Ductile Mg-Te-Pb Thermoelectric Materials with Ultralow Lattice Thermal Conductivity Predicted by a Deep Learning Potential Model

Ductile Mg-Te-Pb Thermoelectric Materials with Ultralow Lattice Thermal Conductivity Predicted by a Deep Learning Potential Model | 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 Ductile Mg-Te-Pb Thermoelectric Materials with Ultralow Lattice Thermal Conductivity Predicted by a Deep Learning Potential Model Xin-Xuan Wang, Zhen-Shuai Lei, Wen-Juan Li, Xiao-Bin Feng, Gang Chen, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9154062/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Inorganic thermoelectric materials with excellent thermoelectric performance are often brittle. In this work, we introduce functional units into deep learning molecular dynamics-accelerated crystal structure prediction to develop novel functional materials exhibiting both outstanding thermoelectric and mechanical properties. We selected the elements Mg, Te, Pb, and Bi, which are prone to form materials with superior thermoelectric and mechanical performance. A deep learning potential was iteratively trained to accelerate the energy evaluation during structure prediction. Subsequently, the [XY 6 ] functional units were introduced to guide the discovery of novel crystals. Following stability screening, we identified three novel materials that exhibit both outstanding thermoelectric and mechanical performance: I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb. I-Mg 2 Te 3 Pb possesses an ultralow lattice thermal conductivity of 0.065 W/mK, while II-Mg 2 Te 3 Pb achieves a remarkably high Seebeck coefficient of 767 µV/K. All three materials can withstand shear strains exceeding 60% without significant structural failure. The enhancement in thermoelectric performance is attributed to the [PbTe 6 ] units significantly suppressing lattice thermal conductivity, while the improvement in mechanical properties results from the ordered arrangement of [PbTe 6 ] and [MgTe 6 ] units and the “catch-bond” mechanism, which introduces additional potential slip systems. These findings propose a new pathway for developing materials that integrate excellent thermoelectric and mechanical properties. Physical sciences/Materials science Physical sciences/Physics Ternary thermoelectric materials Thermoelectric properties Mechanical properties Crystal structure prediction Deep learning molecular dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1 INTRODUCTION Thermoelectric (TE) materials are highly promising for clean energy conversion, as they can harvest waste heat and convert it into electricity via the Seebeck effect, and enable solid-state cooling through the Peltier effect. Consequently, TE materials hold significant potential in aerospace, industry, microelectronics, environmental monitoring, and healthcare ( 1 – 2 ). The energy conversion efficiency of TE materials is primarily determined by their ZT value, defined as ZT = S 2 σT /( κ L + κ e ), where S , σ , κ L , κ e , and T represent the Seebeck coefficient, electrical conductivity, lattice thermal conductivity, electronic thermal conductivity, and absolute temperature, respectively ( 3 – 4 ). The strong coupling among these transport parameters critically influences the TE performance ( 5 ). Consequently, extensive research has focused on decoupling or optimally balancing these parameters to enhance the heat-to-electricity conversion efficiency of TE materials. When considering practical applications, the mechanical properties of TE materials emerge as another critical performance metric. TE devices often operate under complex thermo-mechanical-electrical multiphysics conditions, where thermal stresses, vibrations, and mechanical shocks can readily induce stress concentration, leading to crack initiation and ultimately fracture failure. Therefore, while optimizing their TE conversion efficiency, it is equally crucial to consider their processability for device fabrication and long-term operational stability. Under these considerations, the development of novel TE materials that simultaneously possess superior TE properties and reliable mechanical performance has become a critical scientific challenge in the field. The crystal structure prediction (CSP) method offers a promising approach to addressing the challenges in developing novel TE materials, having demonstrated remarkable successes in fields such as superconductivity and geophysics. For instance, Duan et al. ( 6 ) employed the USPEX method to predict an H 3 S superconductor with Im- 3 m symmetry, formed from H 2 S-H 2 compounds, which exhibits a superconducting critical temperature ( T c) of up to 191 K at 200 GPa. This prediction was subsequently confirmed by high-pressure experiments conducted by Drozdov et al. ( 7 ), marking a breakthrough in the fundamental research of conventional superconductors. Similarly, Shao et al. ( 8 ) used the CALYPSO method to identify two high-pressure candidate crystal structures of the hydrous mineral MgSiO 4 H 2 . Subsequent experimental studies further demonstrated that its solid solution with AlOOH remains stable over a broad range of temperatures and pressures, providing crucial insights into the circulation and storage of water in Earth’s interior and super-Earth exoplanets. Therefore, compared to the traditional experience-guided paradigm for materials exploration, CSP offers shorter development cycles, lower costs, higher exploration efficiency, and greater success rates. These advantages of CSP closely match the research objective focused on novel TE compounds that exhibit superior properties. The fundamental principle of CSP is to systematically explore the potential energy surface (PES) for a given chemical composition and identify the most stable candidate crystal structures based on the energy minimization criterion. This approach avoids the high randomness inherent in traditional trial-and-error methods, making rational material design possible. CSP typically involves two core components: first, sampling algorithms for exploring the PES, such as random search ( 9 ), particle swarm optimization ( 10 ), hybrid algorithms ( 11 ), genetic algorithms ( 12 ), and adaptive genetic algorithms ( 13 ); second, energy evaluation methods, primarily molecular dynamics (MD) ( 14 ) and density functional theory (DFT) ( 15 ). The effectiveness of the sampling algorithm directly determines the success rate in locating the global minimum on the PES, while the choice of energy evaluation method governs both the accuracy of the PES and the overall computational efficiency of the prediction workflow. The latter directly influences the feasibility of the entire CSP endeavor. Specifically, MD-based energy evaluations offer high computational speed but limited accuracy, whereas DFT provides high accuracy at the expense of extremely high computational cost. Consequently, achieving an optimal balance between accuracy and efficiency remains a significant obstacle that currently hinders the broader application of CSP. In recent years, the development of machine learning potentials (MLPs) has provided an effective solution for accelerating CSP ( 16 – 19 ). MLPs trained on DFT data can achieve accuracy levels comparable to ab initio (AI) MD while improving computational efficiency by several orders of magnitude, thereby drastically reducing computational cost ( 20 ). Consequently, MLP-based PES models have been widely adopted in CSP tasks across diverse material systems. For example, Tong et al. ( 21 ) combined the Gaussian approximation potential (GAP) ( 22 ) with the particle swarm optimization-based CALYPSO method to systematically predict allotropes of boron. Hong et al. ( 23 ) utilized neural network potential (NNP) ( 24 ) integrated with the genetic algorithm-based USPEX package to accurately predict ground-state structures of several compounds, including Ba 2 AgSi 3 , Mg 2 SiO 4 , LiAlCl 4 , and InTe 2 O 5 F, showing excellent agreement with experimental results. Moreover, Wang et al. ( 25 ) coupled deep learning potential (DP) MD ( 26 ) with CALYPSO to successfully reproduce the stable phases of the Mg-Al binary alloy and discovered a new superhydride Li 2 La 2 H 23 with Cmcm symmetry in the Li-La-H ternary system. Notably, their approach reduced computational cost by an order of magnitude compared to conventional DFT calculations. These achievements demonstrate the significant potential of MLP-assisted CSP in enhancing the efficiency of new material development. Despite the remarkable success of MLPs across various domains, their application to TE materials remains in its early stages. Against this backdrop, this work aims to apply the DP model to CSP and property quantification in the Mg-Te-Pb-Bi quaternary TE system. This elemental system was selected based on the following considerations: Firstly, Te, Pb, and Bi are all highly promising candidates for forming high-performance TE materials. For instance, dense dislocation arrays in Bi 2 Te 3 -based room-temperature TE materials significantly reduce lattice thermal conductivity ( κ L ), achieving a ZT of 1.86 at 300 K ( 27 ). PbTe achieves a ZT as high as 2.0 through band engineering strategies such as MgTe doping ( 28 ). Additionally, a range of traditional TE materials, such as PbSe, PbS, SnTe, GeTe, InTe, Cu 2 Te, and BiCuSeO, all exhibit good TE performance. Secondly, Mg-containing materials like Mg 3 Bi 2 , Mg 3 Sb 2 , and MgTe demonstrate favorable plasticity, with the former two also possessing excellent TE properties( 29 – 32 ). It should be noted that InTe also displays good plasticity( 33 ). In addition, the large atomic mass contrast between Mg and the heavier elements (Te, Pb, Bi) is expected to enhance lattice anharmonicity, thereby further reducing κ L . Most importantly, PbTe and Bi 2 Te 3 crystal structures possess six-coordinated resonant bonding ( 34 ). Taking rock-salt structured PbTe as an example, each Pb-Te octahedral unit contains six covalent bonds with each atom contributing three valence electrons on average, resulting in the random occupation of electrons over available covalent bonding positions. This situation creates resonance or hybridization between different electronic configurations, effectively scattering phonons and leading to low κ L ( 35 – 36 ). Furthermore, we are also motivated to explore whether this six-coordinated structural unit harbors additional potential for enhancing mechanical properties. Consequently, we intentionally introduced the [XY 6 ] units as a functional building block for material design during the CSP process in this work, aiming to obtain TE materials with both outstanding TE conversion efficiency and superior mechanical performance. This study employs the DP method to construct a universal interatomic potential for the Mg-Te-Pb-Bi quaternary system, which is integrated with a genetic algorithm to accelerate CSP for quaternary TE material systems. The objectives are to discover novel TE materials that simultaneously exhibit superior TE and mechanical properties, as well as new physical characteristics distinct from those observed in binary systems. The subsequent chapters are organized as follows: Section 2 will detail the construction of the DP model and the specific procedures and parameters used in the accelerated CSP workflow. Section 3 will discuss the fundamental physical properties, TE transport performance, and mechanical behavior of the predicted new materials. The final section will summarize the key findings of this work. 2 THEORETICAL CALCULATIONS The DP-accelerated CSP workflow for the Mg-Te-Pb-Bi system consists of four stages: structure sampling, model training, model iteration, and final CSP, as illustrated in Fig. 1 . In Stage 1, a total of 27 structures—comprising elemental phases, binary compounds, and ternary compounds of Mg, Te, Pb, and Bi (see Supporting Information Table S1 ) are selected, all representing known structures at ambient or low pressures (below 20 GPa). The chosen structures are then subjected to perturbation deformation using the DPGEN ( 37 ) based on the DP method, followed by short AIMD simulations to relax the systems. During these simulations, data including energies, atomic forces, atomic positions, and virial tensors are collected. In stage 2, the DP model is constructed using the DeePMD-kit ( 26 , 38 – 39 ). The model generated at this stage is preliminary and must be refined in Stage 3, where the genetic algorithm-based USPEX software serves as a configuration sampler to improve the DP model. Specifically, the DP potential generated in Stage 2 is used to accelerate the generation of variable-composition structures for the ternary and quaternary systems composed of Mg, Te, Pb, and Bi. These structures are then subjected to DFT single-point energy calculations, and the resulting data are used to update and refine the DP model. The iterative loop between Stages 2 and 3 is performed three times: In the first iteration, the four ternary subsystems (Mg-Te-Pb, Mg-Te-Bi, Mg-Pb-Bi, and Te-Pb-Bi) formed by Mg, Te, Pb, and Bi are considered. All obtained structures are used to update and train the second-generation DP model. This step aims to extend the DP model, originally trained on binary compounds, to ternary systems through a progressive refinement strategy, thereby avoiding the generation of highly unreasonable structures during prediction. In the second iteration, the updated DP model is used to generate variable-composition structures of the Mg-Te-Pb-Bi quaternary system. Similarly, all resulting structures are used to update and train the third-generation DP model, extending its applicability from ternary to quaternary compositions. In the third iteration, the refined DP model is used to generate a comprehensive set of variable-composition structures for the Mg-Te-Pb-Bi quaternary system through large-scale sampling. Similarly, all newly generated structures are used to update and train the fourth-generation DP model, further improving its completeness and reliability. In the final stage of the entire workflow, the refined DP model is employed for ultimate CSP of variable-composition systems composed of Mg, Te, Pb, and Bi. During the prediction process, resonant bonding units are introduced to derive novel TE materials incorporating such bonding features. The predicted structures are subsequently screened according to the following criteria: first, they must satisfy mechanical, dynamical, and thermodynamic stability; second, they should be narrow-bandgap semiconductors; and finally, they must exhibit both excellent TE performance and reliable mechanical properties. Subsequently, the computational tools and parameters employed in each stage are detailed. In this work, all DFT calculations, including geometry optimizations, DPGEN-based perturbative sampling, and the iterative refinement of the DP model, were carried out using the VASP code ( 40 – 41 ). The exchange-correlation interaction was described using the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form ( 42 – 43 ). The interaction between core and valence electrons was treated using the projector augmented-wave (PAW) method ( 44 ). For all structures, the plane-wave cutoff energy was set to 500 eV, and the energy convergence criterion was 1 × 10 − 5 eV. The k -point spacing in the Brillouin zone was set to a minimum of 0.3 Å −1 , and the force on each atom in the unit cell was kept below 0.01 eV/Å. In DPGEN, 27 initial structures were supercell-expanded to ensure that each contained at least 30 atoms. The cell volume and atomic positions were then scaled 0.8–1.2 times in 0.05 increments. AIMD simulations were then performed on all perturbed structures at 300 K with a 1 fs time step for 10 steps. After all AIMD runs were completed, some non-converged structures were discarded, yielding a total of up to 252,000 configurations as the training data for the initial DP potential. During the DP model fitting process, the training and test datasets are randomly split in a 9:1 ratio. The model employed three hidden layers, with an embedding network of 25, 50, 100, and a fitting network of 240, 240, 240, enabling more effective separation of different data types. A cutoff radius of 6 Å was used, and the initial learning rate was set to 1×10 − 3 , decaying exponentially every 10,000 steps until it reached 3.51×10 − 8 at the end of training. To ensure sufficient fitting accuracy and prevent overfitting, the total number of training steps was set to 2 million. In USPEX-based predictions of ternary, quaternary, and broad-composition quaternary systems, structural generation was performed for 20 generations each. The initial generation produced 200, 400, and 1000 structures, respectively, with 150, 300, and 500 new structures generated in each generation thereafter. Over the entire iterative refinement process, a total of 30,663 new structures were generated, and their DFT data were used to train the DP model. In the final variable-composition CSP for Mg, Te, Pb, and Bi, the elemental ratios of generated structures were constrained to exclude unreasonable compositions (e.g., ratios exceeding 10:1). Each generation produced 200 structures, with no preset limit on the number of generations, and the search continued until convergence. Figure 1 outlines the workflow of this work. Figure 1 (a) presents the rationale for selecting the four elements: Mg, Te, Pb, and Bi, and Fig. 1 (b) compares the DP model predictions with DFT-calculated data. As shown, the predicted energies and atomic forces agree closely with the DFT benchmarks, with the vast majority of data points evenly distributed along the y = x line, indicating excellent predictive performance of the DP model. Quantitative analysis further reveals root-mean-square errors (RMSEs) of 0.0295 eV/atom for energy and 0.150 eV/Å for atomic forces lower than those reported for DPMD in most other systems ( 45 ). This result demonstrates high model fitting accuracy, highlighting its strong generalization capability. Figure 1 (c) illustrates the compositional sampling space for quaternary systems during the iterative process, where colors ranging from blue to red indicate increasing formation enthalpy. The sampling points are uniformly distributed and densely packed, demonstrating broad coverage of the composition space and suggesting that the resulting DP model possesses good extrapolation capability. Figure 1 (d) is a schematic diagram of the predicted crystal structure after the active introduction of [XY 6 ] functional units. 3 RESULTS AND DISCUSSION 3.1 Crystal Structures and Intrinsic Properties An extensive DP-accelerated crystal structure search across binary to quaternary systems composed of Mg, Te, Pb, and Bi, not only reproduces known stable phases such as PbTe, Bi 2 Te 3 , and MgTe, but also reveals three new hexagonal structures in the Mg-Te-Pb ternary system: two polymorphs of Mg 2 Te 3 Pb and one MgTe 2 Pb phase. The two Mg 2 Te 3 Pb components crystallize in the P 3 m 1 and P -6 m 2 space groups, respectively, and are denoted as I-Mg 2 Te 3 Pb and II-Mg 2 Te 3 Pb for clarity. MgTe 2 Pb crystallizes in the P -6 m 2 space group. Their lattice parameters are as follows: I- Mg 2 Te 3 Pb with a = b = 4.35 Å, c = 10.76 Å; II-Mg 2 Te 3 Pb with a = b = 4.31 Å, c = 11.06 Å; MgTe 2 Pb with a = b = 4.35 Å, c = 15.16 Å (detailed parameters such as atomic positions are given in Table S2 of the Supporting Information). Figures 2 (a)-(c) respectively show the crystal structures and the electron localization function (ELF) on the (1100) plane for I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb, respectively. In I-Mg 2 Te 3 Pb, Pb and Mg atoms act as symmetry centers and each forms a six-coordinate [PbTe 6 ] and [MgTe 6 ] unit with Te atoms, which aligns with our design objective of incorporating [XY 6 ] functional units (where X = Pb/Mg and Y = Te). These [XTe 6 ] units connect to form Pb-Te and Mg-Te layers, resulting in a stacking sequence along the z -direction consisting of one Pb-Te layer sandwiched between two Mg-Te layers. In II-Mg 2 Te 3 Pb, the [MgTe 6 ] units are identical to those in I-Mg 2 Te 3 Pb, but the Te atoms in the [PbTe 6 ] units deviate from the ideal symmetric positions, forming distorted six-coordinate polyhedra. These distorted units arrange into Pb-Te layers, ultimately establishing the same stacking sequence along the z -direction as in I-Mg 2 Te 3 Pb. The crystal structure of MgTe 2 Pb is structurally similar to that of II-Mg 2 Te 3 Pb, with both featuring stacked layers of [MgTe 6 ] units and distorted [PbTe 6 ] units. The only difference lies in the stacking sequence along the z -direction, which comprises alternating single Pb-Te and single Mg-Te layers. The ELF distribution reveals that Mg-Te interactions in all three structures are predominantly ionic, while Pb-Te pairs exhibit discernible covalent character. In contrast, Mg and Pb atoms are well separated, with no chemical bond formed between them. Among them, the [PbTe 6 ] units act as resonant bonding units in all three structures, suggesting that these materials may exhibit low κ L . Although the [MgTe 6 ] units form a structure similar to that of the resonant [PbTe 6 ] units, the charge on the Mg atoms is almost entirely transferred to Te, and thus they are not typical resonant bonding units. To assess the thermodynamic stability of these three materials, we calculated their formation enthalpies and constructed the ternary convex hull diagram based on all known compounds that can be formed from Mg, Te, and Pb, as shown in Fig. 2 (d). The formation enthalpies of I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb are all negative, with values of -0.6714 eV/atom, -0.6539 eV/atom, and − 0.5638 eV/atom, respectively. Among them, I-Mg 2 Te 3 Pb exhibits the lowest formation enthalpy, suggesting it is likely the ground-state structure in this system, whereas the other two are metastable. Moreover, among all known phases in the Mg-Te-Pb system, only MgTe (-0.881 eV/atom) has a lower formation enthalpy than I-Mg 2 Te 3 Pb and II-Mg 2 Te 3 Pb. This result indicates that the synthesis of both I-Mg 2 Te 3 Pb and II-Mg 2 Te 3 Pb is experimentally more feasible than that of MgTe 2 Pb. Table 1 Elastic constants C , bulk modulus B , Young’s modulus E , shear modulus G , Poisson’s ratio ν , and B / G for I-Mg 2 Te 3 Pb, II- Mg 2 Te 3 Pb, and MgTe 2 Pb (units: GPa) Phase C 11 C 12 C 13 C 33 C 44 C 66 B E G ν B/G I-Mg 2 Te 3 Pb 75.857 27.842 31.742 77.997 29.890 24.008 45.787 64.355 25.422 0.266 1.80 II-Mg 2 Te 3 Pb 61.973 33.837 25.202 90.834 20.471 14.068 42.328 49.510 18.968 0.305 2.23 MgTe 2 Pb 60.479 30.485 26.425 84.696 22.035 14.997 41.077 50.446 19.472 0.295 2.11 In addition, we have also calculated the elastic properties of the three materials, as listed in Table 1 . All three compounds belong to the hexagonal crystal system and exhibit similar values for their six independent elastic constants. Among them, I-Mg 2 Te 3 Pb shows larger elastic moduli, indicating a stronger resistance to elastic deformation compared to the other two. However, its Pugh’s ratio ( 46 ) ( B / G ) is lower, suggesting that its capacity for plastic deformation may be inferior to that of the other two materials. Moreover, mechanical stability can also be evaluated through the elastic stability criteria. For the hexagonal crystal system, the elastic stability conditions ( 47 ) are: C 11 > | C 12 |, 2 0. It can be inferred from the calculated elastic constants that all three materials, I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb, satisfy these conditions, further supporting their potential for stable existence. 3.2 Electrical Transport Properties To investigate the intrinsic physical properties of the Mg-Te-Pb compounds, this work systematically calculates and analyzes the electronic band structures and density of states (DOS) for I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb. As shown in Figs. 3 (a)-(c), the valence band maximum (VBM) and conduction band minimum (CBM) of all three compounds are located at different high-symmetry points, indicating that they are indirect-bandgap semiconductors. Specifically, for both I-Mg 2 Te 3 Pb and II-Mg 2 Te 3 Pb, the VBM is at the Γ point, and the CBM is at the L point, whereas for MgTe 2 Pb, the VBM is at the Γ point and the CBM is at the H point. The band gaps of the three compounds are 0.17 eV for I-Mg 2 Te 3 Pb, 0.46 eV for II-Mg 2 Te 3 Pb, and 0.14 eV for MgTe 2 Pb, all exhibiting pronounced narrow bandgap characteristics, which are favorable for achieving high TE performance. DOS analysis reveals that the VBM is primarily contributed by the Te p orbitals, whereas the CBM is mainly contributed by the Pb p orbitals. This band structure feature indicates that Te plays a dominant role in the valence band, while Pb makes a significant contribution to the formation of the conduction band. Subsequently, we employed the BoltzTraP2 code ( 48 ), which is based on the Boltzmann transport equation (BTE), to calculate the Seebeck coefficient S for the three materials. Figures 3 (d)-(f) show the temperature dependence of S for I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb under both p -type and n -type doping, respectively. Within the temperature ranges where their respective crystal structures remain stable (determined by MD high-temperature relaxation), the absolute Seebeck coefficient, ∣ S ∣, for all three materials gradually decrease with increasing temperature and exhibit distinct doping-type dependencies: for I-Mg 2 Te 3 Pb, the ∣ S ∣ under n -type doping is higher than that under p -type doping; for II-Mg 2 Te 3 Pb, the ∣ S ∣ values for p - and n -type doping are comparable; and for MgTe 2 Pb, the ∣ S ∣ under p -type doping is higher than that under n -type doping. At 300 K, the maximum S values are + 323 µ V/K ( p -type) and − 341 µ V/K ( n -type) for I-Mg 2 Te 3 Pb, + 765 µ V/K ( p -type) and − 766 µ V/K ( n -type) for II-Mg 2 Te 3 Pb, and + 302 µ V/K ( p -type) and − 298 µ V/K ( n -type) for MgTe 2 Pb. Notably, II-Mg 2 Te 3 Pb exhibits a significantly larger S compared with the other two compounds, indicating stronger energy dependence of carrier transport and thus superior TE response characteristics. Figures 3 (g)-(i) show the temperature dependence of the electrical conductivity divided by the relaxation time ( σ / τ ) for the three materials. In the temperature range from room temperature to high temperatures, the σ / τ values of all three compounds continuously increase with rising temperature. At 300 K, the σ / τ values under p - and n -type doping are 2.71×10 17 S/(m·s) and 2.92×10 17 S/(m·s) for I-Mg 2 Te 3 Pb, 1.79×10 15 S/(m·s) and 1.84×10 15 S/(m·s) for II-Mg 2 Te 3 Pb, 1.51×10 17 S/(m·s) and 1.60×10 17 S/(m·s) for MgTe 2 Pb, respectively. Notably, I-Mg 2 Te 3 Pb exhibits a significantly higher σ / τ than the other two structures, indicating superior carrier transport capability. The temperature evolution of S and σ / τ demonstrates that all three materials possess excellent electrical transport properties over a broad temperature range, suggesting excellent TE response characteristics. 3.3 Thermal Transport Properties The primary purpose of introducing the resonant bonding functional units was to reduce the lattice thermal conductivity and enhance the TE performance. The most direct way to evaluate the thermal transport properties of these three TE materials is to study their phonon characteristics. Based on the linear response method with the Phonopy software ( 49 ), we calculated the second-order force constants of the three materials and obtained their phonon dispersion curves, as shown in Figs. 4 (a)-(c). It can be seen that no imaginary frequencies appear throughout the entire Brillouin zone for any of the three materials, indicating that each system possesses the ability to spontaneously recover stability upon perturbation and confirming their dynamical stability. In addition, the phonon spectra of all three materials exhibit characteristic features typical of low thermal conductivity systems. Specifically, the acoustic branches are confined to the low-frequency range of 0–2 THz, indicating weak thermal transport capability. Moreover, there is no pronounced bandgap between the acoustic and optical branches, and a large number of flat and densely packed low-frequency optical modes. This suggests strong anharmonic interactions in the system, which can significantly shorten the phonon mean free path and thereby further reduce the κ L . Combined with the phonon DOS analysis, it is found that the acoustic phonons and low-frequency optical phonons in all three materials are primarily contributed by the heavier Te and Pb atoms. The significant mass contrast between the heavy Te/Pb atoms and the light Mg atoms is the main origin of the pronounced band gaps observed in the phonon spectra across different frequency ranges. These band gaps effectively modulate the scattering channels between distinct phonon branches, thereby suppressing phonon transport efficiency. As a result, the combined effects of the heavy constituent atoms and the resulting bandgap-induced scattering synergistically suppress phonon transport, which is directly reflected in the low κ L of all three materials. To obtain the κ L of I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb, the third-order force constants are calculated using the ShengBTE code( 50 ). In the calculations, the cutoff parameters for the three materials are set to -10, -11, and − 12, respectively; the ngrid values are 25 × 25 × 25, 15 × 15 × 15, and 15 × 15 × 15, respectively; and a uniform scale broad value of 0.3 is adopted. Combined with the second-order force constants, the κ L of the three structures-I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb-along different crystallographic directions is obtained, as shown in Figs. 4 (d)-(f). It can be seen that κ L exhibits pronounced anisotropy in all three materials: the values along the y - and x -directions are identical, whereas those along the z -direction differ. Subsequent analysis, therefore, focuses on the x (or y ) and z -directions. At 300 K, the κ L values of I-Mg 2 Te 3 Pb are 0.125 W/(m·K) and 0.065 W/(m·K) along the x - and z -directions, respectively; for II-Mg 2 Te 3 Pb, they are 0.712 W/(m·K) and 0.613 W/(m·K); and for MgTe 2 Pb, they are 0.430 W/(m·K) and 0.779 W/(m·K). The exceptionally low κ L values of all three materials corroborate the previous analysis of their phonon dispersion curves. In fact, a major factor behind this low κ L is the preservation of [PbTe 6 ] resonant bonding units within the crystal structure. The long-range interactions induced by resonant bonding lead to optical phonon softening, strong anharmonic scattering, and a large phase space for three-phonon scattering processes of which make a non-negligible contribution to the reduction of κ L ( 34 ). Moreover, the [PbTe 6 ] resonant bonding units in I-Mg 2 Te 3 Pb adopt a regular octahedral geometry with ideal six-fold coordination, leading to the strongest resonance (or hybridization) effect and consequently the lowest κ L . Ji et al. ( 35 ) identified K 5 CuSb 2 , a known TE material containing the linear triatomic resonant bonds, through high-throughput computations, which exhibits a low κ L of 0.39 W/(m·K). In contrast, the I-Mg 2 Te 3 Pb structure reported in this work achieves an even lower κ L of 0.065 W/(m·K), further underscoring its exceptional potential as a high-performance TE material. 3.4 Mechanical Properties The TE performance determines the efficiency of a material in heat-to-electricity conversion, whereas its mechanical properties directly govern the yield during fabrication and the operational lifetime. As previously mentioned, to enhance the TE performance of the predicted materials, we deliberately introduced the [XY 6 ] functional units. Its effectiveness in improving TE properties—particularly the role of the [PbTe 6 ] unit—has been well demonstrated. However, we also anticipated that it would contribute to significant advantages in mechanical performance. Accordingly, we next calculated the mechanical properties of I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb under deformation loading, with a focus on analyzing the role played by the [XTe 6 ] functional units. We employ the DP model fitted during structure prediction and perform DPMD simulations using the LAMMPS code ( 51 ) to evaluate the materials’ resistance to deformation. To eliminate the effects of surfaces and finite-size artifacts, periodic boundaries are applied in the x -, y -, and z- directions, and energy minimization is performed using the conjugate gradient algorithm. The simulated systems of I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb contain 7,200, 7,200, and 9,600 atoms, respectively. All simulations are carried out in the NPT ensemble with a time step of 0.001 ps. Before deformation, each structure is relaxed for 50 ps to achieve stress equilibrium. Given that the three structures are stacked along the z -axis, shear loading is applied at 300 K along the (0001)/ direction to investigate interlayer slip and failure mechanisms. The deformation process is run for 1000 ps at a strain rate of 0.001 ps⁻¹, with structural relaxation performed every 1 ps to approximate quasi-static loading conditions. The stress-strain responses and corresponding atomic structural evolution of the three materials are shown in Fig. 5 . As seen in Fig. 5 (a), I-Mg 2 Te 3 Pb initially exhibits a brief stress increase with rising strain, followed by a plateau where the stress remains nearly constant. A sudden stress jump then occurs at a shear strain of 0.127, marking the onset of a strengthening stage. As shown in the atomic configuration at a strain of 0.127 in Fig. 5 (d), partial Mg-Te bonds are broken, transforming the original [MgTe 6 ] coordination units into [MgTe 5 ] coordination units. This transformation leads to the stress plateau observed in the stress-strain curve. Subsequently, as the lattice continues to resist deformation, stress begins to rise again. When the strain reaches 0.226, relative slip between Pb-Te polyhedral layers occurs, releasing stress and causing a downward trend in the stress-strain curve; at a strain of 0.360, the same atomic layer slips again along this direction, leading to another stress release. At a strain of 0.488, the Mg-Te polyhedral layer begins to slip and continues sliding until the end of shear loading. Point defects gradually accumulate within the layer during slip, but without causing significant structural damage. From Fig. 5 (b), it is evident that II-Mg 2 Te 3 Pb experiences a brief initial stress rise, followed by a sudden drop at a strain of 0.044. The corresponding configuration in Fig. 5 (e) shows that at this strain, local structures transform [MgTe 6 ] units to five-coordinate [MgTe 5 ], similar to I-Mg 2 Te 3 Pb. Subsequently, the system regains its resistance to deformation, leading to an increase in stress. As the strain increases to 0.220, Pb-Te polyhedral layers begin to slip continuously. Until the strain reaches 0.356, all Pb-Te layers complete their slip, and their arrangement gradually transforms from the initial five-coordination structure into a regular octahedral arrangement. The Mg-Te layers slip at a strain of 0.460. Thereafter, the individual Mg-Te polyhedral layers slip, and by the time the strain reaches 0.640, all slipping has finished, adopting a uniform, co-oriented tilted arrangement. When the strain further increases to 0.752, the crystal structure collapses. From Figs. 5 (c) and (f), it can be seen that the stress of MgTe 2 Pb first undergoes a linear elastic stage followed by an elastoplastic stage as strain increases. At a strain of 0.135, the stress exhibits continuous small-amplitude fluctuations. The corresponding configurations reveal that these fluctuations result from successive slips of Pb-Te polyhedral layers, which complete their slip by a strain of 0.370 and adopt a regular octahedral arrangement. When the strain reaches 0.496, the stress begins to exhibit large-amplitude oscillations caused by the slip of the Mg-Te polyhedral layers. Thereafter, the individual Mg-Te polyhedral layers slip continuously until all have completed their slip at a strain of 0.652, at which point they adopt a uniform right-tilted arrangement identical to that of II-Mg 2 Te 3 Pb. Further increasing the strain to 0.818 leads to structural collapse. These three materials can maintain the integrity of their crystal lattice over a wide strain range by continuously releasing stress through extensive bond breaking, reconstruction, and interlayer slip, thereby exhibiting a certain capacity for plastic deformation under shear. Notably, II-Mg 2 Te 3 Pb and MgTe 2 Pb further display shear-induced ordering of Pb-Te and Mg-Te polyhedral layers, forming standard octahedral coordination structures. The continuous slip in all three materials is closely linked to the presence of [PbTe 6 ] and [MgTe 6 ] octahedral units. Their highly symmetric local structures provide new pathways for interlayer slip, enabling large plastic deformation without relying on conventional dislocation-mediated mechanisms. In essence, within these two types of octahedral building blocks, Mg and Pb atoms transfer strain to each other via Te atoms. Upon significant stress accumulation, dense arrays of Te atoms facilitate bond breaking and reformation, creating “catch bonds”. Moreover, each layer possesses similar structural features, offering abundant channels for stress release, which underpins their observable plastic deformability. We will subsequently elaborate on the development of this mechanism in detail from the perspectives of microstructural evolution and energetics. 3.5 Analysis of the Slip Mechanisms As revealed by the preceding slip analysis, all three materials share a common origin of their mechanical deformation mechanism—the octahedral structural unit [XTe 6 ], where X = Pb/Mg. Based on atomic trajectories, we have plotted a schematic diagram illustrating the microstructural evolution of the [XTe 6 ] unit during the shearing process, as shown in Fig. 6 (a). In the diagram, blue atoms represent Te, whereas yellow atoms represent Pb or Mg. When the Pb/Mg atom at the center of the [XTe 6 ] unit and the Te atoms in the lower layer remain fixed while only the upper-layer Te atoms slide (i.e., single-layer Te slip), the three upper bonds within the [XTe 6 ] unit undergo stretching, breaking, and reformation, enabling continuous slip, whereas the other bonds remain unchanged. The crystal structure after slip is identical to the initial crystal structure. When the central X atom remains stationary, and the Te atoms in both upper and lower layers slide in opposite directions (i.e., double-layer Te slip), two bonds in the [XTe 6 ] unit break and reform, while the other four bonds only exhibit fluctuations in bond length. This process ultimately yields an [XTe 6 ] unit with its apical direction reversed relative to the initial state, involving fewer bond-breaking and reformation events. After a double-layer Te slip occurs, the resulting inverted [XTe 6 ] unit must slide further in the same direction to recover the initial state. This requires breaking and reforming three bonds. Crucially, the bond at the octahedral apex becomes tightly compressed and experiences strong repulsive forces, which block the original slip path. Therefore, when the system encounters such a blocked slip path, and no alternative slip channels are available, the central atom of the reversed [XTe 6 ] unit naturally shifts along a direction within the slip plane that is perpendicular to the original slip direction to release stress. This shift also restores the initial structure, and involves only two bond-breaking and reformation events together with length fluctuations in the other four bonds-identical to the bond evolution observed during the double-layer Te slip process. It should be noted that although all three materials contain [XTe 6 ] units, their structures exhibit certain differences, as previously mentioned. Specifically, I-Mg 2 Te 3 Pb consists of two types of standard octahedral units—[MgTe 6 ] and [PbTe 6 ]—whose orientations are identical to the initial structure shown in Fig. 6 (a). Consequently, its entire slip process strictly follows the two slip mechanisms: single-layer Te slip and double-layer Te slip. Both II-Mg 2 Te 3 Pb and MgTe 2 Pb contain not only standard [MgTe 6 ] octahedra but also reversed [MgTe 6 ] units, as well as distorted [PbTe 6 ] square pyramids, making their behavior considerably more complex. First, layers with standard [MgTe 6 ] arrangements undergo double-layer Te slip, whereas the already reversed [MgTe 6 ] layers remain unchanged due to blocked slip paths and the availability of alternative slip channels. The distorted [PbTe 6 ] units correspond to the saddle-point configuration along the double-layer Te slip pathway, rendering them highly susceptible to slip and transformation into reversed [PbTe 6 ] octahedra. This is precisely why the structures of II-Mg 2 Te 3 Pb and MgTe 2 Pb gradually become more ordered during shear deformation. In summary, the slip mechanisms of the [XTe 6 ] units in all three materials can be simply described as single- /double-layer Te slip. These two slip mechanisms jointly endow the Mg-Te-Pb system with excellent mechanical properties. To further analyze the single- and double-layer Te slip mechanisms in the Mg-Te-Pb system, we calculate the energy barriers for single and double-layer Te slip in I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb. The energy barriers in I-Mg 2 Te 3 Pb, as shown in Figs. 6 (b)-(d), increase in the following order: single-layer Te slip of [MgTe 6 ], single-layer Te slip of [PbTe 6 ], the first half of the double-layer Te slip for both [MgTe 6 ] and [PbTe 6 ], and finally the second, hindered stage of double-layer Te slip. Under ideal conditions, the system undergoes slip sequentially in this order and eventually becomes trapped in the energy valley of double-layer Te slip. Subsequently, under applied strain, it either fails or experiences parallel displacement of the central atom within the [XTe 6 ] unit. In practice, the system first undergoes double-layer Te slip and single-layer Te slip of the [PbTe 6 ] units, and the process ends with simultaneous double-layer Te slip and single-layer Te slip of the [MgTe 6 ] units. The slip of the double Te layer occurs first because its energy barrier is comparable to that of the single Te layer; at finite temperatures, thermal fluctuations can easily overcome this small energy difference. Moreover, since the displacement required for the double Te slip to reach the first energy barrier is relatively small, atomic vibrations at finite temperature are expected to overcome this barrier, enter the corresponding energy minimum, and stabilize there. Some layers in the structure do not participate in the slip process. This is because the first slip event introduces a certain amount of defects, which lowers the slip barrier within the already slipped layers and promotes further slip along the same layers. This leads to an accumulation of defects and eventual mechanical failure. The II-Mg 2 Te 3 Pb and MgTe 2 Pb are very similar, so their slip energy barriers exhibit analogous characteristics, and we discuss them together. It should be noted that the double-layer Te slip condition for [PbTe 6 ] is not satisfied in either structure, so it is not included. First, we note that the lowest energy barrier corresponds to the single-layer Te slip path of the distorted [PbTe 6 ] units. As previously mentioned, this distorted [PbTe 6 ] is equivalent to a half-completed double-layer Te slip, and thus already resides in a metastable state. Consequently, the system inevitably selects this pathway first, enabling the formation of stable inverted resonant-bond units. Once all distorted [PbTe 6 ] octahedra have undergone slip, the system proceeds along the next lowest-energy slip path—namely, slip involving the [MgTe 6 ] layers. Because the double-layer Te slip involves the shortest displacement, all regular [MgTe 6 ] units gradually undergo double-layer Te slip until every microstructural unit in the system transforms into an inverted [XTe 6 ] configuration, reaching an energetically stable state. Beyond this point, further straining would require the system to overcome the extremely high energy barrier associated with the second-stage double-layer Te slip, which is highly improbable. Therefore, the central atoms of the [XTe 6 ] units either undergo in-plane displacement perpendicular to the original slip direction or the structure fails directly. To further elucidate the structural evolution during the slip process in the Mg-Te-Pb compounds, we analyze the local atomic configurations containing Pb-Te resonant bonds and their bond lengths as a function of shear strain, thereby clarifying the dynamic response behavior of chemical bonds under shear loading. Since the single-layer Te and double-layer Te slip deformation mechanisms in the II-Mg 2 Te 3 Pb and MgTe 2 Pb systems are identical to those in I-Mg 2 Te 3 Pb, we present the analysis using I-Mg 2 Te 3 Pb as an example, as shown in Fig. 7 (the analyses for II-Mg 2 Te 3 Pb and MgTe 2 Pb are provided in Supporting Information Figures S1 and S2). The single-layer Te slip process are shown in Figs. 7 (a)-(d). These atomic snapshots correspond to shear strains increasing from 0.220 to 0.245. The red-labeled Te( 1 ), Te( 2 ), and Te( 3 ) atoms belong to the upper layer of the same [PbTe 6 ] structural unit, while the pink-labeled Te( 4 ), Te( 5 ), and Te( 6 ) atoms belong to the upper layer of the subsequent [PbTe 6 ] unit. These snapshots capture the complete sequence of bond breaking between the leading Te atom and its central Pb atom, followed by bond formation between the trailing Te atoms and the Pb atom. At a shear strain of 0.220, the system exhibits a perfect [PbTe 6 ] unit configuration, in which each Pb atom is bonded to three Te atoms. As the strain increases to 0.232, the Pb( 1 )-Te( 1 ) bond is stretched and breaks. Upon further increasing the strain to 0.237, Pb( 1 ) forms a new bond with the subsequent Te( 4 ) atom, while the bonds between Pb( 1 ) and Te( 2 ) as well as Te( 3 ) break simultaneously. At a strain of 0.245, Pb( 1 ) bonds with the following Te( 5 ) and Te( 6 ) atoms. Figures 7 (e)-(i) illustrate the schematic sliding process of a double-layer Te. Similarly, Te( 1 ) and Te( 2 ) atoms, highlighted in red, bond with the central Pb( 1 ) atom, while Te( 3 ) and Te( 4 ) atoms, marked in pink, are located on the upper level of the subsequent left [PbTe 6 ] unit and the lower level of the preceding right [PbTe 6 ] unit, respectively. When the shear strain is between 0.351 and 0.354, the bonds between Pb( 1 ) and Te( 1 ), as well as Pb( 1 ) and Te( 2 ), are stretched and nearly simultaneously broken. Subsequently, due to the rightward shift of the upper layer atoms and the leftward shift of the lower layer atoms, the Te( 3 ) and Te( 4 ) atoms originally located on the left and right sides moved closer to the central Pb( 1 ) atom. At a strain of 0.360, these atoms formed new bonds, creating an [PbTe 6 ] unit oriented in the opposite direction compared to before the slip. The entire process is dominated by the relative slip between the upper and lower layers of Te atoms, ultimately resulting in the “inversion” phenomenon of the [PbTe 6 ] unit. This single-layer Te slip process involves the sequential breaking and reformation of three pairs of bonds, as shown in Figs. 7 (j)-(l), and overall represents a relatively simple single-layer Te slip translation. However, during the double-layer Te slip process, only two Pb-Te bonds are broken (Figs. 7 (m)-(n)), while the remaining bonds exhibit a behavior of first shortening, followed by elongation. In both slip mechanisms, all bond-breaking and bond-reformation processes occur in a discontinuous manner, with each slip step resulting in a relatively stable atomic configuration. This mechanism is known as the “catch-bond” mechanism ( 52 – 53 ), wherein a covalent or ionic bond breaks and is immediately followed by the formation of a new bond at a first-nearest-neighbor site, thereby preserving structural integrity. These deformation mechanisms are closely related to the functional characteristics of the [XTe 6 ] units, whose role can be summarized in the following two aspects: structurally, the [XTe 6 ] unit possesses two closely packed planes on the top and bottom. The ordered stacking along these densely packed planes gives the entire crystal lattice a pronounced layered structure, which introduces new potential slip systems for inorganic TE materials that originally had limited slip paths, thereby increasing stress‑relief pathways; in terms of slip mode, the centrosymmetric nature of the [XTe 6 ] unit perfectly satisfies the conditions for the formation of a “catch-bond” phenomenon. During the shear process in all three materials, the [XTe 6 ] units can sequentially exhibit a “catch” behavior, promoting coordinated slip of all Pb-Te or Mg-Te layers along the shear direction. This effectively releases internal stress while maintaining structural integrity. Thus, the [XTe 6 ] units synergistically enhance the mechanical properties of I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb through both their ordered structural arrangement and the “catch-bond” deformation mode, which strongly confirms our initial hypothesis that the deliberate introduction of the [XTe 6 ] functional units would improve the mechanical performance of the materials. 3.6 TE and Mechanical Property Analysis The above analysis demonstrates that I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb exhibit excellent TE conversion potential coupled with favorable mechanical properties. Figure 8 systematically compares the intrinsic lattice thermal conductivity κ L and B / G of representative binary TE materials reported in recent years at room temperature. Among known materials, α -Ag 2 S shows the lowest κ L of only 0.25 W/(m·K). Additionally, TE materials such as Bi 2 Te 3 , SnTe, PbTe, PbSe, and PbS all exhibit κ L values below 1 W/(m·K), attributed to the presence of resonant bonding. In this work, the predicted I-Mg 2 Te 3 Pb features both resonant bonds and a large atomic mass contrast, resulting in an ultralow average κ L of 0.095 W/(m·K)—62% lower than that of the best-performing α -Ag 2 S. Moreover, II-Mg 2 Te 3 Pb and MgTe 2 Pb also display κ L values below 1 W/(m·K). In terms of mechanical properties, the B / G ratios of I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb all exceed the ductility threshold of 1.75, outperforming traditional inorganic bulk thermoelectric materials such as PbTe, PbSe, PbS, SnTe, GeTe, Cu 2 Te, Bi 2 Te 3 , and SnSe. This indicates greater potential for processing and practical application. However, their ductility remains inferior to that of intrinsically plastic materials such as the typical layered compounds InTe, Cu 2 S, and α -Ag 2 S, as well as the special intermetallic compound Mg 3 Bi 2 . The primary reason is that the ductility of the three Mg-Te-Pb compounds does not originate from the common dislocation slip mechanism found in metals or layered materials, but rather from the “catch-bond” phenomenon induced by the slip of [XTe 6 ] units. This mechanism allows the three materials to theoretically withstand strains exceeding 60% without significant fracture. Although such an ideal scenario is unlikely to be fully realized in practice, the underlying slip mechanisms would still enhance toughness in real-world applications. Overall, the exceptional TE and mechanical performance of these three materials can be attributed to the presence of the [XTe 6 ] structural units. Additionally, we have preliminarily explored the feasibility of synthesizing the three new TE materials via melt processing, magnetron sputtering, and high-pressure approaches (see Supporting Information Figures S3-S5 and corresponding descriptions). Current characterization results reveal indications of potential phase separation. We hypothesize that successful formation of these multi-component compounds will require precise compositional control under strictly anhydrous conditions to facilitate proper lattice formation—an insight that may offer initial guidance for future experimental studies. 4 CONCLUSION Guided by a functional-unit-based materials design strategy and using the functional units, we performed DP-accelerated CSP. During the training of the DP model, four elements—Mg, Te, Pb, and Bi—which readily form compounds with excellent TE and mechanical properties were selected, along with 27 binary and ternary compounds derived from them. The performance of the model is iteratively optimized through crystal structures generated by CSP. In the final prediction stage, the [XY 6 ] TE/mechanical functional units are introduced, leading to the discovery of three novel TE materials: I‑MgTe 2 Pb, II‑Mg 2 Te 3 Pb, and MgTe 2 Pb. All three materials are narrow‑bandgap semiconductors (0.17 eV, 0.46 eV, and 0.14 eV, respectively) and exhibit outstanding TE transport and mechanical performance. Specifically, I-Mg 2 Te 3 Pb exhibits ultralow κ L of 0.125 W/(m·K) along the x -direction and 0.065 W/(m·K) along the z -direction—significantly lower than that of the benchmark TE material PbTe (~ 2.25 W/(m·K)). Moreover, II-Mg 2 Te 3 Pb demonstrates remarkably high Seebeck coefficients of + 765 µV/K under p -type doping and − 766 µV/K under n -type doping, underscoring its superior TE performance. From a mechanical standpoint, I-Mg 2 Te 3 Pb, II-Mg 2 Te 3 Pb, and MgTe 2 Pb can undergo continuous interlayer slip under shear deformation, sustaining shear strains exceeding 60% without significant structural failure. Their ductility originates from both the ordered structural arrangement of the [XTe 6 ] functional units and the “catch-bond” mechanism. Overall, the complete implementation of this functional-unit-based materials design strategy has not only yielded three promising novel TE materials and provided a universal potential model for the Mg–Te–Pb–Bi system, but also provided a fresh alternative to conventional high-throughput computation for the discovery and development of other functional materials. Declarations Author Contributions Xin-Xuan Wang and Zhen-Shuai Lei wrote the main manuscript text and prepared the figures. They also contributed to the methodology, investigation, formal analysis, data curation, and software. Wen-Juan Li supervised the project. Xiao-Bin Feng, Gang Chen, Bo Duan, Guo-Dong Li, and Qing-Jie Zhang acquired funding and provided resources. Peng-Cheng Zhai contributed to the conceptualization. Xiao-Bin Feng performed validation. Guo-Dong Li reviewed and edited the manuscript. All authors reviewed the manuscript. Competing interests All authors declare that they have no conflict of interest. Data availability All data supporting the findings of this study are available within the paper and its Supplementary Information. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 92463309, 92163212, 92463301, and 92363001), and the Natural Science Foundation of Hubei Province of China (No. 2023AFB175). References DiSalvo, F. J., Thermoelectric cooling and power generation. Science 1999, 285 (5428), 703–706. Bell, L. E., Cooling, heating, generating power, and recovering waste heat with thermoelectric systems. Science 2008, 321 (5895), 1457–1461. 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ACS Applied Materials & Interfaces 2019, 11 (34), 31237–31244. Jana, M. K.; Pal, K.; Waghmare, U. V.; Biswas, K., The origin of ultralow thermal conductivity in InTe: lone-pair-induced anharmonic rattling. Angewandte Chemie International Edition 2016, 55 (27), 7792–7796. Feng, Q.; He, J.; Wang, W.; Liu, H., Low Thermal Conductivity in Single Crystalline Mg 3 Bi 2 and Its Thermopower Enhanced by Electron-Phonon Interaction. Advanced Science 2025, 12 (22), 2416518. Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G., Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals. Nature 2014, 508 (7496), 373–377. Yu, J.; Li, T.; Nie, G.; Zhang, B.-P.; Sun, Q., Ultralow lattice thermal conductivity induced high thermoelectric performance in the δ-Cu 2 S monolayer. Nanoscale 2019, 11 (21), 10306–10313. Zhao, X.; Yu, T.; Zhou, B.; Ning, S.; Chen, X.; Qi, N.; Chen, Z., Extremely low lattice thermal conductivity and significantly enhanced near-room-temperature thermoelectric performance in α-Cu 2 Se through the incorporation of porous carbon. ACS Applied Materials & Interfaces 2023, 16 (1), 1333–1341. Zhou, W.-X.; Wu, D.; Xie, G.; Chen, K.-Q.; Zhang, G., α-Ag 2 S: A ductile thermoelectric material with high ZT. ACS Omega 2020, 5 (11), 5796–5804. Li, G.; Aydemir, U.; Duan, B.; Agne, M. T.; Wang, H.; Wood, M.; Zhang, Q.; Zhai, P.; Goddard III, W. A.; Snyder, G. J., Micro-and macromechanical properties of thermoelectric lead chalcogenides. ACS Applied Materials & Interfaces 2017, 9 (46), 40488–40496. Kumar, J.; Tanwar, P.; Paliwal, U.; Joshi, K., Ab initio study of elastic, electronic, and vibrational properties of SnTe and PbTe. Journal of Molecular Modeling 2023, 29 (11), 335. Kagdada, H. L.; Jha, P. K.; Śpiewak, P.; Kurzydłowski, K. J., Structural stability, dynamical stability, thermoelectric properties, and elastic properties of GeTe at high pressure. Physical Review B 2018, 97 (13), 134105. Hasan, S.; Baral, K.; Ching, W.-Y., Total bond order density as a quantum mechanical metric for materials design: Application to chalcogenide crystals. Preprints 2019, 2019060199 . Xiong, Z.; An, X.; Li, Z.; Xiao, T.; Chen, X., Phase transition, electronic, elastic and thermodynamic properties of Bi 2 Te 3 under high pressure. Journal of Alloys and Compounds 2014, 586 , 392–398. Kayadibi, F.; GÜNAY, S.; TAŞSEVEN, Ç., Studying static, dynamic and transport properties of Mg 3 Bi 2 . Acta Physica Polonica A 2015, 128 (3). Li, G.; Aydemir, U.; Wood, M.; Goddard III, W. A.; Zhai, P.; Zhang, Q.; Snyder, G. J., Ideal strength and deformation mechanism in high-efficiency thermoelectric SnSe. Chemistry of Materials 2017, 29 (5), 2382–2389. Liang, Y.; Ahmad, A. S.; Zhao, J.; Song, G.; Zhou, X.; Ji, J.; Zhang, W.; Han, Z.; Liu, J.; Stahl, K., Isosymmetric phase transitions, ultrahigh ductility, and topological nodal lines in α-Ag 2 S. Physical Review B 2020, 102 (14), 140101. Additional Declarations No competing interests reported. Supplementary Files Supplementarymaterial.docx The Supplementary material is available free of charge. Provides structural data for training the first-generation Mg-Te-Pb-Bi quaternary general-purpose potential model (Table S1); Lattice parameters of Mg-Te-Pb ternary thermoelectric materials (Table S2); Analysis of the intralayer slip mechanisms in II-Mg 2 Te 3 Pb and MgTe 2 Pb (Figures. S1-S2 and accompanying descriptions); Attempted experimental synthesis with characterization results (Figures. S3-S5, Tables S3- S4); (PDF) Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 06 Apr, 2026 Reviews received at journal 03 Apr, 2026 Reviews received at journal 01 Apr, 2026 Reviewers agreed at journal 26 Mar, 2026 Reviewers agreed at journal 24 Mar, 2026 Reviewers invited by journal 24 Mar, 2026 Editor assigned by journal 20 Mar, 2026 Submission checks completed at journal 19 Mar, 2026 First submitted to journal 17 Mar, 2026 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. 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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-9154062","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":611687330,"identity":"be367cd9-a97a-4c97-8404-0113ca5a9a09","order_by":0,"name":"Xin-Xuan Wang","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Xin-Xuan","middleName":"","lastName":"Wang","suffix":""},{"id":611687332,"identity":"61ada16a-2164-4b83-a620-99d2ca015778","order_by":1,"name":"Zhen-Shuai Lei","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Zhen-Shuai","middleName":"","lastName":"Lei","suffix":""},{"id":611687333,"identity":"bcfe4ddc-2373-4532-b89d-a8d05f4f8e31","order_by":2,"name":"Wen-Juan Li","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Wen-Juan","middleName":"","lastName":"Li","suffix":""},{"id":611687334,"identity":"9052a085-0d5d-4f9d-a3eb-0dcc5894aca7","order_by":3,"name":"Xiao-Bin Feng","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Xiao-Bin","middleName":"","lastName":"Feng","suffix":""},{"id":611687335,"identity":"115a5ede-64d1-46ac-b9a7-4c657a543277","order_by":4,"name":"Gang Chen","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Gang","middleName":"","lastName":"Chen","suffix":""},{"id":611687336,"identity":"053ee152-777a-444b-aba6-771125608018","order_by":5,"name":"Peng-Cheng Zhai","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Peng-Cheng","middleName":"","lastName":"Zhai","suffix":""},{"id":611687337,"identity":"453bcee8-0f74-41f0-b224-130f35d58ca1","order_by":6,"name":"Bo Duan","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Bo","middleName":"","lastName":"Duan","suffix":""},{"id":611687338,"identity":"2a2ea0cb-30dd-445b-85d4-1d0671312bd4","order_by":7,"name":"Guo-Dong Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYJACCSCWYWBgPsAM4ScQp4WHgYEtAajFgCQtPAbEaZGPSD544+OOWh5+9p5v0oVtfxj42XMMGH7uwK3F8EZasuXMM8d5JHvObpOe2WbAINnzxoCx9wweLTNyzKR5247xGNzI3XabF6jF4EaOATNjGxFa7O+/eQbWYk9Ii7wEWEsNj4EEDxvEFgkCWgx4ngH90naAR+JMmvlvnnPGQMazgoO9+GxpB4VYW50cf/vhx8Y8ZXJARvLGBz/x2XIATB2GC/CAiAO4NQBtaQBTdfjUjIJRMApGwUgHAAFES+m9eCYTAAAAAElFTkSuQmCC","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Guo-Dong","middleName":"","lastName":"Li","suffix":""},{"id":611687339,"identity":"f2b1b204-c22f-49ca-8012-c54b306bf1fb","order_by":8,"name":"Qing-Jie Zhang","email":"","orcid":"","institution":"Wuhan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Qing-Jie","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2026-03-18 03:28:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9154062/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9154062/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105566784,"identity":"617de0ed-4b51-4917-bf32-7ff66e792ab8","added_by":"auto","created_at":"2026-03-27 12:57:19","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":508138,"visible":true,"origin":"","legend":"\u003cp\u003eWorkflow diagram, including structure sampling (blue), model training (yellow), model iteration (purple), and final CSP (green). The left side shows the overall workflow schematic, while the right side details the procedures for each stage.\u003c/p\u003e","description":"","filename":"img1.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/67fc9572e2557d7e557933ec.png"},{"id":105491405,"identity":"cee60dc2-6d13-4d05-b276-16e352dead9b","added_by":"auto","created_at":"2026-03-26 15:33:40","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":307730,"visible":true,"origin":"","legend":"\u003cp\u003e(a)-(c) Crystal structures and Electron Localization Function (ELF) distributions on the (1100) plane for I- Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, respectively; along with (d) the ternary convex hull. In the ELF maps, the color scale from blue to red corresponds to ELF values ranging from 0 to 1.0. In the structural diagrams, Te, Mg, and Pb atoms are represented by green, orange, and gray spheres, respectively.\u003c/p\u003e","description":"","filename":"img2.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/b44178122e333642a8ed10a7.png"},{"id":105491411,"identity":"ed1d73ee-228f-4ccd-ad3f-7bd3b465f619","added_by":"auto","created_at":"2026-03-26 15:33:40","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":5143807,"visible":true,"origin":"","legend":"\u003cp\u003e(a)-(c) Electronic band structures and DOS of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, respectively; (d)-(f) temperature dependence of the Seebeck coefficient \u003cem\u003eS\u003c/em\u003e; and (g)-(i) temperature dependence of \u003cem\u003eσ\u003c/em\u003e/\u003cem\u003eτ\u003c/em\u003e.\u003c/p\u003e","description":"","filename":"img3.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/27b154b84750233bb792fdb2.png"},{"id":105491412,"identity":"605d5c0b-9f37-4148-9a6e-9ccb49e4364c","added_by":"auto","created_at":"2026-03-26 15:33:40","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":750901,"visible":true,"origin":"","legend":"\u003cp\u003e(a)-(c) Phonon dispersion relations and DOS for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, respectively. (d)-(f) Temperature-dependent \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e along the \u003cem\u003ex\u003c/em\u003e-, \u003cem\u003ey\u003c/em\u003e-, and \u003cem\u003ez\u003c/em\u003e-directions for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, respectively.\u003c/p\u003e","description":"","filename":"img4.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/19ac3fa8492468c408caf67d.png"},{"id":105566515,"identity":"9d9edf79-ba0f-447f-b18a-defa1f98d645","added_by":"auto","created_at":"2026-03-27 12:56:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1305994,"visible":true,"origin":"","legend":"\u003cp\u003eShear stress–strain curves of (a) I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, (b) II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and (c) MgTe\u003csub\u003e2\u003c/sub\u003ePb, the corresponding atomic configurations of (d) I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, (e) II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and (f) MgTe\u003csub\u003e2\u003c/sub\u003ePb during shear deformation along the (0001)/\u0026lt;01–10\u0026gt; direction.\u003c/p\u003e","description":"","filename":"img5.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/267ca8144fe20de2d884a59c.png"},{"id":105491406,"identity":"646c4090-8a74-46b2-8234-b633cb48b900","added_by":"auto","created_at":"2026-03-26 15:33:40","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":134098,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic illustration of the plastic deformation mechanism in the Mg-Te-Pb system along the (0001)/\u0026lt;01-10\u0026gt; direction, and (b)-(d) slip energy profiles corresponding to different slip modes for (b) I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, (c) II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and (d) MgTe\u003csub\u003e2\u003c/sub\u003ePb.\u003c/p\u003e","description":"","filename":"img6.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/d6b8090433229dc27ca6ba3a.png"},{"id":105566320,"identity":"d0972d35-1111-48ba-87cc-152c37342e3a","added_by":"auto","created_at":"2026-03-27 12:56:08","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":4588565,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic illustrations of the slip processes within the [PbTe\u003csub\u003e6\u003c/sub\u003e] layers in the I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb system: (a-d) single-layer Te slip process, (e-i) double-layer Te slip process; the corresponding bond-length responses are shown in (j-l) for the single-layer slip and (m, n) for the double-layer slip.\u003c/p\u003e","description":"","filename":"img7.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/1c050688b4aeb3578e7c33d2.png"},{"id":105566830,"identity":"b29dd796-488e-458f-a4aa-25a73df34e14","added_by":"auto","created_at":"2026-03-27 12:57:28","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":3498701,"visible":true,"origin":"","legend":"\u003cp\u003eSummary of the intrinsic lattice thermal conductivity (\u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e) and \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e of representative binary TE materials at room temperature, compared with the \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG \u003c/em\u003eof the new TE materials predicted in this work: I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb (\u003ca href=\"#_ENREF_33\" title=\"Bencheikh, 2025 #101\"\u003e33\u003c/a\u003e\u003cstrong\u003e, \u003c/strong\u003e\u003ca href=\"#_ENREF_54\" title=\"Pei, 2012 #71\"\u003e54-72\u003c/a\u003e).\u003c/p\u003e","description":"","filename":"img8.png","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/a17084329cd9182ea416be08.png"},{"id":105570449,"identity":"8a36b2d6-208d-4dc2-9b7e-a644c0ba27e8","added_by":"auto","created_at":"2026-03-27 13:17:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":16440875,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/72ae56a5-df66-489e-bb83-e65635b54474.pdf"},{"id":105491409,"identity":"229ad58d-aced-42c5-8294-0af693972552","added_by":"auto","created_at":"2026-03-26 15:33:40","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1725978,"visible":true,"origin":"","legend":"\u003cp\u003eThe Supplementary material is available free of charge.\u003c/p\u003e\n\u003cp\u003eProvides structural data for training the first-generation Mg-Te-Pb-Bi quaternary general-purpose potential model (Table S1); Lattice parameters of Mg-Te-Pb ternary thermoelectric materials (Table S2); Analysis of the intralayer slip mechanisms in II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb (Figures. S1-S2 and accompanying descriptions); Attempted experimental synthesis with characterization results (Figures. S3-S5, Tables S3- S4); (PDF)\u003c/p\u003e","description":"","filename":"Supplementarymaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-9154062/v1/5f90d39f003a1ad1bad3c940.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Ductile Mg-Te-Pb Thermoelectric Materials with Ultralow Lattice Thermal Conductivity Predicted by a Deep Learning Potential Model","fulltext":[{"header":"1 INTRODUCTION","content":"\u003cp\u003eThermoelectric (TE) materials are highly promising for clean energy conversion, as they can harvest waste heat and convert it into electricity via the Seebeck effect, and enable solid-state cooling through the Peltier effect. Consequently, TE materials hold significant potential in aerospace, industry, microelectronics, environmental monitoring, and healthcare (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e). The energy conversion efficiency of TE materials is primarily determined by their \u003cem\u003eZT\u003c/em\u003e value, defined as \u003cem\u003eZT\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eS\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e\u003cem\u003eσT\u003c/em\u003e/(\u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e), where \u003cem\u003eS\u003c/em\u003e, \u003cem\u003eσ\u003c/em\u003e, \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003ee\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eT\u003c/em\u003e represent the Seebeck coefficient, electrical conductivity, lattice thermal conductivity, electronic thermal conductivity, and absolute temperature, respectively (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). The strong coupling among these transport parameters critically influences the TE performance (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e). Consequently, extensive research has focused on decoupling or optimally balancing these parameters to enhance the heat-to-electricity conversion efficiency of TE materials. When considering practical applications, the mechanical properties of TE materials emerge as another critical performance metric. TE devices often operate under complex thermo-mechanical-electrical multiphysics conditions, where thermal stresses, vibrations, and mechanical shocks can readily induce stress concentration, leading to crack initiation and ultimately fracture failure. Therefore, while optimizing their TE conversion efficiency, it is equally crucial to consider their processability for device fabrication and long-term operational stability. Under these considerations, the development of novel TE materials that simultaneously possess superior TE properties and reliable mechanical performance has become a critical scientific challenge in the field.\u003c/p\u003e \u003cp\u003eThe crystal structure prediction (CSP) method offers a promising approach to addressing the challenges in developing novel TE materials, having demonstrated remarkable successes in fields such as superconductivity and geophysics. For instance, Duan et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e) employed the USPEX method to predict an H\u003csub\u003e3\u003c/sub\u003eS superconductor with \u003cem\u003eIm-\u003c/em\u003e3\u003cem\u003em\u003c/em\u003e symmetry, formed from H\u003csub\u003e2\u003c/sub\u003eS-H\u003csub\u003e2\u003c/sub\u003e compounds, which exhibits a superconducting critical temperature (\u003cem\u003eT\u003c/em\u003ec) of up to 191 K at 200 GPa. This prediction was subsequently confirmed by high-pressure experiments conducted by Drozdov et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e), marking a breakthrough in the fundamental research of conventional superconductors. Similarly, Shao et al. (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e) used the CALYPSO method to identify two high-pressure candidate crystal structures of the hydrous mineral MgSiO\u003csub\u003e4\u003c/sub\u003eH\u003csub\u003e2\u003c/sub\u003e. Subsequent experimental studies further demonstrated that its solid solution with AlOOH remains stable over a broad range of temperatures and pressures, providing crucial insights into the circulation and storage of water in Earth\u0026rsquo;s interior and super-Earth exoplanets. Therefore, compared to the traditional experience-guided paradigm for materials exploration, CSP offers shorter development cycles, lower costs, higher exploration efficiency, and greater success rates. These advantages of CSP closely match the research objective focused on novel TE compounds that exhibit superior properties. The fundamental principle of CSP is to systematically explore the potential energy surface (PES) for a given chemical composition and identify the most stable candidate crystal structures based on the energy minimization criterion. This approach avoids the high randomness inherent in traditional trial-and-error methods, making rational material design possible. CSP typically involves two core components: first, sampling algorithms for exploring the PES, such as random search (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e), particle swarm optimization (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e), hybrid algorithms (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e), genetic algorithms (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e), and adaptive genetic algorithms (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e); second, energy evaluation methods, primarily molecular dynamics (MD) (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e) and density functional theory (DFT) (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e). The effectiveness of the sampling algorithm directly determines the success rate in locating the global minimum on the PES, while the choice of energy evaluation method governs both the accuracy of the PES and the overall computational efficiency of the prediction workflow. The latter directly influences the feasibility of the entire CSP endeavor. Specifically, MD-based energy evaluations offer high computational speed but limited accuracy, whereas DFT provides high accuracy at the expense of extremely high computational cost. Consequently, achieving an optimal balance between accuracy and efficiency remains a significant obstacle that currently hinders the broader application of CSP.\u003c/p\u003e \u003cp\u003eIn recent years, the development of machine learning potentials (MLPs) has provided an effective solution for accelerating CSP (\u003cspan additionalcitationids=\"CR17 CR18\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e). MLPs trained on DFT data can achieve accuracy levels comparable to \u003cem\u003eab initio\u003c/em\u003e (AI) MD while improving computational efficiency by several orders of magnitude, thereby drastically reducing computational cost (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e). Consequently, MLP-based PES models have been widely adopted in CSP tasks across diverse material systems. For example, Tong et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e) combined the Gaussian approximation potential (GAP) (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e) with the particle swarm optimization-based CALYPSO method to systematically predict allotropes of boron. Hong et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e) utilized neural network potential (NNP) (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e) integrated with the genetic algorithm-based USPEX package to accurately predict ground-state structures of several compounds, including Ba\u003csub\u003e2\u003c/sub\u003eAgSi\u003csub\u003e3\u003c/sub\u003e, Mg\u003csub\u003e2\u003c/sub\u003eSiO\u003csub\u003e4\u003c/sub\u003e, LiAlCl\u003csub\u003e4\u003c/sub\u003e, and InTe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003eF, showing excellent agreement with experimental results. Moreover, Wang et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e) coupled deep learning potential (DP) MD (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e) with CALYPSO to successfully reproduce the stable phases of the Mg-Al binary alloy and discovered a new superhydride Li\u003csub\u003e2\u003c/sub\u003eLa\u003csub\u003e2\u003c/sub\u003eH\u003csub\u003e23\u003c/sub\u003e with \u003cem\u003eCmcm\u003c/em\u003e symmetry in the Li-La-H ternary system. Notably, their approach reduced computational cost by an order of magnitude compared to conventional DFT calculations. These achievements demonstrate the significant potential of MLP-assisted CSP in enhancing the efficiency of new material development.\u003c/p\u003e \u003cp\u003eDespite the remarkable success of MLPs across various domains, their application to TE materials remains in its early stages. Against this backdrop, this work aims to apply the DP model to CSP and property quantification in the Mg-Te-Pb-Bi quaternary TE system. This elemental system was selected based on the following considerations: Firstly, Te, Pb, and Bi are all highly promising candidates for forming high-performance TE materials. For instance, dense dislocation arrays in Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e-based room-temperature TE materials significantly reduce lattice thermal conductivity (\u003cem\u003eκ\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e), achieving a \u003cem\u003eZT\u003c/em\u003e of 1.86 at 300 K (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e). PbTe achieves a \u003cem\u003eZT\u003c/em\u003e as high as 2.0 through band engineering strategies such as MgTe doping (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e). Additionally, a range of traditional TE materials, such as PbSe, PbS, SnTe, GeTe, InTe, Cu\u003csub\u003e2\u003c/sub\u003eTe, and BiCuSeO, all exhibit good TE performance. Secondly, Mg-containing materials like Mg\u003csub\u003e3\u003c/sub\u003eBi\u003csub\u003e2\u003c/sub\u003e, Mg\u003csub\u003e3\u003c/sub\u003eSb\u003csub\u003e2\u003c/sub\u003e, and MgTe demonstrate favorable plasticity, with the former two also possessing excellent TE properties(\u003cspan additionalcitationids=\"CR30 CR31\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e). It should be noted that InTe also displays good plasticity(\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e). In addition, the large atomic mass contrast between Mg and the heavier elements (Te, Pb, Bi) is expected to enhance lattice anharmonicity, thereby further reducing \u003cem\u003eκ\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e. Most importantly, PbTe and Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e crystal structures possess six-coordinated resonant bonding (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e). Taking rock-salt structured PbTe as an example, each Pb-Te octahedral unit contains six covalent bonds with each atom contributing three valence electrons on average, resulting in the random occupation of electrons over available covalent bonding positions. This situation creates resonance or hybridization between different electronic configurations, effectively scattering phonons and leading to low \u003cem\u003eκ\u003c/em\u003e\u003csub\u003eL\u003c/sub\u003e (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e). Furthermore, we are also motivated to explore whether this six-coordinated structural unit harbors additional potential for enhancing mechanical properties. Consequently, we intentionally introduced the [XY\u003csub\u003e6\u003c/sub\u003e] units as a functional building block for material design during the CSP process in this work, aiming to obtain TE materials with both outstanding TE conversion efficiency and superior mechanical performance.\u003c/p\u003e \u003cp\u003eThis study employs the DP method to construct a universal interatomic potential for the Mg-Te-Pb-Bi quaternary system, which is integrated with a genetic algorithm to accelerate CSP for quaternary TE material systems. The objectives are to discover novel TE materials that simultaneously exhibit superior TE and mechanical properties, as well as new physical characteristics distinct from those observed in binary systems. The subsequent chapters are organized as follows: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e will detail the construction of the DP model and the specific procedures and parameters used in the accelerated CSP workflow. Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e will discuss the fundamental physical properties, TE transport performance, and mechanical behavior of the predicted new materials. The final section will summarize the key findings of this work.\u003c/p\u003e"},{"header":"2 THEORETICAL CALCULATIONS","content":"\u003cp\u003eThe DP-accelerated CSP workflow for the Mg-Te-Pb-Bi system consists of four stages: structure sampling, model training, model iteration, and final CSP, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In Stage 1, a total of 27 structures\u0026mdash;comprising elemental phases, binary compounds, and ternary compounds of Mg, Te, Pb, and Bi (see Supporting Information Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e) are selected, all representing known structures at ambient or low pressures (below 20 GPa). The chosen structures are then subjected to perturbation deformation using the DPGEN (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e) based on the DP method, followed by short AIMD simulations to relax the systems. During these simulations, data including energies, atomic forces, atomic positions, and virial tensors are collected. In stage 2, the DP model is constructed using the DeePMD-kit (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e). The model generated at this stage is preliminary and must be refined in Stage 3, where the genetic algorithm-based USPEX software serves as a configuration sampler to improve the DP model. Specifically, the DP potential generated in Stage 2 is used to accelerate the generation of variable-composition structures for the ternary and quaternary systems composed of Mg, Te, Pb, and Bi. These structures are then subjected to DFT single-point energy calculations, and the resulting data are used to update and refine the DP model. The iterative loop between Stages 2 and 3 is performed three times: In the first iteration, the four ternary subsystems (Mg-Te-Pb, Mg-Te-Bi, Mg-Pb-Bi, and Te-Pb-Bi) formed by Mg, Te, Pb, and Bi are considered. All obtained structures are used to update and train the second-generation DP model. This step aims to extend the DP model, originally trained on binary compounds, to ternary systems through a progressive refinement strategy, thereby avoiding the generation of highly unreasonable structures during prediction. In the second iteration, the updated DP model is used to generate variable-composition structures of the Mg-Te-Pb-Bi quaternary system. Similarly, all resulting structures are used to update and train the third-generation DP model, extending its applicability from ternary to quaternary compositions. In the third iteration, the refined DP model is used to generate a comprehensive set of variable-composition structures for the Mg-Te-Pb-Bi quaternary system through large-scale sampling. Similarly, all newly generated structures are used to update and train the fourth-generation DP model, further improving its completeness and reliability. In the final stage of the entire workflow, the refined DP model is employed for ultimate CSP of variable-composition systems composed of Mg, Te, Pb, and Bi. During the prediction process, resonant bonding units are introduced to derive novel TE materials incorporating such bonding features. The predicted structures are subsequently screened according to the following criteria: first, they must satisfy mechanical, dynamical, and thermodynamic stability; second, they should be narrow-bandgap semiconductors; and finally, they must exhibit both excellent TE performance and reliable mechanical properties. Subsequently, the computational tools and parameters employed in each stage are detailed.\u003c/p\u003e \u003cp\u003eIn this work, all DFT calculations, including geometry optimizations, DPGEN-based perturbative sampling, and the iterative refinement of the DP model, were carried out using the VASP code (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e). The exchange-correlation interaction was described using the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e). The interaction between core and valence electrons was treated using the projector augmented-wave (PAW) method (\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e). For all structures, the plane-wave cutoff energy was set to 500 eV, and the energy convergence criterion was 1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV. The \u003cem\u003ek\u003c/em\u003e-point spacing in the Brillouin zone was set to a minimum of 0.3 \u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e, and the force on each atom in the unit cell was kept below 0.01 eV/\u0026Aring;. In DPGEN, 27 initial structures were supercell-expanded to ensure that each contained at least 30 atoms. The cell volume and atomic positions were then scaled 0.8\u0026ndash;1.2 times in 0.05 increments. AIMD simulations were then performed on all perturbed structures at 300 K with a 1 fs time step for 10 steps. After all AIMD runs were completed, some non-converged structures were discarded, yielding a total of up to 252,000 configurations as the training data for the initial DP potential. During the DP model fitting process, the training and test datasets are randomly split in a 9:1 ratio. The model employed three hidden layers, with an embedding network of 25, 50, 100, and a fitting network of 240, 240, 240, enabling more effective separation of different data types. A cutoff radius of 6 \u0026Aring; was used, and the initial learning rate was set to 1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e, decaying exponentially every 10,000 steps until it reached 3.51\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;8\u003c/sup\u003e at the end of training. To ensure sufficient fitting accuracy and prevent overfitting, the total number of training steps was set to 2\u0026nbsp;million. In USPEX-based predictions of ternary, quaternary, and broad-composition quaternary systems, structural generation was performed for 20 generations each. The initial generation produced 200, 400, and 1000 structures, respectively, with 150, 300, and 500 new structures generated in each generation thereafter. Over the entire iterative refinement process, a total of 30,663 new structures were generated, and their DFT data were used to train the DP model. In the final variable-composition CSP for Mg, Te, Pb, and Bi, the elemental ratios of generated structures were constrained to exclude unreasonable compositions (e.g., ratios exceeding 10:1). Each generation produced 200 structures, with no preset limit on the number of generations, and the search continued until convergence.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e outlines the workflow of this work. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) presents the rationale for selecting the four elements: Mg, Te, Pb, and Bi, and Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b) compares the DP model predictions with DFT-calculated data. As shown, the predicted energies and atomic forces agree closely with the DFT benchmarks, with the vast majority of data points evenly distributed along the \u003cem\u003ey\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ex\u003c/em\u003e line, indicating excellent predictive performance of the DP model. Quantitative analysis further reveals root-mean-square errors (RMSEs) of 0.0295\u0026nbsp;eV/atom for energy and 0.150 eV/\u0026Aring; for atomic forces lower than those reported for DPMD in most other systems (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e). This result demonstrates high model fitting accuracy, highlighting its strong generalization capability. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c) illustrates the compositional sampling space for quaternary systems during the iterative process, where colors ranging from blue to red indicate increasing formation enthalpy. The sampling points are uniformly distributed and densely packed, demonstrating broad coverage of the composition space and suggesting that the resulting DP model possesses good extrapolation capability. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d) is a schematic diagram of the predicted crystal structure after the active introduction of [XY\u003csub\u003e6\u003c/sub\u003e] functional units.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"3 RESULTS AND DISCUSSION","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Crystal Structures and Intrinsic Properties\u003c/h2\u003e \u003cp\u003eAn extensive DP-accelerated crystal structure search across binary to quaternary systems composed of Mg, Te, Pb, and Bi, not only reproduces known stable phases such as PbTe, Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e, and MgTe, but also reveals three new hexagonal structures in the Mg-Te-Pb ternary system: two polymorphs of Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and one MgTe\u003csub\u003e2\u003c/sub\u003ePb phase. The two Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb components crystallize in the \u003cem\u003eP\u003c/em\u003e3\u003cem\u003em\u003c/em\u003e1 and \u003cem\u003eP\u003c/em\u003e-6\u003cem\u003em\u003c/em\u003e2 space groups, respectively, and are denoted as I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb for clarity. MgTe\u003csub\u003e2\u003c/sub\u003ePb crystallizes in the \u003cem\u003eP\u003c/em\u003e-6\u003cem\u003em\u003c/em\u003e2 space group. Their lattice parameters are as follows: I- Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb with \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e = 4.35 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10.76 \u0026Aring;; II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb with \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e = 4.31 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;11.06 \u0026Aring;; MgTe\u003csub\u003e2\u003c/sub\u003ePb with \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e = 4.35 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15.16 \u0026Aring; (detailed parameters such as atomic positions are given in Table S2 of the Supporting Information). Figures\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a)-(c) respectively show the crystal structures and the electron localization function (ELF) on the (1100) plane for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, respectively. In I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, Pb and Mg atoms act as symmetry centers and each forms a six-coordinate [PbTe\u003csub\u003e6\u003c/sub\u003e] and [MgTe\u003csub\u003e6\u003c/sub\u003e] unit with Te atoms, which aligns with our design objective of incorporating [XY\u003csub\u003e6\u003c/sub\u003e] functional units (where X\u0026thinsp;=\u0026thinsp;Pb/Mg and Y\u0026thinsp;=\u0026thinsp;Te). These [XTe\u003csub\u003e6\u003c/sub\u003e] units connect to form Pb-Te and Mg-Te layers, resulting in a stacking sequence along the \u003cem\u003ez\u003c/em\u003e-direction consisting of one Pb-Te layer sandwiched between two Mg-Te layers. In II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, the [MgTe\u003csub\u003e6\u003c/sub\u003e] units are identical to those in I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, but the Te atoms in the [PbTe\u003csub\u003e6\u003c/sub\u003e] units deviate from the ideal symmetric positions, forming distorted six-coordinate polyhedra. These distorted units arrange into Pb-Te layers, ultimately establishing the same stacking sequence along the \u003cem\u003ez\u003c/em\u003e-direction as in I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb. The crystal structure of MgTe\u003csub\u003e2\u003c/sub\u003ePb is structurally similar to that of II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, with both featuring stacked layers of [MgTe\u003csub\u003e6\u003c/sub\u003e] units and distorted [PbTe\u003csub\u003e6\u003c/sub\u003e] units. The only difference lies in the stacking sequence along the \u003cem\u003ez\u003c/em\u003e-direction, which comprises alternating single Pb-Te and single Mg-Te layers. The ELF distribution reveals that Mg-Te interactions in all three structures are predominantly ionic, while Pb-Te pairs exhibit discernible covalent character. In contrast, Mg and Pb atoms are well separated, with no chemical bond formed between them. Among them, the [PbTe\u003csub\u003e6\u003c/sub\u003e] units act as resonant bonding units in all three structures, suggesting that these materials may exhibit low \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e. Although the [MgTe\u003csub\u003e6\u003c/sub\u003e] units form a structure similar to that of the resonant [PbTe\u003csub\u003e6\u003c/sub\u003e] units, the charge on the Mg atoms is almost entirely transferred to Te, and thus they are not typical resonant bonding units.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo assess the thermodynamic stability of these three materials, we calculated their formation enthalpies and constructed the ternary convex hull diagram based on all known compounds that can be formed from Mg, Te, and Pb, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d). The formation enthalpies of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb are all negative, with values of -0.6714\u0026nbsp;eV/atom, -0.6539\u0026nbsp;eV/atom, and \u0026minus;\u0026thinsp;0.5638\u0026nbsp;eV/atom, respectively. Among them, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb exhibits the lowest formation enthalpy, suggesting it is likely the ground-state structure in this system, whereas the other two are metastable. Moreover, among all known phases in the Mg-Te-Pb system, only MgTe (-0.881\u0026nbsp;eV/atom) has a lower formation enthalpy than I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb. This result indicates that the synthesis of both I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb is experimentally more feasible than that of MgTe\u003csub\u003e2\u003c/sub\u003ePb.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eElastic constants \u003cem\u003eC\u003c/em\u003e, bulk modulus \u003cem\u003eB\u003c/em\u003e, Young\u0026rsquo;s modulus \u003cem\u003eE\u003c/em\u003e, shear modulus \u003cem\u003eG\u003c/em\u003e, Poisson\u0026rsquo;s ratio \u003cem\u003eν\u003c/em\u003e, and \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II- Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb (units: GPa)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePhase\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e11\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e13\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e44\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e66\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eB\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cem\u003eG\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cem\u003eν\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cem\u003eB/G\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eI-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e75.857\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27.842\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e31.742\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e77.997\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e29.890\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e24.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e45.787\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e64.355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e25.422\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.266\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e1.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eII-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e61.973\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e33.837\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e90.834\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.471\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e14.068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e42.328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e49.510\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e18.968\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.305\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e2.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMgTe\u003csub\u003e2\u003c/sub\u003ePb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e60.479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e30.485\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e26.425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e84.696\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e22.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e14.997\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e41.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e50.446\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e19.472\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.295\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e2.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn addition, we have also calculated the elastic properties of the three materials, as listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. All three compounds belong to the hexagonal crystal system and exhibit similar values for their six independent elastic constants. Among them, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb shows larger elastic moduli, indicating a stronger resistance to elastic deformation compared to the other two. However, its Pugh\u0026rsquo;s ratio (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e) (\u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e) is lower, suggesting that its capacity for plastic deformation may be inferior to that of the other two materials. Moreover, mechanical stability can also be evaluated through the elastic stability criteria. For the hexagonal crystal system, the elastic stability conditions (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e) are: \u003cem\u003eC\u003c/em\u003e\u003csub\u003e11\u003c/sub\u003e \u0026gt; |\u003cem\u003eC\u003c/em\u003e\u003csub\u003e12\u003c/sub\u003e|, 2\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003e\u0026thinsp;\u0026lt;\u0026thinsp;\u003cem\u003eC\u003c/em\u003e\u003csub\u003e33\u003c/sub\u003e(\u003cem\u003eC\u003c/em\u003e\u003csub\u003e11\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;\u003cem\u003eC\u003c/em\u003e\u003csub\u003e12\u003c/sub\u003e), \u003cem\u003eC\u003c/em\u003e\u003csub\u003e44\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0. It can be inferred from the calculated elastic constants that all three materials, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, satisfy these conditions, further supporting their potential for stable existence.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Electrical Transport Properties\u003c/h2\u003e \u003cp\u003eTo investigate the intrinsic physical properties of the Mg-Te-Pb compounds, this work systematically calculates and analyzes the electronic band structures and density of states (DOS) for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb. As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a)-(c), the valence band maximum (VBM) and conduction band minimum (CBM) of all three compounds are located at different high-symmetry points, indicating that they are indirect-bandgap semiconductors. Specifically, for both I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, the VBM is at the \u003cem\u003eΓ\u003c/em\u003e point, and the CBM is at the \u003cem\u003eL\u003c/em\u003e point, whereas for MgTe\u003csub\u003e2\u003c/sub\u003ePb, the VBM is at the \u003cem\u003eΓ\u003c/em\u003e point and the CBM is at the \u003cem\u003eH\u003c/em\u003e point. The band gaps of the three compounds are 0.17 eV for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, 0.46 eV for II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and 0.14 eV for MgTe\u003csub\u003e2\u003c/sub\u003ePb, all exhibiting pronounced narrow bandgap characteristics, which are favorable for achieving high TE performance. DOS analysis reveals that the VBM is primarily contributed by the Te \u003cem\u003ep\u003c/em\u003e orbitals, whereas the CBM is mainly contributed by the Pb \u003cem\u003ep\u003c/em\u003e orbitals. This band structure feature indicates that Te plays a dominant role in the valence band, while Pb makes a significant contribution to the formation of the conduction band.\u003c/p\u003e \u003cp\u003eSubsequently, we employed the BoltzTraP2 code (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e), which is based on the Boltzmann transport equation (BTE), to calculate the Seebeck coefficient \u003cem\u003eS\u003c/em\u003e for the three materials. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(d)-(f) show the temperature dependence of \u003cem\u003eS\u003c/em\u003e for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb under both \u003cem\u003ep\u003c/em\u003e-type and \u003cem\u003en\u003c/em\u003e-type doping, respectively. Within the temperature ranges where their respective crystal structures remain stable (determined by MD high-temperature relaxation), the absolute Seebeck coefficient, ∣\u003cem\u003eS\u003c/em\u003e∣, for all three materials gradually decrease with increasing temperature and exhibit distinct doping-type dependencies: for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, the ∣\u003cem\u003eS\u003c/em\u003e∣ under \u003cem\u003en\u003c/em\u003e-type doping is higher than that under \u003cem\u003ep\u003c/em\u003e-type doping; for II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, the ∣\u003cem\u003eS\u003c/em\u003e∣ values for \u003cem\u003ep\u003c/em\u003e- and \u003cem\u003en\u003c/em\u003e-type doping are comparable; and for MgTe\u003csub\u003e2\u003c/sub\u003ePb, the ∣\u003cem\u003eS\u003c/em\u003e∣ under \u003cem\u003ep\u003c/em\u003e-type doping is higher than that under \u003cem\u003en\u003c/em\u003e-type doping. At 300 K, the maximum \u003cem\u003eS\u003c/em\u003e values are +\u0026thinsp;323 \u003cem\u003e\u0026micro;\u003c/em\u003eV/K (\u003cem\u003ep\u003c/em\u003e-type) and \u0026minus;\u0026thinsp;341 \u003cem\u003e\u0026micro;\u003c/em\u003eV/K (\u003cem\u003en\u003c/em\u003e-type) for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, +\u0026thinsp;765 \u003cem\u003e\u0026micro;\u003c/em\u003eV/K (\u003cem\u003ep\u003c/em\u003e-type) and \u0026minus;\u0026thinsp;766 \u003cem\u003e\u0026micro;\u003c/em\u003eV/K (\u003cem\u003en\u003c/em\u003e-type) for II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and +\u0026thinsp;302 \u003cem\u003e\u0026micro;\u003c/em\u003eV/K (\u003cem\u003ep\u003c/em\u003e-type) and \u0026minus;\u0026thinsp;298 \u003cem\u003e\u0026micro;\u003c/em\u003eV/K (\u003cem\u003en\u003c/em\u003e-type) for MgTe\u003csub\u003e2\u003c/sub\u003ePb. Notably, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb exhibits a significantly larger \u003cem\u003eS\u003c/em\u003e compared with the other two compounds, indicating stronger energy dependence of carrier transport and thus superior TE response characteristics. Figures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(g)-(i) show the temperature dependence of the electrical conductivity divided by the relaxation time (\u003cem\u003eσ\u003c/em\u003e/\u003cem\u003eτ\u003c/em\u003e) for the three materials. In the temperature range from room temperature to high temperatures, the \u003cem\u003eσ\u003c/em\u003e/\u003cem\u003eτ\u003c/em\u003e values of all three compounds continuously increase with rising temperature. At 300 K, the \u003cem\u003eσ\u003c/em\u003e/\u003cem\u003eτ\u003c/em\u003e values under \u003cem\u003ep\u003c/em\u003e- and \u003cem\u003en\u003c/em\u003e-type doping are 2.71\u0026times;10\u003csup\u003e17\u003c/sup\u003e S/(m\u0026middot;s) and 2.92\u0026times;10\u003csup\u003e17\u003c/sup\u003e S/(m\u0026middot;s) for I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, 1.79\u0026times;10\u003csup\u003e15\u003c/sup\u003e S/(m\u0026middot;s) and 1.84\u0026times;10\u003csup\u003e15\u003c/sup\u003e S/(m\u0026middot;s) for II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, 1.51\u0026times;10\u003csup\u003e17\u003c/sup\u003e S/(m\u0026middot;s) and 1.60\u0026times;10\u003csup\u003e17\u003c/sup\u003e S/(m\u0026middot;s) for MgTe\u003csub\u003e2\u003c/sub\u003ePb, respectively. Notably, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb exhibits a significantly higher \u003cem\u003eσ\u003c/em\u003e/\u003cem\u003eτ\u003c/em\u003e than the other two structures, indicating superior carrier transport capability. The temperature evolution of \u003cem\u003eS\u003c/em\u003e and \u003cem\u003eσ\u003c/em\u003e/\u003cem\u003eτ\u003c/em\u003e demonstrates that all three materials possess excellent electrical transport properties over a broad temperature range, suggesting excellent TE response characteristics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Thermal Transport Properties\u003c/h2\u003e \u003cp\u003eThe primary purpose of introducing the resonant bonding functional units was to reduce the lattice thermal conductivity and enhance the TE performance. The most direct way to evaluate the thermal transport properties of these three TE materials is to study their phonon characteristics. Based on the linear response method with the Phonopy software (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e), we calculated the second-order force constants of the three materials and obtained their phonon dispersion curves, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a)-(c). It can be seen that no imaginary frequencies appear throughout the entire Brillouin zone for any of the three materials, indicating that each system possesses the ability to spontaneously recover stability upon perturbation and confirming their dynamical stability. In addition, the phonon spectra of all three materials exhibit characteristic features typical of low thermal conductivity systems. Specifically, the acoustic branches are confined to the low-frequency range of 0\u0026ndash;2 THz, indicating weak thermal transport capability. Moreover, there is no pronounced bandgap between the acoustic and optical branches, and a large number of flat and densely packed low-frequency optical modes. This suggests strong anharmonic interactions in the system, which can significantly shorten the phonon mean free path and thereby further reduce the \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e. Combined with the phonon DOS analysis, it is found that the acoustic phonons and low-frequency optical phonons in all three materials are primarily contributed by the heavier Te and Pb atoms. The significant mass contrast between the heavy Te/Pb atoms and the light Mg atoms is the main origin of the pronounced band gaps observed in the phonon spectra across different frequency ranges. These band gaps effectively modulate the scattering channels between distinct phonon branches, thereby suppressing phonon transport efficiency. As a result, the combined effects of the heavy constituent atoms and the resulting bandgap-induced scattering synergistically suppress phonon transport, which is directly reflected in the low \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of all three materials. To obtain the \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb, the third-order force constants are calculated using the ShengBTE code(\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e). In the calculations, the cutoff parameters for the three materials are set to -10, -11, and \u0026minus;\u0026thinsp;12, respectively; the ngrid values are 25 \u0026times; 25 \u0026times; 25, 15 \u0026times; 15 \u0026times; 15, and 15 \u0026times; 15 \u0026times; 15, respectively; and a uniform scale broad value of 0.3 is adopted. Combined with the second-order force constants, the \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of the three structures-I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb-along different crystallographic directions is obtained, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(d)-(f). It can be seen that \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e exhibits pronounced anisotropy in all three materials: the values along the \u003cem\u003ey\u003c/em\u003e- and \u003cem\u003ex\u003c/em\u003e-directions are identical, whereas those along the \u003cem\u003ez\u003c/em\u003e-direction differ. Subsequent analysis, therefore, focuses on the \u003cem\u003ex\u003c/em\u003e (or \u003cem\u003ey\u003c/em\u003e) and \u003cem\u003ez\u003c/em\u003e-directions. At 300 K, the \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e values of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb are 0.125 W/(m\u0026middot;K) and 0.065 W/(m\u0026middot;K) along the \u003cem\u003ex\u003c/em\u003e- and \u003cem\u003ez\u003c/em\u003e-directions, respectively; for II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, they are 0.712 W/(m\u0026middot;K) and 0.613 W/(m\u0026middot;K); and for MgTe\u003csub\u003e2\u003c/sub\u003ePb, they are 0.430 W/(m\u0026middot;K) and 0.779 W/(m\u0026middot;K). The exceptionally low \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e values of all three materials corroborate the previous analysis of their phonon dispersion curves.\u003c/p\u003e \u003cp\u003eIn fact, a major factor behind this low \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e is the preservation of [PbTe\u003csub\u003e6\u003c/sub\u003e] resonant bonding units within the crystal structure. The long-range interactions induced by resonant bonding lead to optical phonon softening, strong anharmonic scattering, and a large phase space for three-phonon scattering processes of which make a non-negligible contribution to the reduction of \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e). Moreover, the [PbTe\u003csub\u003e6\u003c/sub\u003e] resonant bonding units in I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb adopt a regular octahedral geometry with ideal six-fold coordination, leading to the strongest resonance (or hybridization) effect and consequently the lowest \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e. Ji et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e) identified K\u003csub\u003e5\u003c/sub\u003eCuSb\u003csub\u003e2\u003c/sub\u003e, a known TE material containing the linear triatomic resonant bonds, through high-throughput computations, which exhibits a low \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of 0.39 W/(m\u0026middot;K). In contrast, the I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb structure reported in this work achieves an even lower \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of 0.065 W/(m\u0026middot;K), further underscoring its exceptional potential as a high-performance TE material.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Mechanical Properties\u003c/h2\u003e \u003cp\u003eThe TE performance determines the efficiency of a material in heat-to-electricity conversion, whereas its mechanical properties directly govern the yield during fabrication and the operational lifetime. As previously mentioned, to enhance the TE performance of the predicted materials, we deliberately introduced the [XY\u003csub\u003e6\u003c/sub\u003e] functional units. Its effectiveness in improving TE properties\u0026mdash;particularly the role of the [PbTe\u003csub\u003e6\u003c/sub\u003e] unit\u0026mdash;has been well demonstrated. However, we also anticipated that it would contribute to significant advantages in mechanical performance. Accordingly, we next calculated the mechanical properties of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb under deformation loading, with a focus on analyzing the role played by the [XTe\u003csub\u003e6\u003c/sub\u003e] functional units. We employ the DP model fitted during structure prediction and perform DPMD simulations using the LAMMPS code (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e) to evaluate the materials\u0026rsquo; resistance to deformation.\u003c/p\u003e \u003cp\u003eTo eliminate the effects of surfaces and finite-size artifacts, periodic boundaries are applied in the \u003cem\u003ex\u003c/em\u003e-, \u003cem\u003ey\u003c/em\u003e-, and \u003cem\u003ez-\u003c/em\u003edirections, and energy minimization is performed using the conjugate gradient algorithm. The simulated systems of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb contain 7,200, 7,200, and 9,600 atoms, respectively. All simulations are carried out in the \u003cem\u003eNPT\u003c/em\u003e ensemble with a time step of 0.001 ps. Before deformation, each structure is relaxed for 50 ps to achieve stress equilibrium. Given that the three structures are stacked along the \u003cem\u003ez\u003c/em\u003e-axis, shear loading is applied at 300 K along the (0001)/\u0026lt;01\u0026ndash;10\u0026thinsp;\u0026gt;\u0026thinsp;direction to investigate interlayer slip and failure mechanisms. The deformation process is run for 1000 ps at a strain rate of 0.001 ps⁻\u0026sup1;, with structural relaxation performed every 1 ps to approximate quasi-static loading conditions.\u003c/p\u003e \u003cp\u003eThe stress-strain responses and corresponding atomic structural evolution of the three materials are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a), I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb initially exhibits a brief stress increase with rising strain, followed by a plateau where the stress remains nearly constant. A sudden stress jump then occurs at a shear strain of 0.127, marking the onset of a strengthening stage. As shown in the atomic configuration at a strain of 0.127 in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d), partial Mg-Te bonds are broken, transforming the original [MgTe\u003csub\u003e6\u003c/sub\u003e] coordination units into [MgTe\u003csub\u003e5\u003c/sub\u003e] coordination units. This transformation leads to the stress plateau observed in the stress-strain curve. Subsequently, as the lattice continues to resist deformation, stress begins to rise again. When the strain reaches 0.226, relative slip between Pb-Te polyhedral layers occurs, releasing stress and causing a downward trend in the stress-strain curve; at a strain of 0.360, the same atomic layer slips again along this direction, leading to another stress release. At a strain of 0.488, the Mg-Te polyhedral layer begins to slip and continues sliding until the end of shear loading. Point defects gradually accumulate within the layer during slip, but without causing significant structural damage.\u003c/p\u003e \u003cp\u003eFrom Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b), it is evident that II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb experiences a brief initial stress rise, followed by a sudden drop at a strain of 0.044. The corresponding configuration in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(e) shows that at this strain, local structures transform [MgTe\u003csub\u003e6\u003c/sub\u003e] units to five-coordinate [MgTe\u003csub\u003e5\u003c/sub\u003e], similar to I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb. Subsequently, the system regains its resistance to deformation, leading to an increase in stress. As the strain increases to 0.220, Pb-Te polyhedral layers begin to slip continuously. Until the strain reaches 0.356, all Pb-Te layers complete their slip, and their arrangement gradually transforms from the initial five-coordination structure into a regular octahedral arrangement. The Mg-Te layers slip at a strain of 0.460. Thereafter, the individual Mg-Te polyhedral layers slip, and by the time the strain reaches 0.640, all slipping has finished, adopting a uniform, co-oriented tilted arrangement. When the strain further increases to 0.752, the crystal structure collapses.\u003c/p\u003e \u003cp\u003eFrom Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c) and (f), it can be seen that the stress of MgTe\u003csub\u003e2\u003c/sub\u003ePb first undergoes a linear elastic stage followed by an elastoplastic stage as strain increases. At a strain of 0.135, the stress exhibits continuous small-amplitude fluctuations. The corresponding configurations reveal that these fluctuations result from successive slips of Pb-Te polyhedral layers, which complete their slip by a strain of 0.370 and adopt a regular octahedral arrangement. When the strain reaches 0.496, the stress begins to exhibit large-amplitude oscillations caused by the slip of the Mg-Te polyhedral layers. Thereafter, the individual Mg-Te polyhedral layers slip continuously until all have completed their slip at a strain of 0.652, at which point they adopt a uniform right-tilted arrangement identical to that of II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb. Further increasing the strain to 0.818 leads to structural collapse.\u003c/p\u003e \u003cp\u003eThese three materials can maintain the integrity of their crystal lattice over a wide strain range by continuously releasing stress through extensive bond breaking, reconstruction, and interlayer slip, thereby exhibiting a certain capacity for plastic deformation under shear. Notably, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb further display shear-induced ordering of Pb-Te and Mg-Te polyhedral layers, forming standard octahedral coordination structures. The continuous slip in all three materials is closely linked to the presence of [PbTe\u003csub\u003e6\u003c/sub\u003e] and [MgTe\u003csub\u003e6\u003c/sub\u003e] octahedral units. Their highly symmetric local structures provide new pathways for interlayer slip, enabling large plastic deformation without relying on conventional dislocation-mediated mechanisms. In essence, within these two types of octahedral building blocks, Mg and Pb atoms transfer strain to each other via Te atoms. Upon significant stress accumulation, dense arrays of Te atoms facilitate bond breaking and reformation, creating \u0026ldquo;catch bonds\u0026rdquo;. Moreover, each layer possesses similar structural features, offering abundant channels for stress release, which underpins their observable plastic deformability. We will subsequently elaborate on the development of this mechanism in detail from the perspectives of microstructural evolution and energetics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Analysis of the Slip Mechanisms\u003c/h2\u003e \u003cp\u003eAs revealed by the preceding slip analysis, all three materials share a common origin of their mechanical deformation mechanism\u0026mdash;the octahedral structural unit [XTe\u003csub\u003e6\u003c/sub\u003e], where X\u0026thinsp;=\u0026thinsp;Pb/Mg. Based on atomic trajectories, we have plotted a schematic diagram illustrating the microstructural evolution of the [XTe\u003csub\u003e6\u003c/sub\u003e] unit during the shearing process, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a). In the diagram, blue atoms represent Te, whereas yellow atoms represent Pb or Mg. When the Pb/Mg atom at the center of the [XTe\u003csub\u003e6\u003c/sub\u003e] unit and the Te atoms in the lower layer remain fixed while only the upper-layer Te atoms slide (i.e., single-layer Te slip), the three upper bonds within the [XTe\u003csub\u003e6\u003c/sub\u003e] unit undergo stretching, breaking, and reformation, enabling continuous slip, whereas the other bonds remain unchanged. The crystal structure after slip is identical to the initial crystal structure. When the central X atom remains stationary, and the Te atoms in both upper and lower layers slide in opposite directions (i.e., double-layer Te slip), two bonds in the [XTe\u003csub\u003e6\u003c/sub\u003e] unit break and reform, while the other four bonds only exhibit fluctuations in bond length. This process ultimately yields an [XTe\u003csub\u003e6\u003c/sub\u003e] unit with its apical direction reversed relative to the initial state, involving fewer bond-breaking and reformation events. After a double-layer Te slip occurs, the resulting inverted [XTe\u003csub\u003e6\u003c/sub\u003e] unit must slide further in the same direction to recover the initial state. This requires breaking and reforming three bonds. Crucially, the bond at the octahedral apex becomes tightly compressed and experiences strong repulsive forces, which block the original slip path. Therefore, when the system encounters such a blocked slip path, and no alternative slip channels are available, the central atom of the reversed [XTe\u003csub\u003e6\u003c/sub\u003e] unit naturally shifts along a direction within the slip plane that is perpendicular to the original slip direction to release stress. This shift also restores the initial structure, and involves only two bond-breaking and reformation events together with length fluctuations in the other four bonds-identical to the bond evolution observed during the double-layer Te slip process. It should be noted that although all three materials contain [XTe\u003csub\u003e6\u003c/sub\u003e] units, their structures exhibit certain differences, as previously mentioned. Specifically, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb consists of two types of standard octahedral units\u0026mdash;[MgTe\u003csub\u003e6\u003c/sub\u003e] and [PbTe\u003csub\u003e6\u003c/sub\u003e]\u0026mdash;whose orientations are identical to the initial structure shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a). Consequently, its entire slip process strictly follows the two slip mechanisms: single-layer Te slip and double-layer Te slip. Both II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb contain not only standard [MgTe\u003csub\u003e6\u003c/sub\u003e] octahedra but also reversed [MgTe\u003csub\u003e6\u003c/sub\u003e] units, as well as distorted [PbTe\u003csub\u003e6\u003c/sub\u003e] square pyramids, making their behavior considerably more complex. First, layers with standard [MgTe\u003csub\u003e6\u003c/sub\u003e] arrangements undergo double-layer Te slip, whereas the already reversed [MgTe\u003csub\u003e6\u003c/sub\u003e] layers remain unchanged due to blocked slip paths and the availability of alternative slip channels. The distorted [PbTe\u003csub\u003e6\u003c/sub\u003e] units correspond to the saddle-point configuration along the double-layer Te slip pathway, rendering them highly susceptible to slip and transformation into reversed [PbTe\u003csub\u003e6\u003c/sub\u003e] octahedra. This is precisely why the structures of II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb gradually become more ordered during shear deformation. In summary, the slip mechanisms of the [XTe\u003csub\u003e6\u003c/sub\u003e] units in all three materials can be simply described as single- /double-layer Te slip. These two slip mechanisms jointly endow the Mg-Te-Pb system with excellent mechanical properties.\u003c/p\u003e \u003cp\u003eTo further analyze the single- and double-layer Te slip mechanisms in the Mg-Te-Pb system, we calculate the energy barriers for single and double-layer Te slip in I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb. The energy barriers in I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b)-(d), increase in the following order: single-layer Te slip of [MgTe\u003csub\u003e6\u003c/sub\u003e], single-layer Te slip of [PbTe\u003csub\u003e6\u003c/sub\u003e], the first half of the double-layer Te slip for both [MgTe\u003csub\u003e6\u003c/sub\u003e] and [PbTe\u003csub\u003e6\u003c/sub\u003e], and finally the second, hindered stage of double-layer Te slip. Under ideal conditions, the system undergoes slip sequentially in this order and eventually becomes trapped in the energy valley of double-layer Te slip. Subsequently, under applied strain, it either fails or experiences parallel displacement of the central atom within the [XTe\u003csub\u003e6\u003c/sub\u003e] unit. In practice, the system first undergoes double-layer Te slip and single-layer Te slip of the [PbTe\u003csub\u003e6\u003c/sub\u003e] units, and the process ends with simultaneous double-layer Te slip and single-layer Te slip of the [MgTe\u003csub\u003e6\u003c/sub\u003e] units. The slip of the double Te layer occurs first because its energy barrier is comparable to that of the single Te layer; at finite temperatures, thermal fluctuations can easily overcome this small energy difference. Moreover, since the displacement required for the double Te slip to reach the first energy barrier is relatively small, atomic vibrations at finite temperature are expected to overcome this barrier, enter the corresponding energy minimum, and stabilize there. Some layers in the structure do not participate in the slip process. This is because the first slip event introduces a certain amount of defects, which lowers the slip barrier within the already slipped layers and promotes further slip along the same layers. This leads to an accumulation of defects and eventual mechanical failure.\u003c/p\u003e \u003cp\u003eThe II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb are very similar, so their slip energy barriers exhibit analogous characteristics, and we discuss them together. It should be noted that the double-layer Te slip condition for [PbTe\u003csub\u003e6\u003c/sub\u003e] is not satisfied in either structure, so it is not included. First, we note that the lowest energy barrier corresponds to the single-layer Te slip path of the distorted [PbTe\u003csub\u003e6\u003c/sub\u003e] units. As previously mentioned, this distorted [PbTe\u003csub\u003e6\u003c/sub\u003e] is equivalent to a half-completed double-layer Te slip, and thus already resides in a metastable state. Consequently, the system inevitably selects this pathway first, enabling the formation of stable inverted resonant-bond units. Once all distorted [PbTe\u003csub\u003e6\u003c/sub\u003e] octahedra have undergone slip, the system proceeds along the next lowest-energy slip path\u0026mdash;namely, slip involving the [MgTe\u003csub\u003e6\u003c/sub\u003e] layers. Because the double-layer Te slip involves the shortest displacement, all regular [MgTe\u003csub\u003e6\u003c/sub\u003e] units gradually undergo double-layer Te slip until every microstructural unit in the system transforms into an inverted [XTe\u003csub\u003e6\u003c/sub\u003e] configuration, reaching an energetically stable state. Beyond this point, further straining would require the system to overcome the extremely high energy barrier associated with the second-stage double-layer Te slip, which is highly improbable. Therefore, the central atoms of the [XTe\u003csub\u003e6\u003c/sub\u003e] units either undergo in-plane displacement perpendicular to the original slip direction or the structure fails directly.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further elucidate the structural evolution during the slip process in the Mg-Te-Pb compounds, we analyze the local atomic configurations containing Pb-Te resonant bonds and their bond lengths as a function of shear strain, thereby clarifying the dynamic response behavior of chemical bonds under shear loading. Since the single-layer Te and double-layer Te slip deformation mechanisms in the II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb systems are identical to those in I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, we present the analysis using I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb as an example, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e (the analyses for II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb are provided in Supporting Information Figures \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e and S2). The single-layer Te slip process are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(a)-(d). These atomic snapshots correspond to shear strains increasing from 0.220 to 0.245. The red-labeled Te(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e), Te(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e), and Te(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) atoms belong to the upper layer of the same [PbTe\u003csub\u003e6\u003c/sub\u003e] structural unit, while the pink-labeled Te(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e), Te(\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e), and Te(\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e) atoms belong to the upper layer of the subsequent [PbTe\u003csub\u003e6\u003c/sub\u003e] unit. These snapshots capture the complete sequence of bond breaking between the leading Te atom and its central Pb atom, followed by bond formation between the trailing Te atoms and the Pb atom. At a shear strain of 0.220, the system exhibits a perfect [PbTe\u003csub\u003e6\u003c/sub\u003e] unit configuration, in which each Pb atom is bonded to three Te atoms. As the strain increases to 0.232, the Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e)-Te(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) bond is stretched and breaks. Upon further increasing the strain to 0.237, Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) forms a new bond with the subsequent Te(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) atom, while the bonds between Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) and Te(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) as well as Te(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) break simultaneously. At a strain of 0.245, Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) bonds with the following Te(\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e) and Te(\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e) atoms. Figures\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(e)-(i) illustrate the schematic sliding process of a double-layer Te. Similarly, Te(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) and Te(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e) atoms, highlighted in red, bond with the central Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) atom, while Te(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) and Te(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) atoms, marked in pink, are located on the upper level of the subsequent left [PbTe\u003csub\u003e6\u003c/sub\u003e] unit and the lower level of the preceding right [PbTe\u003csub\u003e6\u003c/sub\u003e] unit, respectively. When the shear strain is between 0.351 and 0.354, the bonds between Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) and Te(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e), as well as Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) and Te(\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e), are stretched and nearly simultaneously broken. Subsequently, due to the rightward shift of the upper layer atoms and the leftward shift of the lower layer atoms, the Te(\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e) and Te(\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) atoms originally located on the left and right sides moved closer to the central Pb(\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e) atom. At a strain of 0.360, these atoms formed new bonds, creating an [PbTe\u003csub\u003e6\u003c/sub\u003e] unit oriented in the opposite direction compared to before the slip. The entire process is dominated by the relative slip between the upper and lower layers of Te atoms, ultimately resulting in the \u0026ldquo;inversion\u0026rdquo; phenomenon of the [PbTe\u003csub\u003e6\u003c/sub\u003e] unit. This single-layer Te slip process involves the sequential breaking and reformation of three pairs of bonds, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(j)-(l), and overall represents a relatively simple single-layer Te slip translation. However, during the double-layer Te slip process, only two Pb-Te bonds are broken (Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e(m)-(n)), while the remaining bonds exhibit a behavior of first shortening, followed by elongation. In both slip mechanisms, all bond-breaking and bond-reformation processes occur in a discontinuous manner, with each slip step resulting in a relatively stable atomic configuration. This mechanism is known as the \u0026ldquo;catch-bond\u0026rdquo; mechanism (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e), wherein a covalent or ionic bond breaks and is immediately followed by the formation of a new bond at a first-nearest-neighbor site, thereby preserving structural integrity.\u003c/p\u003e \u003cp\u003eThese deformation mechanisms are closely related to the functional characteristics of the [XTe\u003csub\u003e6\u003c/sub\u003e] units, whose role can be summarized in the following two aspects: structurally, the [XTe\u003csub\u003e6\u003c/sub\u003e] unit possesses two closely packed planes on the top and bottom. The ordered stacking along these densely packed planes gives the entire crystal lattice a pronounced layered structure, which introduces new potential slip systems for inorganic TE materials that originally had limited slip paths, thereby increasing stress‑relief pathways; in terms of slip mode, the centrosymmetric nature of the [XTe\u003csub\u003e6\u003c/sub\u003e] unit perfectly satisfies the conditions for the formation of a \u0026ldquo;catch-bond\u0026rdquo; phenomenon. During the shear process in all three materials, the [XTe\u003csub\u003e6\u003c/sub\u003e] units can sequentially exhibit a \u0026ldquo;catch\u0026rdquo; behavior, promoting coordinated slip of all Pb-Te or Mg-Te layers along the shear direction. This effectively releases internal stress while maintaining structural integrity. Thus, the [XTe\u003csub\u003e6\u003c/sub\u003e] units synergistically enhance the mechanical properties of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb through both their ordered structural arrangement and the \u0026ldquo;catch-bond\u0026rdquo; deformation mode, which strongly confirms our initial hypothesis that the deliberate introduction of the [XTe\u003csub\u003e6\u003c/sub\u003e] functional units would improve the mechanical performance of the materials.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.6 TE and Mechanical Property Analysis\u003c/h2\u003e \u003cp\u003eThe above analysis demonstrates that I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb exhibit excellent TE conversion potential coupled with favorable mechanical properties. Figure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e systematically compares the intrinsic lattice thermal conductivity \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e of representative binary TE materials reported in recent years at room temperature. Among known materials, \u003cem\u003eα\u003c/em\u003e-Ag\u003csub\u003e2\u003c/sub\u003eS shows the lowest \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of only 0.25 W/(m\u0026middot;K). Additionally, TE materials such as Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e, SnTe, PbTe, PbSe, and PbS all exhibit \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e values below 1 W/(m\u0026middot;K), attributed to the presence of resonant bonding. In this work, the predicted I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb features both resonant bonds and a large atomic mass contrast, resulting in an ultralow average \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of 0.095 W/(m\u0026middot;K)\u0026mdash;62% lower than that of the best-performing \u003cem\u003eα\u003c/em\u003e-Ag\u003csub\u003e2\u003c/sub\u003eS. Moreover, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb and MgTe\u003csub\u003e2\u003c/sub\u003ePb also display \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e values below 1 W/(m\u0026middot;K).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn terms of mechanical properties, the \u003cem\u003eB\u003c/em\u003e/\u003cem\u003eG\u003c/em\u003e ratios of I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb all exceed the ductility threshold of 1.75, outperforming traditional inorganic bulk thermoelectric materials such as PbTe, PbSe, PbS, SnTe, GeTe, Cu\u003csub\u003e2\u003c/sub\u003eTe, Bi\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003e, and SnSe. This indicates greater potential for processing and practical application. However, their ductility remains inferior to that of intrinsically plastic materials such as the typical layered compounds InTe, Cu\u003csub\u003e2\u003c/sub\u003eS, and \u003cem\u003eα\u003c/em\u003e-Ag\u003csub\u003e2\u003c/sub\u003eS, as well as the special intermetallic compound Mg\u003csub\u003e3\u003c/sub\u003eBi\u003csub\u003e2\u003c/sub\u003e. The primary reason is that the ductility of the three Mg-Te-Pb compounds does not originate from the common dislocation slip mechanism found in metals or layered materials, but rather from the \u0026ldquo;catch-bond\u0026rdquo; phenomenon induced by the slip of [XTe\u003csub\u003e6\u003c/sub\u003e] units. This mechanism allows the three materials to theoretically withstand strains exceeding 60% without significant fracture. Although such an ideal scenario is unlikely to be fully realized in practice, the underlying slip mechanisms would still enhance toughness in real-world applications. Overall, the exceptional TE and mechanical performance of these three materials can be attributed to the presence of the [XTe\u003csub\u003e6\u003c/sub\u003e] structural units.\u003c/p\u003e \u003cp\u003eAdditionally, we have preliminarily explored the feasibility of synthesizing the three new TE materials via melt processing, magnetron sputtering, and high-pressure approaches (see Supporting Information Figures S3-S5 and corresponding descriptions). Current characterization results reveal indications of potential phase separation. We hypothesize that successful formation of these multi-component compounds will require precise compositional control under strictly anhydrous conditions to facilitate proper lattice formation\u0026mdash;an insight that may offer initial guidance for future experimental studies.\u003c/p\u003e \u003c/div\u003e"},{"header":"4 CONCLUSION","content":"\u003cp\u003eGuided by a functional-unit-based materials design strategy and using the functional units, we performed DP-accelerated CSP. During the training of the DP model, four elements\u0026mdash;Mg, Te, Pb, and Bi\u0026mdash;which readily form compounds with excellent TE and mechanical properties were selected, along with 27 binary and ternary compounds derived from them. The performance of the model is iteratively optimized through crystal structures generated by CSP. In the final prediction stage, the [XY\u003csub\u003e6\u003c/sub\u003e] TE/mechanical functional units are introduced, leading to the discovery of three novel TE materials: I‑MgTe\u003csub\u003e2\u003c/sub\u003ePb, II‑Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb. All three materials are narrow‑bandgap semiconductors (0.17 eV, 0.46 eV, and 0.14 eV, respectively) and exhibit outstanding TE transport and mechanical performance. Specifically, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb exhibits ultralow \u003cem\u003eκ\u003c/em\u003e\u003csub\u003e\u003cem\u003eL\u003c/em\u003e\u003c/sub\u003e of 0.125 W/(m\u0026middot;K) along the \u003cem\u003ex\u003c/em\u003e-direction and 0.065 W/(m\u0026middot;K) along the \u003cem\u003ez\u003c/em\u003e-direction\u0026mdash;significantly lower than that of the benchmark TE material PbTe (~\u0026thinsp;2.25 W/(m\u0026middot;K)). Moreover, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb demonstrates remarkably high Seebeck coefficients of +\u0026thinsp;765 \u0026micro;V/K under \u003cem\u003ep\u003c/em\u003e-type doping and \u0026minus;\u0026thinsp;766 \u0026micro;V/K under \u003cem\u003en\u003c/em\u003e-type doping, underscoring its superior TE performance. From a mechanical standpoint, I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb can undergo continuous interlayer slip under shear deformation, sustaining shear strains exceeding 60% without significant structural failure. Their ductility originates from both the ordered structural arrangement of the [XTe\u003csub\u003e6\u003c/sub\u003e] functional units and the \u0026ldquo;catch-bond\u0026rdquo; mechanism. Overall, the complete implementation of this functional-unit-based materials design strategy has not only yielded three promising novel TE materials and provided a universal potential model for the Mg\u0026ndash;Te\u0026ndash;Pb\u0026ndash;Bi system, but also provided a fresh alternative to conventional high-throughput computation for the discovery and development of other functional materials.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eXin-Xuan Wang and Zhen-Shuai Lei wrote the main manuscript text and prepared the figures. They also contributed to the methodology, investigation, formal analysis, data curation, and software. Wen-Juan Li supervised the project. Xiao-Bin Feng, Gang Chen, Bo Duan, Guo-Dong Li, and Qing-Jie Zhang acquired funding and provided resources. Peng-Cheng Zhai contributed to the conceptualization. Xiao-Bin Feng performed validation. Guo-Dong Li reviewed and edited the manuscript. All authors reviewed the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAll authors declare that they have no conflict of interest.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data supporting the findings of this study are available within the paper and its Supplementary Information.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work is supported by the National Natural Science Foundation of China (No. 92463309, 92163212, 92463301, and 92363001), and the Natural Science Foundation of Hubei Province of China (No. 2023AFB175).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eDiSalvo, F. 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S.; Zhao, J.; Song, G.; Zhou, X.; Ji, J.; Zhang, W.; Han, Z.; Liu, J.; Stahl, K., Isosymmetric phase transitions, ultrahigh ductility, and topological nodal lines in α-Ag\u003csub\u003e2\u003c/sub\u003eS. \u003cem\u003ePhysical Review B\u003c/em\u003e 2020, \u003cem\u003e102\u003c/em\u003e (14), 140101.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Ternary thermoelectric materials, Thermoelectric properties, Mechanical properties, Crystal structure prediction, Deep learning molecular dynamics","lastPublishedDoi":"10.21203/rs.3.rs-9154062/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9154062/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eInorganic thermoelectric materials with excellent thermoelectric performance are often brittle. In this work, we introduce functional units into deep learning molecular dynamics-accelerated crystal structure prediction to develop novel functional materials exhibiting both outstanding thermoelectric and mechanical properties. We selected the elements Mg, Te, Pb, and Bi, which are prone to form materials with superior thermoelectric and mechanical performance. A deep learning potential was iteratively trained to accelerate the energy evaluation during structure prediction. Subsequently, the [XY\u003csub\u003e6\u003c/sub\u003e] functional units were introduced to guide the discovery of novel crystals. Following stability screening, we identified three novel materials that exhibit both outstanding thermoelectric and mechanical performance: I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb, and MgTe\u003csub\u003e2\u003c/sub\u003ePb. I-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb possesses an ultralow lattice thermal conductivity of 0.065 W/mK, while II-Mg\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3\u003c/sub\u003ePb achieves a remarkably high Seebeck coefficient of 767 \u0026micro;V/K. All three materials can withstand shear strains exceeding 60% without significant structural failure. The enhancement in thermoelectric performance is attributed to the [PbTe\u003csub\u003e6\u003c/sub\u003e] units significantly suppressing lattice thermal conductivity, while the improvement in mechanical properties results from the ordered arrangement of [PbTe\u003csub\u003e6\u003c/sub\u003e] and [MgTe\u003csub\u003e6\u003c/sub\u003e] units and the \u0026ldquo;catch-bond\u0026rdquo; mechanism, which introduces additional potential slip systems. These findings propose a new pathway for developing materials that integrate excellent thermoelectric and mechanical properties.\u003c/p\u003e","manuscriptTitle":"Ductile Mg-Te-Pb Thermoelectric Materials with Ultralow Lattice Thermal Conductivity Predicted by a Deep Learning Potential Model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-26 15:33:35","doi":"10.21203/rs.3.rs-9154062/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-06T09:05:56+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-03T05:15:47+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-02T00:11:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"54894150778494397900568965535101476901","date":"2026-03-27T03:59:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"131563987425602862409151262636590461486","date":"2026-03-25T02:28:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-25T02:24:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-20T07:32:27+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-19T11:57:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Computational Materials","date":"2026-03-18T03:09:41+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"90a3d727-00c7-4e57-8bab-9488e2dd85e8","owner":[],"postedDate":"March 26th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":65083369,"name":"Physical sciences/Materials science"},{"id":65083370,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-13T13:40:22+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-26 15:33:35","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9154062","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9154062","identity":"rs-9154062","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}