exhibits the highest thermoelectric performance among the samples. These results indicate that the structural evolution, particularly the amorphous–crystalline fraction, contributes to the tuning of carrier concentration, enabling effective optimization without additional doping. Consequently, high thermoelectric performance at room temperature is achieved through carrier concentration optimization. Based on the measured thermoelectric properties, finite-element simulations were performed using COMSOL Multiphysics to evaluate the device-level impact of structural heterogeneity. The experimentally determined transport parameters were implemented under identical boundary conditions to enable direct comparison between samples (Fig. 3 g, h). Details of the simulation setup and parameters are provided in the Supplementary Information. The simulated temperature and electrical potential distributions reveal a clear dependence on thermal transport properties. Samples with lower thermal conductivity exhibit steeper temperature gradients and larger temperature differences under identical heat flux conditions. Consequently, a higher electrical potential is generated, with a maximum increase of ~ 176% as the amorphous fraction decreases. In addition, the theoretical coefficient of performance ( COP ) was evaluated to assess the cooling performance 45 , 46 . $$\:COP=\:\frac{{T}_{c}}{{T}_{h}-{T}_{c}}\frac{{\left(1+Z\stackrel{-}{T}\right)}^{1/2}-{T}_{h}/{T}_{c}}{{(1+Z\stackrel{-}{T})}^{1/2}+1}$$ where T c and T h ​ are the cold- and hot-side temperatures, respectively, and \(\:Z\stackrel{-}{T}\) is ZT value at average temperature. The cold-side temperature was fixed at 288 K, while the hot-side temperature was varied from 293 to 318 K. Under these conditions, AM60 exhibits the highest COP of 0.47 at ΔT = 30 K (Fig. 3 i). These results demonstrate that the structural heterogeneity enables enhanced device-level cooling performance under near-room-temperature operating conditions. Mechanical Properties in Amorphous-Crystalline AgSTe The mechanical response of Ag 2 S 0.4 Te 0.6 arises from its structural heterogeneity. This enables multiple deformation modes, including slip in crystalline regions and shear deformation in amorphous domains, which collectively contribute to enhanced ductility. In addition, nanoscale precipitates are expected to influence the mechanical strength by acting as obstacles to dislocation motion. As a result, the overall mechanical behavior reflects a balance between deformation mechanisms that accommodate strain and microstructural features that resist plastic flow. Vickers hardness measurements were performed to evaluate the mechanical response under localized deformation (Fig. 4 a). The average hardness decreases with decreasing amorphous fraction. Optical microscopy images of the indented surfaces reveal distinct bright and dark regions (Fig. S8). Hardness measurements confirm that these regions exhibit different hardness values, as evidenced by the variation in Vickers hardness within individual indents. The absence of compositional differences in SEM-EDS (Fig. S6, S7) suggests that this contrast originates from structural heterogeneity rather than chemical inhomogeneity. Based on these observations, the lower-hardness regions are inferred to correspond to crystalline domains, whereas the higher-hardness regions are associated with amorphous areas. Thus, the averaged hardness values decrease as the fraction of the amorphous phase decreases, reflecting the lower intrinsic hardenss of the ordered structure. This interpretation is supported by previous reports showing that crystalline Ag 2 S 0.4 Te 0.6 exhibits enhanced ductility 30 , combined with the general relationship between increased ductility and reduced hardness 47 . Based on this understanding, AM60 was selected for further mechanical evaluation, as it combines the highest ZT with the lowest hardness among the samples. A three-point bending test was conducted to further probe the deformation behavior (Fig. 4 b). AM60 exhibits a maximum strain of 22% at a stress of 145 MPa, demonstrating high ductility, which is also evident from the bent sample maintaining structural integrity without fracture. The stress–strain curve shows a clear hardening behavior, indicating that the material sustains increasing stress with continued deformation. This behavior arises from structural heterogeneity, where nanoscale precipitates interact with dislocations and limit their motion during continued loading, leading to strain hardening. In addition, the serrated features observed below ~ 5% strain are attributed to shear deformation within amorphous regions. SEM images of the deformed surface reveal well-developed slip bands extending over macroscopic regions, accompanied by localized shear features (Fig. 4 c). Shear deformation is initially observed within the amorphous regions, as evidenced by the serrated features observed in the early stage of the bending stress–strain curve. As shear bands propagate, they are impeded by crystalline boundaries and precipitates, leading to dislocation generation. These dislocations migrate to form slip within the crystalline domains, while being partially pinned by embedded precipitates, contributing to strain hardening (Fig. 4 d). As a result, localized shear is suppressed and distributed into multiple shear bands, enabling sustained plastic deformation and enhanced ductility, as observed in the SEM image. The combined thermoelectric and mechanical performance is summarized in Fig. 4 e, where AM60 shows high ZT and bending ductility compared with previously reported Ag 2 S-based materials 20 , 21 , 22 , 48 , 49 , 50 , 51 . In summary, the thermoelectric performance of Ag 2 S 0.4 Te 0.6 is governed by the interplay between carrier transport and phonon scattering, both controlled by the amorphous–crystalline phase fraction. This structural tuning enables simultaneous optimization of electrical and thermal transport properties. Importantly, the phase fraction governs the carrier concentration, enabling effective electronic tuning without additional doping. These results show that improved thermoelectric performance is achieved not by maximizing individual transport parameters, but by approaching an optimal balance between them through structural control. Furthermore, the heterogeneous structure supports cooperative deformation mechanisms, allowing high ductility to be retained alongside enhanced thermoelectric performance. Overall, phase-fraction engineering of amorphous–crystalline heterostructures provides a design strategy for developing high-performance, mechanically compliant thermoelectric materials. This approach offers broad applicability to other disordered or metastable systems where competing transport and mechanical properties must be optimized concurrently. Methods Synthesis of Ag 2 S 0.4 Te 0.6 ingots High-purity Ag (99.999%), S (99.99%), and Te (99.99%) were weighed to the desired atomic ratio and sealed in carbon-coated quartz tube under vacuum. The sealed materials were heat-treated at 1273 K for 12 h. Subsequently, the samples were annealed at 823 K for 24 h and then at 393 K for 10 h. The heating and cooling rates for all processes were fixed at 3 K min - 1 . The low-temperature annealing at 393 K was selected based on the Ag–S and Ag–Te phase diagrams, which indicate that monoclinic phases can form at low temperatures. The synthesized ingots were cut and polished to measure their properties. Density functional theory calculation of AgSTe ingots All density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) with the projector-augmented wave (PAW) method 52 , 53 . Structural relaxations were carried out using the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) 54 , while electronic structure calculations were performed using the meta-GGA modified Becke-Johnson (MBJ) potential 55 , 56 . The plane-wave energy cutoff was set to 520 eV. The convergence criteria for electronic self-consistency were set to 1 × 10 − 5 eV for structural relaxation and 1 × 10 − 8 eV for electronic structure calculations. Atomic positions and lattice parameters were fully relaxed until the Hellmann-Feynman forces were less than 0.01 eV Å⁻¹ for unit-cell models and 0.03 eV Å⁻ 1 for supercell models. Brillouin zone sampling was performed using Monkhorst-Pack k-point meshes with a reciprocal-space density of 100 Å - 3 , generated using pymatgen 57 . A 2 × 2 × 2 supercell (96 atoms) based on monoclinic Ag 2 S was constructed using the special quasi-random structure (SQS) 58 approach to model the Ag 2 S 0.4 Te 0.6 solid solution. The amorphous structure was generated by melt-quenching the optimized SQS model using machine-learning molecular dynamics based on CHGNet 59 . The system was melted at 2200 K and subsequently quenched to 300 K with a cooling rate of 10 K ps - 1 . The quenched amorphous structure was further relaxed using DFT to obtain the final atomic configuration. Thermoelectric Characterization of AgSTe ingots X-ray diffraction (XRD) analysis was performed on ingots for the phase characterization (Rigaku, SmartLab XE, Japan). The amorphous and crystalline fractions were determined by fitting the XRD patterns using a combination of sharp crystalline peaks and a broad amorphous background and evaluating their respective integrated areas. Microstructure was examined using field emission scanning electron microscope (FE-SEM, HITACHI, SU-6600, Japan) and field emission transmission electron microscope (FE-TEM, JEOL, JEM-F200, Japan). σ and S were measured by four-probe method based thermoelectric measurement system (NETZSCH, SBA-458, Germany) from 300 to 673 K. Carrier concentration ( n ) and mobility ( µ ) was confirmed by Hall effect measurement (Ecopia, AHT55T3, South Korea). Based on the measured n, µ was calculated using the \(\:\sigma\:=ne\mu\:\) . Thermal diffusivity ( D ) was measured by the laser flash method (Netzsch, LFA 457, Germany). The specific heat ( C p ) was calculated by the Dulong-Petit law ( \(\:{C}_{P}=3nR/M\) , where n, R, and M are number of atoms per formula unit, the gas constant, and molar mass of the compound, respectively). Density( ρ ) of the sample was measured by Archimedes method. Total thermal conductivity was calculated from the measured data \(\:(\kappa\:=\rho\:{C}_{P}D)\) . Dimensionless figure of merit( ZT ) was calculated based on the measured thermoelectric properties ( \(\:ZT={S}^{2}\sigma\:T/\kappa\:\) ). Mechanical Characterization of Ag 2 S 0.4 Te 0.6 ingots The Vickers hardness of the samples was measured using a micro-Vickers hardness tester (HM-200, Mitutoyo, Japan). A load of 0.05 kgf (HV0.05) was applied using a diamond pyramidal indenter. The indentations were made on the prepared surface of the samples, and the hardness values were calculated from the diagonal lengths of the indentation marks. Multiple indentations were performed at different locations, and the average hardness value was reported. Three-point bending tests were conducted using a universal testing machine (Model 5982, Instron, USA). Rectangular specimens with dimensions of 1.5 × 3 × 13.5 mm 3 were tested at a loading rate of 0.5 mm min - 1 . Declarations Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author contributions J. M. Park contributed to conceptualization, methodology, investigation, formal analysis, visualization, and writing-original draft. J. M. Lee contributed to methodology, investigation, formal analysis, and visualization. S.-H. Jung and S. Jo contributed to investigation. L. B. Vu and H. W. Kim contributed to visualization. H. Kim and S. B. Cho contributed to conceptualization. X.Shi contributed to writing & review manuscript. K.-I. Park and W. H. Shin contributed to supervision and writing-review & editing. K. T. Kim contributed to supervision, writing-review & editing, funding acquisition, project administration, and resources. J. M. Park and J. M. Lee contributed equally to this work. K.-I. Park, W. H. Shin, and K. T. Kim are corresponding authors. Acknowledgement This work was financially supported by National Research Foundation of Korea(NRF) grant funded by the Korea government (RS-2022-NR068194 and RS-2024-00448499). Data availability The authors declare that all data supporting the findings of this study are available within the article and its Supplementary Information files or from the corresponding author. References Parida K, Bark H, Lee PS (2021) Emerging Thermal Technology Enabled Augmented Reality. Adv Funct Mater 31:2007952 Cheng R et al (2024) Unraveling electronic origins for boosting thermoelectric performance of p-type (Bi,Sb) 2 Te 3 . Sci Adv 10:eadn9959 Xu P et al (2024) High-Performance Bi 2 Te 3 ‐Based Thermoelectrics Enabled by ≈ 1 nm Metal Chalcogenide Clusters with Size‐Dependent Electron and Phonon Structures. Adv Funct Mater 34:2401240 Zhou M et al (2025) Ultrahigh thermoelectricity obtained in classical BiSbTe alloy processed under super-gravity. 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Phys Rev Lett 65:353–356 Deng B et al (2023) CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nat Mach Intell 5:1031–1041 Additional Declarations There is NO Competing Interest. Supplementary Files NatCommSupplementaryInformationver5.1.docx Supplementary Information Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9531103","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":629779916,"identity":"5bc8ca5e-1384-4fd3-bae6-6eec593193d5","order_by":0,"name":"Kyung Tae Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVRIiWNgGAWjYBACCQY2hgMMFQk8UH4CEVrYQFrOkKqFgbENrpIILZLz2xIP3ZyXJqPbf4DtwweGtHyCWqTZ2A4czt2Ww2N2I4F55gyGHMsGQlrk2NgbgFoqgFoYmJl5GCoMCNoC0TIHqOX8AWbmP8RogTisAeiwAwnMzAwMOYS1SLalJRzOOZYGdFhiM2OPQRphLRKHjxl/zqlJtjc7f/gww4+KZMJakABjAwMDSRpGwSgYBaNgFOAEAGUXNpa6w7M0AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-2045-095X","institution":"Korea Institute of Materials Science","correspondingAuthor":true,"prefix":"","firstName":"Kyung","middleName":"Tae","lastName":"Kim","suffix":""},{"id":629779917,"identity":"7c66ca1b-5b80-4ffd-a644-4891e0b58a62","order_by":1,"name":"Jong Min Park","email":"","orcid":"","institution":"Korea Institute of Materials Science","correspondingAuthor":false,"prefix":"","firstName":"Jong","middleName":"Min","lastName":"Park","suffix":""},{"id":629779918,"identity":"20604982-529f-4e19-9597-9eefc334d8f1","order_by":2,"name":"Jeong Min Lee","email":"","orcid":"https://orcid.org/0009-0005-3842-6992","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jeong","middleName":"Min","lastName":"Lee","suffix":""},{"id":629779919,"identity":"cbdc5833-53e6-46a2-96b4-ede37b119b28","order_by":3,"name":"Seungki Jo","email":"","orcid":"","institution":"Ulsan National Institute of Science and Technology (UNIST)","correspondingAuthor":false,"prefix":"","firstName":"Seungki","middleName":"","lastName":"Jo","suffix":""},{"id":629779920,"identity":"2bb0b562-d3eb-4a5b-b787-79c4b9908e25","order_by":4,"name":"Soo-ho Jung","email":"","orcid":"","institution":"Korea Institute of Materials Science","correspondingAuthor":false,"prefix":"","firstName":"Soo-ho","middleName":"","lastName":"Jung","suffix":""},{"id":629779921,"identity":"2b62006d-0ff4-4024-8e51-dcbe214aa148","order_by":5,"name":"Linh Vu","email":"","orcid":"","institution":"Korea Institute of Materials Science","correspondingAuthor":false,"prefix":"","firstName":"Linh","middleName":"","lastName":"Vu","suffix":""},{"id":629779922,"identity":"dae05fbe-0156-4899-95e8-34c3c75730a6","order_by":6,"name":"Hyun-Sik Kim","email":"","orcid":"https://orcid.org/0000-0001-8934-4042","institution":"University of Seoul","correspondingAuthor":false,"prefix":"","firstName":"Hyun-Sik","middleName":"","lastName":"Kim","suffix":""},{"id":629779923,"identity":"cad0f44e-44f7-4d49-bf10-3b47ef5e370a","order_by":7,"name":"Hyeon Woo Kim","email":"","orcid":"","institution":"Ajou University","correspondingAuthor":false,"prefix":"","firstName":"Hyeon","middleName":"Woo","lastName":"Kim","suffix":""},{"id":629779924,"identity":"e757ffa7-f8a7-4f76-b77d-a8a7b1a129f6","order_by":8,"name":"Sung Beom Cho","email":"","orcid":"https://orcid.org/0000-0002-3151-0113","institution":"Ajou University","correspondingAuthor":false,"prefix":"","firstName":"Sung","middleName":"Beom","lastName":"Cho","suffix":""},{"id":629779925,"identity":"7f80b7ca-6992-4fdd-9493-66da82d9d4f4","order_by":9,"name":"Xun Shi","email":"","orcid":"https://orcid.org/0000-0002-8086-6407","institution":"Shanghai Institute of Ceramics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Xun","middleName":"","lastName":"Shi","suffix":""},{"id":629779926,"identity":"d1136cfc-9284-437f-a222-e333604800eb","order_by":10,"name":"Kwi-Il Park","email":"","orcid":"https://orcid.org/0000-0002-9140-6641","institution":"Kyungpook National University","correspondingAuthor":false,"prefix":"","firstName":"Kwi-Il","middleName":"","lastName":"Park","suffix":""},{"id":629779927,"identity":"b33fb2ba-3a2f-40c6-99a7-64cd2c1eba3c","order_by":11,"name":"Weon Ho Shin","email":"","orcid":"https://orcid.org/0000-0003-0487-5480","institution":"Kwangwoon University","correspondingAuthor":false,"prefix":"","firstName":"Weon","middleName":"Ho","lastName":"Shin","suffix":""}],"badges":[],"createdAt":"2026-04-26 10:20:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9531103/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9531103/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108804907,"identity":"70a3bcd4-3e6c-4158-afeb-2369b0992440","added_by":"auto","created_at":"2026-05-08 15:24:12","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":950389,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Crystalline and Amorphous Structures of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e. (b) Electronic DOS of monoclinic and amorphous Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e calculated by DFT. (c) Partial charge distributions illustrating localized band‑tail states associated with the amorphous Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e. (d) XRD patterns of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots synthesized with identical composition and process conditions. (e) TEM images of the matrix and nanoprecipitates in an Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingot with the corresponding SAED patterns. (f) Quantified amorphous-crystalline phase ratio using peak area integration method.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-9531103/v1/4a83f9e03b1e6bcc84707476.png"},{"id":108804172,"identity":"44988962-3016-4cf6-ad63-d3486e030f8d","added_by":"auto","created_at":"2026-05-08 15:17:04","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":426174,"visible":true,"origin":"","legend":"\u003cp\u003eElectrical transport properties of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots. (a) Electrical conductivity, (b) Seebeck coefficient and power factor (inset), (c) carrier concentration and mobility, (d) weighted mobility, and (e, f) Pisarenko plots of Seebeck coefficient and power factor as a function of carrier concentration.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9531103/v1/572ad5c901ee57905b0e8c47.png"},{"id":108805257,"identity":"81150336-df22-4082-aa39-2ebba6f54aff","added_by":"auto","created_at":"2026-05-08 15:25:23","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":535817,"visible":true,"origin":"","legend":"\u003cp\u003eThermal transport properties and thermoelectric performance of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots. (a) Total thermal conductivity, (b) electronic thermal conductivity, and (c) lattice thermal conductivity as a function of temperature. (d) Schematic illustration of phonon scattering mechanism in Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e (e) Quality factor (\u003cem\u003eB\u003c/em\u003e) and (f) Figure of merit (\u003cem\u003eZT\u003c/em\u003e) of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots as a function of temperature. (g) Simulated temperature and electrical potential distributions, (h) generated electrical potential for each sample, and (i) COP calculated using the measured \u003cem\u003eZT\u003c/em\u003e values.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9531103/v1/5e00e3547603f3eaf69f60bb.png"},{"id":108804537,"identity":"390e33b1-d507-40b0-aefb-c38274460cb1","added_by":"auto","created_at":"2026-05-08 15:21:24","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":484299,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Vickers hardness of the Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots. (b) Three-point bending stress-strain curve of AM60. (c) SEM image of the bent surface of AM60. (d) Schematic illustration of deformation mechanisms in Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e under applied strain. (e) ZT-bending ductility for AM60 and reported Ag\u003csub\u003e2\u003c/sub\u003eS-based materials \u003csup\u003e20, 21, 22, 48, 49, 50, 51\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9531103/v1/7061d84ef68a7a90cc4ca16e.png"},{"id":108811796,"identity":"41a308ab-280c-45a5-bdd3-f452e18bc40f","added_by":"auto","created_at":"2026-05-08 16:07:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2778870,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9531103/v1/5a8cd9a7-c071-469c-b3f4-1b45e744955a.pdf"},{"id":108540573,"identity":"6ed9df2e-de70-4b44-8309-52d30b888cee","added_by":"auto","created_at":"2026-05-05 18:36:28","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4802211,"visible":true,"origin":"","legend":"Supplementary Information","description":"","filename":"NatCommSupplementaryInformationver5.1.docx","url":"https://assets-eu.researchsquare.com/files/rs-9531103/v1/aebae57477c3265e12e74578.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Tuning amorphous-crystalline heterogeneity enables simultaneous optimization of thermoelectric performance and ductility in silver chalcogenides","fulltext":[{"header":"Introduction","content":"\u003cp\u003eDuctile thermoelectric (TE) materials are essential for enabling mechanically compliant, on skin energy harvesting and thermal management devices; however, achieving high thermoelectric performance near room temperature while maintaining mechanical flexibility remains a fundamental challenge due to the intrinsic coupling between electronic and thermal transport \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Conventional inorganic TE materials such as Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e exhibit excellent performance at room temperature \u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e but suffer from intrinsic brittleness \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, whereas organic systems offer mechanical compliance \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e at the expense of low thermoelectric efficiency \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Bridging this performance-ductility trade-off remains a central challenge in the development of next-generation TE materials.\u003c/p\u003e \u003cp\u003eSilver chalcogenides, particularly Ag\u003csub\u003e2\u003c/sub\u003eS-based systems \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e, have recently emerged as promising alternatives, combining moderate thermoelectric performance with intrinsic ductility. However, their relatively low carrier concentration (\u003cem\u003en\u003c/em\u003e) remains a key limitation for further performance enhancement \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Despite extensive efforts to optimize Ag₂S-based systems through alloying and compositional tuning, these approaches primarily focus on adjusting carrier concentration and phonon scattering, while lacking a generalizable structural design parameter that can simultaneously control electronic transport, thermal transport, and mechanical behavior. Therefore, establishing such a structural design parameter represents a critical unmet challenge in ductile thermoelectric materials.\u003c/p\u003e \u003cp\u003eAlloying strategies, such as Te or Se incorporation, have been widely explored to optimize the electronic and thermal transport properties of Ag\u003csub\u003e2\u003c/sub\u003eS \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. Among these, Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e has attracted considerable attention due to its intrinsically low thermal conductivity (\u003cem\u003eκ\u003c/em\u003e), which has been attributed to nanoscale structural disorder \u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e. While this material has often been described as amorphous-like, recent studies suggest that its structural state is highly sensitive to external perturbations and can readily transition between crystalline and amorphous configurations during processing \u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. This indicates that the material inherently exhibits a heterogeneous amorphous-crystalline structure, rather than a purely amorphous phase.\u003c/p\u003e \u003cp\u003eThe coexistence of amorphous and crystalline phases is expected to strongly influence thermoelectric transport. Amorphous regions introduce localized electronic states and band-tail features that can alter carrier concentration, while enhancing phonon scattering and suppressing thermal conductivity \u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. In contrast, crystalline domains provide ordered pathways that facilitate carrier transport and improve mobility (\u003cem\u003e\u0026micro;\u003c/em\u003e) \u003csup\u003e33\u003c/sup\u003e. This contrast suggests that armorphous-crystalline heterogeneity may provide a route to decouple electronic and thermal transport. However, a systematic understanding of how amorphous-crystalline phase fractions govern transport behavior and mechanical properties in ductile thermoelectric systems remains lacking.\u003c/p\u003e \u003cp\u003eHere, we demonstrate that amorphous-crystalline structural heterogeneity serves as an effective structural design parameter to regulate both thermoelectric and mechanical behavior in Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e. Density functional theory calculations are first employed to elucidate how structural transitions influence electronic structure and carrier transport. Guided by these insights, samples with tunable amorphous-to-crystalline phase fractions are synthesized by controlling heat-treatment conditions while maintaining identical compositions. Additional low-temperature annealing is introduced to induce controlled crystallization of secondary phases. By correlating structural state with transport and mechanical properties, we demonstrate that phase-fraction engineering enables simultaneous optimization of thermoelectric performance and ductility. The optimized material achieves a room-temperature figure of merit (\u003cem\u003eZT\u003c/em\u003e) of ~\u0026thinsp;0.47 together with a bending strain of ~\u0026thinsp;22%, highlighting amorphous-crystalline heterogeneity as a design paradigm for high-performance, mechanically compliant thermoelectric materials.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eAmorphous-Crystalline Structural heterogeneity of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e\u003c/h2\u003e \u003cp\u003eStructural heterogeneity provides a versatile mechanism for reconfiguring electronic structures and tailoring the resultant physical properties. In Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e, which exhibits amorphous\u0026ndash;crystalline coexistence, this effect is directly reflected in the evolution of its atomic and electronic structures. While the crystalline phase maintains a well-defined atomic arrangement, increasing structural heterogeneity introduces significant atomic disorder (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). This structural variation leads to a clear modification of the electronic structure. The crystalline phase exhibits a bandgap of ~\u0026thinsp;0.47 eV.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIncreasing structural heterogeneity reduces the bandgap to ~\u0026thinsp;0.29 eV and introduces band-tail states extending into the gap region. These results indicate that structural heterogeneity broadens the electronic states near the band edges and reduces the effective bandgap (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, c). Based on these changes in the electronic structure, structural heterogeneity was induced by external stimuli through reducing the heat-treatment time or varying applied strain to generate an amorphous\u0026ndash;crystalline mixed structure. A subsequent low-temperature annealing step further promoted precipitate formation (Fig. S3). X-ray diffraction patterns of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e show the coexistence of broad amorphous features and crystalline peaks, confirming the formation of structural heterogeneity (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed). Peaks near ~\u0026thinsp;35\u0026deg; and ~\u0026thinsp;43\u0026deg; are consistently located between the corresponding reflections of cubic Ag\u003csub\u003e2\u003c/sub\u003eS and Ag\u003csub\u003e2\u003c/sub\u003eTe, indicating S\u0026ndash;Te substitution within a single lattice rather than a simple phase mixture. In addition, peaks in the 20\u0026ndash;30\u0026deg; range emerge with decreasing amorphous fraction and are consistent with monoclinic Ag\u003csub\u003e2\u003c/sub\u003eTe- and Ag\u003csub\u003e2\u003c/sub\u003eS-related structures (Fig. S4). A peak near ~\u0026thinsp;21\u0026deg; appears at an intermediate position between monoclinic Ag\u003csub\u003e2\u003c/sub\u003eS and Ag\u003csub\u003e2\u003c/sub\u003eTe reflections, consistent with substitutional mixing within the lattice. These diffraction results indicate a mixed amorphous\u0026ndash;crystalline structure with substitutional effects and locally ordered domains.\u003c/p\u003e \u003cp\u003eConsistent with the X-ray diffraction results, transmission electron microscopy reveals pronounced structural heterogeneity at the nanoscale (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee). Selected area electron diffraction (SAED) patterns from the matrix region show either cubic diffraction features or diffuse rings with discontinuous intensity, indicating the coexistence of locally ordered crystalline domains and disordered regions. In addition, precipitates with distinct contrast relative to the surrounding matrix are observed and can be primarily indexed to monoclinic Ag\u003csub\u003e2\u003c/sub\u003eTe. These precipitates are randomly dispersed and embedded within the disordered matrix, further contributing to the structural heterogeneity. Although Ag\u003csub\u003e2\u003c/sub\u003eS-related reflections are present in the X-ray diffraction patterns, corresponding precipitates are not directly observed in the TEM analysis. Their presence can be inferred from the diffraction results and from their relative thermodynamic stability compared to Ag\u003csub\u003e2\u003c/sub\u003eTe (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). These observations indicate that Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e forms a hierarchical amorphous\u0026ndash;crystalline heterostructure, in which crystalline domains and secondary precipitates are distributed within a disordered matrix.\u003c/p\u003e \u003cp\u003eThe amorphous-to-crystalline fraction was quantified using peak-area integration of the background-subtracted XRD patterns (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef) \u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, allowing the samples to be categorized as AM72, AM67, and AM60 according to their amorphous fractions of 72%, 67% and 60%. All samples are dominated by the disordered phase, with the crystalline fraction accounting for approximately one-third of the structure. Further separation of the crystalline contributions into matrix and precipitate components (Fig. S5) shows that both increase with overall crystallinity, with a more pronounced increase in the precipitate phase. However, these precipitates are not clearly resolved in scanning electron microscopy (SEM) images, indicating that they exist at the nanoscale beyond the spatial resolution of SEM. Energy-dispersive X-ray spectroscopy (EDS) analysis confirms that all ingots exhibit nearly identical overall compositions (Fig. S6, S7). These results indicate that the observed structural heterogeneity originates from differences in local phase distribution within the same nominal composition rather than from variations in bulk composition.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eElectrical Transport in Amorphous-Crystalline AgSTe\u003c/h3\u003e\n\u003cp\u003eThe electrical transport behavior of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e is governed by a competition between disorder-induced carrier generation and crystallinity-driven mobility enhancement. Structural disorder reduces the effective bandgap and introduces band-tail states, as indicated by the DFT results, thereby increasing the carrier concentration. At the same time, disorder introduces local potential fluctuations and structural irregularities that enhance carrier scattering, resulting in reduced mobility \u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. As the crystalline fraction increases, disorder-induced carrier generation is suppressed, leading to a decrease in carrier concentration \u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. In parallel, the formation of crystalline domains and precipitates establishes more continuous and ordered transport pathways, resulting in enhanced carrier mobility \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThese effects are reflected in the measured electrical transport properties (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). As the amorphous fraction decreases, the electrical conductivity decreases, whereas the Seebeck coefficient increases. This trend reflects systematic changes in carrier concentration and mobility. From AM72 to AM60, the carrier concentration decreases, while the mobility initially decreases and then increases. This behavior correlates with the formation of precipitates observed in the X-ray diffraction patterns. At intermediate crystallinity (AM67), the increased number of precipitates is accompanied by a higher density of interfaces. This can enhance carrier scattering and reduce mobility.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith further increase in crystallinity (AM60), the connectivity between crystalline domains becomes more pronounced. This enables more continuous transport pathways and leads to enhanced mobility. The increase in mobility mitigates the effect of reduced carrier concentration, thereby suppressing the decrease in electrical conductivity. Although the Hall mobility partially recovers at higher crystallinity, the weighted mobility decreases with decreasing amorphous fraction (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). This indicates that the intrinsic carrier transport quality does not continuously improve with increasing crystallinity.\u003c/p\u003e \u003cp\u003eThe Seebeck coefficient (S) exhibits an opposite trend, increasing as the carrier concentration decreases. This behavior is consistent with the single parabolic band (SPB) model, which describes the relationship between Seebeck coefficient, carrier concentration, and density-of-states effective mass (\u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e*\u003c/em\u003e). While strictly valid in the degenerate regime, the following expression provides an intuitive description of the S\u0026ndash;n relationship \u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:S\\:=\\:\\frac{8{\\pi\\:}^{2}{k}_{B}^{2}T}{3q{h}^{2}}{m}_{d}^{*}{\\left(\\frac{\\pi\\:}{3n}\\right)}^{2/3}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e is the Boltzmann constant, \u003cem\u003eq\u003c/em\u003e is the carrier charge, \u003cem\u003eh\u003c/em\u003e is the Planck constant, and \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e*\u003c/em\u003e is the density of states effective mass. Consistent with this trend, the Pisarenko plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee) shows that the experimental data follow the SPB trend with a nearly constant effective mass, confirming that the variation in the Seebeck coefficient is primarily driven by shifts in the Fermi level. In addition, the enhanced Seebeck coefficient may reflect an energy-dependent carrier filtering effect associated with bandgap variation and structural heterogeneity. This interpretation is supported by the reduced weighted mobility in AM60 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed), indicating enhanced overall carrier scattering. Such enhanced scattering may preferentially affect low-energy carriers, contributing to the increase in the Seebeck coefficient. Consequently, the opposing trends of electrical conductivity and Seebeck coefficient lead to comparable power factor values among the samples at room temperature (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb inset). In particular, AM60 exhibits a carrier concentration closest to the optimal range, resulting in a balanced combination of electrical conductivity and Seebeck coefficient.\u003c/p\u003e\n\u003ch3\u003eThermal Transport and Thermoelectric Performance in Amorphous-Crystalline AgSTe\u003c/h3\u003e\n\u003cp\u003eThe thermal transport properties of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e are strongly influenced by structural heterogeneity, which introduces multiple phonon scattering mechanisms. The coexistence of amorphous regions, crystalline domains, and nanoscale precipitates provides a hierarchical scattering environment that suppresses phonon transport. As the amorphous fraction increases, structural disorder becomes more pronounced, leading to enhanced phonon scattering due to lattice distortion and increased lattice disorder. In addition, nanoscale precipitates introduce interfacial scattering, further suppressing phonon propagation.\u003c/p\u003e \u003cp\u003eThese effects are reflected in the measured thermal transport properties (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea\u0026ndash;c), where the total thermal conductivity decreases with increasing amorphous fraction. To further analyze the thermal transport behavior, the electronic contribution (\u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e) was estimated using the Wiedemann\u0026ndash;Franz law, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\kappa\\:}_{e}=L{\\sigma\\:}T\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eL\u003c/em\u003e is the Lorenz number. The lattice thermal conductivity (\u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e) was then obtained by subtracting electronic thermal conductivity from the total thermal conductivity. The lattice thermal conductivity remains nearly unchanged across the samples, indicating that phonon transport is already strongly suppressed by structural disorder and exhibits limited sensitivity to the amorphous\u0026ndash;crystalline fraction. To evaluate the lower bound of lattice thermal conductivity, the minimum value was estimated using the Cahill\u0026ndash;Pohl model \u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. The calculated minimum (~\u0026thinsp;0.38 Wm\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003eK\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) is higher than the experimentally measured value (~\u0026thinsp;0.2 Wm\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003eK\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e). This discrepancy can be attributed in part to the tendency of the Cahill\u0026ndash;Pohl model to overestimate the minimum lattice thermal conductivity \u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. In addition, the model parameters were interpolated from crystalline Ag\u003csub\u003e2\u003c/sub\u003eS and Ag\u003csub\u003e2\u003c/sub\u003eTe \u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e, whereas the present samples contain a substantial amorphous fraction and enhanced disorder-induced phonon scattering. These factors collectively contribute to the lower experimentally observed lattice thermal conductivity. These results indicate that the variation in total thermal conductivity is primarily governed by the electronic contribution, which scales with electrical conductivity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBased on the evaluated thermoelectric properties, the quality factor (\u003cem\u003eB\u003c/em\u003e) and \u003cem\u003eZT\u003c/em\u003e were derived (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee, f). The quality factor exhibits the lowest value for AM60 (~\u0026thinsp;0.22), whereas the room-temperature \u003cem\u003eZT\u003c/em\u003e reaches its maximum (~\u0026thinsp;0.47) compared to those of AM67 and AM72. This contrasting behavior suggests that the enhancement in thermoelectric performance is not solely dictated by the intrinsic quality factor, but instead arises from the optimization of carrier transport conditions. This interpretation is consistent with the SPB analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef), where AM60 is located closest to the optimal transport condition among the samples. Although AM67 and AM72 exhibit higher quality factors, their \u003cem\u003eZT\u003c/em\u003e could only be improved through carrier concentration tuning that inevitably alters the structural state. As a result, independent optimization of carrier concentration while preserving their structural characteristics is difficult, and AM60, which is closest to the optimal carrier concentration, exhibits the highest thermoelectric performance among the samples. These results indicate that the structural evolution, particularly the amorphous\u0026ndash;crystalline fraction, contributes to the tuning of carrier concentration, enabling effective optimization without additional doping. Consequently, high thermoelectric performance at room temperature is achieved through carrier concentration optimization.\u003c/p\u003e \u003cp\u003eBased on the measured thermoelectric properties, finite-element simulations were performed using COMSOL Multiphysics to evaluate the device-level impact of structural heterogeneity. The experimentally determined transport parameters were implemented under identical boundary conditions to enable direct comparison between samples (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg, h). Details of the simulation setup and parameters are provided in the Supplementary Information. The simulated temperature and electrical potential distributions reveal a clear dependence on thermal transport properties. Samples with lower thermal conductivity exhibit steeper temperature gradients and larger temperature differences under identical heat flux conditions. Consequently, a higher electrical potential is generated, with a maximum increase of ~\u0026thinsp;176% as the amorphous fraction decreases. In addition, the theoretical coefficient of performance (\u003cem\u003eCOP\u003c/em\u003e) was evaluated to assess the cooling performance \u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e.\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:COP=\\:\\frac{{T}_{c}}{{T}_{h}-{T}_{c}}\\frac{{\\left(1+Z\\stackrel{-}{T}\\right)}^{1/2}-{T}_{h}/{T}_{c}}{{(1+Z\\stackrel{-}{T})}^{1/2}+1}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ec\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e​ are the cold- and hot-side temperatures, respectively, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Z\\stackrel{-}{T}\\)\u003c/span\u003e\u003c/span\u003e is \u003cem\u003eZT\u003c/em\u003e value at average temperature. The cold-side temperature was fixed at 288 K, while the hot-side temperature was varied from 293 to 318 K. Under these conditions, AM60 exhibits the highest COP of 0.47 at \u003cem\u003eΔT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;30 K (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ei). These results demonstrate that the structural heterogeneity enables enhanced device-level cooling performance under near-room-temperature operating conditions.\u003c/p\u003e\n\u003ch3\u003eMechanical Properties in Amorphous-Crystalline AgSTe\u003c/h3\u003e\n\u003cp\u003eThe mechanical response of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e arises from its structural heterogeneity. This enables multiple deformation modes, including slip in crystalline regions and shear deformation in amorphous domains, which collectively contribute to enhanced ductility. In addition, nanoscale precipitates are expected to influence the mechanical strength by acting as obstacles to dislocation motion. As a result, the overall mechanical behavior reflects a balance between deformation mechanisms that accommodate strain and microstructural features that resist plastic flow.\u003c/p\u003e \u003cp\u003eVickers hardness measurements were performed to evaluate the mechanical response under localized deformation (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). The average hardness decreases with decreasing amorphous fraction. Optical microscopy images of the indented surfaces reveal distinct bright and dark regions (Fig. S8). Hardness measurements confirm that these regions exhibit different hardness values, as evidenced by the variation in Vickers hardness within individual indents. The absence of compositional differences in SEM-EDS (Fig. S6, S7) suggests that this contrast originates from structural heterogeneity rather than chemical inhomogeneity. Based on these observations, the lower-hardness regions are inferred to correspond to crystalline domains, whereas the higher-hardness regions are associated with amorphous areas. Thus, the averaged hardness values decrease as the fraction of the amorphous phase decreases, reflecting the lower intrinsic hardenss of the ordered structure. This interpretation is supported by previous reports showing that crystalline Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e exhibits enhanced ductility \u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, combined with the general relationship between increased ductility and reduced hardness \u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBased on this understanding, AM60 was selected for further mechanical evaluation, as it combines the highest \u003cem\u003eZT\u003c/em\u003e with the lowest hardness among the samples. A three-point bending test was conducted to further probe the deformation behavior (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). AM60 exhibits a maximum strain of 22% at a stress of 145 MPa, demonstrating high ductility, which is also evident from the bent sample maintaining structural integrity without fracture. The stress\u0026ndash;strain curve shows a clear hardening behavior, indicating that the material sustains increasing stress with continued deformation. This behavior arises from structural heterogeneity, where nanoscale precipitates interact with dislocations and limit their motion during continued loading, leading to strain hardening. In addition, the serrated features observed below ~\u0026thinsp;5% strain are attributed to shear deformation within amorphous regions. SEM images of the deformed surface reveal well-developed slip bands extending over macroscopic regions, accompanied by localized shear features (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). Shear deformation is initially observed within the amorphous regions, as evidenced by the serrated features observed in the early stage of the bending stress\u0026ndash;strain curve. As shear bands propagate, they are impeded by crystalline boundaries and precipitates, leading to dislocation generation. These dislocations migrate to form slip within the crystalline domains, while being partially pinned by embedded precipitates, contributing to strain hardening (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). As a result, localized shear is suppressed and distributed into multiple shear bands, enabling sustained plastic deformation and enhanced ductility, as observed in the SEM image. The combined thermoelectric and mechanical performance is summarized in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee, where AM60 shows high \u003cem\u003eZT\u003c/em\u003e and bending ductility compared with previously reported Ag\u003csub\u003e2\u003c/sub\u003eS-based materials \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn summary, the thermoelectric performance of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e is governed by the interplay between carrier transport and phonon scattering, both controlled by the amorphous\u0026ndash;crystalline phase fraction. This structural tuning enables simultaneous optimization of electrical and thermal transport properties. Importantly, the phase fraction governs the carrier concentration, enabling effective electronic tuning without additional doping. These results show that improved thermoelectric performance is achieved not by maximizing individual transport parameters, but by approaching an optimal balance between them through structural control. Furthermore, the heterogeneous structure supports cooperative deformation mechanisms, allowing high ductility to be retained alongside enhanced thermoelectric performance. Overall, phase-fraction engineering of amorphous\u0026ndash;crystalline heterostructures provides a design strategy for developing high-performance, mechanically compliant thermoelectric materials. This approach offers broad applicability to other disordered or metastable systems where competing transport and mechanical properties must be optimized concurrently.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eSynthesis of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots\u003c/h2\u003e \u003cp\u003eHigh-purity Ag (99.999%), S (99.99%), and Te (99.99%) were weighed to the desired atomic ratio and sealed in carbon-coated quartz tube under vacuum. The sealed materials were heat-treated at 1273 K for 12 h. Subsequently, the samples were annealed at 823 K for 24 h and then at 393 K for 10 h. The heating and cooling rates for all processes were fixed at 3 K min\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. The low-temperature annealing at 393 K was selected based on the Ag\u0026ndash;S and Ag\u0026ndash;Te phase diagrams, which indicate that monoclinic phases can form at low temperatures. The synthesized ingots were cut and polished to measure their properties.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eDensity functional theory calculation of AgSTe ingots\u003c/h3\u003e\n\u003cp\u003eAll density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) with the projector-augmented wave (PAW) method \u003csup\u003e\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e, \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e. Structural relaxations were carried out using the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) \u003csup\u003e\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e, while electronic structure calculations were performed using the meta-GGA modified Becke-Johnson (MBJ) potential \u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e. The plane-wave energy cutoff was set to 520 eV. The convergence criteria for electronic self-consistency were set to 1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV for structural relaxation and 1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e eV for electronic structure calculations. Atomic positions and lattice parameters were fully relaxed until the Hellmann-Feynman forces were less than 0.01 eV \u0026Aring;⁻\u0026sup1; for unit-cell models and 0.03 eV \u0026Aring;⁻\u003csup\u003e1\u003c/sup\u003e for supercell models. Brillouin zone sampling was performed using Monkhorst-Pack k-point meshes with a reciprocal-space density of 100 \u0026Aring;\u003csup\u003e-\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, generated using pymatgen \u003csup\u003e\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. A 2 \u0026times; 2 \u0026times; 2 supercell (96 atoms) based on monoclinic Ag\u003csub\u003e2\u003c/sub\u003eS was constructed using the special quasi-random structure (SQS) \u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e approach to model the Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e solid solution. The amorphous structure was generated by melt-quenching the optimized SQS model using machine-learning molecular dynamics based on CHGNet \u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e. The system was melted at 2200 K and subsequently quenched to 300 K with a cooling rate of 10 K ps\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. The quenched amorphous structure was further relaxed using DFT to obtain the final atomic configuration.\u003c/p\u003e\n\u003ch3\u003eThermoelectric Characterization of AgSTe ingots\u003c/h3\u003e\n\u003cp\u003eX-ray diffraction (XRD) analysis was performed on ingots for the phase characterization (Rigaku, SmartLab XE, Japan). The amorphous and crystalline fractions were determined by fitting the XRD patterns using a combination of sharp crystalline peaks and a broad amorphous background and evaluating their respective integrated areas. Microstructure was examined using field emission scanning electron microscope (FE-SEM, HITACHI, SU-6600, Japan) and field emission transmission electron microscope (FE-TEM, JEOL, JEM-F200, Japan). \u003cem\u003eσ\u003c/em\u003e and \u003cem\u003eS\u003c/em\u003e were measured by four-probe method based thermoelectric measurement system (NETZSCH, SBA-458, Germany) from 300 to 673 K. Carrier concentration (\u003cem\u003en\u003c/em\u003e) and mobility (\u003cem\u003e\u0026micro;\u003c/em\u003e) was confirmed by Hall effect measurement (Ecopia, AHT55T3, South Korea). Based on the measured n, \u0026micro; was calculated using the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sigma\\:=ne\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e. Thermal diffusivity (\u003cem\u003eD\u003c/em\u003e) was measured by the laser flash method (Netzsch, LFA 457, Germany). The specific heat (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e) was calculated by the Dulong-Petit law (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{P}=3nR/M\\)\u003c/span\u003e\u003c/span\u003e, where n, R, and M are number of atoms per formula unit, the gas constant, and molar mass of the compound, respectively). Density(\u003cem\u003eρ\u003c/em\u003e) of the sample was measured by Archimedes method. Total thermal conductivity was calculated from the measured data \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(\\kappa\\:=\\rho\\:{C}_{P}D)\\)\u003c/span\u003e\u003c/span\u003e. Dimensionless figure of merit(\u003cem\u003eZT\u003c/em\u003e) was calculated based on the measured thermoelectric properties (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:ZT={S}^{2}\\sigma\\:T/\\kappa\\:\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eMechanical Characterization of Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e ingots\u003c/h2\u003e \u003cp\u003eThe Vickers hardness of the samples was measured using a micro-Vickers hardness tester (HM-200, Mitutoyo, Japan). A load of 0.05 kgf (HV0.05) was applied using a diamond pyramidal indenter. The indentations were made on the prepared surface of the samples, and the hardness values were calculated from the diagonal lengths of the indentation marks. Multiple indentations were performed at different locations, and the average hardness value was reported. Three-point bending tests were conducted using a universal testing machine (Model 5982, Instron, USA). Rectangular specimens with dimensions of 1.5 \u0026times; 3 \u0026times; 13.5 mm\u003csup\u003e3\u003c/sup\u003e were tested at a loading rate of 0.5 mm min\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e\u003cp\u003e\u003cstrong\u003eJ. M. Park\u003c/strong\u003e contributed to conceptualization, methodology, investigation, formal analysis, visualization, and writing-original draft. \u003cstrong\u003eJ. M. Lee\u003c/strong\u003e contributed to methodology, investigation, formal analysis, and visualization. \u003cstrong\u003eS.-H. Jung\u003c/strong\u003e and \u003cstrong\u003eS. Jo\u003c/strong\u003e contributed to investigation. \u003cstrong\u003eL. B. Vu\u003c/strong\u003e and \u003cstrong\u003eH. W. Kim\u003c/strong\u003e contributed to visualization. \u003cstrong\u003eH. Kim\u003c/strong\u003e and \u003cstrong\u003eS. B. Cho\u003c/strong\u003e contributed to conceptualization.\u003cstrong\u003eX.Shi\u003c/strong\u003e contributed to writing \u0026amp; review manuscript. \u003cstrong\u003eK.-I. Park\u003c/strong\u003e and \u003cstrong\u003eW. H. Shin\u003c/strong\u003e contributed to supervision and writing-review \u0026amp; editing. \u003cstrong\u003eK. T. Kim\u003c/strong\u003e contributed to supervision, writing-review \u0026amp; editing, funding acquisition, project administration, and resources.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eJ. M. Park and J. M. Lee contributed equally to this work.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eK.-I. Park, W. H. Shin, and K. T. Kim are corresponding authors.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e \u003cp\u003eThis work was financially supported by National Research Foundation of Korea(NRF) grant funded by the Korea government (RS-2022-NR068194 and RS-2024-00448499).\u003c/p\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eThe authors declare that all data supporting the findings of this study are available within the article and its Supplementary Information files or from the corresponding author.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eParida K, Bark H, Lee PS (2021) Emerging Thermal Technology Enabled Augmented Reality. Adv Funct Mater 31:2007952\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCheng R et al (2024) Unraveling electronic origins for boosting thermoelectric performance of p-type (Bi,Sb)\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e. 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Nat Mach Intell 5:1031\u0026ndash;1041\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Amorphous-crystalline heterogeneity, Thermoelectric materials, Silver Chalcogenides, mechanical ductility","lastPublishedDoi":"10.21203/rs.3.rs-9531103/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9531103/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDuctile thermoelectric materials are key to enabling mechanically reliable, self-powered wearable electronics; however, achieving high thermoelectric performance near room temperature without sacrificing mechanical flexibility remains a persistent challenge. Silver chalcogenides have attracted considerable interest due to their intrinsic ductility. However, their propensity for amorphous-crystalline transformation introduces structural heterogeneity whose impact on transport properties remains unclear. Here, we demonstrate that amorphous-crystalline heterogeneity serves as an effective structural parameter to decouple charge and heat transport in Ag\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e0.4\u003c/sub\u003eTe\u003csub\u003e0.6\u003c/sub\u003e by integrating density functional theory calculations with the controlled synthesis of materials featuring tunable phase fractions. We show that decreasing the amorphous fraction reduces carrier concentration while enhancing carrier mobility, resulting in compensated electrical transport behavior. In parallel, the total thermal conductivity decreases primarily due to suppression of the electronic contribution, while the lattice thermal conductivity remains below the Cahill-Pohl minimum. As a result, an optimized composition with ~\u0026thinsp;60% amorphous content achieves a room-temperature \u003cem\u003eZT\u003c/em\u003e of ~\u0026thinsp;0.47 while maintaining a high bending strain exceeding 22%. These findings establish amorphous-crystalline heterogeneity as a design strategy for simultaneously controlling transport properties and mechanical compliance, offering a pathway toward high-performance ductile thermoelectric materials.\u003c/p\u003e","manuscriptTitle":"Tuning amorphous-crystalline heterogeneity enables simultaneous optimization of thermoelectric performance and ductility in silver chalcogenides","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-05-05 18:36:24","doi":"10.21203/rs.3.rs-9531103/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"153d989f-744e-4f03-a6c7-ad2382f7ecc7","owner":[],"postedDate":"May 5th, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Reject before peer review","date":"2026-05-06T05:21:01+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":67030172,"name":"Physical sciences/Energy science and technology/Thermoelectric devices and materials"},{"id":67030173,"name":"Physical sciences/Materials science/Materials for energy and catalysis/Thermoelectrics"}],"tags":[],"updatedAt":"2026-05-06T05:25:25+00:00","versionOfRecord":[],"versionCreatedAt":"2026-05-05 18:36:24","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9531103","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9531103","identity":"rs-9531103","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}